text:
\section{Introduction}
A magnetic spin configuration where the spin directions span the entire unit sphere is called a magnetic skyrmion \cite{Nagaosa2013,Mueller2015}.
Magnetic skyrmions were theoretically predicted to exist as solitons in the continuum two-dimensional isotropic Heisenberg model~\cite{Belavin1975}, but they were demonstrated to be destabilized by the external field, magnetocrystalline anisotropy or lattice discretization effects. Robust mechanisms for the stabilization of skyrmions were identified later, including the \ac{DMI} \cite{dmiD1958, dmiM1960, Bogdanov1994}, four-spin interactions~\cite{Heinze2011} and the frustration of Heisenberg exchange interactions~\cite{Okubo2012,vonMalottki2017}. The first experimental indications for the formation of a skyrmion lattice were found in MnSi via neutron scattering~\cite{Muelbauer2009}. Since then, skyrmions have been directly observed experimentally in other magnetic materials including Fe$_{1-x}$Co$_x$Si \cite{Yu2010,Muenzer2010}, Cu$_2$OSeO$_3$~\cite{Seki2012}, Pd/Fe/Ir(111)~\cite{Romming2013},
and GaV$_4$S$_8$ \cite{Kezsmarki2015}. Skyrmions were even observed close to or at room temperature in Pt/Co/MgO nanostructures~\cite{Boulle2016}, thin films of FeGe~\cite{Yu2011} and Pt/Co/Ta~\cite{Woo2016}, and in Co-Zn-Mn alloys~\cite{Tokunaga2015}.
Skyrmions are often regarded as exceptionally stable, turning them into a candidate for future use in logic and memory devices~\cite{Fert2013,Iwasaki2013,Zhou2014}. The operation of such devices relies on the demonstrated possibility of writing and deleting individual skyrmions~\cite{Hsu2017,Iwasaki2013}, and of moving them with electrical currents~\cite{Yu2012}.

Skyrmions are characterized by an integer topological charge $Q$, counting the number of times the spin configuration wraps the unit sphere. Because the topological charge cannot be changed dynamically in a continuum model, skyrmions are often referred to as topologically protected.
However, the topological charge is not a conserved quantity in lattice spin models as the energy barrier between topologically trivial states and skyrmions is finite, allowing for the possibility of spontaneous creation and annihilation of skyrmions at finite temperature. Therefore, skyrmions should rather be thought of as quasiparticles, with their lifetime following the Arrhenius law as demonstrated in numerical simulations~\cite{Hagemeister2015,Rozsa2016} and experiments~\cite{Wild2017}. The decisive factor for skyrmion stability can be understood based on linear spin-wave theory or the harmonic approximation of the energy functional close to the metastable solution. In contrast to the collinear state, skyrmions are characterized by a number of low-frequency magnon modes which are easily excited by temperature, giving rise to a higher spin-wave entropy and, consequently, a free-energy preference for skyrmions over collinear configurations as the temperature is raised ~\cite{Muelbauer2009}. The larger entropy means that the attempt frequency, i.e. the pre-exponential factor in the Arrhenius law, is lower for skyrmion annihilation than for the creation of a skyrmion from the collinear state~\cite{Hagemeister2015, Desplat2018, Malottki2019}, referred to as entropic stabilization.
However, linear spin-wave theory is expected to gradually lose its validity at elevated temperatures, where magnon-magnon interactions become more prominent and the fast creation and destruction of skyrmions makes the expansion around a well-defined equilibrium state questionable. Numerical simulations are a suitable method for investigating magnetic systems beyond the linear spin-wave approximation, but extracting the free energy or the entropy is typically challenging since these quantities are not defined for single microstates. Therefore, the thermodynamic properties of skyrmions beyond the linear spin-wave approximation remain to be explored.

In this paper, we calculate the free-energy and entropy difference between topologically trivial and skyrmionic states in a wide temperature range through numerical simulations for a (Pt$_{0.95}$Ir$_{0.05}$)/Fe bilayer on a Pd(111) surface. The free-energy difference is shown to decrease with temperature, leading to a range where the free energy of skyrmionic states with $Q=1$ is lower than for topologically trivial states. The dependence of this temperature range on the magnetic field and the system size is demonstrated. Remarkably, we also find a temperature range where skyrmions possess a lower entropy than topologically trivial states, reversing the entropic stabilization. These results highlight the thermodynamic properties and the quasiparticle character of skyrmions.

\section{Methods}
\subsection{Spin dynamics simulations}
The system being modeled is a (Pt$_{0.95}$Ir$_{0.05}$)/Fe bilayer on a Pd(111) surface. The magnetic Fe moments are described by the following classical atomistic Hamiltonian:
\begin{align}
\mathcal{H} = \frac{1}{2} \sum\limits_{i \neq j} \bm{S}_i \mathcal{J}_{ij} \bm{S}_j + \sum\limits_{i} \bm{S}_i \mathcal{K} \bm{S}_i  - \mu_{\textrm{s}} \sum\limits_i \bm{B} \cdot \bm{S}_i.
\end{align}
Here, $i,j$ are site indices and $\mu_{\textrm{s}}$ is the spin magnetic moment. The interaction tensors $\mathcal{J}_{ij}$ include Heisenberg exchange in its diagonal terms $J_{ij}=\dfrac{1}{3}\textrm{Tr}\mathcal{J}_{ij}$, DMI in its antisymmetric part $\bm{D}_{ij}\left(\bm{S}_{i}\times\bm{S}_{j}\right)=\dfrac{1}{2}\bm{S}_{i}\left(\mathcal{J}_{ij}-\mathcal{J}^{T}_{ij}\right)\bm{S}_{j}$, and two-site anisotropy in its traceless symmetric part.
$\mathcal{K}$ denotes the on-site anisotropy tensor. $\bm{B}$ is an applied external field perpendicular to the surface. The exchange coefficients $\mathcal{J}_{ij}$ and $\mathcal{K}$ were determined by {\it ab initio} calculations using the Korringa--Kohn--Rostoker~\cite{Szunyogh1995, Zeller1995} multiple scattering formalism with the relativistic torque~\cite{Udvardi2003} method, and are reported in Refs.~\cite{Rozsa2017,Zazvorka2019}. The interactions were included between pairs of spins up to a distance of $8$ lattice constants. In particular, the competition between ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions leads to the stabilization of localized spin structures with various topological charges, including skyrmions and antiskyrmions~\cite{Rozsa2017,Weissenhofer2019,Weissenhofer2020,Rozsa_2020}.

The dynamics of the spin system is described by the stochastic Landau--Lifshitz--Gilbert (LLG) equation,
\begin{align}
\frac{\partial \bm{S}_i}{\partial t} = - \frac{\gamma}{(1+\alpha^2) \mu_{\textrm{s}}} \bm{S}_i \times (\bm{H}_i + \alpha \bm{S}_i \times \bm{H}_i),
\end{align}
where $\alpha$ is the damping parameter and $\gamma$ the gyromagnetic ratio. $\bm{H}_i$ is the local effective field with $\bm{H}_i = \bm{\zeta}_i - \partial \mathcal{H} / \partial \bm{S}_i$. $\bm{\zeta}_i$ is a Gaussian noise term with $\langle \bm{\zeta}_i(t) \rangle = 0$ and $\langle \zeta_{i,\mu}(t) \zeta_{j,\nu} ( t^{\prime}) \rangle = \delta_{i,j} \delta_{\mu,\nu} \delta(t-t^{\prime}) 2 \alpha k_B T \mu_s / \gamma$, with $i,j$ denoting different spins and $\mu,\nu$ representing different Cartesian coordinate directions.

The simulations were performed on a two-dimensional triangular lattice with periodic boundary conditions. The damping constant was set to $\alpha=1$ in order to increase the speed of relaxation towards thermal equilibrium and to make transitions between states with different topological charges more frequent.
The simulations were started from a collinear field-polarized state or from a configuration with a prepared skyrmionic structure of given topological charge and the time evolution was calculated according to the stochastic LLG equation for a time of $50.4 \, \mu\textrm{s}$ with a total of 5 independent realizations for each temperature and initial condition. The time step of the simulation was set to $50.4 \, \textrm{fs}$ and the topological charge was calculated at each step.

\subsection{Calculation of thermodynamic quantities}
The free energy and the entropy of a skyrmion are not defined for single microstates of the system; therefore, they cannot be calculated as time or ensemble averages. Instead, they were determined from the time dependence of the topological charge and the energy of the system at various values of the external parameters.

The topological charge of a continuous vector field can be calculated as a surface integral with the spin vectors $\bm{S}$ of unit length,
\begin{align}
    Q= -\frac{1}{4\pi} \int \mathrm{d}^2r \, \bm{S} \cdot (\partial_x \bm{S} \times \partial_y \bm{S}).\label{eqn3}
\end{align}
The sign convention is chosen such that a skyrmion on an out-of-plane-oriented collinear background has a topological charge of $Q=1$, while an antiskyrmion is described by $Q=-1$. For our spin model simulation we use a discretized version of Eq.~\eqref{eqn3}~\cite{Boettcher2018}, calculating $Q$ via
\begin{align}
    Q\left(\bm{S}\right) = -\sum_{\left\{i,j,k\right\}}\frac{1}{2\pi} \arctan \left( \frac{\bm{S}_i \cdot \left(\bm{S}_j\times \bm{S}_k\right) }{1+ \bm{S}_i \cdot \bm{S}_j + \bm{S}_i \cdot \bm{S}_k + \bm{S}_j \cdot \bm{S}_k} \right),
\end{align}
where $\bm{S}_i$ ($i=1,2,3)$ denotes the spin unit vectors on a nearest-neighbor triangle on the lattice. This value is calculated for all simulated triangles and summed up to determine the topological charge for the entire system. For the simulated system with periodic boundary conditions, $Q$ is always an integer value.

To each value of the topological charge $Q$ we assign the conditional free energy $F_Q$. This can be connected to the conditional partition function $Z_Q$, defined as the phase-space integral of the Boltzmann exponential factor over all configurations with topological charge $Q$,
\begin{align}
    F_Q = - k_{\textrm{B}} T \ln(Z_Q) = - k_{\textrm{B}} T \ln \left( \int_{Q\left(\bm{S}\right)=Q} \exp\left(-\beta\mathcal{H}\left(\bm{S}\right)\right) \, \mathrm{d}\bm{S} \right),
\end{align}
with $\beta = 1/\left(k_\textrm{B} T\right)$. The direct calculation of the conditional partition functions is numerically not feasible. However, the difference in free energies between two values of the topological charge, for example $1$ and $0$, can be calculated from the ratio of partition functions using the corresponding condition:
\begin{align}
    \Delta F_{10} = F_1 - F_0 = - k_{\textrm{B}} T \ln( Z_1/Z_0).\label{eqn6}
\end{align}
During a numerical simulation, a total number $N$ of spin configurations, or recorded events, are created. Once the system has reached thermal equilibrium, the configurations are generated with the probabilities according to the Boltzmann distribution. Therefore, we expect the number of recorded events $N_Q$ fulfilling condition $Q$ divided by the total number of recorded events $N$ to converge to the ratio of the partition function $Z_Q$ and the total partition function $Z$ in the thermodynamic limit:
\begin{align}
    \lim_{N\rightarrow\infty}N_Q / N = Z_Q / Z.\label{eqn7}
\end{align}
Using Eqs.~\eqref{eqn6} and \eqref{eqn7}, a formula to calculate free-energy differences can be derived, only based on the number of recorded events during simulation time that fulfill a certain condition \cite{vanGunsteren2002},
\begin{align}
\Delta F_{10,\textrm{count}}(T) = \lim_{N\rightarrow\infty} - k_{\textrm{B}} T \ln( N_1 / N_0) = - \Delta F_{01,\textrm{count}}(T), \label{DeltaFN}
\end{align}
which we apply to spin configurations with different topological charges $Q$. Equation~\eqref{DeltaFN} requires that the simulation explores a large part of the phase space, such that a sufficient amount of changes in the topological charge take place during simulation time, with both states being present at a considerable number of time steps.

