text:
\section{Introduction}

 Fluids of elongated particles that interact via a harshly repulsive excluded-volume interaction potential, i.e., hard-rod fluids, have proven immensely useful as a model system for investigating the formation, structure and properties of liquid crystals\cite{deGennes.Prost:1993}. Indeed, hard-rod fluids exhibit a wealth of aggregated states including nematic, smectic and columnar liquid-crystalline phases as well as various plastic and crystalline solid phases, depending on the precise shape, density and composition of the model particles present in the system\cite{bolhuis.frenkel:1997}.
Closest experimental realizations of the hard-rod fluid model are found in fluid dispersions of very stiff polymers, inorganic rod-like colloids,
filamentous viruses, fibrillar or tubular protein assemblies, and carbon
nanotubes\cite{Dogic:2006,Davidson:2005,Kas:1996,Zhang:2008,Vroege:1992}. For this class of system, the transition from an isotropic to a
symmetry-broken liquid-crystalline or crystalline state is entropy rather than
enthalpy driven, and the relevant control parameter is not the temperature but
the concentration or particle density. The transitions between the different
phases are driven by a tradeoff between free volume and configurational
entropy.

Arguably, the experimentally and theoretically by far most extensively studied liquid-crystalline state is the nematic that is characterized by uniaxial and up-down symmetry. The preferred mean
orientation of the particles is described by a director field the ground state
of which is spatially uniform. The transition from the isotropic to the
nematic phase is first order. (See, however, the work by Oakes and
co-workers \cite{Viamontes:2006}.) In the biphasic
region it proceeds via
the formation of nematic droplets called tactoids in the background
isotropic dispersion. Tactoids are typically not spherical but elongated and spindle-shaped, and they have over the past century or so been
observed in a wide variety of systems \cite{Sonin:1998, Bernal:1937,Bernal:1941,
  Zocher:1960, Dogic:2001,Oakes:2007,Kaznacheev:2003,Mourad:2008}. The shape and internal structure of nematic droplets is the
result of the competition between the preferred surface anchoring of the director field and the deformation of the director field that occurs if the preferred anchoring is indeed accommodated.

The shape and director-field configurations of tactoids have recently been studied theoretically in considerable detail within a macroscopic Frank
elasticity theory \cite{prinsen.schoot:2003, prinsen.schoot:2004a,
  prinsen.schoot:2004b,Kaznacheev:2002,Kaznacheev:2003}. Predictions depend on several parameters:
two surface energies (the surface tension and anchoring energy),
three bulk elastic constants associated with the splay,
twist and bend deformations, the saddle-splay surface elastic constant,
and, finally, the size of the droplet. For our purposes, it suffices to
summarize the most important predictions, presuming preferential planar anchoring of the director field to the interface that for rod-like particles seems to hold for entropy reasons: i) The director field of small drops is uniform
and of large ones bipolar; ii) The crossover is smooth
and set by a healing or extrapolation length that is the ratio of an average elastic constant and an anchoring energy; iii) The aspect ratio of
uniform tactoids depends only on
the anchoring energy, and of bipolar ones on their size relative to the healing length.

Some aspects of these theoretical predictions have been verified against
experiment, in particular the size dependence of aspect ratio and opening
angle of the sharp ends of the tactoids \cite{Kaznacheev:2002, Kaznacheev:2003,
  prinsen.schoot:2004a, prinsen.schoot:2004b, Oakes:2007}. The crossover from bipolar
to uniform director field has not been observed and this probably presents quite an experimental challenge because it has been predicted to
occur when the drops are quite small, that is, in the micrometer range.
For such small droplets, not at all very much larger than the particles that they are
made up from, director field patterns are difficult to distinguish in polarization microscopic images.

Clearly, computer simulations are of use here\cite{golemme:1988, erdmann:1990,
prishchepa:2005}, not least because a macroscopic
description might break down for such small drops, in other words, the predicted
transition may be spurious. On the other hand, recent simulations on the nucleation of the nematic phase in a hard-rod fluid have indeed shown that small nuclei of the nematic phase are elongated and
it appears at least that their director field is uniform \cite{Cuetos.Dijkstra:2007}. Simulations on small nematic droplets
of prolate particles interacting via a Gay-Berne potential have been shown to exhibit similar behavior, although fluctuations are large so a
director field is not so easily defined. \cite{Berardi:2003,Bates:2003} Because systematic computational
investigations of the shape and internal structure of nematic droplets
are lacking, we set out to do this for nematics of hard spherocylinders of aspect ratio eleven. Our simulations build on our earlier work on
hard-rod nematics in a spherical cavity of fixed size and shape \cite{trukhina:2008}, but we now focus on actual drops that can adjust their structure.
This we do by placing the spherocylinders in a suspension of spherical particles, which interact via a hard-core repulsion with the spherocylinders yet are transparent with
respect to themselves, i.e., behave like an ideal gas.

