text:
\section{Introduction}

It is generally believed that vortices in Type II superconductors tend to be pinned
in regions where the gap is small~\cite{blatter}.  This is true because a vortex, being a region
where the gradient of the superconducting order parameter is large, locally increases the gradient
part of the free energy.  Since this local increase is less in regions where the gap is smaller than average,
the vortex tends to migrate to such regions, according to this picture.

In this paper, we describe a simple model for vortex pinning in an inhomogeneous two-dimensional (2D) superconductor, in which the vortices tend to be pinned in regions where the gap is {\it larger} than its spatial average.  The model is based on a Ginzburg-Landau (GL) free energy functional in which both the mean-field transition temperature $T_{c0}$ and the zero-temperature penetration depth $\lambda(0)$ are functions
of position, but are correlated in such a way that regions with large $T_{c0}$ also have large $\lambda(0)$.
This assumption seems to apply to some of the high-T$_c$ cuprate superconductors: according to scanning
tunneling microscopy (STM) experiments on cuprates~\cite{cren, pan_oneal_badzey, howald1,
lang_davis, howald2, kato_sakata, fang, mashima}, regions that have a large gap (proportional to
$T_{c0}$ in this model) also have a single-particle local density of states (LDOS) with low, broad peaks, suggestive of a low superfluid density in these regions [proportional to $1/\lambda^2(0)$].  Our model is a generalization of an earlier approach intended to treat inhomogeneous superconductors in zero magnetic
field\cite{valdez_stroud2}.

In order to further test this vortex pinning model, we also examine the quasiparticle LDOS near the
vortex cores within this model.  The proper theoretical description of this LDOS near the cores
is one of the unsolved issues in the field of high-T$_c$
superconductivity.  STM experiments on
YBa$_2$Cu$_3$O$_{6+x}$ (YBCO) \cite{maggio_renner_fischer,
  renner_revaz_fischer} and Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212)
\cite{levy_kugler_fischer, pan_hudson_gupta, matsuba_sakata_kosugi,
  hoogenboom_renner_revaz}, show that the local density of states
(LDOS) near vortex cores in those materials has the
following characteristics: a dip at zero energy, small peaks at
energies smaller than the superconducting gap, and low, broad peaks at
energies above the superconducting gap.  Those features contrast with
the spectra shown by conventional superconductors near vortex
cores, where the LDOS usually has a peak at zero energy
in clean superconductors (i.e., those with a mean-free path larger
than the coherence length) \cite{hess_robinson_waszczak,
  renner_kent_niedermann}, or is nearly energy-independent in dirty superconductors
\cite{renner_kent_niedermann, wilde_iavarone_welp}.

The zero-energy peak in the LDOS near vortex cores of
clean conventional superconductors can be understood in terms of
electronic states with subgap energies bound to vortex cores
\cite{caroli_gennes_matricon, shore_huang_dorsey}. However, the
structure of the spectra near vortex cores of cuprates is still
lacking an explanation.  Several authors have suggested that this
structure is due to some type of competing order which emerges within
the vortex cores when superconductivity is suppressed by a magnetic
field \cite{franz_tesanovic1, arovas_berlinsky_kallin,
  franz_tesanovic2, han_lee, kishine_lee_wen}.  Some of those models,
and other descriptions of the spectra near vortex cores, have used the
Bogoliubov-de Gennes method to solve various microscopic Hamiltonians
\cite{soininen_kallin_berlinsky, wang_macdonnald, franz_tesanovic1,
  zhu_ting, melikyan_tesanovic, vafek_melikyan_franz_tesanovic}, such
as BCS-like models with d-wave symmetry.  One recent model for the
LDOS near the vortex cores, proposed by Melikyan
and Tesanovic\cite{melikyan_tesanovic}, used a Bogoliubov-de Gennes
approach to a tight-binding Hamiltonian.  These authors found that, if
a homogeneous pairing field is used in the microscopic Hamiltonian,
the LDOS exhibits a zero-energy peak on the
atomic sites that are closest to the vortex cores; this peak is,
however, absent from all other sites near the vortex cores.  On the
other hand, they found that introducing an enhanced pairing strength
for electrons on nearest-neighbor atomic sites near the vortex cores
leads to a suppression of the zero energy peak, thus obtaining a better
agreement with experiment.  They speculate that the enhancement could
be due to impurity atoms that pin the vortices, to a distortion of the
atomic lattice by the vortex itself, or to quantum fluctuations of the
superconducting order parameter.   The assumption of an enhanced pairing strength
is consistent with the model that we describe in this paper.

In our model, having introduced this correlation between the GL parameters, we
anneal the system to find both the magnitude and the phase of the
superconducting order parameter that minimize the GL free energy at
low temperatures.  Since the magnetic vector potential enters the GL
free energy functional, this procedure naturally leads to vortex
formation.  The vortex cores can be identified in our simulations as
regions with a large phase gradient. We find that, in inhomogeneous
systems, vortices tend to be pinned in regions where the
superconducting gap is large.  For comparison, we also perform a
similar annealing procedure for homogeneous systems.  In this case,
contrary to inhomogeneous systems, the magnitude of the
superconducting order parameter is reduced near vortex cores.
Thus, the assumption that the gap is large in regions with small
superfluid density in inhomogeneous systems, originally intended to
model superconductors in a zero magnetic field \cite{valdez_stroud2},
leads naturally to pinning of the vortices in large-gap regions.  This
approach might therefore be complementary to that of Ref.\
\cite{melikyan_tesanovic} mentioned above.

To connect our vortex pinning model to previous studies of the LDOS
near vortex cores, we have also studied a microscopic
Hamiltonian for electrons on a lattice.  This is a tight-binding model
in which electrons on nearest neighbor sites experience a pairing
interaction of the BCS type with d-wave symmetry \cite{valdez_stroud2,
  eckl1}. The LDOS is obtained by exact numerical diagonalization of
this Hamiltonian.  We take the pairing stregth between electrons on
nearest neighbor sites to be
proportional to the value of the superconducting order parameter as
determined by the GL simulations using the GL functional just
described.

Using this combination of a GL free energy functional and a
microscopic d-wave BCS Hamiltonian, we find that a number of
experimental results on cuprates are reproduced well by our model for
inhomogeneous systems.  For example, far from vortex cores, the LDOS
shows sharp coherence peaks.  Near the vortex cores, our calculated
LDOS does not show a spurious zero energy peak; instead it exhibits a
large gap, as well as low, broad peaks which occur at energies larger
than the value of the superconducting energy gap observed far from
vortex cores.  Also, in agreement with experiment,
the LDOS curves near vortex cores are similar
to those in the large gap regions in systems
with quenched disorder but {\em zero} magnetic field\cite{valdez_stroud2});
this connection is discussed in
section \ref{results}.  One feature not captured by our model is the
existence of small, low energy peaks in the LDOS observed near the
vortex cores.

The rest of the present article is organized as follows.  In Section
\ref{model}, we present the GL free energy functional, as well the
microscopic Hamiltonian.  In Section \ref{results}, we present results
for homogeneous and inhomogeneous systems in a magnetic field, as well
as results for inhomogeneous systems in a zero magnetic field for
comparison.  Finally, in Section \ref{discussion}, we conclude with a
discussion and a summary of our work.

\section{Model}
\label{model}

\subsection{Ginzburg-Landau free energy functional}

We use a model for a single layer of a cuprate superconductor in a
perpendicular magnetic field based on a GL free energy functional of
the form described previously\cite{valdez_stroud2}:
\begin{eqnarray}
    \frac{F}{K_{1}} =
    \sum_{i=1}^{M} \left(\frac{t}{t_{c0i}}+3\right)\frac{1}{\lambda^{2}_{i}(0)t_{c0i}^2} \left|\psi_{i}\right|^2 +
    \sum_{i=1}^{M} \frac{1}{2(9.38)}\frac{1}{\lambda^{2}_{i}(0)t_{c0i}^4} \left|\psi_{i}\right|^4  \nonumber \\
    -\sum_{\langle ij \rangle}
    \frac{2|\psi_{i}||\psi_{j}|}{\lambda_{i}(0)t_{c0i}\lambda_{j}(0)t_{c0j}}
    \cos(\theta_{i}-\theta_{j}+A_{\vec i \vec j}).
  \label{eq:GLgeneral4}
\end{eqnarray}
In Eq.~(\ref{eq:GLgeneral4}) the first and second sums are
carried over $M$ square cells, each of area equal to the
zero-temperature GL coherence length squared, $\xi_{0}^2$, of a square
lattice into which the superconductor has been discretized for
computational purposes. The third sum is carried out over nearest
neighbor cells $\langle ij \rangle$.  Here
\begin{equation}
  \psi_{i} \equiv \frac{\Delta_{i}}{E_{0}},
  \label{eq:psi_def}
\end{equation}
where $\Delta_{i}$ is the complex superconducting order parameter of
the i$^{th}$ cell, $E_{0}$ is an arbitrary energy scale
(which we take to be the hopping constant $t_{hop}\sim 200$ meV)
\begin{equation}
  t \equiv \frac{k_{B}T}{E_{0}},
  \label{eq:t_def}
\end{equation}
is the reduced temperature, $T$ is the temperature, and $k_{B}$ is the
Boltzmann constant.  Also, $\lambda_{i}(0)$ is the $T = 0$ penetration
depth and $t_{c0i}\equiv k_{B}T_{c0i}/E_{0}$, where $T_{c0i}$ is the
mean-field transition temperature of the i$^{th}$ cell. Therefore, in discretizing the
superconductor, we have assumed that $\lambda(0)$, $T_{c0}$ and
$\Delta$ are constant over distances of order $\xi_{0}$.  Finally,
\begin{equation}
  A_{\vec i \vec j} = \frac{2 e}{\hbar c}\int_{\vec i}^{\vec j}\vec A(\vec r)\cdot d\vec r
  \label{eq:vec_pot1}
\end{equation}
is the integral of the vector potential $\vec A(\vec r)$ from the
center of cell $i$, located at $\vec i$, to the center of cell $j$,
located at $\vec j$, and
$
K_{1} \equiv \hbar^4 d /[32 (9.38) \pi m^{\ast 2} \mu_{B}^{2}]
$,
where $\mu_{B}^2\simeq 5.4\times 10^{-5}$ eV-\AA$^3$ is the
square of the Bohr magneton, $m^{\ast}$ is twice the mass of a free
electron, $e$ is the absolute value of its charge, and $d$ is the
thickness of the superconducting layer.
In all of our simulations we use periodic boundary conditions. A gauge
for the magnetic field that allows this is given in
Ref.~\cite{valdez_stroud2, wenbin_lee_stroud} [see, e.\ g., eq.\ (51) of Ref.\
\cite{valdez_stroud2}, which gives this gauge choice explicitly for $N_v = 1$].

