text:
\section{Introduction}
The recent experimental work on tunable few-fermion systems consisting of ultracold gases in optical traps, that is characterized by the control of the quantum state of the system \cite{jochim11,zurn12,zurn13a}, has opened the way to investigate a variety of aspects of few and many-body physics \cite{bloch08,lode12,guan13}. As described in these works, this can be achieved by exploiting Pauli's principle in a highly degenerate Fermi gas in a trap so that it is possible to control the number of particles by controlling the number of available lowest energy single-particle states. For a few particles, the confining trapping potential consists of a one-dimensional optical potential created by a tight focus of a laser beam and a magnetic field gradient in the axial direction, in such a way that the states above a well defined energy become unbound. The resulting potential is formed by an impenetrable barrier on the left, a barrier of finite height on the right and a well in between with a controlled number of atoms which may decay out of the trap by tunneling through the barrier. The above setup has been used to address experimentally the tunneling decay of two or more atoms \cite{jochim11}, and has motivated theoretical studies on the dynamics of multiparticle decay \cite{cdgcmr06,delcampo11,lode12,longhi12,pons12}, in addition to studies on the decay of two interacting or non-interacting particles \cite{gcm11,kim11,zurn12,rontani12,rontani13,lundmark15,gharashi15}. In Ref. \cite{jochim11} it is also pointed out the possibility to prepare just one atom in the lowest energy level of an optical trap.

In contrast to the widespread view that tunneling decay of an isolated single particle into open space is amply understood
\cite{lode12}, here we call the attention to the old prediction of the deviations of the exponential decay law at short and long times compared with the lifetime of the decaying system. Here, by using an exact analytical approach for decay \cite{gc10,gc11,gcmv12}, we investigate the conditions that need to be fulfilled to be able to observe nonexponential decay of single ultracold atoms tunneling out of  potential profile using realistic parameters. We believe that these systems are the closest realization for tunneling decay in a highly isolated environment and hence might be appropriate to test nonexponential decay at long times. This is a relevant issue from a fundamental point of view that requires experimental verification.

We first provide an overview of the subject of decay of particles by tunneling. It is well known that quantum decay, a subject as old as quantum mechanics, was developed to explain $\alpha$-decay in radioactive nuclei. In 1928, Gamow derived the analytical expression for the exponential decay law $\exp(-\Gamma t/\hbar)$, with $\Gamma$ the decay rate; an expression that has been widely used in the description of particle decay. For single-particle decay, and it seems also in multi-particle decay \cite{delcampo11,pons12}, one may usually identify, in addition to the exponential regime,  two nonexponential regimes that, respectively, occur in general at short and long times compared with the lifetime of the system. The short-time behavior, which is related to the existence of the energy moments of the Hamiltonian \cite{khalfin68}, exhibits typically a $t^2$ behavior (see however \cite{cgc12}) and has been the subject of a great deal of attention, particularly in connection with the quantum Zeno effect \cite{sudarshan77b,koshino05}. The long-time, post-exponential, regime is a consequence of the fact that in most real systems, the energy spectra $E$ is bounded by below, i.e., $E \in (0,\infty)$, leading to integer inverse power in time behaviors, as discussed by Khalfin \cite{khalfin58}. In that work, Khalfin indicated the relevant role of the ratio of the energy of the decaying fragment $\mathcal{E}_r$ to the decaying width $\Gamma_r$, $R=\mathcal{E}_r/\Gamma_r$, in determining the time scale for the transition from  exponential to  nonexponential decay. Subsequent theoretical work investigated further the issue of the approximate nature of the exponential decay law \cite{goldberger64,baz69} and  provided also estimates of the above time scale for values  $R \gg 1$ \cite{winter61,ghirardi78,peres80}. This is of interest because it gave an explanation of the failure of finding deviations of the exponential decay law  at long times in radioactive nuclei \cite{norman88,son98}. Norman et.al. \cite{norman88} looked unsuccessfully for deviations from exponential decay law using $^{56}{\rm Mn}$ up to $65$ lifetimes. Here $R \sim 10^{17}$ and Winter's estimate in lifetime units: $t_0=5\ln(R)$ for the onset of nonexponential decay, yields $t_0 \sim 200$, which is beyond the experimental range of present day technology. Following the work by Khalfin \cite{khalfin58}, it was soon realized that deviations from the exponential decay law could also been obtained for small values of $R$, as the proposal for observing nonexponential decay in isolated autoionizing states located very close to the energy threshold in atomic systems \cite{nicolaides77}, that so far has not been confirmed experimentally.

The above results contributed to the widespread view that nonexponential decay contributions were beyond experimental reach or even to the alternative explanation that the interaction of the decaying system with the environment would enforce exponential decay at all times \cite{ghirardi78,parrot02}. Some years ago, however, short-time deviations from exponential decay \cite{raizen97} and the quantum Zeno effect \cite{raizen01} were finally observed, and more recently, in 2006, the measurement of post-exponential decay in a number of organic molecules in solution, exhibiting distinct  inverse power in time behaviors was reported \cite{monk06}. The above long-time deviations from the exponential decay law, however, were obtained due to the additional broadening of the excited state energy distributions produced by the solvent. That is, instead of looking for states with very small $E$, these authors considered systems with large values of $\Gamma$. It is intriguing that the solvent, which may be regarded as some sort of environment for these complex molecules, favors a nonexponential behavior. To the best of our knowledge, there is not at present time a theoretical approach that explains the above experimental results. It is worthwhile to point out that these experiments refer to luminescence decays after laser pulse excitation and hence do not refer to particle decay as considered in the present work.

In 2005 Jittoh et. al. published a theoretical study on particle decay using a single-pole approximation, where these authors estimate that for values of $R < 0.5$  in $s$-wave spherical symmetric systems or one-dimensional systems, there exists a novel regime where the decay is nonexponential at all times \cite{jittoh05}. These authors, however, did not discuss that regime in actual physical systems. In 2006, Garc\'{\i}a-Calder\'on and Villavicencio  \cite{gcv06} suggested the possibility that this novel full time nonexponential regime could be observed in semiconductor double-barrier resonant quantum structures.

As pointed out at the beginning of this Introduction, in this work we investigate the conditions that need to be fulfilled to be able to observe nonexponential decay in the deterministic preparation of a tunable single atom in an optical trap \cite{jochim11}. As pointed out above, we believe that these systems are the closest realization  of  decay by tunneling of a particle out of a single particle potential. We derive  analytical expressions for the nonescape probability as an expansion involving the full set of decaying states of the system at all times and study the conditions of validity for the single-pole approximation.

It is worth to point out that the formulation considered here refers to the full hamiltonian $H$ to the problem and hence it differs from approaches where the Hamiltonian is separated into a part $H_0$ corresponding to a closed system and a part $H_1$ responsible for the decay which is usually treated to some sort of perturbation theory, as in the work by Weisskopf and Wigner to describe the decay (also exponential) of an excited atom interacting with a quantized radiation field \cite{wigner30a}. These approximate approaches have become a standard procedure for treating a class of decay problems where perturbation theory can be justified, as in studies of  nonexponential decay in atomic spontaneous emission \cite{mostowski73,knight77}.

The manuscript is organized as follows. Section II provides an overview of the theoretical formalism that we consider here. Section III discusses some model calculations and analyzes different post-exponential scenarios and finally, Section IV presents some Concluding Remarks.

\section{Formalism}

The formalism that we shall consider here has its roots in the old work by Gamow which imposed outgoing boundary conditions on the solutions to the Schr\"odinger equation to describe the process of decay \cite{gamow28,gamow49}. As is well known, these boundary conditions lead to complex energy eigenvalues, its imaginary part being twice the decay rate that appears in the expression of the exponential decay law. Outside the interaction region, the amplitude of such solutions, known as decaying, resonant or quasi-normal states, grows exponentially with distance  and hence the usual rules of normalization and completeness do not apply. The approach initiated by Gamow, however, evolved over the years. In particular, significant developments in the 1970s on the analytical properties of the outgoing Green's function to the problem provided a suitable framework to study distinct  approaches to the issues of normalization and eigenfunction expansions involving these states \cite{berggren68,gcp76}. In particular some of these developments have led to an exact analytical description of decay by tunneling \cite{gc10,gc11}.

The effective trap potential  that results after application of the magnetic field to the initially confining trap and of the spilling process that guarantees that the decaying atom remains in the lowest decaying state,
corresponds to a one-dimensional system where the  transmission channel is closed \cite{jochim11,rontani13}. This potential is analogous to a spherical potential of zero angular momentum.

The solution to the time-dependent Schr\"odinger equation as an initial
value problem, may be written at time $t$ in terms of the retarded Green's function $g(x,x';t)$ of the problem as \cite{gc10,gc11}
\begin{equation}
\Psi(x,t)=\int_0^L {\! g(x,x^\prime,t)\Psi(x',0)\,\mathrm{d}x^\prime},
\label{e1}
\end{equation}
where $\Psi(x,0)$ stands for a state initially confined within the internal interaction region
$(0,L)$. Here, for simplicity of the discussion and without loss of generality it is assumed that $\psi(x,0)$ is a real function.
A convenient form of the retarded time-dependent Green's function is expressed in terms of the
outgoing Green's function $G^+(x,x';k)$ of the problem. Both quantities are related by a Laplace transformation
\cite{gc10,gc11}. In the present approach, instead of the common practice of assuming the analytical properties of $G^+(x,x';k)$, we impose the condition, justified on physical grounds, that the potential vanishes after a distance, i.e. $V(x)=0, \,x>L$.  As a consequence, it can be rigorously proved that $G^+(x,x';k)$  may be extended analytically to the whole complex $k$ plane where it has an infinite number of poles  distributed in a well known manner \cite{newtonchap12}.