The method allows us to compress by osmotic stress
droplets of a fixed and predestined number of rod-like particles. This is
achieved in a controlled manner because the density of the
rods in the drop will be set by the imposed pressure of the ideal gas of spheres
(if we ignore a small contribution from a Laplace pressure). Hence, the drop size must then be given by
the number of rods in the simulation box. Note that our making use of what in essence is a depletion agent (the spherical particles)
is not all that dissimilar in spirit to the experiments of Dogic and Fraden\cite{Dogic:2001},
who used the non-adsorbing polymer dextran to induce  phase separation in aqueous dispersions of filamentous
fd virus particles.

Our results may be summarized as follows.
\begin{itemize}
\item[i)] For relatively low densities
of spheres, the droplets are spherical and the rods randomly oriented;
\item[ii)]  Above a critical sphere density, the drops become nematic and elongated;
\item[iii)] Small tactoids have a uniform director field and large ones
a bipolar one;
\item[iv)] At the crossover the drops measure about four rod lengths so indeed are very small;
\item[v)] The surface tension anisotropy and healing length that we
deduce from the simulations are consistent with theoretical estimates.
\end{itemize}

The remainder of this paper is organized as follows.
In section \ref{model} we introduce
the model and define the relevant order parameters.
A detailed discussion of our results is given in section \ref{res}. Finally, in section \ref{summary} we summarize our findings and relate
them to theory and experiment.

\section{Model and Simulation Details}
\label{model}

In the Monte-Carlo simulations, we model the rods as spherocylinders
consisting of a cylindrical part of length $L$ and diameter $D$, capped at both
ends by hemispheres of diameter $D$. In order to stabilize droplets of rods,
we surround them by a liquid of spheres.
The spherocylinders interact via a hard-core
repulsion. The spheres also interact with a hard-core repulsion with
spherocylinders but are able to freely interpenetrate
each other at not energy cost. Hence, our
model is an extension of the Asakura-Oosawa or AO model for colloid-polymer
mixtures \cite{asakura.oosawa:1954, vrij:1976} to anisotropic colloids \cite{Jungblut:2007}. Note that
strictly speaking the spheres
do interact with each other via the rods whilst this is not so in the original
AO model.
This difference is of academic interest only, because we consider only
those concentrations of particles that produce a very
strong phase separation into sphere- and rod-rich phases, so
the former behaves as a (nearly) ideal gas
of spheres that in essence acts
as a barostat for the droplet consisting of only spherocylinders.

As already advertised in the introduction, this implies that by means of
changing the
number of spheres in the system at fixed volume,
we can tune the pressure exerted on the rods in the droplet. Through that we
vary the density of the drop and therefore also the physical properties
of the drop, such as the elastic response if the drop is in a nematic
fluid state. Hence, we use the number density of
spheres $\rho_{\rm{sp}}$ measured far away from the droplet as a
parameter
that characterizes the external conditions imposed on the droplets
formed. The same method has been used in an earlier study to study
the formation of nanocrystals in a simulation\cite{gruenwald:2007}.

The simulations were performed at fixed particle number $N$ and
simulation box volume $V$ (and temperature $T$, but as the system is purely
entropic, temperature is not relevant here) in a
cubic box with periodic boundary conditions.  We focus on
spherocylinders with an aspect ratio of $L/D+1=11$ (i.e. $L/D=10$), and spheres
with a diameter twice that of the thickness of the rods,
$D_{\rm sp}=2D$. Spheres that are much larger than this introduce strong
effects on the surface anchoring, whilst for smaller spheres the
numbers needed in the simulation are so large to be unpractical from a computational point of view.

The number of spherocylinders in the box was varied from
$200$ to $700$, and the number of spheres was fixed such that
phase separation was induced into two phases containing virtually
only spherocylinders or spheres. This corresponded in
our simulations to between approximately 20000 and 70000 spheres.
We chose the simulation box to be $70^3 D^3$, i.e., sufficiently
large to ensure that the spherocylinders
did not interact directly with each other via the periodic boundaries.
We verified the droplets that form are
not system spanning. The systems were equilibrated by local translation and
rotation moves. Depending on the specific concentrations, $10^6 - 10^7$ MC
sweeps were required.

The boundary and volume of a droplet is established as follows.
We first divide the system into small boxes and next verify whether a box contains the center of a sphere or whether it is intersected by any spherocylinder.
In the latter case, this box is counted as a part of the droplet.
If it so happens that a box does not fall into either of the two categories,
it is counted as a part of the droplet if it has a larger number of
nearest neighbouring boxes containing spherocylinders than spheres.