We note that the connection between the local superfluid density $n_{s,i}(T)$ and
penetration depth $\lambda_i(T)$ is such that $n_{s,i}(0) \propto 1/\lambda_i^2(0)$~\cite{valdez_stroud2}.
Thus, the quantity $1/\lambda^2$ in eq.\ (1) is a way of describing the local superfluid density,
which varies over a length scale of $\xi_0$.

We will be using the above free energy functional at both $T = 0$ and finite $T$.  Although
we call this a ``Ginzburg-Landau free energy functional,'' this name is really a misnomer, since the original GL functional was intended to be applicable only near the mean-field transition temperature. Strictly speaking, the correct free energy functional near $T = 0$ should not have the GL form, but would be expected to contain additional terms, such as higher powers of $|\psi|^2$.  We use the GL form for convenience, and because we expect it will exhibit the qualitative behavior, such as vortex pinning in the large-gap regions, that would be seen in a more accurate functional.

We assume that the magnetic field is uniform, which is a good
approximation for cuprate superconductors in their mixed state, provided
the external field is not too close to the lower critical field
$H_{c1}$.  In the cuprates, the approximation is satisfactory because the
penetration depth is of the order of thousands of \AA, while the
intervortex distance for the fields we consider is
$\sim 100$~\AA.  We employ a gauge that permits
periodic boundary conditions, such that the flux through the lattice
can take any integer multiple of $hc/e$ \cite{valdez_stroud2,
  wenbin_lee_stroud}.  Thus, the number $N_v$ of flux quanta $hc/(2e)$
must be an integer multiple of two.

The procedure for choosing the parameters $\lambda_{i}(0)$ and
$t_{c0i}$ is similar to that used in Ref.~\cite{valdez_stroud2}.
Basically, in most of the system ($\alpha$ regions),
we take $\lambda_{i}(0) \sim \lambda(0)$, where $\lambda(0)$ is the
in-plane penetration depth of a bulk cuprate superconductor
[$\lambda(0)\sim 1800$~\AA\ in Bi2212, for example], while $t_{c0i}$ is
determined from the typical energy gap in the LDOS as
observed in STM experiments. However, we will
also introduce regions ($\beta$ regions) in which $t_{c0}$ and
$\lambda(0)$ are larger than those bulk values.  Throughout this
article, when we refer to a ``gap in the LDOS,'' we mean the distance
between the two peaks in the LDOS spectra.  This is the same
gap definition used in Ref.\ \cite{lang_davis}.

In Ref.~\cite{valdez_stroud2}, we generally introduced
inhomogeneities in the superconducting order parameter $\Delta_i$ by
assuming a binary distribution of $t_{ci0}$, randomly distributed in space:
$\alpha$ cells with a small $t_{ci0}$ and
$\beta$ cells with a large $t_{ci0}$.  We also assumed a
correlation between $\lambda_{i}(0)$ and $t_{c0i}$ of the form
\begin{equation}
  \lambda_i^2(0) =  \lambda^{2}(0) \left(\frac{t_{c0i}}{t_{c0}}\right)^{y},
  \label{eq:lambda2_correl}
\end{equation}
with $y=1$. More generally, Eq.~(\ref{eq:lambda2_correl}),
with $y>0$, accounts for the fact that in STM experiments, regions
with a large gap seem to have a small superfluid density (low and
broad peaks.)

In the present article, instead of randomly distributed $\beta$
cells, we introduce two square regions with only $\beta$ cells, while
the rest of the lattice is assumed to have only $\alpha$ cells.  We
make this choice to study the effects of these
inhomogeneities on field-induced vortices.  We also consider a more
general model than Ref.\ \cite{valdez_stroud2}, allowing $y$ to
have values other than only $y = 1$.

As shown in Eq.\ (36) of Ref.~\cite{valdez_stroud2}, in the absence of
thermal fluctuations the coupling constant $J_{XY,ij}$ between cells
$i$ and $j$ is approximately
\begin{equation}
  J_{XY,ij}(t) \simeq \frac{2(9.38)\sqrt{ (1-t/t_{c0i})  (1-t/t_{c0j}) } }{\lambda_{i}(0)\,\lambda_{j}(0)}K_{1}.
  \label{eq:JXY1}
\end{equation}
(The factor of $K_1$ is missing in Ref.\ \cite{valdez_stroud2}.)
If $t<<t_{c0i}$ and $t <<
t_{c0j}$, then
\begin{equation}
  J_{XY,ij}(t) \simeq \frac{2(9.38)K_{1}}{\lambda_{i}(0)\,\lambda_{j}(0)}.
  \label{eq:JXY1_lowt}
\end{equation}
If we further choose a binary distribution of $t_{c0i}$, that is,
\begin{equation}
  t_{c0i} =
  \begin{cases}
    t_{c0}, & \text{if $i$ is on an $\alpha$ cell},\\
    ft_{c0}, & \text{if $i$ is on a $\beta$ cell},
  \end{cases}
  \label{eq:tc0_alpha_beta}
\end{equation}
where $f$ is any positive number (typically $f > 1$), then
\begin{equation}
  J_{XY,ij}(t) \simeq \frac{2(9.38)K_{1}}{\lambda^2(0)}\cdot
  \begin{cases}
    1 & \text{if $i$ and $j\in \alpha$,}\\
    \frac{1}{f^{\frac{y}{2}}} & \text{if $i\in \alpha$ and $j\in \beta$ or if $i\in \beta$ and $j\in \alpha$,}\\
    \frac{1}{f^{y}} & \text{if $i$ and $j\in \beta$.}
  \end{cases}
  \label{eq:J_alpha_beta}
\end{equation}
This expression shows that in regions with a large gap the coupling
between XY cells is small, reflecting the large penetration depth in
those regions.

\subsection{Microscopic Hamiltonian}

Besides using a GL free energy to explore vortex pinning in an
inhomogeneous superconductor, we have also studied the LDOS of
a corresponding microscopic model Hamiltonian, given by~\cite{valdez_stroud2}:
\begin{equation}
  H =   2 \sum_{\langle i,j \rangle,\sigma}t_{ij}c_{i\sigma}^{\dagger}c_{j\sigma}
+2\sum_{\langle i,j \rangle}(\Delta_{ij}c_{i\downarrow}c_{j\uparrow} +
\text{c.c.}) -\mu \sum_{i,\sigma}c_{i\sigma}^{\dagger}c_{i\sigma}
  \label{eq:hamil_bcs}
\end{equation}
Here $\sum_{\langle i, j \rangle }$ denotes a sum over distinct pairs
of nearest neighbor atomic sites on a square lattice with $N$ sites,
$c_{j\sigma}^{\dagger}$ creates an electron with spin $\sigma$
($\uparrow$ or $\downarrow$) at site $j$, $\mu$ is the chemical
potential, and $\Delta_{ij}$ denotes the strength of the pairing
interaction between electrons at sites $i$ and $j$.  Finally, we write
$t_{ij}$ as
\begin{equation}
  t_{ij} = -t_{hop}\, e^{-i A_{\vec i \vec j}^{\prime}},
  \label{hopp_const2}
\end{equation}
with
\begin{equation}
  A_{\vec i \vec j}^{\prime} = \frac{e}{\hbar c}\int_{\vec i}^{\vec j}\vec A(\vec r)\cdot d\vec r.
\end{equation}
Here the integral runs along the line from atomic site $i$, located at $\vec
i$, to the atomic site $j$, located at $\vec j$, and $t_{hop}>0$ is
the hopping integral for nearest neighbor sites on the lattice. Note
that the prefactor in $A_{ij}^{\prime}$ involves the factor of $hc/e$
due to a single electronic charge, and is thus twice as large as
that in $A_{ij}$, which involves the charge of a Cooper pair.

Following Ref.~\cite{valdez_stroud2} we take
$\Delta_{ij}$ to be given by
\begin{equation}
  \Delta_{ij} = \frac{1}{4}\frac{|\Delta_i|+|\Delta_j|}{2} e^{i
  \theta_{ij}},
  \label{delta}
\end{equation}
where
\begin{equation}
  \theta_{ij} =
  \begin{cases}
    (\theta_i+\theta_j)/2, & \text{if bond $\langle i, j \rangle$ is in $x$-direction,}\\
    (\theta_i+\theta_j)/2 + \pi, & \text{if bond $\langle i, j \rangle$ is in $y$-direction,}
  \end{cases}
  \label{eq:thetaij}
\end{equation}
and
\begin{equation}
  \Delta_{j}=|\Delta_j|e^{i\theta_{j}},
  \label{eq:psi_complex}
\end{equation}
is the value of the complex superconducting order parameter at site
$j$.  We will refer to the lattice over which the sums
in~(\ref{eq:hamil_bcs}) are carried out as the {\em atomic} lattice
(in order to distinguish it from the {\em XY} lattice.) The first term
in Eq.~(\ref{eq:hamil_bcs}) thus corresponds to the kinetic energy,
the second term is a BCS type of pairing interaction with $d$-wave
symmetry, and the third is the energy associated with the
chemical potential.

The model we present is similar to the one presented in
Ref.~\cite{valdez_stroud2}, the main differences being the inclusion of
a vector potential in the GL free energy functional, and the spatial
distribution of the inhomogeneities.
Because the vector potential
introduces vortices in the system, our results
differ substantially from our previous work.

\section{Results}
\label{results}

We first present results for homogeneous systems in the presence of an
applied transverse magnetic field equal to two flux quanta through the lattice at low $T$.
This is the lowest magnetic field consistent with the periodic boundary conditions.
In this case,
$t_{c0i}$ and $\lambda_{i}(0)$ are independent of $i$.
Fig.~\ref{fig:psi2_L16_T001_ktc14_f1} shows our calculated maps of $\Delta$ for
a homogeneous system.  In part
(a), the lengths and directions of the arrows represent
the magnitude and phase of $\Delta$ in
each XY cell.  Even though $t_{c0i}$ is homogeneous,
the magnetic field renders $\Delta$ inhomogeneous, especially near the
vortex cores, where $\Delta$ has a large phase gradient and
a smaller magnitude.  This behavior is familiar from Ginzburg-Landau
treatments of homogeneous Type II superconductors in a magnetic field.
Part (b) of Fig.~\ref{fig:psi2_L16_T001_ktc14_f1} shows a map of
$|\Delta|$, with dark (light) regions representing small (large) value
of $|\Delta|$.  The vortex cores are the
darkest regions.