The lifetime of configurations with a given value of the topological charge is expected to follow the Arrhenius law $\tau~\propto\textrm{exp}\left(\Delta E/\left(k_{\textrm{B}} T\right)\right)$, where $\tau$ is the lifetime of the state and $\Delta E$ is the energy barrier separating it from a configuration with a different topological charge. The lifetimes in the simulations have been measured using the method described in Ref.~\cite{Rozsa2016}, and the energy barriers were estimated from an Arrhenius fit to the data. These energy barriers were compared to values obtained from the Geodesic Nudged Elastic Band (GNEB) method~\cite{Bessarab2015} as implemented in the UppASD simulation code~\cite{UppASD}. The GNEB method provides an analytic approximation for the energy barrier and has been used for investigating skyrmion lifetimes in numerous works previously~\cite{Bessarab2018, Desplat2018, Malottki2019}.

At lower temperatures, switching events between configurations with different topological charges become exceedingly rare. In the regime where no changes in topological charge take place during the simulation, another method must be employed to calculate the free energy. Using the internal energy $U_{Q}=\left<\mathcal{H}\left(\bm{S}\right)\right>_{Q\left(\bm{S}\right)=Q}$ and a single value of $\Delta F_{10}$ at a high temperature $T_0$ calculated from Eq.~\eqref{DeltaFN}, $\Delta F_{10}$ can be determined at all temperatures based on the internal energy difference $\Delta U_{10}=U_{1}-U_{0}$ via \cite{vanGunsteren2002,Hinzke2008},
\begin{align}
\Delta F_{10,\textrm{integ}}(T) = \Delta F_{10,\textrm{count}}(T_0) \frac{T}{T_0} - T \int_{T_0}^T \Delta U_{10}(T^\prime) \frac{\mathrm{d}T^\prime}{T^{\prime 2}}. \label{DeltaFInteg}
\end{align}
$\Delta U_{10}$ is easily accessible as the time average of the Hamiltonian, which may be determined from independent simulations initialized in states with different topological charges, rather than requiring a high number of switching events during a single run. Note that Eq.~\eqref{DeltaFInteg} may still become numerically inaccurate close to $T=0$ where the denominator goes to zero.

The entropy difference between skyrmionic and topologically trivial states can be calculated by the negative derivative of the free energy difference,
\begin{align}
\Delta S_{10}=-\frac{\partial\Delta F_{10}}{\partial T}.\label{eqn9}
\end{align}
which is done numerically by using the central finite difference.

The average value of the topological charge can be calculated as a time average of $Q$ using the number of recorded events with corresponding topological charge:
\begin{align}
    \langle Q \rangle_{\textrm{time}} = \frac{\sum_Q Q N_Q }{\sum_Q N_Q}.\label{Qtime}
\end{align}
This method of calculation is appropriate at high temperatures. However, at low temperatures there are no changes in topological charge during the simulation time, making the calculated value dependent on the initial condition.

For the low-temperature calculations, we use the formula
\begin{align}
    \langle Q \rangle_{\textrm{ensemble}} = \frac{\sum_{Q}Q\exp(-\beta \Delta F_{Q0})}{\sum_{Q}\exp(-\beta \Delta F_{Q0})},\label{Qens}
\end{align}
where $\Delta F_{Q0}$ is determined from Eq.~\eqref{DeltaFInteg}. Note that here the free-energy difference of the entire system has to be used and not an average per spin. Since this method requires performing simulations with different initial values of $Q$, we refer to it as an ensemble average. For simplicity, the summation in Eq.~\eqref{Qens} were restricted to the values $Q=-1,0,1$, which is possible since skyrmions and antiskyrmions are both stable at zero temperature in the system~\cite{Rozsa2017}. Calculating the free-energy difference for other values of the topological charge is numerically demanding, and their relative Boltzmann weight is significantly lower. When the number of states with other topological charges increases, this restriction of the sum to $Q=-1,0,1$ is no longer a good approximation, and Eq.~\eqref{Qtime} can be used directly instead.

\subsection{Linear spin-wave theory\label{sec2c}}

At sufficiently low temperatures, the internal and the free energy, as well as the entropy may be determined analytically based on linear spin-wave expansion. In this approximation, the conditional free energy may be expressed as~\cite{Rozsa2015}
\begin{align}
F_{Q}=U_{Q}-TS_{Q},\label{eqn10}
\end{align}
with
\begin{align}
U_{Q}=E_{Q}+\sum_{k=1}^{N_{S}}\frac{\mu_{\textrm{s}}}{\gamma}\omega_{Q,k}n_{Q,k}\label{eqn11}
\end{align}
and
\begin{align}
S_{Q}=k_{\textrm{B}}\sum_{k=1}^{N_{S}}\textrm{ln}\:n_{Q,k},\label{eqn12}
\end{align}
with $E_{Q}$ the energy of the equilibrium spin configuration at zero temperature and $\omega_{Q,k}$ denoting the spin-wave frequencies in the vicinity of the local energy minimum. This method corresponds to approximating the energy landscape close to the minimum with the potential of independent harmonic oscillators. The calculation of the spin-wave frequencies for non-collinear spin configurations is discussed in, e.g., Ref.~\cite{Rozsa2018}.

The occupation number of the spin-wave modes according to classical statistics is calculated as
\begin{align}
n_{Q,k}=\frac{\int q^{2}_{Q,k}\textrm{e}^{-\beta \frac{\mu_{\textrm{s}}}{\gamma}\omega_{Q,k} q^{2}_{Q,k}}\textrm{d}q_{Q,k}}{\int \textrm{e}^{-\beta \frac{\mu_{\textrm{s}}}{\gamma}\omega_{Q,k} q^{2}_{Q,k}}\textrm{d}q_{Q,k}}=\frac{k_{\textrm{B}}T}{\frac{\mu_{\textrm{s}}}{\gamma}\omega_{Q,k}}\:\:\:\textrm{for}\:\:\:\omega_{Q,k}\neq 0,\label{eqn12a}
\end{align}
where the integration limits for the phase space variable $q_{Q,k}$ are extended to infinity. For eigenmodes with $\omega_{Q,k}=0$, the harmonic-oscillator approximation loses its validity. Such Goldstone modes naturally occur for skyrmions in the continuum limit, since translation along one of the two in-plane directions does not influence the energy of the system. As discussed in Ref.~\cite{Bessarab2018}, the phase-space variable belonging to the translational modes can be expressed as
\begin{align}
q_{Q,\mu}=&A_{Q,\mu}r_{\mu},\label{eqn12b}
\\
A_{Q,\mu}=&\left|\partial_{\mu}\boldsymbol{S}^{Q}\right|=\sqrt{\sum_{i=1}^{N_{S}}\left(\partial_{\mu}\boldsymbol{S}_{i}^{Q}\right)^{2}},\label{eqn12c}
\end{align}
where $\mu=x,y$ denotes translation along one of the in-plane coordinates $r_{\mu}$. Substituting Eqs.~\eqref{eqn12b} and \eqref{eqn12c} into Eq.~\eqref{eqn12a} yields
\begin{align}
n_{Q,\mu}=\frac{\int q^{2}_{Q,\mu}\textrm{d}q_{Q,\mu}}{\int \textrm{d}q_{Q,\mu}}=\frac{A_{Q,\mu}^{2}L_{\mu}^{2}}{3},\label{eqn12d}
\end{align}
with $L_{\mu}$ the system size along the given direction. Since the zero as well as the nonzero eigenvalues enter Eq.~\eqref{eqn11} in pairs, the occupation number for the pair of translational modes will be written as $n_{Q,k=1}=\sqrt{n_{Q,x}n_{Q,y}}$.

Equations~\eqref{eqn10}-\eqref{eqn12} imply $\Delta F_{10}=\Delta U_{10}$ at $T=0$~K. Since $\frac{\mu_{\textrm{s}}}{\gamma}\omega_{Q,k}n_{Q,k}=k_{\textrm{B}}T$ is independent of the spin configuration for finite-frequency modes, one has
$\Delta U_{10}=\Delta U_{10}\left(T=0\right)-k_{\textrm{B}}T$ because of the translational mode of the skyrmion. For the entropy difference one obtains
\begin{align}
\frac{1}{k_{\textrm{B}}}\Delta S_{10}=\sum_{k=1}^{N_{S}}\textrm{ln}\:\omega_{0,k}-\sum_{k=2}^{N_{S}}\textrm{ln}\:\omega_{1,k}-\textrm{ln}\frac{k_{\textrm{B}}T}{\frac{\mu_{\textrm{s}}}{\gamma}n_{1,1}}.\label{eqn13}
\end{align}
The main contribution to the temperature dependence of $\Delta F_{10}$ comes from the entropy contribution of the finite-frequency modes, leading to a linear decrease. A logarithmic divergence of the entropy difference due to the Goldstone modes of the skyrmion is predicted from Eq.~\eqref{eqn13} at low temperatures, an effect also observed in the calculation of the configurational entropy of skyrmions~\cite{Zivieri2019}. In the lattice model considered here, this divergence is regularized since the atomic sites create a weak but finite periodic modulation potential for the skyrmion position, and the translational modes obtain a finite frequency. In Ref.~\cite{Desplat2018}, it was argued that the translational modes in a lattice model can be treated like all other spin-wave excitations, rather than Goldstone modes, during the calculation of skyrmion lifetimes. The logarithmic singularity should be less pronounced for larger system sizes, since the number of Goldstone modes does not scale with the number of spins.

Linear spin-wave theory is expected to break down as the temperature becomes comparable to the energy barrier separating the different metastable equilibrium states. For the translation of skyrmions, this effect is observable already at the energy scales corresponding to the atomic modulation potential of the skyrmion position, above which a Brownian motion of the quasiparticles can be observed~\cite{Zazvorka2019,Weissenhofer2020}. Overcoming the energy barrier between the skyrmion and the topologically trivial state requires considerably higher temperatures. Finally, increasing the temperature also enhances the role of magnon--magnon interactions as the spin-wave occupation numbers become higher, further limiting the applicability of the linear approximation.