As is customary, we define the average alignment of the ($N$) rods in
terms of the traceless tensor $\bf{Q}$, with the elements
\[
\label{eq:s2}
 Q_{\alpha\beta} = \frac{1}{2 N} \sum_{i=1}^N
   \left( 3 u_{i\alpha} u_{i\beta} - \delta_{\alpha\beta} \right),
\]
where $u_{i\alpha}$ is the $\alpha$ component ($\alpha = x,y,z$)  of the
unit vector along the axis of particle $i=1,...,N$
 and $\delta_{\alpha\beta}$ the Kronecker delta.
Diagonalization of the tensor yields three eigenvalues, $\lambda_{+}$, $\lambda_{0}$ and
$\lambda_{-}$, where $\lambda_{+}>\lambda_{0}>\lambda_{-}$.
Different authors use different combinations of these eigenvalues to define
the nematic and biaxial order parameters\cite{dijkstra.roij.ea:2001, low:2002}. To avoid confusion,
we shall present all eigenvalues instead.
The case $\lambda_{+}>0$, $\lambda_{0}=\lambda_{-}$ corresponds to a structure with one preferred direction.
The case $\lambda_{+}=\lambda_{0}>0$ corresponds to a structure in which
one direction is avoided and the two other directions are equally favored. All the intermediate cases $\lambda_{+}>0$,
$\lambda_{+}>\lambda_{0}>\lambda_{-}$ correspond to a biaxial structure.
Obviously, in an isotropic phase one finds $\lambda_{+}=\lambda_{0}=\lambda_{-}=0$.

When calculating observables, such as the components of the
order parameter tensor properly averaged over the ensemble of configurations,
all the possible types of symmetry in the system have to be taken into
account. In the case of radial symmetry we calculated the orientational
tensor directly by averaging over all configurations obtained in
the simulations.

If there is a preferred axis in the system
along which the particles tend to align, we need to proceed differently. As
rotations of the director do not cost any (free) energy,
the orientation of this axis can fluctuate strongly during a simulation run.
In order to average the local properties of interest, the configurations have been rotated in such a way that the director always points in the same direction. It is important to point out that this procedure
introduces additional noise to the simulation
results. In the following,
we show all data rotated such that the director is aligned with the $z$-axis.

\section{Results and Discussion}
\label{res}

In the diagram of fig.~\ref{diagram} we have indicated with asterisks
the system conditions for which we ran the simulations.
The letters ``a'' through ``l'' are used in the following to refer to specific
points in this diagram. We have indicated schematically
in the figure the shape and the structure of the droplets, which we
discuss in more detail below. The numbers in the
boxes indicate the aspect ratios of the droplets.

Figs.~\ref{nem} and \ref{iso} give the snapshots of two typical structures given by conditions ``i'' and ``c'', respectively, where only the
spherocylinders are shown for clarity. Two essential
differences between these structures can be seen:
The first of the two droplets shown is i) more elongated
and ii) the spherocylinders in this droplet have a much stronger tendency to orient in one direction. Below we will analyse these effects in a more quantitative fashion.

The difference is caused by the difference in bulk sphere density and hence osmotic stress imposed on the drop by the sphere fluid.
Droplet ``i'' is subject to much higher
pressure and hence is condensed much more than droplet ``c'', and has
crossed over to the nematic phase.
The rod densities $\rho D^3$ in the two drops are $0.034$
and $0.027$ (averaged over each droplet).
From the (remarkably accurate) Lee-Parsons theory of the nematic transition
in bulk fluids of hard rods \cite{Cuetos:2007}, we expect for
spherocylinders of aspect ratio 11 the nematic transition to occur at a
pressure of $P D^3 /k_B T \approx 0.25 $, corresponding
to an ideal gas density of $\rho_{\rm sp}D^3 \approx 0.25$.
This is in reasonable agreement
with the transitional regime around $\rho_{\rm sp}D^3 \approx 0.23$ in the
diagram. We also estimated the transition density by
simulating a compression curve and an expansion curve in the bulk and obtained
 $\rho_{\rm sp}D^3 \approx 0.22$, which again is in good agreement with the
numbers above. We note that due to the effects of Laplace pressure the
nematic transition should occur at a somewhat higher sphere density then
that in bulk solution. For details we refer to the Appendix.