Fig.~\ref{fig:ldos_L16_na1_f1} show the LDOS averaged over regions
near and far from the vortex cores of the system described in
Fig.~\ref{fig:psi2_L16_T001_ktc14_f1}. Since $|\Delta|$ is small near
the core, we have defined an XY cell to be ``near the core'' if
$|\Delta| \leq |\Delta_{\text{avg}}|/2$ in that cell, where
$|\Delta_{\text{avg}}|$ is the value of $|\Delta|$ averaged over all
the XY cells of the lattice. All other cells are considered to be far
from the core. Thus, in order to compute the averaged quantities shown
in Fig.~\ref{fig:ldos_L16_na1_f1}, we first calculated the LDOS on every
atomic site by exact numerical diagonalization of the Hamiltonian
(\ref{eq:hamil_bcs}), and then averaged the LDOS over the the set of
atomic sites near and far from the vortex cores, as defined
above.  We have chosen to enclose nine atomic sites inside
each XY cell for this system, because the
coherence length in cuprates is $\sim 15$~\AA, approximately
three times larger than the atomic lattice constant, $\sim 5$~\AA.

Fig.~\ref{fig:ldos_L16_na1_f1} shows that, in a homogeneous system,
the LDOS far from the core is strongly suppressed near $\omega=0$,
and exhibits sharp coherence peaks, reminiscent of a d-wave
superconductor in the absence of a magnetic field.  Near the vortex
cores, on the other hand, the gap is filled, and the LDOS is large
near $\omega=0$, resembling the spectrum of a gapless tight-binding
model in two dimensions and zero magnetic field \cite{assaad,valdez_stroud2}.
The spectrum near the core has considerable numerical noise, because
it represents an average over only a few atomic sites.  In particular, the
rapid oscillations are probably due to this numerical artifact.

To estimate our magnetic fields, we note that,
because of the numerical implementation of the periodic boundary
conditions \cite{yu_stroud,valdez_stroud2}, the field has to be chosen
so that the number $N_v$ of magnetic flux quanta $\Phi_{0} = hc/(2e)$
through the system is a multiple of two.  Therefore, the magnetic
field can be estimated using $B=N_v \Phi_{0}/S$ where $S$ is the area
of the system, and $\Phi_{0}\equiv hc/(2e)\approx 2\times 10^{-15}$~T-m$^{2}$.
In the present article we use a numerical sample of area
area $S=(48 a_{0})^{2}$, where $a_{0} \sim 5$ \AA \ is the atomic
lattice constant.  Therefore $B\approx N_{v}\times 3$~T, and for the
systems containing two vortices,
$B \sim 6$T.
The magnitude of this magnetic field is comparable
used in STM experiments\cite{levy_kugler_fischer,pan_hudson_gupta}.

We now briefly discuss the temperature evolution of $\langle
|\Delta|^2 \rangle$, defined as an average of $\langle |\Delta_i|^2
\rangle$ over all XY lattice cells $i$, for systems with homogeneous
$t_{c0}$ in a transverse magnetic field. Here, $\langle... \rangle$
denotes a thermal average, obtained using Monte Carlo simulations.
Fig.~\ref{fig:psi2_gl_L16} shows curves of $\langle |\Delta|^2
\rangle(t)$ versus reduced temperature $t$, for systems of the same
size subject to different magnetic fields, and therefore containing
different numbers of vortices $N_v$.  In the zero magnetic field case,
$N_v = 0$, $\langle |\Delta|^2\rangle(t)$ has a minimum as a function
of $t$, which occurs near the phase ordering temperature.
Fig.~\ref{fig:psi2_gl_L16} shows that, as the field is increased, the
phase ordering temperature is reduced, and around $N_v = 36$, it seems
to drop to zero. The fact that of $\langle |\Delta|^2 \rangle(t) $
increases with $t$ for large $t$ is an artifact of the GL functional,
as has been discussed in detail in \cite{valdez_stroud2} for the case
$B = 0$.

We now proceed to show systems with inhomogeneities.
Fig.~\ref{fig:psi2_L16_T001_ktc14_f1_fac3_na3_x3}~shows gap maps of
systems in which $t_{c0i}$, and therefore $J_{XY,ij}$, are are $i$
dependent. Specifically, two square regions, of size 4$\times$4 XY
cells each, have $t_{c0i} = ft_{c0}$, with $f=3$; those are called
$\beta$ cells, as described in the previous section. The remainder of
the XY cells have $t_{c0i}=t_{c0}$, and are called $\alpha$ cells.
Clearly, the vortices are pinned in the $\beta$ regions, where
$|\Delta|$ is large. The fact that $|\Delta|$ is large in $\beta$
regions is of course due to the fact that at low temperatures,
$|\Delta|$ is roughly proportional to $t_{c0}$.
On the other hand, in order to understand why the vortices are pinned
in the large-$|\Delta|$ regions, we note that $J_{XY,ij}$ at low
temperatures can be estimated with the use of eq.\
(\ref{eq:J_alpha_beta}). For the particular parameters used in this
calculation, namely, $x=3$ and $f=3$, $J_{XY,ij}$ is about 27 times
smaller within $\beta$ regions than in the $\alpha$ regions.  Because
of this ratio, phase gradients near the vortex cores cost much less energy
in the $\beta$ regions than in the $\alpha$ regions, even though
$|\Delta|$ is larger in the $\beta$ regions.  Thus, it is
energetically favorable for the vortices to be pinned in the $\beta$
regions.

Fig.~\ref{fig:ldos_L16_t0001_tc014_f1_na3_x3} shows the LDOS averaged
over $\alpha$ and $\beta$ regions of the system shown in
Fig.~\ref{fig:psi2_L16_T001_ktc14_f1_fac3_na3_x3}.  This Figure shows
that, far from the vortex cores ($\alpha$ regions), the LDOS is very
similar to that of regions far from the core in homogeneous system at
low magnetic field [cf.\ Fig.\ \ref{fig:ldos_L16_na1_f1}] - both
spectra have a small gap and sharp coherence peaks.  However, in
contrast to the homogeneous case, the LDOS of the inhomogeneous system
exhibits a large gap and broadened peaks near the vortex core.  This
LDOS spectrum is similar to that calculated for the large gap regions of
systems with quenched disorder and no magnetic field in our previous
work \cite{valdez_stroud2}. In the present case, the gap in the LDOS
is large in the $\beta$ regions, of course, because of the large value
of $t_{c0i}$ and therefore of $|\Delta|$, near the vortex cores.  The
peaks in the LDOS in the $\beta$ region above the gap are low and
broad, on the other hand, because of the large phase gradient of the
superconducting order parameter in these regions.  It is as if the
system has lost phase coherence in those regions due to the presence
of the vortex core.  We can more clearly see this point by comparing
the LDOS of a $\beta$ region containing a pinned vortex core to that
of a $\beta$ region in a system in a zero magnetic field, in which,
therefore, there is no vortex core to be pinned. We now describe this
system.

Fig.~\ref{fig:psi2_L16_T001_ktc14_f1_fac3_na3_f0xy} shows a system at
low temperature with two inhomogeneities, similar to that shown in
Fig.~\ref{fig:psi2_L16_T001_ktc14_f1_fac3_na3_x3}, but with zero
rather than a finite magnetic field.  Clearly, in the ground state, as
expected, the phase of $\Delta$ is almost uniform. Furthermore, and
also as expected, $|\Delta|$ is larger in the $\beta$ regions, which
have a larger value of $t_{c0i}$.  However, when we turn to the LDOS
(Fig.~\ref{fig:ldos_L16_t0001_tc014_f0xy_na3_x3}), the LDOS of the
$\beta$ regions is characterized by much sharper coherence peaks than
that at finite magnetic field described in the previous paragraph,
presumably because of the absence of a large phase gradient.

We have also tested the sensitivity of our results to lattice size and
to the number of atomic sites per XY cell.  To do this, we performed
calculations similar to the ones described above, but with
24$\times$24 instead of 16$\times$16 XY lattices, each XY cell
containing four instead of nine atomic lattice sites.
Fig.~\ref{fig:psi2_L24_T001_ktc14_f1_fac3_na2_x3} shows the results
for a 24$\times$24 XY lattice of an inhomogeneous system in the
presence of a magnetic field. As in the 16$\times$16 case, the
vortices are pinned in the regions with large $\Delta$ and small
$J_{XY,ij}$.  Fig.~\ref{fig:ldos_L24_t0001_tc014_f1_na2_x3} shows that
the LDOS for this system both near and far from the core is nearly the
same as that of the 16$\times$16 system shown in
Fig.~\ref{fig:ldos_L16_t0001_tc014_f1_na3_x3}.
Likewise, a system
with 24$\times$24 XY cells and two atomic sites per XY cell, but with
no magnetic field, is shown in
Fig.~\ref{fig:psi2_L24_T001_ktc14_f1_fac3_na2_f0xy}; the corresponding
LDOS averaged over regions near and far from the core is shown in
Fig.~\ref{fig:ldos_L24_t0001_tc014_f0xy_na2_x3}.  The LDOS shown in
this Figure has the same features as that of the 16$\times$16 system
shown in Fig.~\ref{fig:ldos_L16_t0001_tc014_f0xy_na3_x3}.
We thus conclude that our
results are not very sensitive to the lattice sizes used, nor to the
number of atomic sites per XY cell.

In the calculations described above, have assumed that $\lambda^2
\propto T_{c0}^y $.  If $y \geq 3$, then the vortices are consistently
pinned in the large gap region.  By contrast, if $y = 1$, we find the
vortices may or may not be pinned in the large gap region, depending
on where these regions are located within the computational lattice.
The vortices obviously go to the large gap region because of the
correlation between $\lambda^2$ and $T_{c0}$.
As mentioned earlier, this correlation originates in the fact large
$\lambda^2$ implies a small energy cost to introduce a gradient in the
phase of the order parameter.  Such a gradient must exist near a
vortex core; therefore, the vortex prefers to be in a region where
this gradient is energetically inexpensive.  Melikyan and Tesanovic
\cite{melikyan_tesanovic} discuss various other possible causes of
larger pinning in the large gap region; these include quantum
fluctuations, distortion of the atomic lattice by the vortices, and
the pinning of vortices by impurity atoms.  Our model could be viewed
as a special kind of such impurity pinning, in which the
``impurities'' are superconducting regions with a large gap and large
penetration depth.  We have also looked at how the size of the pinning
regions affects the pinning.  The pinning is generally more effective
for large pinning regions, probably because the vortex energy is
reduced by a larger amount if pinned in a region of large pinning
area, all other parameters being the same.

Finally, we note the similarity between our calculated LDOS
versus energy curves for regions near the vortex cores, and the
corresponding curves for large gap regions of inhomogeneous systems
with quenched disorder in a {\it zero} magnetic field, calculated in
our previous work \cite{valdez_stroud2}.  Those similarities have been
implied in several experimental papers.  For example, Lang {\it et
  al.}\cite{lang_davis} discussed the similarity between the spectra
of large-gap regions of inhomogeneous systems at low temperatures
in a zero field
and those observed in the pseudogap regime of some cuprate
superconductors.  In the pseudogap region, the phase configuration is
disordered and therefore, possibly like the $\beta$ region at zero
field, both might be considered as ``normal'' regions.  Likewise,
Fischer {\it et al.}~\cite{fischer_kugler_maggio} have also noted the
similarity of the low-$T$ spectra near the vortex cores to spectra in
the pseudogap regime.  Once again, the similarity may arise because
both the interior of the vortex cores and the pseudogap region may be
considered as ``normal''.
Thus, both of these reports implicitly suggest a similarity between
the low-$T$ spectra in the large gap regions of a disordered system at
$B = 0$ and the corresponding spectra near vortex cores at finite $B$.