\section{Results}

\begin{figure}
\includegraphics[width=0.9\columnwidth]{Fig1-eps-converted-to.pdf}
\caption{Phase diagram of the (Pt$_{0.95}$Ir$_{0.05}$)/Fe/Pd(111) system. (a) Energy per spin in the spin spiral (SS), skyrmion lattice (SkL) and field-polarized (FP) states as a function of magnetic field at $T=0\,\textrm{K}$. $B_{\textrm{m}}$ and $B_{\textrm{s}}$ denote the metastability field for an isolated skyrmion and the transition field from the spin spiral to the field-polarized state, respectively. (b) Static susceptibility as a function of temperature at $B=0\,\textrm{T}$. $T_{\textrm{c}}$ denotes the transition temperature from the SS to the paramagnetic (PM) phase.
}
\label{phasediag}
\end{figure}

Before discussing the thermodynamic properties of metastable skyrmions, we present the observed phases in the system. The zero-temperature energies of the different states are displayed in Fig.~\ref{phasediag}(a). For lower external fields the ground state is a spin spiral which transforms into a collinear field-polarized state at around $B_{\textrm{s}}\approx0.21$~T~\cite{Rozsa2016v2}. The skyrmion lattice is not a ground state for any value of the external field, since its energy already exceeds that of the field-polarized state at $B_{\textrm{s}}$. A single isolated skyrmion leads to a positive energy contribution to the field-polarized state for fields above $B_{\textrm{m}}\approx0.1$~T. Due to the short-range attractive interaction between the skyrmions, this field is slightly lower than where the energy curves for the skyrmion lattice and the field-polarized states cross in Fig.~\ref{phasediag}(a). In the following, we study the thermal properties of metastable skyrmions at field values higher than $B_{\textrm{m}}$.

As the temperature is increased, the spin spiral phase is transformed into the paramagnetic phase at $T_{\textrm{c}}\approx50$~K for $B=0$~T, as evidenced by the singular behaviour of the static magnetic susceptibility shown in Fig.~\ref{phasediag}(b). Based on previous studies~\cite{Rozsa2016,Boettcher2018}, the critical temperature only changes weakly as the field is increased to $B_{\textrm{s}}$. The field-polarized regime is part of the paramagnetic phase, with a continuous crossover in the physical observables as the temperature is increased. Above the critical temperature, strong thermal fluctuations lead to the formation of a considerable number of metastable skyrmions in an intermediate regime reaching approximately up to $120$~K, where an inflection point in the static susceptibility is found. This intermediate regime extends to considerably higher field values than $B_{\textrm{s}}$, as has been investigated for similar systems in Refs.~\cite{Rozsa2016,Boettcher2018}.

As a first step, it has to established whether configurations with topological charge $Q=1$ may indeed be identified as skyrmions in our simulations, while $Q=0$ states remain close to the collinear configuration. This question is especially relevant in the strongly fluctuating regime above $T_{\textrm{c}}\approx50$~K, illustrated at $T=80$~K in Figs.~\ref{QoverT}(a) and (b).
Besides the localized, cylindrically symmetric equilibrium skyrmion known at zero temperature, a $Q=1$ spin configuration may denote a combination of two skyrmions plus an antiskyrmion or a completely disordered state with various signs of the local topological charge density. However, the latter configurations turn out to be significantly higher in energy and are consequently expected to occur very rarely in our simulations for a wide temperature range. In Fig.~\ref{QoverT}(c), the topological charge is shown over a short timescale for a sample run with visible changes in the topological charge over time. We calculate a time average of each spin's Cartesian coordinates over the time intervals denoted by thick lines in Fig.~\ref{QoverT}(c)  in order to demonstrate that the recorded spin structures with $Q=1$ are actually skyrmions. Note that the individual spins do not have unit length after taking the average. Figure~\ref{QoverT}(a) demonstrates that the average structure still consists of a downwards-pointing core in an upwards-pointing background, with the spin directions spanning the whole unit sphere as indicated by the color-coding. The time average over configurations with $Q=0$, shown in Fig.~\ref{QoverT}(b), still resembles the collinear state even at this elevated temperature.

By determining the skyrmion lifetime as a function of temperature between $T=60$~K and $T=85$~K, an energy barrier of $\Delta E/k_{\textrm{B}}\approx 922$~K was obtained using the system parameters in Fig.~\ref{QoverT}.

\begin{figure}
\includegraphics[width=0.9\columnwidth]{Fig2.pdf}
\caption{Time-averaged spin configurations for topological charges (a) $Q=1$ and (b) $Q=0$. (c) Time evolution of the topological charge for a sample run with external field strength $B=1$~T, $T=80$~K and number of spins $N_{S} = 25 \times 25$. The spin configurations in (a) and (b) result from a time average for each spin's Cartesian coordinates over the indicated time intervals.}
\label{QoverT}
\end{figure}

The difference in internal and free energy between the $Q=0$ and $Q=1$ states can be seen in Fig.~\ref{DeltaEF}(a). For using Eq.~\eqref{DeltaFInteg}, $\Delta F_{10,\textrm{count}}$ was determined at a temperature of $T_0 = 190$~K by comparing the number of states with different topological charges. Because the free-energy differences agree between the counting and the integral methods for temperatures $T>70$~K , the choice of $T_0$ is not critical for our results. The deviations at lower temperature can be attributed to the limitations of the simulation length discussed after Eq.~\eqref{DeltaFN}.

Since the metastability field $B_{\textrm{m}}$ for skyrmions in Fig.~\ref{phasediag} is significantly lower than the value of $B=1$~T used in Fig.~\ref{DeltaEF},  at low temperatures the topologically trivial configuration
is strongly preferred. $\Delta F_{10}$ has a minimum at around $T\approx85$~K with a value below $0$, showing that the skyrmion quasiparticles with the short lifetimes shown in Fig.~\ref{QoverT} are energetically preferred for a certain temperature range in this system even for such a high value of the external field. From Eq.~\eqref{DeltaFN}, it is clear that skyrmions occur more often at these temperatures than topologically trivial states. For higher temperatures, $\Delta F_{10}$ is slightly positive, but rapid changes in $Q$ may be observed in this regime.

Up to $T\approx50$~K, the
weak temperature dependence of the internal-energy difference and the linear decrease of the free-energy difference agree with the predictions of linear spin-wave theory in Sec.~\ref{sec2c}. The negative slope of $\Delta F_{10}$ indicates the entropic stabilization of skyrmions~\cite{Hagemeister2015, Desplat2018, Malottki2019}.
Note that for the considered external field and system size, the free-energy difference only reaches negative values at higher temperature where deviations from linear spin-wave theory are observed, particularly in the rapid reduction of the internal-energy difference.

\begin{figure}
\includegraphics[width=0.9\columnwidth]{Fig3a-eps-converted-to.pdf}
\includegraphics[width=0.9\columnwidth]{Fig3b-eps-converted-to.pdf}
\caption{(a) Internal- and free-energy difference per spin between skyrmion ($Q=1$) and topologically trivial ($Q=0$) states as a function of temperature, for $B=1$~T and $N_{S} = 25 \times 25$. The free-energy difference $\Delta F_{10,\textrm{count}}$ is calculated from Eq.~\eqref{DeltaFN} and $\Delta F_{10,\textrm{integ}}$ from Eq.~\eqref{DeltaFInteg}. (b) Difference in entropy per spin between skyrmionic and topologically trivial states as a function of temperature, for the same parameters. Dashed lines denote the prediction of linear spin-wave theory, Eq.~\eqref{eqn10}, \eqref{eqn11}, and \eqref{eqn13}.
}
\label{DeltaEF}
\end{figure}

From $\Delta F_{10}$, we calculate $\Delta S_{10}$ using Eq.~\eqref{eqn9}, with the result shown in Fig.~\ref{DeltaEF}(b). Between $25$~K and $50$~K, the entropy difference is slightly decreasing, in agreement with Eq.~\eqref{eqn13} derived from linear spin-wave theory and indicated by the dashed line in the figure. Unfortunately, at very low temperature where the logarithmic dependence would dominate, the inaccuracies caused by the numerical integration in Eq.~\eqref{DeltaFInteg} and differentiation in Eq.~\eqref{eqn9} obscure its influence.

Above $50$~K, approximately corresponding to the critical temperature determined at zero field in Fig.~\ref{phasediag}(b), the entropy difference between the considered states is drastically reduced. As shown in the figure, spin-wave theory loses its validity in this regime due to the strong thermal fluctuations, which lead to the rapid creation and destruction of metastable skyrmions. Remarkably, the skyrmion quasiparticles actually have a lower entropy for certain temperatures than $Q=0$ states. The temperature range where $\Delta S_{10}$ is negative is confined between the extrema of $\Delta F_{10}$, as expected from the derivative expression~\eqref{eqn9}, and shifted towards higher temperatures as compared to the temperature range with negative $\Delta F_{10}$. It is established that in the low-temperature limit where spin-wave theory is applicable, the competition between positive internal-energy difference and negative entropy difference contributions causes the free energy of skyrmions to become lower than that of the collinear state as the temperature is increased~\cite{Muelbauer2009}. However, these results indicate that for skyrmion quasiparticles with reduced lifetimes in the strongly fluctuating regime
the stabilization mechanism is more complex, and the role of the internal-energy and the entropy terms may become reversed as both of them change sign. In the skyrmion lifetime, the pre-exponential factor of the Arrhenius law is similarly affected by the entropy of the different states~\cite{Hagemeister2015, Desplat2018, Malottki2019, Bessarab2018,Wild2017},
meaning that the observed decrease in $\Delta S_{10}$ may also influence the lifetime in this regime. The temperature in this regime is still relatively low compared to the energy barrier $\Delta E/k_{\textrm{B}}\approx 922$~K, reinforcing the validity of the Arrhenius expression.

In Fig.~\ref{Compare}, $\Delta F_{10}$ is calculated for different external magnetic fields applied perpendicular to the surface and different sizes of the simulated system. It is visible in Fig.~\ref{Compare}(a) that strong external fields increase the internal- and free-energy difference at zero temperature, which can suppress the minimum in $\Delta F_{10}$, meaning that skyrmion quasiparticles cannot become favored even at elevated temperatures. At lower magnetic fields, the temperature range where skyrmions are energetically preferred is larger and it extends to lower temperatures. Also the minimum value of $\Delta F_{10}$ is even lower than for higher field values. The lower limit of the temperature range where skyrmions are stable is expected to reach $0$~K at $B_{\textrm{m}}\approx0.1$~T, where isolated skyrmions on an infinite collinear background become energetically preferable (cf. Fig.~\ref{phasediag}(a)).

Simulations with different system sizes are compared in Fig.~\ref{Compare}(b). In our finite-size system, the skyrmions interact with themselves via the periodic boundary conditions, thereby raising the internal-energy difference and with that also the free-energy difference. Since even isolated skyrmions have a higher internal energy at zero temperature than the collinear state, the free-energy per spin also decreases with increasing the system size for a fixed number of skyrmions as the relative size of the field-polarized areas increase. However, the increased ratio of the field-polarized areas decreases the entropy difference as well, as indicated by the reduced slopes of the free-energy curves in the low-temperature regime in Fig.~\ref{Compare}(b). It is obvious that simulating with too small systems can cause the minimum in $\Delta F_{10}$ to only have positive values, which means that topologically trivial states are always preferred over $Q=1$ states. On the other hand, increasing the number of simulated spins lowers the free-energy difference per spin, as can be seen by comparing the case $N_{S}=25 \times 25$ to $N_{S}=28 \times 28$, making $Q=1$ states also being preferred over a wider temperature range. Note that further increasing the system size may cause the formation of multiple skyrmions in the system at elevated temperature with a high probability, which effect was to be avoided in our simulations, similarly to Ref.~\cite{Hagemeister2015}. We mention that increasing the system size does not eliminate the interactions between skyrmions: at high temperature, a finite density of interacting skyrmions is observable instead of an isolated skyrmion at zero temperature, which is reflected as a finite probability of finding a skyrmion in the small systems considered here.