In fig.~\ref{density} we have plotted a typical iso-density distribution
in the $r$-$z$-plane for nematic droplet ``i''. Inside the droplet the spherocylinders have an approximately constant rod density equal to
 $\rho D^3 = 0.039$, which rapidly decays when approaching
 the interface to the fluid of spheres. It is clear that the drop is not spherical, the aspect ratio being approximately 1.8. For comparison,
 and in order to determine the shape of the droplets, we cut a slice from
the $r-z$-density profile at half of its maximum value. That is where we
expect the Gibbs plane to be situated. The curves obtained in this way are shown in fig.~\ref{density_profiles} for several systems
consisting of the same amount or spherocylinders ($N_{\rm rods}=500$) but
with various densities of spheres, corresponding to the points
``a'',``b'',``c'',``f'',``i'', and ``k''.

At low pressures the droplets are (nearly) spherical. This is to be expected if the rods are in their isotropic state. However, if the
pressure is increased
the droplets crossover to the nematic phase and hence become elongated
in order to reduce
either the elastic deformation
of the director field if the anchoring is strong, or the anchoring free energy
if the anchoring is weak. As already advertised, the crossover occurs when the
typical drop dimension exceeds the healing length, which we are going to
discuss in more depth in the following section.

On increase of the density of rods, the elastic constants in all likelihood
 increase, too, as should the interfacial tension and potentially also the anchoring strength.
We expect from scaling arguments that the ratio of the anchoring strength and the surface tension is a weak function of the pressure \cite{schoot:1999}, however, and in the weak anchoring regime it is this ratio that dictates the aspect ratio of the drops \cite{prinsen.schoot:2003}.  In the strong anchoring
regime the aspect ratio is an increasing function of the healing
length that in the equal-constant approximation
is given by the ratio of the elastic constant and the surface tension. Hence,
whether the droplets become more elongated then depends on how strongly these two energies depend on the pressure. Apparently, the elastic constants increase
more strongly with pressure because the aspect ratio increases from about 1.1 to 1.8
with increasing sphere concentration.

We observe the same tendency for the systems of 700 spherocylinders.
At low pressures the droplet is more or less spherical (state point ``e'', aspect ratio 1.1) and at high
pressures the droplet becomes elongated (state point ``j'', aspect ratio 1.8). We have to note, however,
that droplet size also affects the aspect ratio: it decreases with increasing size.
This has been observed experimentally and is predicted theoretically based
on macroscopic theory\cite{Kaznacheev:2003,
  prinsen.schoot:2004b, Oakes:2007}.
The aspect ratios for all the state points are shown in the boxes in the ``shape'' diagram fig.~\ref{diagram}, with an estimated error of $0.1$.

We now turn to the orientational state of the
rods in the droplets.
This is described in
terms of the eigenvalues of the orientational tensor $\bf{Q}$
(see \ref{model}). In fig.~\ref{eigenvalues} we show the r- and z-profiles
of these eigenvalues for the drops ``i'', ``f'', and ``c'' (that each consist
of 500 spherocylinders). The droplets become less ordered
and less elongated.
Droplet ``i'' has a high nematic ordering in its center, which slightly
decays on approach of the interface to the gas of spheres in both,
the r- and the z-direction.
Droplet ``f'' has a lower density and also
a nematic order parameter that is smaller.
Droplet ``c'' has even lower values of the nematic order parameter, and
at the interfaces all the eigenvalues become equal to $0$, indicating
an isotropic configuration. This drop probably is close to the conditions where
the isotropic-nematic transition takes place.

By analysing the tensor $\bf{Q}$ for all the investigated droplets, we construct scalar order parameter profiles as well as
the nematic director-field configuration. The results are indicated
schematically in the
diagram \ref{diagram}:
\begin{itemize}
\item[1)] Droplets ``a'' and ``b'' are spherical
 droplets of an isotropic rod fluid;
\item[2)] Droplets ``c'', ``d'' and ``e'' are in
the isotropic-nematic transition region, exhibiting a strongly
fluctuating orientational order;
\item[3)] States ``f'' to ``l'' are strongly nematic drops;
\item[4)] The director field of drops ``i'', ``j'', ``k'' and ``l'' is more or less uniform,
those of ``g'' and``h'' bipolar, and of ``f'' in between these two.
\end{itemize}

To illustrate these findings, we show the director field (the axis
given by the eigenvector corresponding to the largest eigenvalue of
the orientation tensor)
as a function
of the radial and axial distances $\bf{r}$ and $\bf{z}$ in fig.~\ref{S2_homog} for the case ``k'' and in fig.~\ref{S2_bip} for the case ``h''. The director
field of the tactoid ``k'' is more or less uniform and oriented
along the main axis of the drop. That of ``h'' is bipolar, i.e., curved along the elongated drop surface toward
the tips, where the scalar order parameter drops to zero. This signifies
the melting of the nematic near the tips, where theoretically one would expect
the surface point defects (``boojums'') to reside \cite{prinsen.schoot:2003}.