The relevant point here is that the residue of $G^+(x,x';k)$ at a pole $\kappa_n$
is proportional to the functions $u_n(x)$ and $u_n(x^{\prime})$ and provides its normalization condition \cite{gcp76,gc10,gc11}.
The  decaying or resonant states $u_n(x)$ satisfy the Schr\"{o}dinger equation of the problem
\begin{equation}
[E_n-H]u_n(x)=0,
\label{en1}
\end{equation}
where $H$ is the full Hamiltonian $H=-(\hbar^2/2m)d^2/dx^2 + V(x)$, with $m$ the mass of the decaying particle. Equation (\ref{e1}) satisfies outgoing  boundary conditions at $x=L$, namely,
\begin{equation}
u_n(0)=0,\qquad \left[\frac{du_n(x)}{dx}\right]_{x=L}=i\kappa_n u_n(L),
\label{en2}
\end{equation}
with $\kappa_n=\alpha_n-i\beta_n$. The quantity $E_n$ in (\ref{en1}) refers to the complex energy eigenvalue  $ E_n= (\hbar^2/2m)\kappa_n^2=\,\mathcal{E}_n-i\Gamma_n/2$, where $\mathcal{E}_n$ yields the resonance energy of the decaying fragment and $\Gamma_n$ stands for the corresponding decaying width. Using Cauchy's Integral Theorem allows  to obtain a discrete expansion of $G^+(x,x^{\prime};k)$ in terms of the functions $\{u_n(x)\}$ and the poles $\{\kappa_n\}$ along the internal potential region. This expansion may be used to obtain a representation of $g(x,x^{\prime},t)$ that may be inserted into Eq. (\ref{e1}) to obtain the time-dependent solution \cite{gc10,gc11}
\begin{equation}
\Psi(x,t)=\sum_{n=-\infty}^{\infty}
\left \{ \begin{array}{cc}
C_nu_n(x)M(y^\circ_n), & \quad  x \leq L \\[.3cm]
C_nu_n(L)M(y_n), & \quad  x \geq  L,
\end{array}
\label{e2}
\right.
\end{equation}
where the coefficients $C_n$ are given by
\begin{equation}
C_n=\int_0^L \Psi(x,0) u_n(x) dx,
\label{3c}
\end{equation}
and the functions $M(y_n)$ are defined as \cite{gc10}
\begin{eqnarray}
M(y_n)&=&\frac{i}{2\pi}\int_{-\infty}^{\infty}\frac{{\rm e}^{ik(x-L)}{\rm e}^{-i\hbar k^2t/2m}}{k-\kappa_n}dk\nonumber \\ [.3cm]
&&=\frac{1}{2}{\rm e}^{(imr^2/2 \hbar t)} w(iy_n),
\label{e3}
\end{eqnarray}
where $y_n={\rm e}^{-i\pi /4}(m/2\hbar t)^{1/2}[(x-L)-(\hbar \kappa_n/m)t]$, and the function $w(z)=\exp(-z^2)\rm{erfc(-iz)}$ stands for the Faddeyeva or complex error function \cite{abramowitzchap7} for which there exist efficient computational tools \cite{poppe90}. The argument $y_n^{\circ}$ of the functions $M(y_n^0)$ in (\ref{e2}) is that of $y_n$ given above with $x=L$.

Notice that the sums in (\ref{e2}) run, respectively, over the poles  $\kappa_{-n}= -\alpha_n -i \beta_n$, located on the third quadrant of the $k$ plane, and the poles $\kappa_{n}= \alpha_n -i \beta_n$, located on the fourth quadrant. It follows from time reversal invariance that $\kappa_{-n}=-\kappa_n^*$ \cite{newtonchap12}.

The functions $\{u_n(x)\}$ are normalized according to the condition
\begin{equation}
\int_0^L u_n^2(x) dx + i\frac{u_n^2(L)}{2\kappa_n}=1,
\label{norm}
\end{equation}
and satisfy a closure relationship along the internal region of the potential
which,  provided the initial state is normalized to unity, leads to the expression \cite{gc10,gc11},
\begin{equation}
{\rm Re}\left \{ \sum_{n=1}^\infty C^2_n \right\}= 1,
 \label{e5}
\end{equation}
Equation (\ref{e5}) indicates that  the terms ${\rm Re}\,\{C^2_n\}$ cannot be interpreted as a probability, since in general they are not positive definite quantities, however, each of them  represents the `strength'  or `weight' of the initial state in the corresponding decaying state. One might see the coefficients  ${\rm Re}\,\{C^2_n\}$ as some sort of quasi-probabilities \cite{halliwell13}.

The equivalence between the non-Hermitian formulation that leads to the time-dependent solution given by Eq. (\ref{e2}) and the  Hermitian formulation based on continuum wave functions is discussed in Ref. \cite{gcmv12}. There, the advantage of using the  analytical expressions for the distinct decaying regimes that follow from the former formulation is contrasted  with the `black box'  numerical treatment that characterizes the latter formulation.

It is worth mentioning that the formalism outlined above differs from the so called rigged Hilbert space formulation in many respects, as discussed in Refs. \cite{mgcm05,gc10}. For example, since in that approach the poles located on the third quadrant of the $k$ plane are not taken explicitly into consideration, there is no analytical description of the nonexponential contributions to decay, as given by the Eq. (\ref{e11}) discussed below. It might also be worthwhile to mention here that decaying states, in spite of its non-Hermitian nature, have been used in a large variety of topics yet with different names: resonant states, quasinormal modes or Siegert states, as for example in quantum transients \cite{gcr97,cgcm09}, gravitational waves and black holes \cite{starinets09} and nonadiabatic processes involving molecules \cite{tolstikhin08}.

\subsection*{Nonescape probability}

Two quantities of interest in decaying problems are the survival probability $S(t)$, that yields the probability that at time $t$ the system remains in the initial state, and the nonescape probability $P(t)$, that provides the probability that at time $t$ the particle remains within the confining region of the potential. When the initial state overlaps strongly with the lowest decaying state,  both quantities exhibit a very similar behavior with time \cite{gcmv07}.  It  seems that such is the case for atom decay in ultracold traps, where the spilling process leaves just one atom in the lowest decaying state \cite{jochim11}.

Here we consider the nonescape probability which is defined as
\begin{equation}
P(t) = \int_0^L \Psi^*(x,t)\Psi(x,t) \,dx.
\label{e8}
\end{equation}
In order to calculate the above quantity one  requires  the time-dependent solution along the internal region of the potential. Hence one may insert the top expression of Eq. (\ref{e2}) into Eq. (\ref{e8}),  to obtain the expansion of the nonescape probability in terms of decaying states,
\begin{equation}
P(t)=\sum_{m,n=-\infty}^{\infty}C_m C_n^*I_{mn}M(y_{m})M^*(y_{n}).
\label{pfull}
\end{equation}
where
\begin{equation}
I_{mn}= \int_{0}^{L} u_m(x) u^*_n(x) dx.
\label{imn}
\end{equation}
Equations (\ref{e2}) and (\ref{pfull}) are given in terms of $M$ functions, and consequently their exponential and nonexponential behavior is not exhibited explicitly. This may be obtained by using the symmetry relations $\kappa_{-n}=-\kappa_n^*$ and $u_{-n}(x)=u_n^*(x)$, to write the sums over the poles located on the fourth quadrant. Here one may use the relation $M(y^{\circ}_n)=\exp(-i\mathcal{E}_n t/\hbar)\exp(-\Gamma_n t/\hbar)-M(-y^{\circ}_n)$ \cite{gc10,abramowitzchap7}, to write the time-dependent wave function along the internal region as,
\begin{equation}
\Psi(x,t) = \sum_{n=1}^{\infty} C_nu_n(x){\rm e}^{-i\mathcal{E}_nt\hbar }{\rm e}^{-\Gamma_nt/2\hbar} - I_n(x,t), \quad x \leq L,
\label{e9}
\end{equation}
where the nonexponential contribution $I_n(x,t)$ is given by
\begin{equation}
I_n(x,t)= \sum_{n=1}^{\infty} C_nu_n(x)M(-y^{\circ}_n) - C^{*}_nu^{*}_n(x)M(y^{\circ}_{-n}).
\label{e10}
\end{equation}
In this last expression the argument $y^{\circ}_{-n}$ is equal to $y^{\circ}_{n}$ with $\kappa_{n}$ substituted by $\kappa_{-n}=-\kappa_n^*$.

Substitution of Eqs. (\ref{e9}) and (\ref{e10}) into Eq. (\ref{e8}) provides, therefore, an expression for the nonescape probability that exhibits explicitly the exponential and nonexponential contributions to decay.  Notice, that assuming an initial state that overlaps strongly with the longest lifetime state, say $n=r$, it may be seen  in view of (\ref{e5}), that ${\rm Re}\,\{C^2_r\} \approx 1$, and also that $I_{rr} \approx 1$, and ignoring  the nonexponential contributions, one obtains the well known exponential decay law $P(t)=\exp(-\Gamma t/\hbar)$.

Equations (\ref{e2}) and (\ref{pfull}) are exact and may be used to find out the validity of different approximations.