A numerical comparison of the entropy differences obtained from the simulations and from linear spin-wave theory at $T=25$~K is presented in Table~\ref{table1}.
Treating the translational degrees of freedom as Goldstone modes following Eq.~\eqref{eqn13} provides reasonable agreement with the simulation data. This is expected since the energy barrier between different positions of the skyrmion created by the modulating potential of the atomic lattice, which technically breaks the continuous translational symmetry, is negligible at all simulated temperatures ($\Delta E/k_{\textrm{B}}\approx 10^{-8}$~K based on GNEB calculations). If the finite frequency of the translational modes is taken into account, similarly to the procedure in Refs.~\cite{Desplat2018,Desplat2020}, then achieving agreement with the simulation results requires assuming a frequency which is around three orders of magnitude higher than the numerically calculated value for the translation mode. Treating the translations as a finite-frequency mode does not reproduce the weak logarithmic temperature dependence, which is more pronounced for smaller system sizes, in agreement with
Eq.~\eqref{eqn13}; see Supplemental Fig.~1~\cite{supp}

Linear spin-wave theory apparently reproduces the decrease of the entropy difference for larger system sizes observable in Fig.~\ref{Compare}(b) and discussed above. While the entropy difference only depends weakly on the external field in the considered regime, it is remarkable that the linear regime in the free-energy difference, indicative of the validity of the linear spin-wave approximation, extends over a larger temperature range for higher field values. On the one hand, this effect is rather counterintuitive when only considering the energy barriers, namely the energy differences between the stable states and the saddle point configuration $S$: $\Delta E_{S1}$ for skyrmion annihilation decreases as the field is increased, while $\Delta E_{S0}$ for skyrmion creation stays mostly constant (see Table~\ref{table2} for the numerical values), which would point towards a reduced skyrmion stability and less reliability of the linear spin-wave approximation. On the other hand, the spin-wave frequencies also increase for higher field values, as shown in Ref.~\cite{Rozsa_2020} for the present system. This means that although the energy barriers become lower as the field is increased, the minima simultaneously become sharper, and less magnons are excited at the same temperature. The reduced number of magnons suppresses the interaction between them, which may explain why the non-interacting linear spin-wave model remains applicable in a wider temperature range. This observation also agrees with the phase diagrams obtained in Refs.~\cite{Rozsa2016,Boettcher2018}: the crossover temperature from the field-polarized regime to the completely disordered paramagnetic regime is increasing for higher external field values, and this temperature value marks the maximum of spin fluctuations at a fixed field value.

\begin{figure}
\includegraphics[width=0.9\columnwidth]{Fig4a-eps-converted-to.pdf}
\includegraphics[width=0.9\columnwidth]{Fig4b-eps-converted-to.pdf}
\caption{(a) Free-energy difference per spin as a function of temperature for different magnetic fields at a simulated system size of $N_{S} = 25 \times 25$ spins. (b) Free-energy difference per spin as a function of temperature for different simulated system sizes at an external magnetic field of $B=1$~T. All curves are calculated using Eq.~\eqref{DeltaFInteg}.
}
\label{Compare}
\end{figure}

\begin{table}
 \caption{\label{table1} Entropy difference between the $Q=1$ and $Q=0$ states at $T=25$~K, obtained from numerical simulations
and from linear spin-wave theory Eq.~\eqref{eqn13}, respectively.
 }
\begin{ruledtabular}
 \begin{tabular}{cccc}
   $N_{S}$                        & $B$~(T)                       & $\Delta S_{10,\textrm{sim}}$~(nRy/K) & $\Delta S_{10,\textrm{SW}}$~(nRy/K) \\\hline
   $20\times20$     & 1.00 & 82.05 & 91.78  \\
   $25\times25$     & 0.75 & 61.08 & 64.38  \\
   $25\times25$     & 1.00 & 57.55 & 62.92  \\
   $25\times25$     & 1.50 & 56.05 & 63.09  \\
   $28\times28$     & 1.00 & 47.42 & 52.08  \\
 \end{tabular}
\end{ruledtabular}
\end{table}

\begin{table}
 \caption{\label{table2} Energy barriers for skyrmion annihilation $\Delta E_{S1}$ and skyrmion creation $\Delta E_{S0}$, where $S$ denotes the saddle-point configuration between the $Q=1$ and $Q=0$ states. The annihilation barrier was determined from an Arrhenius fit to the skyrmion lifetimes obtained from the simulations in the range $60~\textrm{K}\le T\le 85~\textrm{K}$, while for the creation barrier the relation $\Delta E_{S0}=\Delta E_{S1}+\Delta E_{10}$ was used. Values obtained from the GNEB method are provided for comparison, displaying the same trends when varying the system size and field strength
 }
\begin{ruledtabular}
 \begin{tabular}{cccccc}
   $N_{S}$                       & $B$~(T)                       & \multicolumn{2}{c}{$\Delta E_{S1}/k_{\textrm{B}}$~(K)} & \multicolumn{2}{c}{$\Delta E_{S0}/k_{\textrm{B}}$~(K)} \\
    & & sim & GNEB & sim & GNEB \\\hline
   $20\times20$     & 1.00 & 918  & 800 & 1306 & 1190 \\
   $25\times25$     & 0.75 &  1008 & 850 & 1328 & 1170 \\
   $25\times25$     & 1.00 &  922 & 800 & 1310 & 1190 \\
   $25\times25$     & 1.50 & 835  & 720 & 1335 & 1220 \\
   $28\times28$     & 1.00 & 929  & 800 & 1321 & 1190 \\
 \end{tabular}
\end{ruledtabular}
\end{table}

At high temperatures, the topological charge can take many different values during a single simulation, and the time average in Eq.~\eqref{Qtime} was used for calculating the average topological charge. The resulting average of the topological charge $\left<Q\right>$ as a function of temperature $T$ is shown in Figure~\ref{pQ}. At low temperature where the transition times between different topological charges exceeds the simulation times, the ensemble average in Eq.~\eqref{Qens} was approximated by using the free energies of topological charges $Q=-1, 0$, and $1$. For the data with topological charge $Q = -1$ we performed simulations with an antiskyrmion as the initial condition. Since the antiskyrmion has considerably higher energy than the skyrmion in the system~\cite{Rozsa2017}, we found no minimum either in the free-energy difference $\Delta F_{-10}$ or in the entropy difference $\Delta S_{-10}$; see Supplemental Fig.~2~\cite{supp}.
\begin{figure}
\includegraphics[width=0.9\columnwidth]{Fig5-eps-converted-to.pdf}
\caption{Average value of Q calculated with ensemble average using free-energy values of topological charges $Q=-1, 0, 1$ (green) and time average over all topological charges (blue). System simulated with $N_{S}=25 \times 25$ spins and $B = 1$~T external field.
}
\label{pQ}
\end{figure}

In Fig.~\ref{pQ} it can be observed that the thermal fluctuations cause a considerable increase in the average topological number in the system, especially in the regime directly above $T_{\textrm{c}}\approx50$~K. This is in agreement with the results of Refs.~\cite{Rozsa2016,Boettcher2018} in skyrmionic systems similarly described by spin models based on \textit{ab initio} calculations. Notice that at around $T\approx85$~K, there is a regime with average topological charge above $0.5$ for the time average. This provides further evidence that skyrmions are thermodynamically preferred at elevated temperatures in the considered system. Note that the ensemble average is close to the time average between $50$ and $80$~K, but it stays below $0.5$ for all temperature values. Although the $Q=1$ state has lower free energy than the collinear state close to the maximum of the average topological charge, taking the presence of antiskyrmions into account reduces the average value below $0.5$. However, a lot of changes of the topological charge are recorded at this temperature range, as can be seen in Fig.~\ref{QoverT}, and considering higher $Q$ values in the time average increases the average above $0.5$. At low temperature, the average topological charge vanishes since skyrmions are energetically unfavorable compared to the topologically trivial state. At very high temperature, $\left<Q\right>$ again converges to zero since all microstates, including those with positive and negative topological charges, contribute with similar weights to the total partition function in this limit. Figure~\ref{pQ} demonstrates that combining Eq.~\eqref{Qtime} accurate at high temperature with Eq.~\eqref{Qens} which can be applied at low temperature enables the calculation of the average topological charge ranging from the completely ordered to the completely disordered regime, with reasonable agreement between the two methods in the intermediate temperature range where both of them are valid.

\section{Conclusion}
We calculated the free-energy and entropy difference between a skyrmion and the topologically trivial state in a (Pt$_{0.95}$Ir$_{0.05}$)/Fe bilayer on a Pd(111) surface by means of numerical simulations. We found that the free-energy difference turns from positive to negative as the temperature is increased, meaning structures with $Q=1$ are thermodynamically preferred over topologically trivial states in a certain temperature range. We demonstrated that this range vanishes at higher magnetic fields or smaller system sizes, where the internal energy of skyrmions with respect to the collinear state becomes higher. We showed that $Q=1$ configurations in a time average can still be identified with skyrmion-like spin structures in this temperature range, although they are frequently created and destroyed by thermal fluctuations. The preference for the formation of skyrmions at elevated temperature agrees with the prediction of entropic stabilization based on linear spin-wave theory, but qualitative deviations from this approximation have been observed in the thermodynamic quantities. In particular, we found that while skyrmions have higher entropy at low temperature, their presence reduces the entropy at elevated temperatures. We calculated a composite average of the topological charge via combining an approximate average in the canonical ensemble based on the free-energy calculations at low temperature with a time average at higher temperatures. We found the time average of the topological charge to reach values over $0.5$ in the temperature range where we found skyrmions to be thermodynamically preferred.

Although skyrmions are preferred by the free energy in a certain parameter regime, this does not mean that these topologically non-trivial states are stable at this temperature. The deviations from linear spin-wave theory based on stable equilibrium structures are pronounced in this regime characterized by strong thermal fluctuations, and the lifetime of skyrmions is considerably reduced as confirmed by our simulations. This shows that skyrmions cannot be interpreted as particles with a conserved topological charge, but should rather be seen as quasiparticles with a finite chemical potential. The non-integer average topological number in this regime corresponds to the probability of finding a skyrmion in the system, if the contributions from higher or opposite topological charges can be neglected. These results should stimulate further studies on the properties of topologically non-trivial spin structures in the presence of strong thermal fluctuations.

\begin{acknowledgments}

The authors would like to thank Bertrand Dup\'{e} for stimulating discussions. Financial support by the German Research Foundation via SFB 1432 and via Project No. 403502522 and by the National Research, Development and Innovation Office of Hungary via Project No. K131938 is gratefully acknowledged.