\section{Discussion}
\label{discussion}

We have presented a model for the pinning of vortices by
inhomogeneities in a two-dimensional type II superconductor at low
temperatures. The model is based on a GL free energy functional, and
it is inspired by our previous study \cite{valdez_stroud2} of the LDOS
in an inhomogeneous superconductor in zero magnetic field.
In our model, we have
proposed a GL free energy functional in which regions with a large
value of the superconducting order parameter have a large penetration
depth, as suggested by zero-field STM experiments on cuprates. Using an annealing process and Monte Carlo simulations, we have found that the pinning of vortices by those large-gap regions
emerges naturally from the functional form of our GL free energy.
The vortices are attracted to the large-gap regions, in our model,
because the large penetration depth leads to a small coupling between cells in
those regions. Therefore, the phase of the
superconducting order parameter can more easily bend in these regions, and this in
turn allows the large-gap regions to accomodate a vortex more easily
than regions with a small gap.  By contrast, in the absence of
quenched inhomogeneities, minimization of the GL free energy
functional yields a spatial configuration in which the superconducting
order parameter is suppressed near vortex cores.

It is worth commenting further on the qualitative physics underlying the pinning of the vortices in the region of enhanced local $T_c$.  Basically, this pinning behavior occurs because, in our model, a locally enhanced Tc corresponds to a locally suppressed superfluid density.   This superfluid density is proportional to the local $1/\lambda^2$, and is related to the Ginzburg-Landau coefficients, as we have described earlier.  The vortices can be more easily accommodated in these large-$T_c$ regions because the large phase gradients which characterize the vortices cost less energy in such regions.  Although we describe the pinning in terms of the variation of $1/\lambda^2$, the pinning is not due to any kind of ``magnetic'' forces - the quantity $1/\lambda^2$ is just a way of describing the local superfluid density.   Thus, just as in conventional pinning, the vortices are attracted to regions of lower free energy.  The major difference is that the superfluid density (and $1/\lambda^2$) is proportional to $T_c$ in the present model, rather than being independent of, or inversely correlated with $T_c$ as in more conventional pinning.  This leads to pinning in a large-$T_c$ region rather than a small-$T_c$ region.  We also emphasize that, although our pinning results are obtained using rather elaborate numerical calculations, the underlying physics is straightforward: the pinning behavior is consistent with qualitative expectations, given the model.

It may seem strange to consider the spatial variation in $1/\lambda^2$ as occurring over a scale
of $\xi_0 \sim 15 \AA$, when $\lambda$ itself is of order $10^3$ $\AA$ or more.  However, it should be remembered that $1/\lambda^2$ is related to the coefficients of the
Ginzburg-Landau free energy [see eq.\ (1)], and these coefficients are, in fact, expected to
vary over a scale of $\xi_0$.  Thus, the model is, indeed, reasonable and consistent with the expected physics.   It is the local superfluid density (proportional to $1/\lambda^2$) which varies over a scale of $\xi_0$.

It is also worth commenting on what kind of real systems could be described by our model.   Even if one neglects the weak Josephson coupling between the layers of a high-T$_c$ material, there will still be magnetic interactions between pancake vortices in adjacent layers, so that the system will not be truly 2D.  Likewise, if we wish to use this model to describe a very thin 2D high-T$_c$ film, there are stray fields in vacuum extending into the third dimension, which will contribute to the total energy.  In both cases, our model is definitely an oversimplification.   Nonetheless, our model does seem to describe some observed features in real high-T$_c$ materials, suggesting that it captures some significant physics in these systems.  Thus, we consider our model as a possible starting point for a fully realistic treatment of either 3D high-T$_c$ materials or very thin 2D
high-T$_c$ layers.

We have connected our work on the pinning of vortices to continuing
efforts by several groups to describe the density of states near
vortices in cuprates superconductors.  To do this, we have
studied a model BCS Hamiltonian with d-wave symmetry, in which the
pairing field is obtained from simulations of the GL free energy
functional.  We use exact diagonalization to compute the local density of states
on each atomic site of the
lattice described by this Hamiltonian.  For homogeneous systems, we found that
the LDOS near the vortex cores resembles that of a gapless
tight-binding model in two dimensions, with a Van Hove peak at zero
energy. However, when we introduce the inhomogeneities with a large
pairing field and large penetration depth that pin the vortices, the
LDOS near the vortex cores is markedly different from that of the
homogeneous systems.  Namely, this LDOS exhibits a large gap as well as
low and broadened peaks at energies greater than that of the
superconducting gap fa.r from the vortex core.  Also, our calculated
LDOS near the vortex cores in this inhomogeneous case does not exhibit
the spurious zero-energy peak which is present in several other
theoretical studies but is absent from experiments. All of these
features in our calculations are consistent with results observed in
STM experiments on YBCO \cite{maggio_renner_fischer,
  renner_revaz_fischer} and Bi2212 \cite{levy_kugler_fischer,
  pan_hudson_gupta, matsuba_sakata_kosugi, hoogenboom_renner_revaz}.

Our results are also consistent with those obtained of
Ref.\ \cite{melikyan_tesanovic}, using a somewhat
different model.  Those authors obtain better agreement between their
calculated LDOS spectra and experiment\cite{pan_hudson_gupta}, if they assume
an enhanced rather than uniform pairing field near the vortex cores. In particular,
introducing this large pairing field near the vortex core in their model suppresses
the unphysical zero-energy peak.  Our approach, in which a large
gap is correlated with a large penetration depth, may
heop justify the occurrence of this larger pairing field in the vortex cores.

Finally, we briefly comment on the possible physical origin of correlation between large
gap and large penetration depth.  The origin of the spatial fluctuations of $T_{c0}$ observed
in the cuprates may be the local fluctuations in concentration, which are highly likely since
the cuprates are mostly disordered alloys and the local concentration would involve an average
a coherence length, which is only about 15 $\AA$ .  But $T_{c0}$ is proportional to the gap (i.\ e.,
presumably, the pseudogap), which increases with decreasing concentration of charge carriers, whereas
$1/\lambda^2(0)$ is proportional to the superfluid density, which should decrease with decreasing
charge carrier concentration.  Therefore, we expect $T_{c0}$ to be positively correlated with
$\lambda^2(0)$, as seen experimentally and as used in the present model.

\section{Acknowledgments}
This work was supported by NSF grant DMR04-13395.  The computations described here
were carried out through a grant of computing time from the Ohio Supercomputer Center.
We thank Prof.\ J.\ Orenstein for a useful conversation about the
origin of the correlation between superconducting gap and penetration depth.