The director field in a nematic droplet is determined by the interplay of
surface anchoring and elastic forces. The bipolar structure can only be formed if the energy for bending is small enough compared to
the surface energy. This can be achieved
if the density of the suspension is small (but the droplet still
has a nematic
structure), or if the droplet is big (and, therefore, the curvature of the
interface is small). Systems ``g'' and ``h'' fit into this category.

The aspect ratio of the droplets does not depend on their size if the director
field inside the droplets is homogeneous. This follows directly
from the well-known Wulff construction of the droplet shape given any polar
angle-dependent
surface tension \cite{prinsen.schoot:2003}. Indeed, all the droplets with an approximately
homogeneous director field, droplets ``i'', ``j'', ``k'', and ``l'',
that we obtained
in our simulations have the same aspect ratio of 1.8
within a statistical error of the simulation of about 0.1,
in agreement with this theoretical prediction.
From the aspect ratio observed in the simulations we can in fact deduce
a dimensionless anchoring strength. Let us presume
that the anisotropic surface
tension $\gamma$  has a functional form
of the Rapini-Papoular type, so
$\gamma = \tau [1+\omega (\bf{q} \cdot \bf{n})^2]$, with $\tau$ the bare surface
tension, $\omega$ the dimensionless anchoring strength, $\bf{q}$ the
surface normal and $\bf{n}$ the director field at the
surface of the drop. For planar anchoring to be favored, $\omega > 0$.
From the Wulff construction we then deduce that the aspect ratio of
the drop equals $1+\omega$ for $0\leq \omega \leq 1$ and $2\sqrt{\omega}$ for $\omega>1$ \cite{prinsen.schoot:2003}.
Hence, we find from our simulations a value for $\omega$ of 0.8, quite close the value of 0.65 found by Dijkstra and co-workers in a simulation
study of nematic drops nucleated in a super-saturated dispersion of hard
rods\cite{cuetos:2008}.

Finally, from the crossover from bipolar to homogeneous director fields, we obtain an estimate for the healing length. According to fig.~ 1,
the crossover occurs for drops of a volume about  $1.7\times 10^4 D^3$. This value may actually depend on the
sphere density, but because of the lack of any detailed information
we shall ignore this for
simplicity. Presuming that the bend elastic constant is
about ten times larger than the splay elastic constant, which seems
reasonable on account of predictions for hard rods in the Onsager limit,
the crossover occurs at a droplet
volume equal to about 10 times the healing length $\lambda \equiv
(K_{11}-K_{24})/\tau \omega$ cubed according
to macroscopic theory \cite{prinsen.schoot:2004a, prinsen.schoot:2004b},
where $K_{11}$ denotes the splay elastic constant and $K_{24}$
the saddle-splay surface elastic constant. So, we find for the healing length $\lambda \approx 12 D$, which is about a rod length.
Clearly, macroscopic theories, such as those of Kaznacheev and collaborators
\cite{Kaznacheev:2003, Kaznacheev:2002}, and of Prinsen and
van der Schoot \cite {prinsen.schoot:2003, prinsen.schoot:2004a,
  prinsen.schoot:2004b}, could perhaps be expected to break down at such
small length scales, yet the predicted crossover from uniform to bipolar
director fields apparently still survives.

From the estimate of the healing length, we can obtain an order of
magnitude estimate of the interfacial tension between the rods
and the spheres that we can compare with the scaling estimate
given in the Appendix.
If we presume the Saupe-Nehring relation to hold, implying that
$K_{24} = (K_{11}-K_{22})/2$ $\;$\cite{Nehring:1971}, and make use of the approximate
expression $K_{22}=K_{11}/3$ $\;$\cite{Lee:1986}, we obtain $\lambda \approx 2K_{11}/3\tau \omega$. Hence, $K_{11}/\tau \approx 14 D$, or, $\beta \tau D^2 \approx \beta K_{11} D/14$. Within
a second-virial approximation, which admittedly is not very accurate
for rods of aspect ratio below 20, we expect $\beta K_{11} D \approx 0.9$ to hold near the transition \cite{Vroege:1987}. Hence, for the interfacial tension between the rods and the
spheres we obtain the estimate $\beta \tau D^2 \approx 0.07$. According to our
scaling estimate cited in the Appendix, we have $\beta \tau D^2 \approx 0.25
\alpha \xi/D$ with $\alpha$ a prefactor that should be of order 0.1
\cite{schoot:1999} and $\xi$ the interfacial width. If $\xi \approx L$, this then implies that $\alpha \approx 0.03$, which is somewhat smaller than expected \cite{schoot:1999}.