The functions $M(-y_{n}^{\circ})$ and $M(y_{-n}^{\circ})$ that appear in the nonexponential contribution given by Eq. (\ref{e10}), exhibit at long times a  $t^{-3/2}$  behavior with time \cite{gc10}. As a consequence, the time-dependent solution may be written along the exponential and long-time regimes as \cite{gc10},
\begin{eqnarray}
\Psi(x,t) &\approx & \sum_{n=1}^{\infty} C_nu_n(x){\rm e}^{-i\mathcal{E}_nt/\hbar}{\rm e}^{-\Gamma_nt/2\hbar} - \nonumber \\ [.3cm]
&&ib\,{\rm Im} \left\{\sum_{n=1}^{\infty}\frac{C_nu_n(x)}{\kappa_n^3} \right\} \,\frac{1}{t^{\,3/2}};\,\,x \leq L,
\label{e11}
\end{eqnarray}
with
\begin{equation}
b= \frac{e^{-i \pi /4}}{2 \sqrt{\pi}} \left(\frac{2m}{\hbar} \right)^{3/2}.
\label{b}
\end{equation}

\subsection*{Decay of a single level}

In what follows we restrict the discussion to the situation that corresponds to an atom located in the lowest decaying state, $n=1$,  of the effective ultracold trap potential. On physical grounds one expects that the initial state overlaps strongly with that state, and therefore  ${\rm Re} \{C^2_1\}$ may provide the main contribution to Eq. (\ref{e5}). This justifies to consider the single pole approximation, $n=1$, in the expansion of the decaying wave function given by Eq. (\ref{e11}). This is a good approximation except near the time origin where more poles are needed \cite{cgc12}. Hence we may write,
\begin{eqnarray}
\Psi(x,t) &\approx & C_1u_1(x){\rm e}^{-i\mathcal{E}_1t/\hbar}{\rm e}^{-\Gamma_1t/2\hbar} - \nonumber \\ [.3cm]
&&ib\,{\rm Im}\left \{\frac{C_1u_1(x)}{\kappa_1^3} \right\} \,\frac{1}{t^{\,3/2}};\,\,x \leq L.
\label{e11s}
\end{eqnarray}
Inserting Eq. (\ref{e11s}) into Eq. (\ref{e8}) allows to write the nonescape probability as
\begin{equation}
P(t) \approx P^e(t)+P^{e,ne}(t)+P^{ne}(t),
\label{pa}
\end{equation}
where $P^e(t)$ stands for the purely exponential decay contribution,
\begin{equation}
P^e(t)=|C_1|^2I_1 e^{-\Gamma_1 t/\hbar},
\label{pe}
\end{equation}
$P^{e,ne}(t)$ refers to the interference term that involves exponential and nonexponential contributions,
\begin{eqnarray}
P^{e,ne}(t) &=& -{\rm Re}\left\{\left[\frac{|C_1|^2I_1}{{\kappa^*_1}^3}-\frac{C_1^2Y_1}{\kappa_1^3} \right] b^*  e^{-i\mathcal{E}_1 t /\hbar}  \right\} \nonumber \\ [.3cm]
&& \times \, e^{-\Gamma_1 t/2\hbar } \frac{1}{t^{3/2}}
\label{pnee}
\end{eqnarray}
and $P^{ne}(t)$ stands for the long-time post-exponential contribution,
\begin{equation}
P^{ne}(t)=\frac{|b|^2}{2}{\rm Re}\left\{\left[\frac{|C_1|^2I_1}{|\kappa_1^3|^2}-\frac{C_1^2Y_1}{(\kappa_1^3)^2} \right] \right\}\frac{1}{t^{3}}.
\label{pne}
\end{equation}
In the above expressions $I_1$ y $Y_1$ are defined, respectively, as
\begin{equation}
I_1= \int_{0}^{L} |u_1(x)|^2 dx.
\label{in}
\end{equation}
and
\begin{equation}
Y_1= \int_{0}^{L} u^2_1(x) dx.
\label{yn}
\end{equation}

We end this Section by referring to an exact single-level resonance expression for the survival probability \cite{gcrr01}, that allows to derive an approximate expression for the time $t_0$, in lifetime units, for the transition from exponential to post-exponential decay,
\begin{equation}
t_0 \approx 5.41\,\ln (R)+12.25,
\label{t0}
\end{equation}
where we recall that $R=\mathcal{E}_1/\Gamma_1$. Equation (\ref{t0}) yields a good estimate of $t_0$ for values of $R \gtrsim 1$ which is more accurate than those given in Refs. \cite{winter61,peres80}.

\section{Models}

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.0in]{fig1a.pdf}}
\rotatebox{0}{\includegraphics[width=3.0in]{fig1b.pdf}}
\caption{(Color online) (a) Trapping potential $V(x)$ (blue solid line) obtained by smoothing the squared barriers (green dashed line) using Eq.  (\ref{pot}).  (b) Two potential profiles appropriate for the analysis of the transition from exponential to post exponential decay. See parameters in the Table \ref{tabla1}.}
\label{figure1}
\end{figure}

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.3in]{fig2.pdf}}
\caption{(Color online) Example of the trajectories followed by a few poles located on the complex energy plane as the tunneling barrier is gradually reduced. We consider neV units, where $1 {\rm neV}= 241.8$ ${\rm kHz}$. The poles in blue solid circles correspond to the potential profile depicted with a blue dashed line in Fig. \ref{figure1} (b) ($R=13.02$), whereas the poles in red diamonds refer to the potential with the thin tunneling barrier shown by the red solid line in  Fig. \ref{figure1} (b) ($R=0.64$).}
\label{figure2}
\end{figure}

As pointed out in the Introduction, a relevant aspect of the recent developments on the preparation of tunable few-body quantum systems is the control of the quantum states in these systems \cite{jochim11,zurn12,zurn13a}. For tunneling decay, the resulting potential corresponds to an impenetrable barrier on the left, a barrier of finite height on the right and a well in between that, in particular, it may be used to study tunneling decay of a single  atom located in the lowest energy level of the system \cite{jochim11}.

Here we consider two potential profiles  to study the  decaying regimes corresponding to different values of $R$ for single $^6{\rm Li}$ atom decay. The first potential profile is the bathtub potential, which has been considered in  Ref. \cite{pons12} to study multiparticle tunneling decay, and the second potential profile refers to the tunneling decay potential considered by the Heidelberg group on tunable few-fermion systems, which consists of the summation of the optical one-dimensional confinement potential plus a linear magnetic term \cite{jochim11}.

\subsection*{Bathtub potential}

Let us first refer to the bathtub potential. Figure \ref{figure1} (a) exhibits a profile for this potential (blue solid line), given by the formula
\begin{eqnarray}
V(x)=\frac{1}{2}V_1 \left[ \tanh{X_1} -  \tanh{X_2}   \right] \Theta \left(\frac{w}{2}-x\right) + \nonumber  \\
 \frac{1}{2}V_2 \left[ \tanh{X_1} -  \tanh{X_2}   \right] \Theta \left( x-\frac{w}{2} \right),\nonumber \\ [.1cm]
\label{pot}
\end{eqnarray}
where $\Theta(u)$ is the Heaviside step function, $X_1=  \left( |x-\frac{w}{2}|-\frac{w}{2} \right) / \sigma$, $X_2=  \left( x-L\right) / \sigma$, and $L=w+b$ being the total width of the potential depicted in Fig. \ref{figure1}(a) (green dashed line). The parameter $\sigma$ determines the smoothness of the potential. As required for single atom decay, the potential supports only one decaying state ($n=1$), with the higher states ($n \ge 2$) lying above the tunneling barrier height, \textit{i.e.}, $\mathcal{E}_n > V_2$ for $n=2,3,4,...$. The above may be accomplished by choosing appropriately the parameters of the potential shown in Fig. \ref{figure1}(a) and the value of $\sigma$. Here we fix for all calculations a large value for $V_1$, namely, $V_1/h=241.8\,{\rm kHz}$, so that the decay process occurs, as pointed out above, by tunneling through the second barrier $V_2$. Figure \ref{figure1}(b) displays two potential profiles which may be appropriate for the analysis of the distinct decaying regimes.

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.1in]{fig3.pdf}}
\caption{(Color online) Plot of the natural logarithm of the nonescape probability as a function of time (in units of the lifetime $\tau$) for different values of the ratio $R=\mathcal{E}_1/\Gamma_1$. The transition from the exponential to the post-exponential regime is clearly appreciated in each curve.}
\label{figure3}
\end{figure}

Using an appropriate combination of the system parameters may allow to select the transition time at which the decay changes from exponential to the post-exponential regime. According to Eq. (\ref{t0}), this transition time is tunable through variations of the ratio $R=\mathcal{E}_1/\Gamma_1$, which may be manipulated by realizing that the location of the poles on the complex wave number or energy planes depends on the system parameters.
The equation for the complex poles follows by imposing the outgoing boundary condition to Eq. (\ref{en1}). The poles may be easily calculated for potentials with rectangular shapes by well known procedures \cite{gcr97,cgc10a} that may be implemented to potentials of arbitrary shape by noticing that a given potential profile can be described as a sequence of rectangles of appropriate high and width.
As an example, Fig. \ref{figure2} shows that the main effect of diminishing the barrier width is to increase the values of the imaginary energies of the poles. One appreciates in Fig. \ref{figure2} the trajectories followed by some poles on the fourth quadrant of the energy plane (dashed line).

We model the initial state $\Psi(x,0)$ as the lowest energy state of a potential with infinite walls, namely,
\begin{equation}
\Psi(x,0)=\left(\frac{2}{w}\right)^{1/2} \sin{\left[\frac{\pi}{w}x\right]}.
\label{eini}
\end{equation}
We choose the initial state (\ref{eini}), in addition to its mathematical simplicity, because it has the essential physical ingredient that initially there must a large probability to find the particle within the interaction region.  The above initial state guarantees that ${\rm Re}\{C_1^2\}$ is the largest contribution to Eq. (\ref{e5}) that is the condition that justifies the single pole approximation in the expansion of the decaying wave function, as discussed in the previous Section.