redpajama_set_name: RedPajamaArXiv


Few life events require as much planning and preparation as weddings and purchasing a home. But that's not the only reason why buying a new home is similar to planning a wedding. And believe it or not, some couples actually do both at the same time. If you're planning your dream wedding and buying your dream home, you'll notice the following similarities.
You both need to get on the same page about expectations.
They say that opposites attract. However, it's certainly helpful for both partners to be similar in certain ways. Both of you will need to get on the same page regarding the expectations for the wedding and the home. When you're checking out the listings of Wilmington-area homes for sale, each of you should keep a separate list of must-have and nice-to-have amenities. For instance, if you have your heart set on a single-family home, but your partner is partial to townhomes, some compromising is in order.
You need to develop a comprehensive budget.
Some couples spend only a few hundred dollars on a bare bones wedding, believing that love is more important than materialism. Others decide to make that perfect day as special as possible, and spend thousands on the florist, venue, band or DJ, caterer, dress, and cake. Regardless of your approach, you and your partner need to develop a comprehensive budget for the wedding that includes allowances for every type of expense. The same method applies to buying a home. Knowing how much home you can afford is only part of the equation. You'll also have to figure out your down payment, develop a budget for moving expenses, and figure out how much you'll spend on furnishings and décor. And unless you're buying a new construction, move-in ready home, you might also have to shell out some cash for repairs.
It's all about location, location, location.
Selecting the right location is one of the most important steps in the process of either buying a home or planning a wedding. For the wedding, you'll want a beautiful location that will look great in the wedding photos. You'll have to decide whether you want to stay close to home or opt for a destination wedding. For your new home, location is even more important, since you expect to be there for years or decades, rather than a day. Look for a community that's convenient to major attractions and major cities nearby, but also has the right family-friendly atmosphere for your future.
Looking for new construction homes near Philadelphia?
Preparing to purchase a home can be a long, difficult process, but Montchanin Builders makes it easy through our partnership with our preferred lender. Our new home communities in Delaware are close to major attractions and transportation hubs. They're also neighborly, walkable communities that are perfect for families, individuals, and seniors who are looking for a peaceful sanctuary to call home.
Call Montchanin Builders today at 302-472-7212 or fill out our online form. Schedule a tour of our move-in ready Wilmington homes for sale at our communities of Darley Green, The Overlook at Rockford Falls or The Town of Whitehall.
One of the fun aspects of buying your own townhome is that you can customize the interior however you wish. Want to recreate the distinctive looks of the 50s or 70s? Go for it! Want to paint a mural in your bedroom? No problem! Have fun with your interior design ambitions, and don't be afraid to think outside the box. The bedroom is the perfect place to experiment with new design concepts, since it's generally off-limits to guests. Here are a few ideas to inspire you.
If you're trying for a traditional look, you could choose a large wooden or ornate metal headboard. But why not try something stylishly different? Use painter's tape to square off an area on the wall behind your bed and paint it a strikingly different color than the rest of the wall. Extend the painted edge to line up with the edge of your bed. Or, ditch the conventional headboard for a soothing work of art instead.
You can also play with shapes. Instead of a square block of painted wall or artwork behind your bed, you could nail up a circular, rustic-looking, woven sisal or hemp throw rug. To make this idea work, you'll have to find a visually intriguing rug with braided or woven textures. A similar headboard alternative is to lay a visually pleasing folding screen against the wall behind the bed.
It's common for homeowners to allocate much of the lighting fixture budget for a fancy chandelier in the entryway, and for dramatic, statement lighting in the kitchen and dining room. The bedroom often gets shortchanged. It's time to change that. Look for truly unique ceiling lighting fixtures for your private sanctuary, like a fixture in the shape of a giant magnolia blossom, with elegant gunmetal-colored "petals." Or, if you're feeling regal, consider a ceiling light in the shape of a king's crown. There are virtually limitless options to choose from. Try browsing specialty lighting shops instead of big box stores.
Another way to carve out a sanctuary in your townhome is by adding an elegant sitting area to the master bedroom. It's the perfect place to relax with a good book on a rainy Sunday. Pair a comfortable recliner with a small occasional table, and place both by the window. Then, add some items for décor, like a large potted plant in the corner and an oil painting on the opposite wall.
Montchanin Builders is known for building elegant homes in Delaware. In addition to our Wilmington, DE single family homes, we're pleased to offer luxurious, yet affordable townhomes for sale in our planned communities. You can tour Darley Green or The Overlook at Rockford Falls today to find your beautiful new home. You can call 302.472.7212 for more information about our homes for sale in Wilmington, Delaware.
Townhomes are an increasingly popular option for homeowners, particularly those who are purchasing their first home. This is because, while townhomes are more affordable than single family homes, they offer the same lifestyle perks. Plus, they tend to have generous square footage for home buyers who are interested in growing their family. In particular, Montchanin Builders in Delaware is known for designing spacious and beautiful townhomes that are perfectly suited to young couples and retirees alike.
Not all townhouses look alike from the outside. You have lots of options to consider, from stacked townhouses with two to three stories, to twin homes, to manor townhouses. Stacked townhomes are what you would think of as a traditional townhouse, including a one-car garage. Twin homes are two townhomes positioned together. These offer the option of a two-car garage.
If you're looking for something a little different, consider purchasing a manor townhome. Manor townhomes are the height of upscale luxury. The Monroe, The Montgomery, and The Maxwell offered by Montchanin Builders are manor townhomes with unique architectural features on the exterior. Inside, you'll find up to 2,500 square feet of finished living space, with 9' ceilings and a gourmet kitchen.
Every home should be personalized to suit its owners' unique style preferences. No matter which architectural style you choose, you'll have the option to customize your new townhome. Choose from stainless kitchen appliances, granite countertops in your choice of colors, recessed lighting, and upgraded kitchen cabinets with designer hardware. You can also choose your own flooring, including hardwood or ceramic tile.
One of the reasons why townhomes are such a popular investment is that they are typically thousands of dollars less than single family homes. But unlike an apartment or condo, you'll own the land you live on. Treat yourself to some new furnishings, but don't buy everything until after you've moved in. You should have the essentials, of course, like the beds, mattresses, table, and seating options. But wait to go to the furniture store until after you get a better sense of your ideal furniture layout. Take measurements and do plenty of online window shopping so you can get your new townhouse looking exactly how you want it.
If you're interested in getting $15,000* toward your new home purchase, as well as favorable rates from one of the most reputable home lenders in the country, then it's time to get in touch with Montchanin Builders. We are a premier home building and community planning company, offering exquisitely designed new homes in Wilmington. We invite you to tour our beautiful, family-friendly communities in the Wilmington, Delaware area, including Darley Green and The Overlook at Rockford Falls. Call our office today at 302.472.7212 to inquire about our Wilmington, DE townhomes for sale.
*$15,000 towards your new home purchase with the use of NCC WF Program, Preferred Lender and Settlement Attorney.
The Philadelphia and Lancaster Turnpike is hailed as America's first engineered road, and its first long-distance paved road. It was first used at the tail-end of the 18th century, and fortunately, it's improved quite a lot since then. Today, travelers on Philly Pike can take a break from the road to enjoy the rich diversity of restaurants and eateries along their route.
The fantastic dining scene on Philadelphia Pike is just one of the many reasons why singles, couples, and families have been moving to the North Wilmington, Delaware area. The area is also known for its beautifully designed, courtesy of Montchanin Builders. Browse our website to view our available properties in Darley Green or The Overlook at Rockford Falls. Our luxurious, new townhomes in North Wilmington are selling quickly, and we've partnered with a reputable lender to make it even easier for you to come home to our community!
Mazzella's is one of the best kept secrets of the Philadelphia Turnpike. It's an award-winning restaurant that consistently gets rave reviews from its diners. The menu includes everything you'd expect from an Italian restaurant, including hot sandwiches, specialty pizzas (try the seafood toppings!), calzones, and Stromboli. Entrees include fettucine carbonara, penne primavera, and penne vodka with chopped prosciutto. Diners with special dietary requirements will be pleased to know that gluten-free penne is available. Don't leave without checking out the dessert menu, which features limoncello mascarpone cake, homemade tiramisu, and homemade New York cheesecake.
Cajun Kate's is run by husband and wife team, Don and Kate Applebaum, who met at culinary school. Both worked the famed restaurants of New Orleans before heading back up north to Delaware. Cajun Kate's has earned a reputation for serving up authentic, made from scratch N'Awlins specialties like crawfish pies, crispy Cajun mac n'cheese, beignets, and Southern-style pralines. Currently, the restaurant is open Fridays and Saturdays for breakfast, lunch, dinner, and dessert.
Just a few blocks from Philadelphia Pike, Bellefonte Café is one of those rare places where you can instantly feel at home as soon as you walk in the door. This casual, homey eatery exudes a bohemian ambience, and the staff is unfailingly friendly and attentive, without being overbearing. Housed in a residential-style building, you can relax on the beautiful wraparound porch, check out the herb gardens out back, or head inside to dine while being serenaded by live music.
The menu is pleasantly eclectic. Start with a Greek salad, roasted beet salad, or Thai chicken salad, or try the Moroccan sampler for a shareable appetizer. Try their unbeatable Philly cheesesteak, paired with apple slaw, or try the chickpea fajitas. In the mood for something a little different? Try the mango brie quesadilla or the vegan "cheesesteak" with chopped seitan, Portobellos, and melted Daiyo cheese.
To schedule a tour of the luxurious new North Wilmington townhomes brought to you by Montchanin Builders, call (302) 472-7212 today!
Just HOW big is New Year's Eve in Philadelphia? The city is ringing in 2017 not once, but twice!
The SugarHouse New Year's Eve Fireworks on the Delaware River Waterfront will take place at 6 p.m., and again at midnight. Inside, there is a grand celebration with live music from Burnt Sienna and an open bar. You can reach the casino by taking a cab or the SEPTA Blue Line to Old City and walking five minutes to Penn's Landing. By car, you can park in one of the lots down Columbus Boulevard.
Aside from the main attraction, there are many other ways to celebrate New Year's Eve in Philly.
Having trouble deciding on just one place to party? The adventurous can purchase a NYE All Access Pass for $109 from Finn McCool's at 118 S. 12th Street, which gets you into open bars at 1925 Lounge, Brü Craft & Wurst, Finn McCool's, Mad River Bar & Grille, and Recess Lounge. DJs will be spinning Top 40, Hip Hop, Dance/House music from 9 p.m. to 2 a.m.
The Blue Cross RiverRink Winterfest is a popular spot for music, food, drinks and ice skating. The fire pits and cozy warming huts offer a nice respite from the cold — not to mention, one of the best views of the fireworks celebration. There will be a Kids Lodge set up with arcade games, food and drink from Garces and Chickie's and Pete's. Don't forget to grab dessert at the Franklin Fountain Confectionary Cabin. All ice skating passes sell out early, but you can still come by the beautiful wintry scene as a "spectator" for $30, which includes live entertainment, a spot for the fireworks, and a party favor.
North Bowl Lounge N Lanes is hosting New Year's Eve festivities for the whole family from 5-8 pm, which will include bowling, a "ball drop", food, games, DJ tunes, face-painting, balloon art, and caricaturist drawings. Tickets are $18 per person. You'll have your choice of 17 bowling lanes, two full bars, pool tables, and arcade games.
New Year's Eve on the Moshulu offers a celebration aboard the oldest and largest square-rigged sailing vessel still afloat. The deck provides top-notch fireworks viewing, a dessert buffet, a cash bar and live music. You can also opt for the four-course prix fixe dinner that includes beef tenderloin, lobster tail, tuna steak, braised lamb shank, crab-crusted grouper, or beef short rib. Music options include a DJ spinning mid-deck, a pianist, in the dining room, and a jazz trio in the Orchid room. The cost ranges from $35 for children, to $125 from 3:30 – 6:45 p.m., or $195 from 7 – 10:30 p.m. Beverages are extra. If you are not dining, you can still join the party for $50, which includes dessert, access to a cash bar, and music.
These are just a few of the many, many places to party on New Year's Eve in Philadelphia. Philly, and all it has to offer, is only a short drive from Montchanin communities like Darley Green, Shipley Road and Town of Whitehall.
Contact our office for an exciting start to 2017 with a tour of available homes in Delaware.
In the market for a beautiful new home in Delaware or Pennsylvania? Prospective homebuyers have more inviting options than ever before within the upscale communities offered by Montchanin Builders. This innovative residential construction firm, headquartered in Wilmington, has put their expertise and talents to work in five distinct communities in some of the most sought-after areas of New Castle County and Chester County, PA.
Montchanin's "5 Hottest Communities in Delaware and Pennsylvania," were recently featured in Delaware Today, giving families a sneak peek into the amenities, floor plans, community highlights and picturesque locales of each unique development.
Whether you're searching for a luxurious estate home to grow your family, or a contemporary condo with an easy city commute, these new construction homes promise the best in architectural design, high-end finishes, and proximity to nightlife and recreation.