In order to go beyond this quantitative analysis, simulation data of the
elastic constants of the bulk nematic and of the surface tension between
the co-existing bulk fluids would be necessary. Unfortunately, these are not
available yet for spherocylinders of aspect ratio 11, as, in particular,
simulations to determine elastic constants are computationally rather
expensive. (To our knowledge, elastic constants have been computed only for
spherocylinders of aspect ratio 6 \cite{Tjipto:1992}.)

\section{Summary}
\label{summary}
By means of computer simulations we have shown that fluid droplets of hard
rods, osmotically compressed by the presence of spherical particles, undergo
an isotropic-nematic transition at sufficiently high osmotic stress. We find
the nematic droplets not to be spherical but elongated. The director field of
the drops is uniform if smaller than a critical size and bipolar if larger
than that. We interpret our findings in terms of the predictions of continuum
mechanical theory that minimizes the combined effect of an elastic deformation
of the director field and an anchoring frustration of this director field at
the surface of the drops. Although in our simulations the drops are not at all
large on the scale of the rods, and continuum theory should perhaps not be
expected to be accurate, results from both levels of description seem to be
consistent with each other down to drop sizes that are as small as a few times the particle length.

\section{Appendix}
\label{Appendix}
An estimate for the rod density in the droplet as a function of the number
$N_{\rm rods}$ of rods and the density of spheres $\rho_{\rm sp}$ can be obtained by presuming complete demixing of the two components and by presuming that the interface between them is sharp. Let $R$ be the radius of the drop, assumed perfectly
spherical, then
$\rho =3 N_{\rm rods}/4\pi R^3 $ is the density of the rods in drop. The bulk pressure of the hard rods is to a very good approximation equal to the expression
put forward by Parsons and by Lee \cite{Vroege:1992}
\[
\beta P = \rho \left(1 + \frac{2\phi(2-\phi)}{(1-\phi)^3}\left[
1+\frac{3\pi}{8}\Lambda\right]\right),
\]
at least in the isotropic phase, where $\phi = \rho (\pi D^3/6 + \pi LD^2/4)$ denotes the packing fraction, $\Lambda = (L/D)^2/\pi(1+3L/2D)$ for slender rods is
proportional to their aspect ratio and $\beta$ denotes the reciprocal thermal
energy $1/k_BT$ with $k_B$ Boltzmann's constant and $T$ the absolute
temperature. The pressure of the ideal gas of spheres obeys
\[
\beta P_{\rm sp} = \rho_{\rm sp}.
\]
Mechanical equilibrium between the gas of hard rods and that of ideal spheres demands that
\[
P + \frac{2\gamma}{R}= P_{\rm sp},
\]
where the second term on the left-hand side is the contribution from the Laplace pressure across the curved interface, with $\gamma$ the interfacial tension that presumably depends on the bulk densities of both the rods and the spheres.
For any given number of rods $N_{\rm rods}$, this equation sets the equilibrium size of the drop.

An estimate of the magnitude of the Laplace pressure may be given by making
use of the scaling Ansatz $\gamma \approx P_{\rm sp}\xi$, with
$\xi \approx L$ the actual interfacial width \cite{schoot:1999}. Hence,
$P/P_{\rm sp} \approx 1 - 2\alpha\xi /R$ with $\alpha$ a constant of proportionality
that we estimate to be of order 0.1 $\;$ \cite{schoot:1999}. So,
the presence of the interface reduces the pressure
in the drop relative to that in the reservoir of spheres
and hence postpones the onset of the nematic phase to higher densities
of spheres the smaller the drop.

From Table I of Lee \cite{Lee:1987}, we deduce by linear extrapolation that for rods of $L/D=10$ the
bulk nematic phase sets in at a dimensionless pressure
$\beta P D^3 \approx 0.247$, corresponding to a sphere fraction of $\rho_{\rm sp} D^3 \approx
0.247$, in reasonable agreement with what we find in the simulations. See fig.~ 1.

\acknowledgments We thank K.~Binder and M.~Allen
for helpful suggestions. CPU time was provided on the JUMP by the John
von Neumann Centre in J\"ulich. We thank the Deutsche Forschungsgemeinschaft
(DFG, Emmy Noether Program and SFB Tr6) and the MWFZ Mainz for financial support.

\newcommand{\noopsort}[1]{} \newcommand{\printfirst}[2]{#1}
  \newcommand{\singleletter}[1]{#1} \newcommand{\switchargs}[2]{#2#1}


On Saturday May 4th, Runna Muck make their triumphant return to the Albany area with a one-time-only show at the Low Beat. From 1999-2004, Runna Muck made an indelible mark on the Albany rock scene. The power trio, made up of heavy hitters, Brendan Hackett (guitar), Dave Trump (bass), Kevin Wassink (drums) weaved eclectic hard driven rock riffs with memorable well crafted songs. Their shows at Valentines were legendary and the group is excited to return to Albany and make their mark again at another premiere rock venue, The Low Beat. Becca Frame and the Tall Boys open.