\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Jonathan Borte (ball in hand) stands next to Jake Davies warming up before their first game against Emerald Ridge. Photo by Ben Ray/Sound Publishing
Kentridge grads launch water polo program
There are 18 sports sanctioned by the Washington Interscholastic Activities Association (WIAA) — but water polo is not one of them.
by Benjamin Ray
Tuesday, December 6, 2022 1:12pm
Jake Davies and Jonathan Borte have revitalized their former high school water polo program at Kentridge High School. Both coaches played for the Chargers water polo program for four years and wanted to give back to the community that had given them so much.
"Realistically, these boys will only play water polo for three to four years, but we are hoping the teamwork and punctuality, all these skills we can teach them will help them become better young men for the community," Borte said.
Borte played Division 1 water polo at Wagner College in Staten Island, NY, and Davies swam at Whitworth University in Spokane. They have been friends since they were 8 years old.
"Another reason I started was also to reconnect with this guy. We have played on a lot of local teams at a bunch of different levels. I wouldn't have wanted to do it with anyone else. It's been incredible," Borte said of Davies.
One troubling aspect of the program that Borte and Davies have started is they are not officially recognized by Kentridge High School. Therefore the coaches have to rely on parents and older teammates for transportation to things like pool time, for which they go to another school district.
"We rent out time from Lindbergh, which they are awesome to us. We have a really good relationship with the Renton School District and appreciate the leadership there," Davies said.
Ever since the two coaches were in the pool, they have battled the same circumstances. With those challenges, the team powers forward. Some teams in the area are supported by their respective schools. But as one who isn't, Davies sees this as a badge of honor.
"Because there were schools who were funded, and we were like 'Oh look what we can do with this.' I can't say that about all of our athletes, but I think it is impressive to do so much with less," he said.
The beginning of the season was quite difficult for the brand new coaches.
"It is trying to learn from square one. Neither of us have any substantial coaching experience. It isn't something that people haven't done before, but it's new to us," Davies said.
They were also uncertain if they would even have enough players to start the season.
"We had five guys we knew we had for sure. We were worried when we had our first initial meeting at a park up in Fairwood and four players showed up. We were thinking, that's half a team. We weren't going to have the numbers to compete," Borte said.
But now at the end of the season, the Chargers have 15 players and nearly enough to field a JV team.
Most of the players who joined the team were swimmers. Only one player had experience playing prior to this season — sophomore Ryan Lloyd, who is also the goaltender for the Chargers.
"I definitely try to share my knowledge as much as I can with the defense," Lloyd said.
Jake Davies (left) and Jonathan Borte (right) drumming up a strategy at the ASD Spookfest Water Polo Tournament. Photo by Ben Ray/Sound Publishing
Junior Anders Erickson is in his first year as a water polo player. He has swam for as long as he could remember. His brother played water polo for Kentridge for three years, but he joined for other reasons.
"At first I just joined for the conditioning. I thought it would help me prepare for the swim season in the winter. But I just fell in love with the sport. It's awesome," Erickson said.
Both players echoed each other's frustration at not being called an official sport.
"We are trying to build it to be more than just a club," Erickson said.
Kentridge competed in the Auburn School District Spookfest Tournament where they finished sixth out of eight teams. Davies, similar to his assistant coach, sees value in playing tough opponents.
"The real wins haven't even really been counted as W's. Maybe it is playing the 9-0 team and showing that you can hang with the best…The significance comes from playing at a higher level. Some of these kids have really stepped up," he said.
The goal for both coaches is to expand interest in the state, and they believe they can do it.
"You know, in a dream I want it to be a sport that is seen much frequently at the high school level," Davies said. "The exciting thing is we have some serious plans here to help not only our program, but also help create opportunities for an underserved region."
T-Birds to play hockey game at Climate Pledge Arena in Seattle
Gonzaga women's basketball to honor ex-Kentwood star Vandersloot
WNBA player to have Gonzaga jersey retired and hung at McCarthey Athletic Center in Spokane
Federal Way drops Kentridge boys in heavyweight bout
Eagles pull away in second quarter en route to 76-62 victory
Kentwood High boys and girls basketball teams fall to Tahoma
Bears dominate Conquerors in both NPSL games
Kentwood's Sarah Wright goes undefeated at girls wrestling meet
Kentwood, Kentridge, Kent Meridian and Kentlake compete beginning at 5 p.m. Thursday, Jan. 26 at Kentwood High School.
King Showcase: Kentridge boys and Kentwood girls come out on top
Kent high school basketball teams went 2-1 in the accesso ShoWare Center… Continue reading
Basketball: Kentwood drops close game to defending state champs
On Jan. 13, the Kentwood Conquerors fell to the Auburn Trojans, 65-61,… Continue reading
Martin Sortun and Lake Youngs win Kent elementary schools volleyball crown
Martin Sortun and Lake Youngs were crowned champions at the Kent elementary… Continue reading
Todd Beamer wrestling team takes down Kentlake
Todd Beamer High School began their boys wrestling duel season Dec. 7… Continue reading
Kentridge beats Lions by 18, extends win streak to three games | Basketball
The Kentridge Chargers took down the Lions of Auburn Mountainview 76-58 on… Continue reading
Seattle Thunderbirds move to No. 1 in Canadian Hockey League poll
First top ranking of the season for Kent-based team
565 participate in 40th Kent Christmas Rush 10K/5K run/walk
Tahoma High senior Daniel Castelluccio, 17, wins 10K

redpajama_set_name: RedPajamaCommonCrawl


text:
Tigers have trouble handling ball, quarterback
9/2/2005 - by Jake Donelan
Bellevue, KY - Bellevue, KY – It didn't take long for the Indian Hill Braves to play spoiler to an optimistic Bellevue Tigers team that has started the season with two straight wins.
Bellevue, who has opened the season by leading all Northern Kentucky teams in scoring with a total of 95 points in two contests, but fell to the Braves 48-20 at Gilligan Stadium.
The right arm of the Braves' senior quarterback Mike Scherpenberg had plenty to do with the demise of the Tigers. The first play from scrimmage was a 62-yard strike from Scherpenberg to senior receiver Jake Kendell for the game's first score just 10 seconds into the first quarter.
The Braves got the ball back quickly after recovering a fumble deep in Tigers' territory. The Braves' then caught the Tigers defense on a blitz and set up there second score in as many plays when Scherpenberg hit running back Case Cousino with a screen pass. Cousino took the pass 20 yards untouched to the endzone.
Turnovers were a key in the seemingly uncharacteristic lack of offense for the Tigers tonight. They put the ball on the ground seven different times and lost possession on four of those.
After throwing for 337 yards and 4 touchdowns last week, Scherpenberg picked up right where he left off. By halftime he was 12-14 with 255 yards and three touchdowns.
Scherpenberg finished 19-27 for 396 yards, five touchdowns and one interception. He hit five different receivers. His favorite target was Jake Kendell who caugth 9 passes for 157 yards and 3 touchdowns.
Despite the score, Bellevue had a bright-spot in senior running back Lincoln Adams. Adams finished the game with 247 all-purpose yards. He gained 104 yards on 11 rushes and had 138 yards on 6 kickoff returns.
Next week Bellevue will try to get back on the winning side of the scoreboard as they travel to the banks of the Ohio River to take on the Ludlow Panthers.
Remember, you can view pictures of tonight's game later in the week by clicking on the photos tab at the top of the site. All pictures are available for sale.


text:
Viewership for Lifetime Continues to Grow
Lifetime spins the numbers for the year to date.
[via press release from Lifetime]
Network Logs in Strongest November-to-November Growth among Key Demographics in Nearly Two Decades
LOS ANGELES, CA (November 29, 2012) - Viewership for Lifetime continued to grow during the month of November, marking double digit jumps and the network's strongest November-to-November growth among the key demographics in nearly two decades.
Among Adults 25-54, Lifetime posted a +18% increase vs. November 2011, the best year-to-year growth in eight years, while it was up +25% in Women 18-49, +22% among Adults 18-49 and +20% with Women 25-54 - a network best for all three demos in 17 years, according to Nielsen Research. Lifetime also made significant jumps in rankings during November, including ranking #9 among Women 25-54 (vs. #14 last year), #11 in Women 18-49 (vs. #18); #19 with both Total Viewers and Adults 25-54 (vs. #24); and #21 among Adults 18-49 (vs. #26).
Supported by last Sunday's premiere of the Lifetime Original Movie Liz & Dick, Lifetime was the November's top cable network for movies in total day among Women 25-54. Liz & Dick was the number one original cable movie of the month among Total Viewers, Adults 25-54, Women 25-54, Adults 18-49, Women 18-49, Adults 18+ and Women 18+. It was also November's number one primetime movie telecast among Total Viewers, Women 25-54, Women 18-49, Adults 18+ and Women 18+.
Year-to-date, Lifetime is continuing to pace ahead of 2011, registering a +16% increase in Women 18-49, its strongest year-to-year jump in 14 years; +10% in Adults 18-49, a network best in 11 years; +9% among Women 25-54, Lifetime's strongest in a decade; and +4% in Adults 25-54, a best in seven years. Lifetime is ranking #5 YTD among Women 25-54 (vs. #9 last year), #6 with Women 18-49 (vs. #12), #14 in Adults 25-54 (vs. #17), #17 in Adults 18-49 (vs. #22) and #16 among Total Viewers (vs. #19). Among the top 10 basic cable networks, Lifetime is the second fastest growing with Women 18-49. Lifetime's YTD median age of 48 is its youngest in 16 years.
Lifetime's YTD highlights include:
·	Lifetime is the #1 basic cable network for original movies in 2012 YTD among Total Viewers, Adults 25-54, Women 25-54, Adults 18-49, Women 18-49, Adults 18+ and Women 18+.
·	Steel Magnolias, Drew Peterson: Untouchable, Abducted: The Carlina White Story and Liz & Dick are the #1, #2, #3 and #4 original movie premieres across ad supported cable among Total Viewers, Adults 18+, Women 18+, Adults 25-54, Women 25-54, Adults 18-49 and Women 18-49 (excluding miniseries).
·	Steel Magnolias premiered with 6.5 million total viewers to become Lifetime's third most-watched telecast ever. Also, it was the number one movie across ad-supported cable networks with Total Viewers since 2007, with Adults 25-54 since 2006 and with Women 25-54 since 2004 (excluding mini-series). Steel Magnolias was Lifetime's best original movie ever with Women 25-54, since 2006 with Total Viewers and since 1995 with Adults 25-54.
·	Liz & Dick was the 4th most watched original ad supported cable movie premiere of the year among Total Viewers, Adults 25-54, Women 25-54, Adults 18-49, Women 18-49, Adults 18+ and Women 18+, behind Steel Magnolias, Drew Peterson: Untouchable and Abducted: The Carlina White Story.
·	Project Runway Season 10 propelled Lifetime to be the #1 cable network in the Thu 9-10:30pm time period among Women 25-54.
·	The season premiere of Project Runway All-Stars Season 2 was the #1 unscripted series across cable in its Thu 9-10pm time period among Women 25-54.
·	Dance Moms season 2 was the #1 unscripted cable series in its Tuesday 9-10pm time period among Women 18-49 and Women 2+. Season 2 over-delivered season 1 by +69% with Adults 18-49, +72% Women 18-49, +64% with Adults 25-54 and +66% with Women 25-54. It is Lifetime's youngest skewing current series with a Season 2 median age of 32 years old, five years younger than Season 1.
·	Abby's Ultimate Dance Competition has seen steady increases throughout the season among Adults 25-54, Adults 18-49 and Women 18-49. The most recent episode was up vs. the series premiere by +4% among Adults 25-54, +17% among Adults 18-49 and +9% among Women 18-49.
·	The Houstons: On Our Own series premiere was the #1 telecast in its Wed 9-10pm time period across cable among Women 25-54 and Women 18-49. The Houstons has improved the 2012 YTD Wed 9-10p time period average by +47% among Adults 25-54, +57% among Women 25-54, +33% among Adults 18-49 and +43% among Women 18-49.
·	Army Wives and Drop Dead Diva launched Lifetime to the #1 cable network on Sundays 9-11pm among Women 25-54.
·	Army Wives Season 6 was the #1 ad-supported cable series in its premiere time period among Women 18+. YTD it ranks as top 5 ad-supported cable drama among Women 18-49 (#5).
·	Drop Dead Diva ranked as the #1 drama across ad-supported cable in the Sunday 9-10pm time period with Women 25-54, Women 18-49, Women 2+ and Women 18+.
·	The Client List delivered Lifetime's strongest freshman season for an original series since Drop Dead Diva (Jul-Oct 2009) among Total Viewers, Adults 25-54 and Women 25-54. Among A18-49 and W18-49, it was the best freshman season since Army Wives premiered in Jun-Aug 2007. The Client List propelled Lifetime to #1 in the Sunday 10-11pm hour among Women 18+.
·	America's Most Wanted has improved the Friday 9-10pm daypart by +42% with Adults 25-54, +21% with Women 25-54, +38% with Adults 18-49, +19% with Women 18-49 and +36% with Total Viewers.
Last month, Lifetime registered a +16% increase among Women 25-54 and +13% in Adults 25-54, the network's strongest October-to-October growth for the two demographics in 11 years. It also posted jumps of +20% among Women 18-49 and +14% with Adults 18-49 vs. October 2011 -- both network bests for the month since 2007. In First Quarter 2012, Lifetime posted major growth in viewership among the key demos versus First Quarter 2011, including a +9% jump in Adults 25-54, +12% with Women 25-54, +14% with Adults 18-49 and +18% with Women 18-49. For Second Quarter 2012, the network continued to enjoy growth compared to Second Quarter 2011, posting a 13% jump among Women 18-49, +5% among Adults 18-49 and +1% in Women 25-54. In Third Quarter 2012, Lifetime registered a +14% increase among Women 18-49 versus Third Quarter 2011, its strongest year-to-year growth for a Third Quarter in 11 years; +9% in Women 25-54, its strongest in a decade; and +5% among Adults 18-49, a 3Q best for Lifetime in 11 years. Lifetime's median age of 48 marked 3Q'12 as its youngest Third Quarter in 14 years.
ABOUT LIFETIME
Lifetime Television is committed to offering the highest quality entertainment and information programming, and advocating a wide range of issues affecting women and their families. In the Third Quarter 2012, the network posted major growth in viewership versus Third Quarter 2011, including a 14% increase among Women 18-49, +9% in Women 25-54 and +5% among Adults 18-49, marking the third straight quarter Lifetime has registered year-on-year growth among the key demographics. Lifetime Television(R), LMN(R), Lifetime Real Women(R) and Lifetime Digital(TM) are part of Lifetime Entertainment Services, LLC, a subsidiary of A+E Networks. A+E Networks is a joint venture of the Disney-ABC Television Group and Hearst Corporation.
· ABBY'S ULTIMATE DANCE COMPETITION (LIFETIME)
· ABDUCTED: THE CARLINA WHITE STORY (LIFETIME)
· AMERICA'S MOST WANTED (LIFETIME)
· ARMY WIVES (LIFETIME)
· CLIENT LIST, THE (LIFETIME)
· DANCE MOMS (LIFETIME)
· DREW PETERSON: UNTOUCHABLE (LIFETIME)
· DROP DEAD DIVA (LIFETIME)
· HOUSTONS, THE: ON OUR OWN (LIFETIME)
· LIZ & DICK (LIFETIME)
· PROJECT RUNWAY (BRAVO)
· PROJECT RUNWAY ALL STARS (LIFETIME)
· STEEL MAGNOLIAS (LIFETIME)