Darley Green is a 67-acre master-planned community that is Wilmington's best kept secret. Its enviable location in the Claymont Renaissance District is attracting attention as the state's first transit oriented, urban style community. Darley Green features elegant condominiums and townhomes along with its own town center, and is just steps from the SEPTA R2 line and the Claymont commuter train. Homeowners can walk to retail shops, dining establishments and a state-of-the-art library, and walking trails and communal green spaces.
Situated just outside of Middletown, DE, the Town of WhiteHall is the area's premier walkable community that seamlessly integrates nature, recreation, locally-owned businesses and stunning 3, 4 and 5-bedroom single family estate homes. Residents enjoy a backdrop of mature hardwoods and miles of scenic trails that lead to Lums Pond State Park. Homebuyers can choose from several floorplans that feature grand front porches, covered back porches, walkout basements and options to customize for an office or quaint reading nook.
Shipley's Circle is a unique three-lot community nestled in heart of the Brandywine Hundred. Each 4 bedroom, 2.5 bath semi-custom estate home boasts a spacious 2-garage garage and dozens of luxurious amenities. These elegant single-family homes offer 2,825 square feet of living space and are centrally located close to shopping and entertainment as well as award-winning schools.
Renowned for its tranquil rural setting on the historic Bancroft Mills site, the new community of Rockford Falls is currently under construction. The community is slated to have 3,000 square foot Delaware townhomes perched on the hillside, each with three spacious bedrooms, two car garages, and gorgeous views of the Brandywine Creek.
Also under development is Pennsylvania's newest "agrihood," on a 26-acre property in Unionville. What sets this neighborhood apart from the pack is its community gardens, harvest barn and working fields. Montchanin will be lending its building expertise in the craftsmanship of 17 custom single family homes, each situated on a 10,000 square foot lot.
Schedule a home tour today!
Montchanin Builders is proud to bring quality affordable housing solutions for first (and second time!) home buyers in the Tri-state area. To learn more about our distinctive communities and move-in ready homes, we invite you to contact our sales team today. You can reach us online, or by calling (302) 376-1100.
Philadelphia's Best Festivals & Events Are Just Around The Corner!
Spring is in the air and the warm weather is bringing people out of their homes for fun festivals and area events.
Montchanin Builders offers a low-maintenance condo and townhomes in Wilmington, Delaware — just 30 minutes from Philadelphia.
Check out these family favorites coming up soon.
Who doesn't love food? The annual Philadelphia Magazine Wine and Food Festival is the ideal opportunity to get out and sample some of Philly's best food and drink. Event highlights include sips of over 650 exclusive wines samples from around the globe, as well as new product tastings and classic bites from the most popular restaurants in the city. Eateries featured include 1100 Social, Bank & Bourbon, Crow and the Pitcher, Davio's, Fat Jack's and Laurel, to name a few. An on-site Fine Wine & Good Spirits store will be available to purchase take-home souvenirs of your favorite finds. Don't miss this spring festival, held on May 3rd.
Spanning 12 city blocks, the 3rd annual South Street Spring Festival and Maifest is a German food and drink enthusiast's delight, but also a free family-friendly gathering. This year's festivities on May 7th will encompass 125 vendors, 35 participating restaurants, and 40 bands on 3 stages. Highlights include: burgers and sausages al fresco from The Twisted Tail; banana cream pies from The Sweet Life Bakeshop; giant pizza slices from Lorenzo's; famous cheesesteaks from Jim's; and frozen daiquiris from Fat Tuesday. Maifest is held at Brauhaus Schmitz, offering German beers, along with roast pork sandwiches, sausage sandwiches and bratwurst. Adding to the ambiance are the authentic dancers, the city's largest maypole, and traditional German music.
This year, Franklin Square turns 10. To celebrate the historic landmark park, Philadelphia's kicking off the first-ever Chinese Lantern Festival in the Northeastern United States. The nightly light spectacle will include 25 illuminated lanterns, giant flowers, a three-story pagoda and a 200-foot-long Chinese dragon. Daytime admission is free, where your family can enjoy rides on a carousel, mini golf, craft booths and vendors selling authentic Chinese goods. By night, you'll need a ticket ($17 adults, $15 seniors and military, $12 kids) for the light show and food specials, in addition to live performances by acrobats, opera performers, dancers, and musicians. The festival runs from April 22 – June 12.
Living in Delaware has many advantages for people currently living in nearby Philadelphia, Pennsylvania. For starters, there is NO SALES TAX in Delaware. You can also get more space for your money and enjoy below-market prices with brand new homes starting in the low $200s.
We offer retail shopping at Brandywine Town Centre and Concord Mall in close proximity, as well as recreational paths and restaurants within walking distance. Commuting to Philadelphia for work is a breeze with easy access to I-95, as well as the SEPTA R2 line and Wilmington Amtrak station. Book your tour of the Darley Green community today!
Along with the warmer Wilmington weather comes an influx of calls about our new homes in Delaware. We're not the only ones experiencing increased activity.
According to Realtor.com, about 40 percent of home sales take place from April through July. Homes are available all year round, but many shoppers take advantage of the spring season for several strategic reasons.
If you're looking for a home with very specific features or wish to live in a particular neighborhood, it's best to look in the spring when there are more homes on the market. Even in new developments where individual sellers are not a factor in determining when to put a home up for sale, builders like basing deadlines for completion to coincide with the increase in buyer interest, so spring is still a great time to look. Unlike the existing home market, you're not likely to run into competitive rifts with other prospective buyers in a new homes community like Darley Green.
Since it could take four to six weeks to close on a new home, depending on a variety of factors, families who wish to move in the summer when the kids are off school should ideally start their search in the spring. Particularly for new homes where customization options exist, early house hunting gives you time to "get your house in order," so to speak, and make desired modifications prior to a summer move-in.
With the tax filing deadline coming up on April 15th and refund checks going out within 21 days after that, buyers will have a little extra padding in their wallets to put toward closing, moving costs or new furnishings. For Delaware residents, the average tax refund is around $2,563, according to SmartAsset.com.
The CoreLogic Home Price Index reports that home prices have appreciated 6.3% over the past year. Their panel of over 100 economists, investment strategists and housing market analysts predicts that prices will continue to rise another 5.5% in the coming year. While mortgage rates have remained around a super low 4% rate, the National Association of Realtors and the Mortgage Bankers Association predict that the rate will be up almost three-quarters of a percentage point by this time next year, which will impact monthly mortgage payments.
Ready to buy a new home in Wilmington, DE?
Spring is a time of rejuvenation and fresh starts. If you're considering a big move, why not get the property and lifestyle of your dreams sooner rather than later to begin life anew? Call us at 302-655-2600 to schedule a walk-through of Darley Green's move-in ready condos.
We are located in the excellent Brandywine School District in a safe neighborhood with tree-lined streets, community gathering space, a state-of-the-art library, walking and jogging trails, a stream, green space and waterfront recreation and sports just minutes away. In the master-planned community of Darley Green you'll find townhomes with up to 2,100 sq. ft. of living space and two-car garages, as well as two-story condos with up to 2,500 sq. ft. of space and one-car garages.
If you're looking for a new home in Philadelphia, why not expand your search to Wilmington, which is just 15 minutes from the Philadelphia International Airport – but with lower taxes? We look forward to helping you with your spring home search!
Though the weather outside may be "frightful," it doesn't stop local residents from getting out to enjoy all the delightful festivities of the holiday season.
Whether your idea of fun consists of hot cocoa and ice skating or shopping at Macy's and high-tech light shows, the best of Philadelphia at Christmastime is less than 30 minutes from the Delaware townhomes of Darley Green.
Philadelphia's annual transformation of Love Park into "Christmas Village" has been called "the Best Outdoor Event" by Philly Happening Magazine. Open from Thanksgiving through the last Sunday of December, the outdoor holiday market is modeled after traditional Christmas markets in Germany with vendors at more than 60 wooden booths, traditional European sweets, international gifts, arts and crafts, thousands of lights and a festive holiday tree.
The centerpiece of Winterfest is the Olympic-size skating rink overlooking the Delaware River lined with holiday trees. You'll also find a ski-chalet style lodge, a winter garden, heated tents, fire pits, food vendors, themed parties, and holiday flea market.
Starting the Friday after Thanksgiving and running through the end of December, Macy's shoppers will be treated to over 34,500 LED lights on a towering pine, with another 65,000 lights decorating the scene. The voice of Julie Andrews and a Wanamaker Organ accompany your journey through classic holiday tales like The Nutcracker and Frosty The Snowman. The third floor of Macy's flagship Philadelphia store is transformed into a 6,000-square-foot 1840s village with more than 100 animated characters telling the story of Charles Dickens' A Christmas Carol.
No matter how many times you've been to Franklin Square, you don't want to miss the Electrical Spectacle Holiday Light Show that runs every 30 minutes from 4:30 to 8 p.m. from November 12 through December 31. More than 50,000 lights flash in accordance with holiday music played by the Philly Pops – but that's not all! Revelers can also ride a holiday train and carousel, nosh at Ben's Bites & Brews food truck, play a round of mini-golf while staying cozy with warming stations, shop for unique gifts at the holiday market, visit with Santa, or participate in one of the many fun themed events like Star Wars Night, Frozen Night or Nutcracker Night.
Not sure what you'd like to see?
Hop aboard the Philadelphia PHLASH, which departs from the Independence Visitor Center every 15 minutes and makes 22 stops in Center City Philadelphia. For just $2, you can take the Holiday Evening Loop from 6-10 p.m. to experience Franklin Square's Holiday Festival, Macy's Christmas Light Show, Christmas Village at LOVE Park and more.
All the best is just a half hour drive from the master-planned community of Darley Green. To learn more about Montchanin Builders' walkable, family-friendly community located in Delaware's Claymont Renaissance District, please call 302-655-2600.
There are certain American cities that seem to come alive in the summer but possibly none more so than Philadelphia with its rich riverfront setting, multicultural residents, and spectacular historic traditions. The city seems to explode from Memorial Day to Labor Day with a calendar full of art, food, and music festivals, blockbuster attractions, sporting events, and family-friendly happenings.
One spectacular sight that never fails to catch everyone's breath is the vision of a fleet of two to three hundred foot long three masted ships gliding under full sail into port. That's what you'll experience from June 25 to June 28 at the Tall Ships Challenge Philadelphia Camden 2015 as you'll be able to climb aboard one of these beauties and go for a sail on the Delaware.
If you're appreciating Philly for the first time or looking at Philadelphia condos as an option to make this gorgeous city your own, be sure to take a break from the many summer events to visit Darley Green, the master planned community of beautiful condos and townhouses just a quick twenty minutes away from downtown Philadelphia in Wilmington, DE.
You'll find a wide selection of affordable condos and townhouses, great design, top amenities, and a wonderful small town feel. At Darley Green, you'll get the best of both worlds—a dynamic and vibrant city full of culture and opportunity in Philadelphia and a delightful maintenance-free home base at Darley Green.
One of the best urban beaches in the world is in Philadelphia?
Yes, that's exactly what the Huffington Post proclaimed Spruce Street Harbor Park on the Delaware River in Philadelphia. It called SSHP "a summer-festival-meets-urban-beach-mash-up that brings together pop-up restaurants, a sand pit strung with hammocks and a small beach with loungers and cozy fire pits. The highlight is a traditional wooden boardwalk lined with street food stalls and arcade games in old shipping containers." Philadelphians wait all winter for this eclectic riverfront scene with its bocce court, beer garden, and a floating restaurant that Travel + Leisure Magazine calls one of "the coolest floating restaurants in the world." And what's also cool is that it's FREE!
Follow Philadelphia folks in the know to another great pop up experience, the Oval, the City of Brotherly Love's eight acre "Park on the Parkway" located next to the Philadelphia Museum of Art at Eakins Oval. Open all summer, the Oval is where you go for the latest art installations, live music, the best food trucks in town, not to mention craft beer and movie nights. It's all summer and it's also free!
Didn't get enough ice skating this winter at RiverRink's Winterfest downtown on the Delaware River? Revisit your "inner kid" this summer and roller skate at Philadelphia's brand new Blue Cross RiverRink Summerfest. It's got a great lodge, a play area for the kids, and will stay open until the end of September.
The condos and townhomes at Darley Green in Wilmington, DE are a fantastic and affordable option for the smart buyer who wants all the big city amenities that Philadelphia has to offer but wants the luxury of a gorgeous maintenance free home just minutes away by car or train.
No matter where you live, what's summer without one of America's greatest 4th of July celebrations. Come to WaWa Welcome America in Philadelphia, a blockbuster Independence Day extravaganza of concerts, fireworks, and fun activities celebrating America's independence.
Finally, we all hate for summer to end but what a great bookend for all the non-stop summer activities in Philadelphia is the two-day Made in America Music Festival over Labor Day weekend. Dozens of top music acts on multiple stages set up on the Benjamin Franklin Parkway and all curated by Jay Z provide a perfect cap to the summer.
There are way too many summer fairs, festivals, and events in and around Philadelphia to list here. If you're thinking Philadelphia condos are your only option, you'll find there may be no more affordable and luxurious ways to experience Philadelphia than owning a move-in ready home at Darley Green, situated just five minutes from downtown Wilmington and 20 minutes from Philly.
Call 302-472-7213 to learn more about the many benefits of this master-planned community or to schedule a home tour of Darley Green.