This year we've had a lot of fun writing about game design, exchanging ideas with designers and conversing with the board game design community. We've been thrilled with the response we've received over the past year and we've received plenty of great comments, criticism and questions. As part of our year in review we thought it would be fun to look back at some of our favorite interactions.
Games Precipice: Evaluated by a jury of our peers.
I love the examples! I've been reading your blog over the past month and I enjoy reading about these games the most. I've noticed you tend to use several favorites as examples. What would you say is your favorite game and why is it Power Grid?
Games Precipice: We had several readers who noticed Power Grid was our go-to example. One of the challenges in our writing is citing attributes in popular games alongside games that demonstrate really strong examples of an idea. Power Grid seems to be a little of each.
To be fair I've only mentioned Power Grid in 17% of relevant articles. On the other hand Matt has mentioned Power Grid an astounding nine times over the past year. In fact in articles posted on a Sunday after 4PM, Matt has an astounding 1.89 PGMPTW (Power Grid mentions per thousand words) which ranked #1 among bloggers over the month of August. Gamermetrics would be proud.


CARR is a manufacture that makes aluminum truck steps, light bars, handles and Jeep cover ups. These stylish, functional products make them a nice addition to your vehicle.
Check out the Recently Listed Grab Bars and Handles.
CARR_headquarters_jpg3All CARR accessories are manufactured for a precise fit for today's vehicles. Our manufacturing processes allows us to design products that give your vehicle unique personal style and appeal. Our cast aluminum construction is time-proven for durability and strength. All CARR products carry a limited lifetime warranty.
In March of 1945, Vernon Lester Carr started V.L. Carr & Son Pattern Co. in an old metal shop behind his house in Los Angeles, California. His son, wendell Whittaker Carr, joined his father Vernon later that year at the end of World War II after his return from serving as a patternmaker in the Navy. Twenty four years later in 1969 the business changed its name to Carr Pattern Co., its corporate name today. In May of 1972 Vernon Carr passed away, leaving his son Wendell with the family business. Notwithstanding his father?s passing, the business made the necessary adjustments and continued to press forward.
However, several years later in March of 1979, the untimely death of Wendell Carr left his wife and two sons, facing the decision to disband the business or continue making patterns for their existing customer base. The decision was made to stay in business, but the family eventually chose to shift away from pattern-making and pattern-casting and started looking for other buHistoric CARR factorysiness opportunities.
Early in 1983, a whole new industry opened up to them which was an entirely different industry than what had been their mainstay since 1945-the automotive aftermarket. Once the decision was made to change the course of the business into the automotive industry, investment money was gathered and the production facility was expanded. Extensive research, development, and design resulted in the introduction of aluminum cast light bars and truck steps, which were introduced at SEMA, where one of CARR?s products won second place, clearly establishing them as serious new competitors.
Today, CARR, as it is popularly known, is in virtually every major warehouse across the United States and Canada, and has established itself as a company whose accessories place it among the major competitors in the industry. With over 60 years of manufacturing excellence, CARR is a third-generation business, who remains firmly committed to product innovation and design, hassle-free customer service, and offering the consumer various choices in steps, light bars, and other accessories.
we hope that as you browse our web-site you find items that work for your vehicle, smartly enhancing its appearance, at practical affordability.


text:
Ruardean Hill is a prominent hill and a village in the English county of Gloucestershire,  west of Gloucester. It lies in the Forest of Dean, in the parish of Drybrook.

The southern slopes are wooded and are part of the northern edge of the Forest of Dean. The hill forms part of a low range of hills separating the River Severn from the River Wye. The hill's summit is the highest point in the Forest of Dean.  A mostly friendly community, there is a local post office and village shop in neighbouring Ruardean Woodside. The village and surrounding areas are well served by Ruardean Hill Sports and Social Club.

Nearest places
 Drybrook
 Steam Mills
 Brierley
 Ruardean Woodside
 Ruardean

External links

 photos of Ruardean Hill and surrounding area on geograph

Marilyns of England
Hills of Gloucestershire
Villages in Gloucestershire
Forest of Dean

redpajama_set_name: RedPajamaWikipedia


text:
Stylophorum (celandine-poppy) is a genus of three species of herbaceous perennial plants native to woodland in eastern North America and China.

Stems are bristly, and leaves are lobed and have wavy edges.

Flowers are yellow and have four petals and an unusually long style, for which the genus is named. Several may be found on each stem.