Using the initial state given by Eq. (\ref{eini}) and the set of poles $\{\kappa_n\}$ and decaying states $\{u_n(r)\}$ corresponding to a given set of potential parameters, allows to calculate the nonescape probability given by Eq. (\ref{pfull}). Figure  \ref{figure3} exhibits a plot of  the time evolution of the nonescape probability as a function of time for different values of $R$ in units of the corresponding lifetime. One may clearly appreciate the transitions from  exponential to nonexponential behavior for distinct values of $R$. The potential parameters that correspond to the above systems for distinct values of $R$ are given in the Table \ref{tabla1}, which
in addition, displays the corresponding values of the lifetimes $\tau$ and the expansion coefficients ${\rm Re}\,\{C_1^2\}$. Notice that the barrier width $b$ is a relevant parameter to diminish the values of $R$.

\begin{table}[!tbp]
\caption{\label{tabla1} Potential parameters for the distinct values of $R$ shown in Fig. \ref{figure3}.  $V_e/h$ $({\rm kHz})$ is the effective potential height that results from the right hand side of Eq. (\ref{pot}), where  $V_2/h$ $({\rm kHz})$ is the potential height, $w$ $(\mu m)$ is the well width, $\sigma$ the smoothness of the potential, $b$ $(\mu m)$ is the barrier width, $R=\mathcal{E}_1/\Gamma_1$,  $\tau$ $(ms)$ the lifetime, and ${\rm Re}\,\{C_1^2\}$ the expansion the coefficient for $n=1$. The mass of $^6{\rm Li}$ is taken as $10,964.898\,m_e$, with $m_e$ the electron mass. See text.}
\begin{ruledtabular}
\begin{tabular}{cccccccc}
 $V_{e}/h $ & $V_2/h$& $w$ & $\sigma$  &  $b$ & $R$ & $\tau$ &${\rm Re}\,\{C_1^2\}$\\
   \hline
  4.19 & 5.56 &2.7 & 0.10 &0.53 &  13.26 & 1.844 & 0.849 \\
       \hline
  3.88 & 5.56 & 2.7&0.09 & 0.42 & 7.75 & 1.166 & 0.868 \\
       \hline
  3.60 & 6.04& 2.7  &0.07 & 0.26 & 4.14 & 0.719 & 0.908 \\
       \hline
  3.37 & 6.04& 2.7 &0.05 & 0.17 & 2.37 &  0.482 & 0.950 \\
       \hline
  2.23 & 6.04& 3.0 &0.03 & 0.07 & 0.96 & 0.308 & 1.079 \\
       \hline
  1.32 & 6.04& 3.0 &0.03 &0.04 &  0.57 & 0.223 & 1.214 \\
       \hline
  0.66 & 6.04& 3.0 &0.03 & 0.02 & 0.30 & 0.164 & 1.498 \\
\end{tabular}
\end{ruledtabular}
\end{table}

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.3in]{fig4.pdf}}
\caption{(Color online) Comparison of $\ln P(t)$ vs $t/\tau$ with $R=0.30$ calculated from the formal solution, Eq (\ref{pfull}) with $N=10$ resonant terms (solid line) and the values the sum $P^{e,ne}+P^{pne}$ (long dashed line) calculated from Eqs.  (\ref{pnee}) and  (\ref{pne}) respectively. The purely exponential contribution (dashed line) is included to help the eye.}
\label{figure4}
\end{figure}

It is worth emphasizing a number of features exhibited by Fig. \ref{figure3}. A first one is that the transition time is reduced as the values of $R$  decrease; a second one, is that the frequency of oscillations that arise from the interference between the purely exponential and the long-time inverse power contributions in (\ref{e11}) also diminishes as $R$ decreases; the third one is that for values of $R \lesssim 1$, the nonescape probability starts to exhibit a departure from purely exponential decay before the transition to the $t^{-3}$ long-time behavior occurs, and finally, as $R$ diminishes further, as exemplified by $R=0.30$, the decay becomes nonexponential at all times.

Previous studies involving distinct systems have shown that the single-pole approximation for the nonescape probability, given by Eq. (\ref{pa}), is an excellent approximation for $R > 1$ \cite{gcmv07}. As mentioned before, for values of $R$ much larger than unity the exponential decay law holds for many lifetimes and hence the long-time nonexponential contribution is very small.

On the other hand, it follows also from inspection of Fig. \ref{figure3}, that for values of $R \sim 1$, as $R=0.96$, or even with $R=0.57$, the nonescape probability  exhibits a clear departure from exponential decay just after a few lifetimes to then follow a
nonexponential  behavior as $t^{-3}$, according to Eq. (\ref{pne}).  This suggests  that in systems around these values of $R$ nonexponential decay could be amenable to experimental verification.

We have found that for values of $R < 1$, the single-pole approximation is still a good approximation. As pointed out above, the case $R =0.30$ is particularly interesting because it exhibits nonexponential decay in the full time interval. Figure \ref{figure4} provides a comparison of a calculation of the nonescape probability (solid line) using Eq. (\ref{pfull}), where 10 poles are sufficient to get convergence of the expansion, with the single-pole approximate calculation $P^{e,ne}+P^{ne}$ (long-dash), using, respectively, Eqs. (\ref{pnee}) and (\ref{pne}). One sees that the interference term $P^{e,ne}$, that goes as $\exp(-\Gamma_1 t/2\hbar)t^{-3/2}$, describes the decay for the first few lifetimes whereas the last term $P^{ne}$, that goes as $t^{-3}$, becomes the dominant contribution from approximately fourteen lifetimes onwards. The above suggests that systems with $R \lesssim 0.3$  could also be appropriate to verify experimentally nonexponential decay.

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.3in]{fig5.pdf}}
\caption{Color online) Potential profiles $V(x)$, given by  Eq. (\ref{pot2}), for three distinct values of the parameter $B^{\prime}$, as indicated in each curve. Each curve is shifted so that $V/h=0$ at the trap bottom. The dashed lines indicate the energies of the lowest decaying levels of each potential. The level with the largest energy corresponds to the potential with the highest barrier, and thus successively in descending order. See text.}
\label{figure5}
\end{figure}

\begin{figure}[!tbp]
\rotatebox{0}{\includegraphics[width=3.3in]{fig6.pdf}}
\caption{Color online) Plot of the natural logarithm of the nonescape probability $P(t)$ as a function of time in lifetime units $\tau$ for three different values of the $R=\mathcal{E}_1/\Gamma_1$, as indicated in each curve. See text.}
\label{figure6}
\end{figure}

\subsection*{Heidelberg potential}

Let us now refer to the second potential profile. This consists of a cigar-shaped cylindrically symmetric optical potential created by the sum of two terms, the first one a tightly focused laser beam which accounts by for an optical one-dimensional confinement of atoms and the second one, a linear magnetic potential term, that allows for tunneling decay. The potential is given by the formula \cite{jochim11,zurn13a,rontani13},
\begin{equation}
V(x)= p V_0 \left[1- \frac{1}{1+ (x/x_R)^2} \right] - {\mu}_m B^{\prime} x,
\label{pot2}
\end{equation}
where  $V_0=(3.326 \mu K) k_B$ is the initial depth at the center of the optical dipole trap, with $k_B$ the Boltzmann constant;  $p=0.6338$, the optical trap depth as a fraction of the initial depth; $x_R = \pi \omega_0^2/\lambda$ stands for the Rayleigh range, with $\lambda=1064 nm$,  the wavelength of the the trapping light; $\mu_m$ is the Bohr magneton; and $B^{\prime}=18.92\,G/cm$, is the magnetic field gradient \cite{jochim11,zurn13a,rontani13}. The above parameters determine a  value for $R$. The analysis by Rontani on single atom decay \cite{rontani13}, which is based on the experiments reported in Ref.  \cite{zurn13a}, gives a value of $R \approx 70$,  where
$\mathcal{E}_1= (316.3\,{\rm Hz})h$ and $\Gamma_1^{WKB}=(\gamma_{s0}/2\pi)=(4.516\,{\rm Hz})h$, with $h$ the Planck  constant and $\gamma_{s0}=(1/35.24) ms$ \cite{rontani13}. The above value of $R \approx 70$ yields using (\ref{t0}), an onset for nonexponential decay around $t_0  \approx 35$ lifetimes, which lies well beyond the range of $6$ lifetimes that were considered in these experiments. That analysis involves a trap parametrization involving a WKB analysis. In recent theoretical work, however, it is argued that the trap calibration via a WKB analysis leads to an inaccurate trap parametrization \cite{gharashi15}. Our own analysis, involving the complex pole for the above potential parameters,  gives $R=27.36$ (see below) which  gives an onset for nonexponential decay around $t_0 \approx 30$ lifetimes, that still lies beyond experimental verification.

It turns out that varying slightly the value of the magnetic field gradient $B^{\prime}$ modifies the potential profile. This is exemplified in Fig. \ref{figure5} which exhibits three potential profiles corresponding  respectively, to  $B^{\prime}=18.92$ $G/cm$, the case considered above,  $B^{\prime}=19.49$ $G/cm$ and $B^{\prime}=19.77$ $G/cm$, as indicated for each curve in that figure. Notice that we have shifted the origin of energy to the bottom of the potential for each case. The lowest energy decaying levels for each potential profile are indicated by  dashed lines in Fig. \ref{figure5}. The first level from above corresponds to the potential profile with $B^{\prime}=18.92$, and thus successively in descending order, as shown in Table \ref{tabla2}.

Figure \ref{figure6} displays the natural logarithm of the nonescape probability as a function of time in lifetime units for the above potential profiles corresponding, as indicated in the figure,  to values  of $R=1.09$, $2.85$ and $27.36$. In these calculations the box model initial state given by (\ref{eini}) is chosen to yield, as expected on physical grounds, values of ${\rm Re}\,\{C_1^2\}$ around unity. The largest value of $R$, namely, $R=27.36$,  corresponds to the potential profile with the smallest value of $B^{\prime}$ in Fig. \ref{figure5}, that is, $B^{\prime}=18.92$, and thus respectively for the other cases as indicated in Table \ref{tabla2}.  One sees, therefore,  that by varying slightly the values of the magnetic field gradient allows for the design of potential profiles with distinct values of  $R$ including values $R <1$. Presumably one might also vary some other parameters of the potential, as the optical trap depth $p$, in order to look for values of $R$ which might be adequate for the experimental verification of  nonexponential decay. Table \ref{tabla2} groups also some other relevant parameters for the calculations shown in Figs. \ref{figure5} and \ref{figure6}.

There is a feature that is worth pointing out here that results from our treatment concerning the potential given by Eq. (\ref{pot2}). It occurs for values of $R \lesssim 2.5$ and may be exemplified by the case with $R=1.09$ appearing in Fig. \ref{figure6} and refers to the fact  that the lowest energy decaying level has an energy that lies above the top of the corresponding potential barrier $(B^{\prime}=19.77)$, as exhibited in Fig. \ref{figure5}. The reason that the nonescape probability for this decaying level behaves in a similar fashion as for decaying levels that are located below the potential height, as for example for $R=0.96$ in Fig. \ref{figure3}, follows from the fact that both cases have a large value of the coefficient ${\rm Re}\,\{C_1^2\}$, as shown in Tables \ref{tabla1} and  \ref{tabla2}. This follows from the notion that the initial state overlaps strongly with the lowest decaying level. In these calculations the values of $w$  for the initial states are given in Table \ref{tabla2} and the  maxima of the corresponding probability densities are centered at the maxima of the corresponding probability decaying densities. Hence, it does not seem to matter if the lowest decaying level is located above or below the potential barrier height. The higher energy decaying levels, in addition that decay much faster, have very small values of the coefficients  ${\rm Re}\,\{C_n^2\}$, with $n=2,3,...$, as follows from Eq. (\ref{e5}), and hence do not play a relevant role in the decay process except at very small times. Clearly the above considerations lie beyond the WKB framework.