text:
Q: How to change the default screen background color of all the pages in React JS(Next JS) using tailwind CSS I am trying to change the default screen background colour of all the pages of the web application.
Technologies I used:

*

*React JS

*Next JS

*Tailwind CSS

I want to make the screen background colour of all pages light grey as shown in the image instead of the default white colour.

Is there any way to do that all at once, or do we need to add background colour manually to every page?

A: If you are using NextJS you can make use of a custom file _app.jsx (if you are using javascript) or _app.tsx (if you are using TypeScript) to change the background colour (and many more by the way) of all your web pages.
You can create a div in the file and add background colour to the className, it will be applied to all pages being rendered in the web application.
Code example :
function MyApp({ Component, pageProps }) {
 return (
  <div className="bg-gray-500">
    <Component {...pageProps}/>
  </div>
 );
}

NextJS has a more detailed explanation about this.

A: You can go to styles -> globals.css
and there add the following
html {
  width: 100%;
  height: 100%;
  background-color: {color of your choice};
}

By this; all your pages will have the specified background color unless you specify a separate background color for any component.

A: Adding bg-color to a div only adds color to a div... I think the html { background-color: {color of your choice}; is more likely to yield the desired result. Having same issue. Applied your solution but it only filled the div that fell short of page view. Of course the previous comment's coding is incorrect.
should be:
html {
    background-color: #yourcolor
}

redpajama_set_name: RedPajamaStackExchange


A lady in Berlin (Germany) has a website on which she posts any news what so ever concerning elephants in zoo's all over the world.
She asked me if I could ask people I know for 'old' photo's of elephants, no matter which zoo in the world… because she wants to add a category to her website about elefants in zoo's in the past.
So… all photographers under you…. if you have old foto's of elephants, and you don't object to them being posted on that lady's Elephants-Lexicon, then please let me know. All photo's are very welcome, b&w, colour etc. If there can be given some info also it would be highly appreciated!
I want to thank you in advance for taking the effort!!


text:
Rissoella paupercula is een slakkensoort uit de familie van de Rissoellidae. De wetenschappelijke naam van de soort is voor het eerst geldig gepubliceerd in 1852 door C.B. Adams.

Rissoellidae

redpajama_set_name: RedPajamaWikipedia


This summer, Sanan and I visited Prague and Budapest on one trip and made a camping trip to the Matterhorn and back. Here are some pix….
I absolutely loved your pics of the fountains in Provence–I love finding a theme and going with it. I hope to get back to France someday and visit Provence, particularly. Also enjoyed looking at your website! Blessings.


Most academics and marketing practioners consider that there are two basic methods to marketing which are generally categorised as being traditional or marriage based. The traditional approach to marketing has the acquisition of new customers as its central tenet. Indeed, Peter Drucker (1964, p. 91) recommended a business only existed 'to produce a customer'. However, organisations have significantly begun to recognise that customer retention is as important, or even more so, than customer acquisition. The traveling make behind this change in thinking has been the ever increasing cost of acquiring clients (Holmlund and Koch, 1996). Therefore, as opposed to traditional marketing, the basic premise of romance marketing is the introduction of customer associations with a view to cost lowering within the company and increased shareholder value through the creation of high degrees of customer satisfaction (Perrien and Ricard, 1995). Indeed, many romantic relationship marketing theorists summarise the difference between relationship marketing and traditional marketing as the creation of 'customer satisfaction' as opposed to the 'creation of the customer' (Perrien and Ricard, 1995). In terms of the competitive edge aspect of Doyle's explanation, Porter's 'General Strategies' model (1980, p. 39 - see Appendix I) suggests that the traditional approach to marketing relies closely on a strategy of cost command and price competiveness. In contrast, relationship marketing focuses on differentiation, in terms of product and/or brand features, as a way to obtain sustainable competitive advantage.
It can be seen, therefore, that Doyle's definition of marketing is closely allied to the partnership marketing school of thinking. However, Doyle's meaning will not take account of the fact that the implementation of an relationship based method of marketing alone will not necessarily guarantee an company will achieve a ecological competitive advantage, or, therefore, a following maximisation of shareholder earnings. To have the prospect of this, a romance marketing programme must include attractive and relevant value propositions for customers, which should distinguish an organisation's brand and/or products from those of its rivals. In addition, these differentiated value propositions should not be easy for opponents to imitate (Barney, 1991). It is important, therefore, that an organisation establishes precisely what value its customers would like in order for it to be able to design and deliver the appropriate value-enhancing benefits that will assist in the building of important long-term, and mutually beneficial, customer human relationships (Christopher et al, 2002, p. 22).
Doyle's definition relates and then "valued customers" suggesting that they are a homogenous group. However, not absolutely all customers are as well and Newell (2003, p. 17) articulates this when he suggests that "Customers don't desire to be treated equally. They would like to be treated individually". Therefore, not only does indeed successful relationship marketing rely on the creation of customer value propositions but also on the procedure of segmenting and concentrating on the most likely customers and then tailoring and setting value propositions to appeal to the many, identified consumer sections. Furthermore, the segmentation of consumers by psychographic and behavioural characteristics enables an company to understand different motivational factors that effect those consumers in their purchasing behaviour towards specific brands or products, thus facilitating a more individual approach to customers. In addition, segmentation by this method provides an organisation with an information into the specific value benefits that its customers, and potential prospects, are seeking when they make a purchase. This, in turn, helps in the creation of desired and differentiated brands and/or products, and enables their effective setting for the identified segments (Dibb et al. , 1997). The segmentation, targeting, and positioning process is summarised in Appendix II.
Doyle's meaning of marketing specifically identifies "developing associations with respected customers" as a means of fabricating a competitive advantage. However, this is makes no reference to some other stakeholder groups an company may have, and will certainly need to interact with, if it's to make and preserve a competitive gain. The 'six market segments' stakeholder model indentifies the main element stakeholder groups that require attention from any organisation that adopts a comprehensive relationship marketing method of the success of its business development and profitability targets (Christopher et al. , 2002, p. 76 - see Appendix III) Whilst this model is certainly customer centric, it recognises different stakeholder groupings as having the potential to engage in active human relationships with the organisation and. , therefore, be considered for addition within its marketing strategy. It is necessary for organisations to effectively deal with relationships with all of these groupings especially as they have an interrelationship with each other. For instance, shareholders in an organisation are customers of the Influencer Marketplaces, but can also be area of the Referral Markets and the client Markets. Finally, and perhaps most importantly, in terms of support for Doyle's classification, research has shown that there surely is a direct hyperlink between your adoption of an effective relationship marketing strategy and revenue (Bhote, 1996).
None of the is to say, however, that traditional marketing doesn't have a role that can be played in the modern-day commercial environment. There is absolutely no doubt that many consumers have a short-term perspective, in terms of these purchasing behavior, and are not necessarily devoted to particular brands. Indeed, such consumers may buy particular brands out of behavior or they could actively seek out brands regardless of whether or not they are really being targeted by marriage marketing programmes (Kotler and Armstrong, 2011, p. 150). Within this sense, Doyle's description will not recognise the idea or value of traditional marketing. However, the countless exponents of the traditional approach to marketing regard it as a definite and dedicated management function in a organisation that is in charge of creating deals with certain sets of customers that fulfill their immediate needs and wishes whilst, at the same time, interacting with the marketing aims set by the organisation (Gr¶nroos, 2006).
Organisations that deploy traditional marketing methods have a tendency to view the marketing function as being accountable for the so-called four Ps, namely Product, Place (distribution), Price, and Promotion, rather than the management of customer associations. Research in addition has shown that, in reality, very few organisations deploy specifically either traditional marketing or marriage marketing. Generally you will see a blending of both marketing disciplines and, in conditions of responsibility within an company, traditional marketing may be the website of the marketing section with customer marriage management being a standalone function. Regardless, the decision between using one of the two methods, and using both, should always be based on the industry involved and the needs of the client. (Zinedlin and Philipson, 2007).
However, there remains without doubt that many consumers are happy, and able, to form psychological, as well as useful, transaction-based connections with organisations. This is particularly the circumstance where an organisation has a recognisable brand as individuals are more likely to identify with a brandname, and remain faithful to that brand, than they are to an company. Commitment by customers to a brand may be a prime factor in the creation of ecological competitive advantage and, therefore, business progress and profitability (Aggarwal, 2004). It really is therefore that, matching to Kotler and Armstrong (2011, p. 259), of all the assets held by an organisation, the brand is the possibly the most long lasting and valuable in conditions of its potential to generate shareholder wealth. Therefore, although Doyle's description of marketing has been seen to exclude the still relevant dimension of traditional marketing, it can be effectively applied to the creation and management of the online marketing strategy of an company. Even so, Doyle's definition does not go very good enough in its tries to encompass the practice and value of relationship marketing as it generally does not specifically refer to the strategically significant role of brands in building lasting competitive advantages.
Consequently, to apply Doyle's definition in a functional sense to the creation and management associated with an organisation's marketing strategy, it is first essential to discuss and evaluate the role that branding and brand reputation has. As has already been shown, true relationship marketing needs that brands, and their natural value propositions, are positioned in a differentiated and competitive sense against the many identified consumer segments. This is only the first rung on the ladder in the branding process which is critical to the building of the sustainable competitive benefit that, as time passes, an organisation can build and preserve its brand reputation. Brand reputation is to do with how customers think and experience a brand and, in order to develop brand reputation organisations have to have certain 'building blocks' in location to enable customers to feel self-confident in developing meaningful human relationships with the brand (Keller, 2003). These blocks include brand salience, performance, imagery, and resonance, which all effect on the judgements consumers make in regards to a brand and, inevitably, how they will behave towards it. This technique of brand reputation building is summarised in Appendix IV.
If the process is adopted effectively, then customers will in the end progress from understanding, and empathising with, the brand's value propositions to presenting a resonance with the brand and being ready to form an mental romance with it. To maximise the value of this potential emotional relationship, organisations have to take benefit of every available opportunity to ensure that engagement between their brand and their customers is positive. These engagements can comprise lots of so called customer 'touchpoints', such as direct marketing, helplines, advertising, and sociable media. Each and every time that a customer engages with a brand via a touchpoint that customer's views and opinions about the brand are produced and, inevitably, this will effect attitudes and behavior towards brand. Indeed, Doyle himself (1998) advised that, by maximising the positive and integrated dynamics of customer engagements using their brands, organisations could improve their overall brand reputations. Consumers who form mental connections with brands can in fact become so enthusiastic about these associations that they develop a loyalty to the brand and may even progress so far as becoming so called 'brand advocates', recommending the brand to friends, family, and participants with their peer and reference teams (Aggarwal, 2004). When the company carefully nurtures these faithful customers and brand advocates, then they can become greatly valuable, in terms of future shareholder results, and sets of them could even form themselves into brand areas on communal networking sites, such as Facebook, where their affect over some other clients and potential clients will be even greater.
Even so, although Doyle's description does flunk in certain areas, it is still a solid groundwork for the framing of organisation's marketing strategy. This is because modern-day organisations have to comprehend that, in order to provide the returns that their shareholders demand, a substantial factor of marketing practice must be focussed on the building of long-term, mutually beneficial relationships with customers rather than on new customer acquisition. This is also true as consumers not just have an extremely heightened awareness of brands but also take more accounts of an brand's reputation when making a purchasing decision. Similarly, consumers are more willing to express their brand consciousness by either defection from, or loyalty to, particular brands. Organisations can encourage customer loyalty to their brands by developing and interacting, at every available opportunity, dependable, relevant, and powerful brand propositions that are customised with their identified market segments. In this way, brands can build competitive gain through differentiation somewhat than through the adoption of low prices regulations which impact negatively on profitability and, in doing so on shareholder comes back.
Slavery: What was its impact on the economy of the South? What were its effects on African American families?.