Pomme Kiwi by Saucy is an exciting, crisp eJuice bursting with fresh flavour! This "Made is Los Angeles" eliquid combines ripened kiwi fruit with a sweet but tart apple for a perfectly balanced, all-day vape.
Comes with: Two convenient 30ml squeeze bottles for a total of 60ml.
POMME KIWI – Apples and Kiwi ejuice.
POMME KIWI – Ripe Kiwi with Juicy Apple Ejuice.
Two 30ml Unicorn Squeeze Bottles. Available in Canada. Shipping from Ontario.


Sound One has launched Boom Wireless Portable Bluetooth speaker in India. According to the company, the Boom Bluetooth speaker can deliver the stereo sound with deep bass and zero distortion by high-sensitivity drivers.
Also, the SoundOne claimed that the speaker on one single charge can provide 6 Hours of continuous music. It also offers built-in Mic for Hands-Free calling.
The SoundOne Boom Bluetooth speaker carries a Bluetooth 4.1 Advance Technology that can connect up to 100 feet away placed device. Apart from the Bluetooth it also supports Aux-In & TF card for Non-Bluetooth Devices. The speaker is Durable, Portable & Water Resistant and made up of durable fabric material and metal finish with plastic housing, triple protection design, said by the SoundOne.
The Sound One Boom Wireless Portable Bluetooth speaker price is 2990 INR, however for the limited period of time, it available at 1790 INR. It carries a 1-year warranty and will be available on Amazon and PaytmMall.


text:
New Adventures from the Canceled Sport Season
Photo Credit: Antonio Hurtado
Judy Ann Quang, Reporter
"If you were to tell me at the beginning of the year that my senior year would fall apart during the second half, I wouldn't believe you," said Senior Antonio Hurtado. People around the world have been affected by a recent pandemic called the coronavirus which began in late 2019 and is continuing to grow even today.
Not only is the coronavirus affecting people, it's also having a major impact on many restaurants, hotels, corporations, resorts, attractions and events as people are forced to shut down in hopes of preventing the coronavirus from spreading.
During this time, a majority of schools have been shut down. This has a major influence on students around the globe as they are forced to do online school and some college students are forced to take their belongings and move out of their college dormitories. As the pandemic is spreading around the world, many teachers are trying to find solutions to give students a chance to learn and complete schoolwork at home.
The Class of 2020 has been a bumpy road ahead as they might not be able to receive a chance to walk during graduation, go to prom, finish their final season of the year, and much more.
Many seniors like Antonio Hurtado are affected by the coronavirus as a track runner for the LHHS Knights. I feel a lot of pain, confusion and anger built up inside from my last season as it ended so quickly. Honestly, it's been really depressing that we may not be able to walk when we've been working so hard our whole lives just to get to that point and walk on the same stage as all of our friends. It was a very emotional time for everyone even for seniors, whether we competed in a spring sport or not
Hurtado had a goal before this final season of track as he enjoyed this sport with a passion and enjoyed the LHHS track team and football team as he will never forget all the memories they have made together. "My goal throughout my whole track career was to hit at least 11.9 on the 100 and 24.9 on the 200 and I only reached my 100-meter goal this season. Occasionally, he felt like these goals were impossible to do, but he worked hard to reach them and felt accomplished when he reached his 100-meter goal.
But the LHHS track team was so much more than just a sport, for it influenced his life heavily. "It was a means of escape from my personal problems where I could freely compete and have fun in the process."
Even though it might be Hurtado"s last season, he still wishes luck to his other teammates and will cherish the memories he made."I can't believe my senior season in track has come to an end in less than a month from the season starting. I want to thank everyone I've met through the track team, and everyone I've competed with and against. And I will do my best to support them, for I am forever a fighting Knight. Good luck to the remaining student-athletes that will compete in their remaining season."
The LHHS track team will always hold a special place in Antionio Hurtado heart and will definitely show as much support as he can for the season yet to come.
Senior Antonio Hurtado isn't the only senior being changed by the coronavirus; multiple seniors are experiencing similar emotions regarding online schooling. Yet, this is not the end of Class of 2020; they are still standing strong in hopes of walking on the graduation stage with their friends.
Judy Ann Quang, Business/Social Media/Advertising/Website Editor
Hey. My name is Judy Ann Quang, and I am the weirdest person you will ever meet. I am currently the Business/Social Media/Advertising/Website Editor. I...
See our Tweets on Twitter!
LHHS Knights in ActionFollow
LHHS Knights in Action@lhhs_knights·
LHHS 2020 Graduation https://youtu.be/zqdQn6OBDuY via @YouTube
Graduation pics brought to you by LHHS Yearbook Staff, https://drive.google.com/drive/folders/15Cud55cc_gGuC1bHyLI3uK1lhZZNVliR?usp=sharing
LHHS Evening of Excellence https://youtu.be/DukEf2-3T4E via @YouTube
If you are interested in being a member of the Freshman Mentor Club, please fill out the link below!
The main function of the Freshman Mentor Club is to help our freshmen transition into high school. There are three main requirements of club members:
Participate in Freshmen...
https://youtu.be/Q6O5KdrOBcE
lhhs_knights
Follow us for the latest updates on what events, games, and fun is happening at LHHS!
Senior sunrise is postponed! See you on November 1
show us your school spirit using #purpleshirtfrida
picture day's coming up!! please read all the in
Wear your purple shirts tomorrow to support our kn
We will remain in distance learning until October
Here are the revised fall sports paperwork due dat
please keep these in mind on your zoom calls!!💜
Swipe over to see the days fall sports paperwork i
Happy first day of school! Since we can't be tog
Top Tips for Acing the ACT
What's better hand washing or hand sanitizing?
Ending divisions: learn to surrender to one another
Video Games Now Being Played as a Sport With Cash Prize Opportunities
Thanksgiving is coming so why do people celebrate unoriginal tradition
CTE cabinetmaking blossoms student's creativity
Medical Terminology opens door to new experiences
Free meals given to any child
How will students take ACT, SAT during pandemic
How Food Waste Affects Our Planet.


text:
Q: Is this cleaning product safe to use on the screen of my laptop? This is the link to the product.
This is the link to my laptop specs.
If you don't want to go there, I'll just paste the display specs here:
15.6" FHD (1920x1080/16:9) LED Retroiluminado 120Hz 300nits 3ms
I think that's all. If you need more info, comment and I'll edit this question. Also, If you want to recommend another product that's better or cheaper maybe, you cando it. I'm from Spain btw, just in case, for the shipping.
Thanks in advance.

A: A clean microfiber cloth with a little bit of clean water has proven really effective for me. I wouldn't mess with vinegar or other stuff - could mess with delicate coatings, and/or leave residue. Get one corner of the microfiber a bit wet, and use that to wipe the whole screen - gets off fingerprints, etc. Then use the dry part of the cloth to completely dry the screen.

A: Although the product is probably safe on computer screens it's not really necessary. As you will never know what coating may be on the screen nor what would dissolve it in seconds, why even risk it?
Microfibre & water alone will do the job just fine.
Microfibre actually doesn't 'like' being used with any kind of detergent cleaner, it clogs the fibres & makes them less effective.
Copied directly from my own answer at Ask Different - Cleaning my Macbook Pro Retina leaves greasy 'streaks' across the screen
Two microfibre cloths, available from any supermarket.
Don't get the 'smooth' ones specially for glass, they can be a bit hard on a plastic screen, get the 'fluffy' ones that make your fingers itch, like picking up tiny velcro.
One cloth completely wetted in lukewarm water [nothing else], then squeezed as dry as you possibly can [trick - fold in 4, then roll & wring. You really want it as dry as possible].
The other cloth totally dry.
If the screen is warm, you may need the first cloth very slightly wetter - but never anywhere near wet enough to dribble if squeezed - you really don't want any water that could run down the screen. The cloths work better when almost dry anyway.
If the screen is cold & also dark, i.e. computer off, you'll also find it much easier to see when it's clean.
Wipe the damp one gently over the screen, multiple times, turning the cloth, pay attention to the edges & corners. The trick is gentle repetition, rather than 'force'.
Then, whilst the screen is still very slightly damp, wipe over again with the dry one, completely drying the surface.
Smears gone forever… well, until next time ;-)
Please don't be tempted to use any type of domestic cleaner or alcohol. You never know what type of screen coating any given screen has & some cleaners can irreparably damage the coating layer of some screens.