It is worth stressing that the behavior with time of the nonescape probability for the potentials considered here  is quite similar, as follows from a comparison between Figs. \ref{figure3} and \ref{figure6}. This suggests that what matters is the value of $R$ independently of the specific shape of the potential profile.

\begin{table}[!tbp]
\caption{\label{tabla2} Values of the magnetic field gradient $B^{\prime}$ $(G/cm)$, $w$ $(\mu m)$, $R=\mathcal{E}_1/\Gamma_1$, the energy of the decaying state $\mathcal{E}_1$ (kHz),  the lifetime $\tau$ $(ms)$, and the expansion coefficient for $n=1$, ${\rm Re}\,\{C_1^2\}$, corresponding to Figs. \ref{figure5} and \ref{figure6}. See text.}
\begin{ruledtabular}
\begin{tabular}{cccccc}
 $B^{\prime}$& $w$  & $R$ & $\mathcal{E}_1$  & $\tau$ &  ${\rm Re}\,\{C_1^2\}$\\
 \hline
  18.92 & 4.51  &27.36 & 0.300 & 14.48 & 0.831 \\
  \hline
  19.49 & 4.80   &2.85 & 0.246 & 1.848 & 0.978 \\
  \hline
  19.77 &  4.80  &1.09 & 0.214 & 0.817 & 1.206  \\
  \end{tabular}
\end{ruledtabular}
\end{table}

\section{Concluding Remarks \label{conclusions}}

The approach discussed in this work provides a consistent analytical framework to discuss exponential and nonexponential contributions to quantum decay. We have exemplified the above for two model calculation for the decay of ultracold atoms out of a  trap having a barrier, with realistic parameters. We have pointed out the relevance of the ratio of the energy of the decaying fragment to the decaying width, $R=\mathcal{E}_1/\Gamma_1$ to determine the decaying regime as a function of time, in particular values of $R <1$ or $R \sim 1$ to obtain a nonexponential behavior  of the decaying system within a few lifetimes. Here, it is important to stress the result that different combinations of potential parameters may lead to similar values of $R$. It is not crucial to know the precise analytical form of the potential. Essentially, the barrier height controls the number of decaying states within the well; the well width controls the energy value of the decaying state, and the barrier width, the value of decaying width.  From an experimental point of view in order to fix a value of $R$ requires to acquire control over these parameters.

We hope that the analysis presented here will stimulate  experimentalists interested in fundamental issues to look for the verification of the nonexponential contributions to quantum decay of ultracold atoms in these systems.

\begin{acknowledgments}
G.G-C. acknowledges the partial financial support of DGAPA-UNAM under grant IN111814.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


I recently added Chitika eMiniMalls to Slaptijack. Since it is a violation of the Google AdSense Terms & Conditions to have other contextual ads along side Google ads, I was forced to use non-contextual ads.
Chitika eMiniMalls has a wide selection of categories that you can choose from to narrow down the selection of ads it sends your readers. Unfortunately, this means hard-coding a category, and I didn't think readers of my TCP Performance Tuning series (a series of articles related to server performance) would want to see ads for routers.
That's when I was hit with a stroke of genius. Instead of using one category for the entire site, I decided to use the default category and then add a query to the ad based on the category of the article being displayed. This means that an article posted in "Networking" displays routers and USB Ethernet adapters, while an article in "Graphics Design" displays ads for Adobe Photoshop.
ch_client = "???"; // Your ID goes here.
Perfect. The code that places the ad can go anywhere. For example on Slaptijack, I've currently got the code that places the ad in my sidebar (thus, outside the loop).
Nothing special there, just the usual stuff. Anyway, that's what I did. Good luck!


So according to the The New Republic, President Donald Trump may have syphilis and should explore treatment options as necessary with his personal physician.
He may have contracted it, according to the magazine, in the 1980s when syphilis was on the rise. If he didn't get it treated, it would be far advanced by now.
Advanced syphilis, neurosyphilis, and manifest itself in numerous ways, according to the article.
And Congressman Ted Lieu, a California Democrat, is introducing legislation that would require the White House to have a psychiatrist on staff. "I'm looking at it from the perspective of, if there are questions about the mental health of the president of the United States, what may be the best way to get the president treatment?" he told the Huffington Post.
It is incredibly important to rule out the disease, according to the article, because it is treatable even at a late date. And yet… we very much doubt Trump has syphilis. Since it is a treatable disease, if he did get it he could easily get rid of it. But surely he didn't get it to begin with. Relatively speaking, very few people have gotten syphilis over the years, even when it was on the rise.
This article, which has been picked up and shared in numerous places in the last day or two, is another example of how low people can stoop to smear someone they don't like.
The birther story was widely shared, but only by a fairly small segment of the alternative media and then widened on Facebook, via email etc. But this assertion has been made by The New Republic among other publications, and The New Republic is a kind of left-wing thought magazine and prestigious in certain circles. The article was written by a doctor with 30 years experience in infectious diseases.
From our point of view the article substantiates as lot of what Trump was talking about in his recent press conference. This article is delivered with both hate and venom from what we can tell.
Of course anything is possible but this is a very low probability event. The New Republic is a very anti-Trump publication. It is interested in embarrassing Trump, which is why it would suggest that Trump has a venereal disease. If they really wanted to get Trump checked, the owner among others would make a discreet call to the White House not blast it all over the news.
We have differences with Trump, big ones, centering around over-policing and the militarization of the US. But we would state these issues directly, as we have, without bringing up some ludicrous side issue like syphilis.
Conclusion: It's an article that truly drips venom and malice and ought not to have been represented in the pages of a magazine that has been taken seriously for decades. That it did appear is more a comment about the magazine and its owner than it is on Donald Trump.


text:
Death of Thai boy inflames debate on Muay Thai's young dreamers
Panu Wongcha-um, Panarat Thepgumpanat
BANGKOK (Reuters) - The death of a 13-year-old boy, knocked out during a Thai boxing match, has inflamed debate about whether children should be allowed to take part in a dangerous sport that many of them see as their only chance of escaping poverty.
Anucha Kochana was pronounced dead from a brain haemorrhage on Monday after he was knocked out in a match on the outskirts of Bangkok on Sunday evening.
Thai boxing, or Muay Thai as it is known, is a passion in Thailand with millions of boys dreaming of glory in the ring, and a life of riches, for them and their families, that success can bring.
But the sport is governed by few rules - children of any age can box in an organized match - leaving them at risk of severe injury, or worse, as Anucha's case has sadly shown.
The boy's grieving relatives told media they would not press charges over his death.
But legislators appointed by a military government have already been looking to tighten regulations to ban children under the age of 12 from professional bouts.
But the effort is opposed by many in the boxing community.
"Those aged 12 to 15 will need to be registered, have the permission of their parents and wear protective gear for professional fights," General Adulyadej Inthapong, the vice chairman of the National Legislative Assembly's committee on sports, told Reuters, referring to the proposed law.
Footage of Anucha's last fight posted on social media shows the boy, without any protective gear, getting punched repeatedly in the head before falling down and banging his head on the mat.
Somchart Charoenwatcharawit, president of the Professional Boxing Association of Thailand, said the proposed changes would hurt the livelihood of an estimated 300,000 child boxers under the age of 15.
"The new rule ... will hurt the children and their parents who earn tens of thousands of baht from boxing in what is a national sport," Somchart said.
He said the referee on Sunday should have stopped the fight when Anucha looked groggy and the match did not meet his association's standards.
The association thinks the minimum age for boys taking part in organized bouts should be 10, he said.
Jiraporn Laothamatas, a neuroradiologist and director of the Advanced Diagnostic Imaging Center, has studied the damage that boxing can inflict.
Her research has fueled the push for change but she says even the proposed minimum age of 12 for competition is a compromise that she disagrees with.
"If I had my way, the minimum age would be 18," she said, while acknowledging that Muay Thai is an important source of income for many, as well as being culturally important.
"The change in the law is being delayed because the industry makes a lot of money from child boxing," she said.
"It will take some guts for the government to push it through."
Reporting by Panarat Thepgumpanat and Panu Wongcha-um; Editing by Robert Birsel

redpajama_set_name: RedPajamaCommonCrawl


Superdry men's Rookie Military parka jacket. This parka style jacket features a fleeced lined hood, zip and popper fastening, four front pockets, one inside pocket and popper cuffs. The Rookie Military parka jacket is fully lined with fleece and features a drawstring waist. The jacket is finished with a Superdry International patch on one sleeve.
© 2005-2019 Cheap Designer Jackets UK Shop . All Rights http://www.windryramadhina.com/ .