DJ Robbie Wilde has almost complete hearing loss, but regularly plays huge events. Here's how.
This is DJ Robbie Wilde.
He's been 90% deaf since the age of 11.
Despite this, he's made a career out of his DJ skills.
Robbie Wilde uses technology that allows him to see and feel the frequencies of the music in order to make his mixes. These include DJ software that help him visualize the differences between vocals, bass, and other musical elements as well as tools that transfer vibrations to his body. Despite his inability to hear, he's been DJing since high school and has made a name for himself by playing such big-name events as the Sundance Film Festival and Consumer Electronics Show. Although he readily embraces the name "That Deaf DJ," which is how he first became known on the DJ circuit in his home state of New Jersey, he also stresses that he prefers being seen as "a great DJ that just happens to be deaf."
Here are some of his mixes.


The Bass Cadet Records duo take us on a percussive journey.
While it would come as no surprise to Berliners that the guys behind the counter at Neukölln's Bass Cadet Recordstore are the real deal, their combined efforts under the Arcarsenal name have recently demanded warm praise further afield thanks to some stormy dub techno works for the French label Rue De Plaisance, a new live set fusing live percussion and hardware synths, plus a continual stream of must-have releases on their labels. Earlier this month the Bass Cadet Records family launched Orbits, a sublabel aimed at sharing music from the artists that have supported and inspired them along the way, with the immeasurably inspiring Ron Trent opening the vaults to two of his classic works that had previously only seen daylight on the digital format. Fittingly it's Trent's inspiration that shines through most in their addition to our series, a soul filled affair showcasing the lifeblood of their extensive record crates.
To start could you give us a brief history of the Bass Cadet label and record shop you guys run in Berlin… Was the transition from label to record store one that you had always hoped to make?
It's a good question as our family can be a little complex to picture exactly. At the very beginning, we met in 2010 when we both moved to Berlin and we started to make some music in Alan's flat. After a short while, we met Atilla and his brother Tolga. We spent nights chatting about music and influences and at some point we decided that we should get together to set up a label and release our material. We started with Brotherhood EP our first release in 2012, then Tolga and Atilla as Helvert in 2013.
At that time, Laura who's Etienne best friend, joined him in Berlin and proposed him to work on a shop project including a record store section. So they naturally named it after the label… It became BCR/DBR our little nest in Neukölln. So the record store wasn't planned at all in the label vision at the very beginning, but it popped up naturally. Since then it has become a hub as most of us live nearby in the neighborhood and we have our headquarters there. Today we have a larger family as Laura started her booking agency On Board Music, where she manages us as Arcarsenal amongst other artists, and we have a little network of labels around Bass Cadet.
Atilla launched Tape Archive, Tolga will follow up with his own very personal project TFR this June, Orbits is the store's in-house label and our friend Matthieu working with us behind the counter is running the Altered Soul Experiment cassette label. Also our good friend Fede of Finest Hour makes the distribution for most of these labels through Off The Grid… And we share a studio space with some of them. So the store helped to gather lot of creative energies around us and we feel now really comfortable within this tiny world.
Earlier this month you released the first of a new series on the label, which you describe as being 'dedicated to the artists who support it and make its life', what can you tell us about Ron Trent's influence on you guys, and how did you go about approaching a reissue of two of his timeless cuts 'Hooked On Your Love' and 'Welcome'?
Since the very beginning of the store we've been supported by artists we are really admiring. It kind of overwhelmed us to see all these people we respected so much to come, put some interest and support what we do. So naturally as the store was taking firm shape, we thought about doing an offshoot and be able to release some of their music. We feel we owe a lot to them so that's a way to give them back, particularly for Aybee, he's been supporting us since the beginning and we exchanged a lot of things, ideas and feelings… He's kind of an older brother for us.
Etienne met Ron Trent through Aybee at the store and we linked up tighter when, with our friends of JAW Family, we organized this party called Young Soul in 2015. That was a really exceptional moment. From then it became clear that Ron would be the best to open the series. Etienne had a crush on these two tracks 5 or 6 years ago, but figured out they weren't available on wax to be played so naturally we asked Ron if he would be ok to release them and here we are. On Ron Trent himself, meeting him was a great honor, to us he's one of the best producers around and brings with him a huge knowledge about dance music, its roots and music in general. You can really feel it in his tracks. He had a really decisive influence on some ways we feel the music. And we always have a good bunch of his records in our DJ bags.
You've been frequent contributors to Varoslav's Rue De Plaisance label in recent times, how did this special connection come about, and what might be next?
The connection with Rue De Plaisance came through our friend Alan Doe who released an EP on the label before us. We sent some tracks to Varoslav and he replied us with this great proposal of releases. He fell in love with the ambient and dub tracks we sent him and offered us to have a full artist EP and to be featured on the Son De La Rue compilation with an ambient track. We are really attached to the fact that we don't want to only feature dance music on our releases. So when he offered us the chance to release a 9 minutes – 110BPM hazy dub/ambient track on the full a-side, we jumped on it! And the artworks from Virassamy are the icing on the cake. It's a great pleasure to work with them as we really need to feel the guys we are working with. Jus-Ed also taught us this "family" behavior within a label and we're really pleased to be able to work with this kind of people. Next up with Rue De Plaisance, we'll be touring with for label nights with our live set, as we'll take part of their Sonar OFF event on 18th of June and their Rex Club residency in July in Paris. Nothing is planned on the release side, but working with them again would be a great pleasure.
We've seen some cheeky snippets and a few gear-heavy pics of your new live set… How have the first few club shows been received, and how have you guys been approaching each set?
Well, this is a truely amazing experience. We always had a DJ approach, working back to back in our sets, and moreover since the store has its reputation set up. But as a production team we always felt that we were missing something in performing and we always wanted to push out the boundaries of our studio work. So we finally made it happen last winter, locking us up in the studio, going through configuration problems and working out the perfect set up for us to start touring. The only logistical restrictions were that we wanted to have live percussions and we didn't want to have a computer with us on stage.
We've been playing it out at Tresor, Le Sucre in Lyon, the amazing party La Serre in Bordeaux and Griessmuehle in Berlin and so far we had great reactions from all the crowds, especially on the live percussion. Every crowd was different but we managed to work with mostly the same tracks in order to make us a first strong experience of bringing your own music live on stage. So now with this experience we're back in the studio to put some more work into it, do new tracks to be able to go further, bringing new ideas, being more flexible and let ourselves go easily in different territories. Most of our next gigs will be live now, and we are really excited about what's waiting for us next. But in the end we'll never give up the deejaying because we are too much attached to this form of expression. It's two very different approaches for us. With one you build up a new story each time and once you've got the crowd drive it wherever you feel like for hours. And with the passion of finding new exciting records you never get bored playing. With the live it's more a concentrate of pure energy. You totally give yourself to the crowd and there's no safety net. It actually reminds us a lot of when we were teenagers and playing gigs in bands.
We worked it out in several takes at the store. There's a good DJ booth there so that's where we usually get to spin some records together. But as we are running after studio time to work on the live set we've tried to record it when the store was open to save some time. It can be a bit complicated with customers around, so we had to redo it couple of times before we were happy with it. But it was a funny experience. We gathered some of the records we bought recently, some from our friends and a couple of obscure oldies coming from the cheap bin that always worked out in our set. We also put an exclusive track from Tolga to be featured on his next release. The recording is bringing different facets of what we like, and we've been trying to showcase what we would build up within the course of a three hour set in natural club conditions but reduced into one hour. Going from some stripped down percussive beats, deeper techno things to some more soulful house, always with a twist. It was a bit weird to record a DJ mix right at the time that we are rehearsing and working a lot on the live set, but it gave us a nice respiration out of all this mess.
Coming next on the label, BCR005 will see Etienne release a solo EP as Solune in September, then we'll have Jenifa Mayanja with DJ Jus-Ed on the remix duty for Orbit 02 and hopefully before the end of the year a BCR006 by Arcarsenal. We'll try to keep up with a busier release schedule than previously now that we have a more fluent flow with the store's organization. But it's always more complicated than what you think. We are also working at the moment on a new Finest Hour EP to be in release before the end of the year too, and we have a lot of new material to record with all the stuff we created for the live set. So the second part of the year will still be busy in the studio, but we are also working on a heavy touring schedule with Laura, so lot of work ahead!


Hope FM is Mpumalanga's first and only Christian Radio Station at 96.0FM!
In a world filled with negativity in media and entertainment – Hope FM is the positive choice aiming to add value, hope and Godliness to your day. We'll keep you company during your day with the very best in local and international Christian music, as well as content that will uplift and encourage you.


Add this gorgeous ombre peacock feather to your next project! It will be perfect on towels, bedding or almost anything! Dreamer Peacock Feather print ready artwork by Hopscotch which is available in Graphic Art and ready for your heat press or direct to garment printer. To see more print ready heat press artwork please visit our Print Art section and search our entire collection of print ready artwork.