A: Your laptop's manual states on page 11:

A: I have used a soft cloth or J-cloth . Make very wet, add a drop or two of "green " dish detergent, work into suds, wring out excess water, clean the screen and keyboard. Just suds - no excess water. Wet the cloth to remove all suds and wring out the water and wipe off the suds. This cleans, removes grease and fingerprints and does not damage screens. I have done this for years on many computers and iPhones. Free (assuming you wash dishes)

redpajama_set_name: RedPajamaStackExchange


text:
Q: Understanding array access with bitwise operators in diamond-square algorithm implementation The question arose from this article which references the implementation of the Diamond-square algorithm found in Notch's "Minicraft". The full source code is available here.
I don't understand how the methods used to access and change the array of values work.
Given a specified  width and  height we initialize a 1-dimensional array of doubles called  values of length  width * height and use the following methods to access and change the value of the point (x,y):
public double sample(int x, int y) {
    return values[(x & (width - 1)) + (y & (height - 1)) * width];
}

public void setSample(int x, int y, double value) {
    values[(x & (width - 1)) + (y & (height - 1)) * width] = value;
}

I don't understand the purpose of the operations x & (width - 1) and y & (height - 1), especially considering the fact that, to my understanding, width and height should equal  for the algorithm to work correctly. If this is the case shouldn't the operations return 0 every time (extremes excluded), since x < width and y < height?
The source mentions that these methods have 'the side effect of allowing the terrain to wrap perfectly across the edge of the generated texture', but I don't understand how's that achieved.


The Cumberland is located on the Eastbourne seafront, overlooking the promenade, the Bandstand, and the Channel. It is a short walk to the town centre and boasts sea views throughout. All rooms have a bathroom with a shower and a bath. Guests can also enjoy tea/coffee making facilities and most rooms have views of the sea. Some rooms have a balcony. The hotel's restaurant has an extensive menu; local produce is used whenever possible. The restaurant also boasts sea views and an extensive wine list. A full English breakfast is served every morning. Guests can relax in the vast lounge or at the Devonshire bar. A sun lounge and regular evening entertainment is also available.


text:
if(__name__ == '__main__'):

    import mavlinkplug.Modules.Module
    import mavlinkplug.Plug
    import logging

    #Handling logging options
    logger = logging.getLogger()
    logger.setLevel(logging.DEBUG)
    handler = logging.StreamHandler()
    handler.setLevel(logging.DEBUG)
    formatter = logging.Formatter("%(levelname)s - %(message)s")
    handler.setFormatter(formatter)
    logger.addHandler(handler)

    #Creating plug
    plug = mavlinkplug.Plug.Plug()
    plug.start()

    test = mavlinkplug.Modules.Module.MAVlinkPlugConnection(('tcp://127.0.0.1:45689', 'tcp://127.0.0.1:45688', 123), 'COM7', dialect='ardupilotmega', baud=115200)
    test.start()
    mavlinkplug.Plug.Plug.server_forever()

redpajama_set_name: RedPajamaGithub


A Brown Bag Lunch Talk is on Thursday, Feb 21 at noon at Schoodic Institute in Winter Harbor. Three live owls are the highlights of this program, which introduces participants to the owls native to Maine and New England. Bring your lunch. No registration is required. For more information, visit schoodicartsforall dot org.
NOTE: DUE TO WEATHER, THIS EVENT HAS BEEN POSTPONED.


This is a MIP Speed Tip 2.0mm Ball End Hex Wrench. These wrenches have high quality precision cut steel tip for accuracy. These tools are awesome for wrenching on your cars with a power screwdriver or electric drill that has a 1/4" quick release mechanism, and are perfect for quick maintenance on your cars.


Just when you thought there were not enough "crapps"
Discussion in 'iOS Apps' started by snow_mani, Dec 14, 2008.
Just when you thought that no one could come up with a new idea for another type of "crapp" to clog up the App Store, along comes Poo Price.
When I saw this on AppShopper.com I thought great. Just great. As if virtual pets, apps that make farting noises and the multitude of other crappy apps were not enough, now someone thinks it is a good idea to create an app that calculates how much of your per hour wage you are being paid while using the toilet.
I wish there was a flush button so I could flush crapps like Poo Price out of the App Store.
The scary thing is that I'm sure someone out there will actually pay money for this piece of crap.
PS: Now I know what I'm getting for Christmas!
Does Apple approve all of these "crapps"? Makes you wonder what their policy is sometimes.
Just don't be referring to iSkate as a "crapp app"!!
Now come on Rich, How could iSkate be a Crapp App? It's so wonderful!
But really, These Apps are starting to get a bit much. Is there now way Apple could implement a system, that after so many users give it a bad review, they check it out again?
There have been a ton of these recently because they were all banned from the app store and then apple finally allowed them so they all came at once.
Sorta makes you sick doesn't it?
So shall we start a campaing aimed at apple to re-instate the ban of the Crapp Apps?
Is there now way Apple could implement a system, that after so many users give it a bad review, they check it out again?
Problem is that people will have to buy it before they can give it a bad review. And I refuse to encourage the further development of crapps!
As I see it, Apple is essentially in a lose lose situation. The more controls they have on the types of apps available, the more they are open to critisism. I know that I would welcome Apple rejecting this type of app, but can you imagine the press they would receive if they made their controls on apps even tighter than they are already? I suspect they are more sensitive to this issue in light of potential competition (Andriod platform phones, etc).
Normally I would just ignore it like Everydaynormalguy and others did, but as Rocketman919 points out there have been a large number of this type of app lately and when I saw an app that has a stated purpose of calculating how much money the boss paid you while you took a dump I really had to vent!
Their policy is not to approve apps that violate their guidelines. If they rejected apps on the grounds of being terrible, there'd be 1,000 on the store instead of 10,000. Although the guidelines are sometimes kinda vague, and don't necessarily apply to everybody (hi, Google!).
Wow, just wow.... This developer obviously knows how to program apps, why doesn't he put it to a better use?
Exactly. They cant restrict it anymore for fear of nobody purchasing anything, yet have to keep the extremely bad stuff out, which will in turn lead to people complaining. Ahh, i wish it was like the android store. You know they even have a gameboy emulator on there?
Forget Gameboy emulators, a Commodore 64 emulator like I have on my PC. Now that would be nice!
I'm pretty damn close to purchasing a fart app, just to play through some of the desk intercoms here at work.


Call (888) 705-8877 or visit www.stratfordsuites.com.
May 12: Jr. Lilac Parade The Jr. Lilac Parade is a treasured, long- standing tradition in Spokane, WA. In fact, our next parade will be the 60th Annual event! Each spring, our community comes together in downtown Spokane to celebrate our children. You'll see elementary and middle school bands and drill units, youth organizations such as Scouts, dance groups, and other clubs. You might even see some of our local mascot celebrities, such as Butch, Swoop, and Spike. Many of our local city and county officials, as well as area businesses, join in the fun. It's an event you don't want to miss. Riverfront Park. Downtown Spokane. For more information, please visit www. spokanejrlilacparade.com.
May 30: 27th Annual AGORA Awards Greater Spokane Incorporated's 27th Annual Agora Awards program will take place on May 30 at The Davenport Hotel. The reception and ceremony are part of the region's premiere business awards event. Over the past twenty years, 400+ members of the regional business community have gathered each year to celebrate business excellence throughout the greater Spokane area. This is a chance for the public and Greater Spokane Incorporated to congratulate each of the businesses for the important role they play in the community and for contributing to the region's economic growth. The Davenport Hotel. 10 South Post St. Spokane, WA 99224. For more information, please contact Greater Spokane Incorporated at www.greaterspokane.org.


text:
package by.triumgroup.recourse.supplier.entity.dto;

import by.triumgroup.recourse.entity.dto.RegistrationDetails;
import by.triumgroup.recourse.entity.model.User;

import java.util.function.Supplier;

public class RegistrationDetailsSupplier implements Supplier<RegistrationDetails> {
    public RegistrationDetails get() {
        RegistrationDetails result = new RegistrationDetails();
        result.setEmail("a@b.c");
        result.setName("Ivan");
        result.setSurname("Shimko");
        result.setPassword("password");
        result.setPasswordConfirmation("password");
        result.setGender(User.Gender.MALE);
        return result;
    }
}


Describe the 6 key steps in the workforce development assessment and planning process, centered around a continuous quality improvement approach.
Demonstrate the series of worksheets to assess and explore strategies within ten core components of workforce development, including: Vision, Mission, Values; Leadership; Job Analysis and Position Requirements; Education and Professional Preparation; Recruitment, Screening and Selection; Incentives and Work Conditions; Professional Development and Training; Organizational Environment; Community Context; and Supervision and Performance Management.
Following the creation of our Workforce Development Framework (WDF) and brief we recognized the need for an accessible companion product to assist teams in an agency setting undertake the process of comprehensive workforce development. Our new Workforce Planning & Assessment Toolkit, developed following a thorough review of the workforce development literature in the public, private, and corporate sectors, guides teams through a comprehensive approach to workforce development including innovative strategies and practices in recruiting, developing and retaining a committed and competent workforce.


text:
Безводовка — название населённых пунктов.

Россия
 Безводовка — деревня в Бугурусланском районе Оренбургской области.
 Безводовка — посёлок в Челно-Вершинском районе Самарской области.
Безводовка — село в Кузоватовском районе Ульяновской области.
Безводовка — станция в Кузоватовском районе Ульяновской области.

Украина
 Безводовка — село в Миргородском районе Полтавской области.
 Безводовка — село в Ичнянском районе Черниговской области.