Unfinished Business looks at how Liverpool became the greatest slaving port in human history. This is the untold story of the greatest slaving nation in history. Up till now, Britain's place in the history of slavery has been as the country that abolished the international slave trade. Britain's Slave Trade reveals the shameful truth behind this liberal facade, showing how the economic, social and cultural life of Britain would have been unrecognisable without slavery. Britain's Slave Trade explains how a middling European power transformed itself into the ruler of the waves, tracing the impact this had on the British way of life and taking in the Industrial Revolution, the beginnings of Empire and the birth of modern racism along the way. It also unearths startling evidence showing how many families that think of themselves as 'pure' English stock are in fact descended from slave ancestors.


text:
List of onshore wind farms List of onshore wind farms in the United Kingdom List of offshore wind farms in the United Kingdom List of offshore wind farms in the United States Lists of offshore wind farms by country Lists of offshore wind farms by water area Lists of wind farms by country List of wind farms in Australia List of wind farms in Canada List of wind farms in Iran List of wind farms in New Zealand List of wind farms in Romania List of wind farms in Sweden List of wind farms in the United States List of wind turbine manufacturers
A heat pump is a device that provides heat energy from a source of heat to a destination called a "heat sink". Heat pumps are designed to move thermal energy opposite to the direction of spontaneous heat flow by absorbing heat from a cold space and releasing it to a warmer one. A solar-assisted heat pump represents the integration of a heat pump and thermal solar panels in a single integrated system. Typically these two technologies are used separately (or only placing them in parallel) to produce hot water.[180] In this system the solar thermal panel performs the function of the low temperature heat source and the heat produced is used to feed the heat pump's evaporator.[181] The goal of this system is to get high COP and then produce energy in a more efficient and less expensive way.
My system has been installed for about a year now. When I first contracted with Envismart, the sales rep was very available and eager to help with my questions but after the installation, he was very hard to make contact with, seldom returned my calls, and when he did seemed to tell me what he thought I wanted hear and very seldom followed through. The system had a shaky start, it died after one day and after two new inverters and several optimizers over several months of on again, off again operation it seems to be running smoothly, at least for the last few months. Customer support was not very good, to be kind, but the service personnel that came out were prompt and there when they said they would be and very open about what the problems were and quickly fixed them. I was told my recurring system problems were a little unusual and I have to take their word on that but they gave me their personnel cell numbers and told me to call them when I couldn't get Customer Support to call - and when I called them, they came through and got me serviced a lot more quickly. They are the main reason I rated the company a 3.I have to say, the last month or so, it seems like the company is starting to work on changing its image. I have been called on several occasions by the "Quality Assurance" group at their initiation and asked if everything was OK with my system and I usually had an issue about something (admittedly, sometimes very minor). They always followed through with answers and corrected my concerns which was a big change from my previous experiences. I want to encourage them to continue improving their Customer Support after the sale in this manner as that is the real reputation for their company. I am still reserving my opinion but I am very much encouraged by their recent efforts - Keep it up!... read more
Climate change concerns coupled with high oil prices and increasing government support are driving increasing rates of investment in the sustainable energy industries, according to a trend analysis from the United Nations Environment Programme. According to UNEP, global investment in sustainable energy in 2007 was higher than previous levels, with $148 billion of new money raised in 2007, an increase of 60% over 2006. Total financial transactions in sustainable energy, including acquisition activity, was $204 billion.[64]
In the case of a "wind turbine generator", the wind pushes directly against the blades of the turbine, which converts the linear motion of the wind into the rotary motion necessary to spin the generators rotor and the harder the wind pushes, the more electrical energy can be generated. Then it is important to have a good wind turbine blade design to extract as much energy out of the wind as possible.
While renewables have been very successful in their ever-growing contribution to electrical power there are no countries dominated by fossil fuels who have a plan to stop and get that power from renwables. Only Scotland and Ontario have stopped burning coal, largely due to good natural gas supplies. In the area of transportation, fossil fuels are even more entrenched and solutions harder to find.[198] It's unclear if there are failures with policy or renewable energy, but twenty years after the Kyoto Protocol fossil fuels are still our primary energy source and consumption continues to grow.[199]
Projections vary. The EIA has predicted that almost two thirds of net additions to power capacity will come from renewables by 2020 due to the combined policy benefits of local pollution, decarbonisation and energy diversification. Some studies have set out roadmaps to power 100% of the world's energy with wind, hydroelectric and solar by the year 2030.
Wind power first appeared in Europe during the Middle Ages. The first historical records of their use in England date to the 11th or 12th centuries and there are reports of German crusaders taking their windmill-making skills to Syria around 1190.[6] By the 14th century, Dutch windmills were in use to drain areas of the Rhine delta. Advanced wind turbines were described by Croatian inventor Fausto Veranzio. In his book Machinae Novae (1595) he described vertical axis wind turbines with curved or V-shaped blades.
Geothermal energy is produced by tapping into the thermal energy created and stored within the earth. It arises from the radioactive decay of an isotope of potassium and other elements found in the Earth's crust.[144] Geothermal energy can be obtained by drilling into the ground, very similar to oil exploration, and then it is carried by a heat-transfer fluid (e.g. water, brine or steam).[144] Geothermal systems that are mainly dominated by water have the potential to provide greater benefits to the system and will generate more power.[145] Within these liquid-dominated systems, there are possible concerns of subsidence and contamination of ground-water resources. Therefore, protection of ground-water resources is necessary in these systems. This means that careful reservoir production and engineering is necessary in liquid-dominated geothermal reservoir systems.[145] Geothermal energy is considered sustainable because that thermal energy is constantly replenished.[146] However, the science of geothermal energy generation is still young and developing economic viability. Several entities, such as the National Renewable Energy Laboratory[147] and Sandia National Laboratories[148] are conducting research toward the goal of establishing a proven science around geothermal energy. The International Centre for Geothermal Research (IGC), a German geosciences research organization, is largely focused on geothermal energy development research.[149]
The US National Renewable Energy Laboratory (NREL), in harmonizing the disparate estimates of life-cycle GHG emissions for solar PV, found that the most critical parameter was the solar insolation of the site: GHG emissions factors for PV solar are inversely proportional to insolation.[125] For a site with insolation of 1700 kWh/m2/year, typical of southern Europe, NREL researchers estimated GHG emissions of 45 gCO2e/kWh. Using the same assumptions, at Phoenix, USA, with insolation of 2400 kWh/m2/year, the GHG emissions factor would be reduced to 32 g of CO2e/kWh.[126]
A: Modern solar panels typically last twenty to thirty years before there's a noticeable increase in output loss. Most residential solar providers offer a 20- to 25-year warranty, but many such warranties only guarantee a certain power output (e.g., a guarantee of 80% output for twenty years). Carefully read through the fine print to make sure you understand the warranty and what it covers.
DOE selected six companies for its 2007 Green Power Supplier Awards, including Constellation NewEnergy; 3Degrees; Sterling Planet; SunEdison; Pacific Power and Rocky Mountain Power; and Silicon Valley Power. The combined green power provided by those six winners equals more than 5 billion kilowatt-hours per year, which is enough to power nearly 465,000 average U.S. households. In 2014, Arcadia Power made RECS available to homes and businesses in all 50 states, allowing consumers to use "100% green power" as defined by the EPA's Green Power Partnership.[86][87]
As local wind speed increases, so does the power output. Since this type of generator uses wind as 'fuel', it is important to choose an appropriate site for mounting the turbine. The ideal location for a wind generator is 20 feet above any surrounding object within a 250-foot radius. Wind speed increases with height above ground, so a taller mast can provide significant gains in energy production.
Energy engineering Oil refinery Fossil-fuel power station Cogeneration Integrated gasification combined cycle Electric power Nuclear power Nuclear power plant Radioisotope thermoelectric generator Solar power Photovoltaic system Concentrated solar power Solar thermal energy Solar power tower Solar furnace Wind power Wind farm High-altitude wind power Geothermal power Hydropower Hydroelectricity Wave farm Tidal power Biomass
The first three are active solar systems, which use mechanical or electrical devices that convert the sun's heat or light to another form of usable energy. Passive solar buildings are designed and oriented to collect, store, and distribute the heat energy from sunlight to maintain the comfort of the occupants without the use of moving parts or electronics.
"[The maps] suggest that our 100 percent renewable energy purchasing goal — which relies on buying surplus renewable energy when it's sunny and windy, to offset the lack of renewable energy supply in other situations — is an important first step toward achieving a fully carbon-free future," Michael Terrell, Google's head of energy markets, wrote in a blog post. "Ultimately, we aspire to source carbon-free energy for our operations in all places, at all times."
We've had our system running for about 6 months now, whole process took a little over 2 months, other than submitting a form to our HOA and reviewing/signing some docs, Brio took care of the whole thing. The system works great, one month after it was running our power bill with Duke went to $0! Even in the summer when it's usually really high, honestly we were kinda skeptical but it's worked as promised. We're in NC and mainly worked with Brendan, he explained everything clearly and has been very responsive whenever we had questions.... read more
Most in the industry agree that 11 m/s (24.6 mph) makes for a good rated wind speed. Go above it and very soon the turbine should be hard at work to protect itself from destruction, by furling, governing, or shutting down. Those that do not will likely face a short and tortured life. If we agree on 11 m/s, an equation for a realistic rated power number is as follows:
The stator is the "stationary" (hence its name) part of the machine and can have either a set of electrical windings producing an electromagnet or a set of permanent magnets within its design. The rotor is the part of the machine that "rotates". Again, the rotor can have output coils that rotate or permanent magnets. Generally, generators and alternators used for wind turbine generators are defined by how they make generate their magnetism, either electromagnets or permanent magnets.
Going forward, there is hope for the small wind future! Certification programs are under way in various places to provide real turbine performance data. In North America this is being spearheaded by the Small Wind Certification Council, which requires third-party certification of turbine performance in a standardized fashion. Manufacturers will no longer be able to fudge power curves, or specify 'rated power' at hurricane-force wind speeds. This will allow you, the consumer, to compare turbines on a much more even footing.
Wind turbines allow us to harness the power of the wind and turn it into energy. When the wind blows, the turbine's blades spin clockwise, capturing energy. This triggers the main shaft, connected to a gearbox within the nacelle, to spin. The gearbox sends that energy to the generator, converting it to electricity. Electricity then travels down the tower to a transformer, where voltage levels are adjusted to match with the grid.
As suppliers of inverters for turbines good, bad, and just plain ugly, we have pretty well seen it all when it comes to turbine failure. We can tell you unequivocally that you get what you pay for. Depending on your sense of adventure that can be good or bad; if you plan to go cheap, plan on (you) being the manufacturer's R&D department and test center. Being a really good do-it-yourselfer with an understanding of wind turbines, alternators, and all things electric will come in very handy too. Just in case you do not believe us, you can read about it in this Green Power Talk thread. There are more threads with similar content on the forum, just browse around a little.
Floating solar arrays are PV systems that float on the surface of drinking water reservoirs, quarry lakes, irrigation canals or remediation and tailing ponds. A small number of such systems exist in France, India, Japan, South Korea, the United Kingdom, Singapore and the United States.[168][169][170][171][172] The systems are said to have advantages over photovoltaics on land. The cost of land is more expensive, and there are fewer rules and regulations for structures built on bodies of water not used for recreation. Unlike most land-based solar plants, floating arrays can be unobtrusive because they are hidden from public view. They achieve higher efficiencies than PV panels on land, because water cools the panels. The panels have a special coating to prevent rust or corrosion.[173] In May 2008, the Far Niente Winery in Oakville, California, pioneered the world's first floatovoltaic system by installing 994 solar PV modules with a total capacity of 477 kW onto 130 pontoons and floating them on the winery's irrigation pond.[174] Utility-scale floating PV farms are starting to be built. Kyocera will develop the world's largest, a 13.4 MW farm on the reservoir above Yamakura Dam in Chiba Prefecture[175] using 50,000 solar panels.[176][177] Salt-water resistant floating farms are also being constructed for ocean use.[178] The largest so far announced floatovoltaic project is a 350 MW power station in the Amazon region of Brazil.[179]
†Offer is available to Texas residential customers who enroll using the Promotion Code "NIGHTSFREE". Plan bills a monthly Base Charge, an Energy Charge, and passes through Utility Transmission and Distribution delivery charges. Energy Charges for usage consumed between 9pm and 7am each day is credited back on your bill. The utility charges, including delivery charges for night time hours, are passed through at cost and aggregated on your bill. See Electricity Facts Label for details.
A wind turbine is made up of two major components and having looked at one of them, the rotor blade design in the previous tutorial, we can now look at the other, the Wind Turbine Generator or WTG's which is the electrical machine used to generate the electricity. A low rpm electrical generator is used for converting the mechanical rotational power produced by the winds energy into usable electricity to supply our homes and is at the heart of any wind power system.
Wind energy research dates back several decades to the 1970s when NASA developed an analytical model to predict wind turbine power generation during high winds.[136] Today, both Sandia National Laboratories and National Renewable Energy Laboratory have programs dedicated to wind research. Sandia's laboratory focuses on the advancement of materials, aerodynamics, and sensors.[137] The NREL wind projects are centered on improving wind plant power production, reducing their capital costs, and making wind energy more cost effective overall.[138] The Field Laboratory for Optimized Wind Energy (FLOWE) at Caltech was established to research renewable approaches to wind energy farming technology practices that have the potential to reduce the cost, size, and environmental impact of wind energy production.[139] The president of Sky WindPower Corporation thinks that wind turbines will be able to produce electricity at a cent/kWh at an average which in comparison to coal-generated electricity is a fractional of the cost.[140]
There is no energy in the wind at those wind speeds, nothing to harvest for the turbine. While it may make you feel good to see your expensive yard toy spin, it is not doing anything meaningful in a breeze like that: To give you some idea, a wind turbine with a diameter of 6 meters (pretty large as small wind turbines go) can realistically produce just 120 Watt at 3.5 m/s wind speed. That same turbine would be rated at 6 kW (or more, see the next section), so energy production at cut-in really is just a drop in the bucket. What is more, due to the way grid-tie inverters work, you are about as likely to be loosing energy around cut-in wind speed to keep the inverter powered, as you are in making any energy, resulting in a net-loss of electricity production.
With that in mind it makes a great deal of sense to use a tilt-up tower for your turbine. It makes maintenance and repairs much safer (on the ground) and cheaper. Crane fees, or having turbine installers hang off the top of a tower for long periods of time, tend to get very expensive. You should also budget for repairs, they will happen. Parts may be free under warranty, your installer's time is not.
Then I pick up a Home Power Magazine, or a Backwoods Home, or a Mother Earth News. I read the letters to the editor and I think, These are my people! This is my tribe—the tribe of folks striving for independence of thought and lifestyle, who are creative in their choice of building materials, who try to make responsible choices about how their choices affect the environment they live in.
While a single dramatic victory against something like the dirty Keystone XL pipeline can be nice to imagine, the truth is this is how we're going to win: fighting at every level and with every tool we've got. We can't stop until governments and fossil fuel corporations finally get the message that we need to put our dirty past behind us and fully commit to a clean future that works for all of us moving forward.
Dale Ross, the mayor of Georgetown, Texas, has a big smile, a big handshake and a big personality. In last year's election, he won big, with 72 percent of the vote. The key to his success? "Without being too self-reflective," he says, "I just like people." He's a Republican, and his priorities are party staples: go light on regulation, be tough on crime, keep taxes low. But the thing that is winning him international renown is straight out of the liberal playbook—green power. Thanks to his (big) advocacy, Georgetown (pop. 67,000) last year became the largest city in the United States to be powered entirely by renewable energy.
Buying a wind turbine generator such as the Windmax HY1000 to produce wind energy is not easy and there are a lot of factors to take into account. Price is only one of them. Be sure to choose an electrical machine that meets your needs. If you are installing a grid-connected system, choose an AC mains voltage generator. If you are installing a battery-based system, look for a battery-charging DC generator. Also consider the mechanical design of a generator such as size and weight, operating speed and protection from the environment as it will spend all of its life mounted at the top of a pole or tower.
Nuclear power. After coal, the next largest source of our electricity is nuclear power. While nuclear plants don't cause air pollution, they do create radioactive waste, which must be stored for thousands of years. As accidents at Three Mile Island and Chernobyl proved, nuclear plants also carry the risk of catastrophic failure. And nuclear power can be very expensive.
Previously, the largest U.S. city fully powered by renewables was Burlington, Vermont (pop. 42,000), home to Senator Bernie Sanders, the jam band Phish and the original Ben & Jerry's. Georgetown's feat is all the more dramatic because it demolishes the notion that sustainability is synonymous with socialism and GMO-free ice cream. "You think of climate change and renewable energy, from a political standpoint, on the left-hand side of the spectrum, and what I've done is toss all those partisan political thoughts aside," Ross says. "We're doing this because it's good for our citizens. Cheaper electricity is better. Clean energy is better than fossil fuels."
Brazil has one of the largest renewable energy programs in the world, involving production of ethanol fuel from sugar cane, and ethanol now provides 18 percent of the country's automotive fuel. As a result of this, together with the exploitation of domestic deep water oil sources, Brazil, which years ago had to import a large share of the petroleum needed for domestic consumption, recently reached complete self-sufficiency in oil.[36][37][38]
Rated power of a wind turbine may not be quite as meaningless as cut-in wind speed, though its use is limited. It could have some utility to quickly compare, or get a feel for, the size of the wind turbine, but only if those rated power numbers were taken at the same rated wind speed, and if the manufacturer is giving you a realistic number (many inflate rated power). A much better measure of turbine size is, simply, their diameter. As shown above it is by far the best predictor for power output.
Green power is a subset of renewable energy and represents those renewable energy resources and technologies that provide the highest environmental benefit. The U.S. Environmental Protection Agency defines green power as electricity produced from solar, wind, geothermal, biogas, biomass and low-impact small hydroelectric sources. Customers often buy green power for avoided environmental impacts and its greenhouse gas reduction benefits.[9]
The International Renewable Energy Agency (IRENA) is an intergovernmental organization for promoting the adoption of renewable energy worldwide. It aims to provide concrete policy advice and facilitate capacity building and technology transfer. IRENA was formed on 26 January 2009, by 75 countries signing the charter of IRENA.[145] As of March 2010, IRENA has 143 member states who all are considered as founding members, of which 14 have also ratified the statute.[146]
Green energy, however, utilizes energy sources that are readily available all over the world, including in rural and remote areas that don't otherwise have access to electricity. Advances in renewable energy technologies have lowered the cost of solar panels, wind turbines and other sources of green energy, placing the ability to produce electricity in the hands of the people rather than those of oil, gas, coal and utility companies.
FEATURES: Integrated automatic braking system to protect from sudden and high wind speed. Easy DIY installation methods with all materials provided. Can be used in conjunction with solar panels. MPPT Maximum power point tracking built into the wind turbine generator. Made with high quality Polypropylene and Glass Fiber material with a weather resistant seal.
A solar cell, or photovoltaic cell (PV), is a device that converts light into electric current using the photovoltaic effect. The first solar cell was constructed by Charles Fritts in the 1880s.[5] The German industrialist Ernst Werner von Siemens was among those who recognized the importance of this discovery.[6] In 1931, the German engineer Bruno Lange developed a photo cell using silver selenide in place of copper oxide,[7] although the prototype selenium cells converted less than 1% of incident light into electricity. Following the work of Russell Ohl in the 1940s, researchers Gerald Pearson, Calvin Fuller and Daryl Chapin created the silicon solar cell in 1954.[8] These early solar cells cost 286 USD/watt and reached efficiencies of 4.5–6%.[9]