redpajama_set_name: RedPajamaWikipedia


text:
Original antique maps of New York City from our store. Our rare New York City map inventory features authentic maps of Colonial and Revolutionary War New York, historic maps of Manhattan, Brooklyn, Queens, the Bronx and Staten Island, as well as Currier and Ives city views and important city plans of Manhattan. Vintage pictorial maps of NYC are also for sale.
Columbia University. Bicentennial Celebration...
Peter Mondello
Columbia University. Bicentennial Celebration 1784-1984
Fine view of Columbia University, drawn by Class of 1978 Alumnus Peter Mondello (School of General Studies).
The view shows Columbia in the foreground, viewed from the north. As noted by Cinty Kaplan in her article about the view in the February 29, 1984 Barnard Bulletin,
In a nutchsell th[e] history of Coumbia appears on a new poster of the Columbia University Campus. Peter Mondello . . . spent a year working on the hand-drawn . . . poster. Mondello is a visual artist who specializes in aerial and architectural photographs and mapping projects for real estate and engineering companies . . .
"This is my own idea," said Mondello in a telephone interview. "It's a venture on my part to see if, one--I can make Money and two-- if I could make an attractive piece in a classical old style pen and ink drawing. "Referring to the present map of Columbia, which is included in catalogs and on folders, Mondello called them "not very attractive." That map depicts the campus in a one dimensional manner. Mondello's version, from an aerial photograph the he took, is three-dimensional and according to him "extremely accurate."
In drawing the buildings, Mondello foound "drawing all those windows" tedious. Another realistic characteristic of his poster is the meticulous representation of every statut from Alma Mater to Alexander Hamilton to Bellerophon Tamine Pegasus in front of the Law building.
Some of the surrounding area is also represented. I turned Harlem into a little forest to make it attractive. Mondello said the poster . . . includes no people. Mondello "originally toyed with the idea of drawing cars on Broadway and on campus" but decided it would look too cluttered. . . .
Mondello will be selling the poster for ten dollars and th same poster on parchmentr for fifteen dollars throug Alpha Phi sorority. . . .
According to Melanie Levinson, Vice President of Alpha Phi, after being on sale for one week in theFerris Booth Hall Lobyy one hundred posters were sold. However, sales have been discontinued until after Spring Break. . . .
Mondello would appear to have gone on to obtain a master's degree in Biblical studies from the Dallas Theological Seminary.
We have not been able to locate any surviving examples of the map.
Minor soiling.
Antique Maps / United States / New York / New York City
(South Street Seaport) Map of Land Situate on Front and South Street's in the Second Ward of the City of New York the Property of the Estate of Teunis Tiebout
The South Street Seaport of Lower Manhattan.
(WPA Manuscript Map of Manhattan) New York (Towne of Manhados or New Amsterdam) 1661 | New York in 1800
Wonderful manuscript map of Manhattan executed for as part of the Works Progress Administration, Federal Writers Project division.
Block 1760 Central Park
Monumental ink on drafting linen map of Central Park from the first half of the 20th century. The map was almost certainly a city planning document during Robert Moses's tenure as New York City Park Commissioner. It is primarily a schematic of water and electricity infrastructure within the Park, and in that respect, it is exceptionally detailed; for instance, main waterlines within the Central Park Zoo and Metropolitan Museum of Art are shown and labeled.
Map of the City of New York with the Adjacent Cities of Brooklyn and Jersey City
Interesting antique Ensign & Bridgeman map of Manhattan from the Battery to 32nd Street, with Williamsburg and Brooklyn Heights to the east (bottom).
Topographical Map of New York and Vicinity Embracing Fifteen Cities and above 1700 Square Miles. Showing Rapid Transit Routes Railroads Roads Canals Soundings Buoys &c. . . .
Detailed hand-colored lithographed map of the New York Metropolitan area, published in New York by Matthew Dripps.
New York: A View of the World
A play on the famous New Yorker cover by Steinberg "A View of the World from Ninth Avenue," expanding its remit to the whole state of New York. This view was published by Harvey Hutter & Co. in New York in c. 1989 and forms part of a series of city-focused views that all play on the famous cover.


At Harry & David, we believe that minimizing our impact on the environment is simply the right thing to do. We demonstrate this commitment in all aspects of our business – from sustainable farming, to recycling, to responsible purchasing … and we've been doing it for nearly three decades.
By increasing our investment in our e-commerce division, we've successfully moved a large number of catalog customers to our Internet site. We've been able to eliminate over 37 million catalogs from the mail-stream, resulting in paper reduction of approximately 35%, or 9,310,000 pounds compared to our 2003 consumption.
Through refined database marketing, targeted product assortments and enhanced Internet promotions, we'll continue to utilize our website to further reduce material consumption. And currently in development is our new Customer Preference Center where our customers can let us know exactly what catalogs they'd like to get, effectively reducing unwanted mailings.
Every year we save over 5,000 megawatt hours of electricity by employing high efficiency lighting, combustion improvements to our steam boilers, and computer-controlled HVAC and refrigeration systems, thereby reducing CO2 emissions by more than 5,000 tons annually.
Helped fund the Jackson County Expo Solar Energy Project.
We recycle more than 75% of our office paper and 99% of all corrugated materials.
Over 64% of the solid waste including cardboard, paper products, all plastic, steel, wood, oil, antifreeze, electrical wire, florescent light bulbs and glass is recycled today.
The Carbon Sequestration rate of our combined orchards is 22,000 tons of CO2 per year.
Harry & David participates with the Oregon Department of Environmental Quality workgroups to identify best management practices and to encourage composting as a means for solid waste management.
Harry & David worked with landowners, state and federal agencies, and environmental advocates on a Rogue River stream channel restoration project to develop high-value salmon-rearing reaches.
The company has three organically certified Royal Riviera® Pear orchards, totaling 94 acres in organic production.
Because of the success using an Integrated Pest Management program to achieve a balance between beneficial and harmful pests and organisms in orchards while continuing to maintain the highest gift quality fruit, Harry and David has been able to eliminate the use of organophosphate pesticides in their orchards for the last five years.
Through field monitoring, tracking of insect life cycles and analyzing leaves in the laboratory we have reduced synthetic insecticide use by almost 50%, and broad-spectrum insecticide use has been decreased by 96%.
Harry & David has upgraded the irrigation systems on most of its orchard properties, to reduce water consumption by over 30%.
Propane-fired heaters are replacing diesel-fired smudge pots for frost protection. Additional frost protection is provided by water systems, plus investment in 165 wind generating machines to keep cold air from settling.
Increased use of ground transportation by strategically locating distribution centers, reducing CO2 output by approximately 4450 tons annually.
By increasing trailer load factors, we've reduced fuel consumption by 333,000 gallons over the past three years.
No paper will contain wood fiber from endangered old growth or endangered forest ecosystems.
All wood fiber must come from forests managed for sustainability. In addition, all suppliers must have a strategic plan, complete with measurable targets to increase the quantity of fiber from third party certified forests. Acceptable third party certifications include Forest Stewardship Council (FSC), Canada's National Standard for Sustainable Forest Management (CAN/CSAZ809), Sustainable Forest Initiative (SFI), Program for the Endorsement of Forest Certification (PEFC), and credible point of harvest certifications systems such as Master Logger and American Tree Farm. Suppliers will report progress on a biannual basis.
A certified "Chain of Custody" procurement system is required of all manufacturers. This certified system ensures accurate reporting of the origin of all wood fiber used in the manufacturing process. Acceptable certifications include: Forest Stewardship Council (FSC) and Sustainable Forest Initiative (SFI).
Bleaching processes will contain no elemental chlorine.
Wastewater effluent in paper making facilities must meet or exceed EPA standards for dioxins.
Paper suppliers must re-forest every acre of land harvested as expressed in the certification for sustainability systems mentioned above.
Paper suppliers will limit the use of chemicals and herbicides and use compounds with low ecological impact.
Paper suppliers will participate in the EPA's Climate Leader program (or similar programs with comparable targets), to reduce emission of greenhouse gases and measure and record progress.
Paper suppliers will have and publish a Code of Ethics, as well as anti-bribery and corruption policies to avoid conflict with environmental goals.
Paper suppliers will report all relevant legal challenges concerning the environment to Harry & David.
Where the net effect of adding post consumer waste to the fiber mix has a positive impact on the environment including but not limited to; resource conservation, energy use and emission levels, paper supplied to Harry & David Operations will contain at least 10% post consumer waste.
All paper supplier facilities will encourage employees to recycle their personal printed material and provide receptacles on site for collection.
All print facilities must have recycling operations for scrap metals, cardboard, pallets, shrink-wrap, printing plates and ink.
Hazardous materials such as solvents and inks must be reclaimed for recycling or reuse.
All paper waste generated must be recycled.
Low volatile organic compounds (VOCs) and alcohol free fountain solutions must be utilized.
Computer-to-plate technology (filmless plating), must be the standard plating process.
All facilities will encourage employees to recycle their personal printed materials and provide receptacles on site for collection.
US Conference of Mayors Recycling at Work Award, Environmental Responsibility.
Silver "Cindy" Audio Visual Communicator Award: "We all live downstream" building awareness of the Bear Creek watershed.
Gold "Cindy" Audio Visual Communication Award: "Sustainability - it's just good business" H&D's stewardship efforts.
Oregon Governor's Occupational Health and Safety Award.
By encouraging customers to shop the Internet, we've been able to eliminate over 37 million catalogs and have saved over 4,500 tons of paper since 2003.
Our paper must contain only wood fiber from sustainable forests, never from endangered forest ecosystems.
Our recycling program began in 1989. We've recycled over 31,000 tons to date!
Royal Riviera® Pear orchards offset more than 22,000 tons of CO2 each year, thanks to our 725,000 trees.
Increasing ground shipments and strategically locating distribution centers reduced our CO2 output by 4,500 tons annually.


text:
var chalk = require('chalk');
var Slack = require('slack-client');
var IRC = require('irc');

var pack = require("./package.json");
var config = require("./config.json");
var consoleLog = require("./lib/log.js");

// Connection
var irc = new IRC.Client(config.irc.server, config.irc.userName, config.irc);
var slack = new Slack(config.slack.token, false, false);
var channel;

// Variables
var status = {
    name: config.irc.userName,
    messages: 0,
    connected: false
};

// Listeners
irc.addListener('message', function(from, to, message) {
    channel.postMessage({channel: config.slack.channel, text: message, username: from, icon_url: 'http://api.adorable.io/avatars/48/' + from});
    consoleLog('message', '[IRC] ' + from + ': ' + message);
    status.messages++;
});

irc.addListener('error', function(message) {
    consoleLog('error', message);
});

irc.addListener('registered', function(message) {
    consoleLog('start', 'Connected to IRC channel');
    status.connected = true;
});

// Callbacks
slack.on('open', function() {
    channel = slack.getChannelGroupOrDMByID(config.slack.channel);
});

slack.on('message', function(message) {
    if(typeof message.text == 'undefined') return;

    var user = slack.getUserByID(message.user);
    var command = message.text.substring(1).split(' ');

    if(message.text.charAt(0) === '!' && message.channel === config.slack.channel && status.connected) {
        switch(command[0].toLowerCase()) {
            case 'say': case 's':
                var message = message.text.substring(5);

                status.messages++;

                client.whois(user.name, function(info) {
                    if(info && info.nick === user.name && status.name !== user.name) {
                        user.name = user.name + '_';
                    }

                    status.name = user.name;
                    irc.send('NICK', user.name);
                    irc.say(config.irc.channels, message);
                });

                consoleLog('message', '[Slack] ' + user.name + ': ' + message);
            break;

            case 'status':
                consoleLog('info', '[' + user.name + '] - Version: ' + pack.version + ' | Uptime: ' + process.uptime() + 's | Messages sent/received: ' + status.messages);
                channel.postMessage({channel: config.slack.channel, text: '<@' + message.user + '> *- Version:* ' + pack.version + ' *| Uptime:* ' + process.uptime() + 's *| Messages sent/received:* ' + status.messages, username: 'status', icon_url: 'http://api.adorable.io/avatars/48/info'});
            break;
        }
    }
});

// Intern
consoleLog('start', 'Initializing...');
slack.login();

process.on('uncaughtException', function (err) {
    console.log('Caught exception: ' + err);
    console.log('Stack trace: ' + err.stack);
});


Bosch KGV36VL32G Tall Fridge Freezer - Silver/Ins/Del/Rec.
The Bosch KGV36VL32G Classixx Fridge Freezer in silver, with an integrated vertical handle and LED interior light in the fridge section features a Crisper Box for fruite and vegetables, LED electronic control, fast-freeze function and automatic defrost in fridge section. Also features four safety glass shelves.
Extendable bottle grid and a large and two small door shelves. Net fridge capacity: 215 litres.
This item includes our FREE Delivery and Recycle Service. Please ensure the old appliance is disconnected prior to delivery. We will collect your old appliance and recycle it for your convenience.
Bought 2 weeks ago the capacity and design good. Was not clear it was low frost when bought frost collects in fridge then drips. Have tried different settings but cannot find ideal to overcome this. As a Bosch fan I am disappointed.
Hi, thanks for getting in touch about your new fridge freezer, Defrosting is actuated automatically.