text:
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Torres Strait Islanders Ask U.N. to Hold Australia to Account on Climate 'Human Rights Abuses'
By Kristen Lyons	 On May 27, 2019 Last updated Oct 10, 2019
Kristen Lyons, The University of Queensland
Climate change threatens Australia in many different ways, and can devastate rural and urban communities alike. For Torres Strait Islanders, it's a crisis that's washing away their homes, infrastructure and even cemeteries.
The failure to take action on this crisis has led a group of Torres Strait Islanders to lodge a climate change case with the United Nations Human Rights Committee against the Australian federal government.
It's the first time the Australian government has been taken to the UN for their failure to take action on climate change. And its the first time people living on a low lying island have taken action against any government.
This case – and other parallel cases – demonstrate that climate change is "fundamentally a human rights issue", with First Nations most vulnerable to the brunt of a changing climate.
The group of Torres Strait Islanders lodging this appeal argue that the Australian government has failed to take adequate action on climate change. They allege that the re-elected Coalition government has not only steered Australia off track in meeting globally agreed emissions reductions, but has set us on course for climate catastrophe.
In doing so, Torres Strait Islanders argue that the government has failed to uphold human rights obligations and violated their rights to culture, family and life.
This case is a show of defiance in the face of Australia's years of political inertia and turmoil over climate change.
It is the first time people living on a low-lying island – acutely vulnerable in the face of rising sea levels – have brought action against a government. But it may also be a sign of things to come, as more small island nations face impending climate change threats.
Breaching multiple human rights obligations
Driving this case is an alliance of eight Torres Strait Islanders, represented by the Torres Strait land and sea council, Gur A Baradharaw Kod, along with a legal team from ClientEarth and 350.org. They argue that their way of life has come under immediate and irreversible threat.
"They are losing everything – they can't just pick it up and go somewhere else; their culture is unique to that region." Torres Strait Islanders lodge a claim against the Australian government for failing to act on climate change. Via @nytimes @livia_ar https://t.co/iX8PN4xNns
— Climate Council (@climatecouncil) May 15, 2019
On this basis, they accuse the Australian government of breaching multiple articles of the UN Human Rights Declaration, including the right to culture, the right to be free from arbitrary interference with privacy, family and home, and the right to life.
In the early 1990s, the Torres Strait Islands were at the centre of struggles to secure Aboriginal and Torres Strait Islander land rights in Australia.
Securing these rights were made possible through the historic Mabo Decision, and these rights remain central to land and human rights debates today as Torres Strait Islanders' land and seas are threatened by climate change.
Torres Straight Islanders are on the frontlines
Some Torres Strait Islands are less than one metre above sea level and are already affected by climate change.
Rising tides have delivered devastating effects for local communities, including flooding homes, land and cultural sites, with dire flooding in 2018 breaking a sea wall built to protect local communities.
Increasing sea temperatures have also affected marine environments, driving coral bleaching and ocean acidification, and disrupting habitat for dugong, salt water crocodiles, and multiple species of turtle.
In the same way settler colonial violence dispossessed First Nations people from their ancestral homelands, climate change presents a real threat of further forced removal of people from their land and seas, alongside destruction of places where deep cultural and spiritual meaning is derived.
Parallel threats across the Pacific
While the Torres Strait appeal to the UN is groundbreaking, the challenges facing Torres Strait Islanders are not unique.
Delegates at the Pacific Islands Forum in Fiji last week described climate change as the "single greatest threat" to the region, with sea level rise occurring up to four times the global average in some countries in the Pacific.
Climate change is already causing migration across parts of the Pacific, including relocation of families from the Carteret Islands to Bougainville with support from local grassroots organisation Tulele Peisa.
What is taking place in the Torres Strait Islands because of rising sea levels and rapid erosion is a tragedy. I fully support what the Torres Strait Islanders are doing at the United Nations with ClientEarth and I hope you will, too. https://t.co/lVJiu4QO8w #ourislandsourhome
— Baz Luhrmann (@bazluhrmann) May 16, 2019
The Alliance of Small Island States, an intergovernmental organisation, has demanded that signatories to the Paris Agreement, including through the Green Climate Fund, recognise fundamental loss and damages communities are facing, and compensate those affected.
The growing wave of climate litigation
Across the Torres Strait, the Pacific, and other regions on the frontline of climate change, there are a diversity of responses in defence of land and seas. These are often grounded in local and Indigenous knowledge.
They show the resolve of First Nations and local communities, as captured in a message from the Pacific Climate Warriors:
We are not drowning. We are fighting.
There are parallel appeals to the Torres Strait Islanders' case. Around the world, First Nations people are calling on the UN to hold national governments to account on human rights obligations, including in the context of mining and other developments that drive greenhouse gas emissions.
The Torres Strait Islanders are among the world's longest surviving cultures. Climate change means their homes are washing away. They're bringing a world-first #HumanRights case against Australia. Wherever you are, add your voice: https://t.co/aNiK0dDg9s #OurIslandsOurHome pic.twitter.com/3sbbidDVso
— Dominique Doyle (@dominiquesdoyle) May 13, 2019
In Australia, Wangan and Jagalingou Traditional Owners have submitted multiple appeals, including last year alleging government violations of six international human rights obligations in their effort to advance Adani's proposed Carmichael mine.
There is an array of other climate litigation underway. This includes citizens suing their governments for failing to take action on climate, such as in the Netherlands, where a judge ordered the government to take hefty action to reduce national emissions.
Similarly, a group of 21 children in the United States are pursuing a lawsuit to demand the right to a safe climate.
Given the parlous state of climate politics in Australia, further litigation can be expected. The significance of the current appeal by a group of Torres Strait Islanders lies in its potential to lay bare the adequacy or otherwise of Australia's response to climate change as a human rights issue.
First Nations people already have a moral authority in defending their human rights in the era of climate change. Over time, they and others, including children, will also test the grounds on which they might have the legal authority to do so.
Kristen Lyons, Professor Environment and Development Sociology, The University of Queensland
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Kristen Lyons 385 posts 0 comments
Kristen Lyons is a social researcher and advocate working on issues related to development, the environment and energy futures. In international settings, Kristen works in East Africa and the Pacific, and has been engaged in work on organic agriculture and international trade, carbon markets, violence and livelihood impacts, and logging and community agro-forestry.
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text:
Questa voce raccoglie le informazioni riguardanti il Građanski nogometni klub Dinamo Zagreb nelle competizioni ufficiali della stagione 2021-2022.

Rosa

Risultati

Prva HNL

Coppa di Croazia

UEFA Champions League

Primo turno preliminare

Secondo turno preliminare

Terzo turno preliminare

Turno di Play-off

UEFA Europa League

Fase a gironi

Fase a eliminazione diretta

Play-off

Statistiche

Statistiche di squadra

Andamento in campionato

2021-2022

redpajama_set_name: RedPajamaWikipedia


text:
package org.horiam.ResourceManager.jms;

import static org.junit.Assert.assertTrue;

import javax.annotation.Resource;
import javax.ejb.EJB;
import javax.ejb.embeddable.EJBContainer;
import javax.jms.Connection;
import javax.jms.ConnectionFactory;
import javax.jms.JMSException;
import javax.jms.MessageConsumer;
import javax.jms.ObjectMessage;
import javax.jms.Session;
import javax.jms.Topic;
import javax.naming.NamingException;

import org.horiam.ResourceManager.mock.TaskMockService;
import org.horiam.ResourceManager.model.Task;
import org.junit.After;
import org.junit.Before;
import org.junit.Test;

public class TestTaskObserver {

	@EJB
	private TaskEventLauncher taskEventLauncher;

	@Resource
    private ConnectionFactory connectionFactory;
	@Resource(name = "jms/tasksTopic")
	private Topic topic;

	private EJBContainer container;

    @Before
    public void before() throws NamingException {
    	container = EJBContainer.createEJBContainer();
    	container.getContext().bind("inject", this);
    }

    @After
    public void after() {
    	if (container != null)
    		container.close();
    }

    @Test
    public void test() throws JMSException {
    	System.out.println("\n Test TaskObserver ...\n");

    	// Subscribe topic
    	Connection connection = connectionFactory.createConnection();
		connection.start();
		Session session = connection.createSession(false, Session.AUTO_ACKNOWLEDGE);
		MessageConsumer consumer = session.createConsumer(topic);

		Task task = TaskMockService.initialTasks[0];
		taskEventLauncher.fireEvent(task);

		ObjectMessage message = (ObjectMessage) consumer.receive(3000);
		Task recvTask = (Task) message.getObject();

		assertTrue("Must be the same", task.equals(recvTask));

		connection.close();
    }
}

redpajama_set_name: RedPajamaGithub


FILL AND RESURFACE CRACKS AND HOLES. Cracks crippling your curb appeal? Use our revolutionary Epoxy Patch system to fill cracks, holes, and pits inside or outside of your home or business.
USE ON MORE THAN JUST PAVEMENT. Epoxy Patch bonds to cracked concrete, asphalt, wood, metal, wood, and other surfaces prone to cracking and spalling. Fill cracks in garage floors, basement floors, driveways, wooden beams, brick walls, etc.
COMES WITH STRONG MIXING AGENTS. Epoxy Patch comes with all three components required to create a strong & dense formula (resin, hardener, and aggregate). Delivered in a sturdy plastic pail. A 50lb. pail covers 10-15 sq. ft. & 25lb. pail covers 5 to 8 sq. ft.
USEFUL FOR ANCHORING EQUIPMENT. Use Epoxy Patch to anchor posts and signs. Epoxy Patch forms a paste-like substance that is 100% waterproof and starts to harden in about an hour after application.
Don't let your curb appeal slip between the cracks. Epoxy Patch is a unique epoxy patching system designed to fill and resurface cracks, holes, and pits in a variety of surface types—not just concrete. Its ultra-strength patching formula is easy to use and even works under the most extreme weather conditions including rain. You can even feather-edge the mortar for the perfect finish.
Epoxy Patch comes with all three components needed to create a strong epoxy patching system (resin, hardener, and aggregate). Use Super Patch indoors or outdoors; in basements or on slabs; in parking lots or in broken brick. It's strong, versatile and quick to bond.
It all starts with a crack. Prevent potholes from forming in your driveway, parking lot, & roadways.
Rain or snow seeps into the pavement, often through small cracks in the road surface, and saturates the sub-base and soil below.
During cold spells, the moisture freezes and the ground expands, pushing up and breaking the road surface.
When temperatures rise, the ground contracts to it's normal level, but the fractured and raised road surface is weakened by the cavity and the ground below.
This damaged road surface cannot support the weight of passing vehicles and begins to break down and collapse into the hollow space.
Prevent a pothole from forming immediately by filling any concrete cracks with our epoxy patching system. Our product will start to harden in about 1 hour, allowing you to safely drive over it after 2 full hours of curing. Plus, it'll very slightly expand completely filling the problem area.
Simple to mix. Easy to use.
Everything you need for the mixture is right in the pail. Combine parts labeled A & B in the container for three minutes. Then add the aggregate in small amounts until the combined material is moist and easy to spread. This can be done by hand with a mixing stick or with an electric drill mixer.
And just like that, you have the perfect concoction for repairs and anchoring equipment, including posts and signs.
Before you apply any of the epoxy mix, wash the surface to clear loose aggregate, dust, dirt, grease and oil. Once you create the mix, trowel it into and over any cracks, holes or pits in the surface.