The closely related Hylomecon vernalis has only one flower on each stem, and the greater celandine (Chelidonium majus) has branched stems and no bracts or bracteoles.

Species
There are three species:

References

 Christopher Grey-Wilson, Poppies (Portland: Timber Press, 2000)  pp. 42–44

External links

Papaveroideae
Papaveraceae genera


Dr. Andy Wood is an author, professor, church leader, consultant, evangelist, and seminar leader. In every role, he has pursued a philosophy he refers to as M.A.D.I.S.E.L. – Make a Difference in Someone Else's Life!
Serving alongside his wife, Robin, Andy offers professional counseling, coaching, consulting, and communication services through The LifeVesting Group.
He blogs consistently and has ghostwritten two books. He has published on both academic and professional levels in magazines and journals and is currently marketing his first e-book, The 12 Pathways to Christmas.
Please join me in welcoming Dr. Andy Wood.
Why do you think it's important for writers to consider blogging?
For me, it's about the discipline to continue writing and developing fresh stuff. Blogging is a great way to test drive ideas that may or may not ever make it into a book.
Blogging also gives you a starter platform for building what Seth Godin calls a "tribe." That is, a group of people who appreciate what you do, keep reading and, hopefully, share your stuff with others.
What are your top tips for potential bloggers?
First – write, write, write.
Second, decide on a realistic schedule and stick to it. If you want regular readers, become a regular writer.
Third, know the purpose of your blog and lean into it.
Please tell us a little bit about your e-book, The 12 Pathways to Christmas.
I've looked closely at the lives of the people who were involved in the first Christmas story. I wanted to create a connection between a 21st-century "real world" and the "real world" of the first century and how the coming of Jesus is relevant to all that. This book offers 12 vignettes of real joy, real pain, real healing, real desperation, real hope.
How did the idea of The 12 Pathways to Christmas develop into an e-book?
It started as a series of posts on the "LifeVesting" blog, in 2009. It took me another Christmas season to finish them up, then another year or two to put them into a book form.
What was the greatest challenge you faced during the e-book process?
Learning how to format the book correctly. It's not super hard, but there was a bit of a learning curve.
What did you enjoy most about the e-book process?
E-book publishing is quick. You can edit or make changes without having to go through the publisher. It also enables you to avoid having to stock piles of book inventory.
I enjoyed the instant awareness of success, or lack thereof. With Amazon, you can always know how sales are going.
Also, it's fun to be part of a larger community of authors who have discovered this format.
What tips do you have for writers who are considering publishing e-books?
First, get several proofreaders to help clean up your writing.
Second, have a good strategy for marketing your work. Nobody will be more committed to your success than you are. There are lots of tools and resources out there for authors to learn to market their stuff.
What words of encouragement would you like to offer aspiring writers?
Use your writing to serve and love people, and the day will come when your writing will serve you.
There has only been one infallible thing ever written, and that's the Bible. Anything short of that has room for improvement.
So, never stop improving and working at your craft.
Thank you for sharing your insights, Dr. Wood.
You can connect with Andy through his blog and check out The 12 Pathways to Christmas.


FREE World wide shipping with track and trace!
If you want a number please ask the numbers! I have the ABBA RSD at the ABBA Museum in Stockholm!
ABBA Summer Night Civic UMC / Polydor 7 "Single" I had the feeling of being in the air "40 years this year since" Summer Night City "was released as a single Clear / Yellow Splatter vinyl.
Check out my eBay shop for more VCRs, hand cameras, manuals, remote controls, tires, DVDs, parts and more!
Verzending vind plaats op Maandag, Dinsdag, Woensdag en Vrijdag!
Bestellingen geplaatst voor 14.00 uur worden dezelfde dag nog verzonden, na 14.00 de volgende aangegeven dag.
Shipment takes place on Monday, Tuesday, Wednesday and Friday!
Orders placed before 14:00 PM will be shipped the same day, after 14.00 the next shipping day.


A written Ministerial Statement of 17 September announced that policy responsibility for data protection, and with it sponsorship of the ICO, is moving from the Ministry of Justice (MoJ) to the Department of Culture Media and Sport (DCMS). Privacy Laws & Business understands that the announcement became operational as of that date. The name of the new responsible minister has not yet been made public.
The government is due to publish the ICO Triennial Review this autumn but a date for publication has not yet been announced. The Triennial Review looks into how the ICO functions but also how it should be funded. The ICO had, in its submission to the Review, said it wished to maintain its existing structure as a single regulatory body, but that it wanted to be directly accountable to Parliament, rather than the ministry. 'For the ICO to do its job while working closely with government, the ICO should be allowed an appropriate degree of operational freedom rather than being subjected to controls more obviously necessary for a traditional non-departmental public body or arms-length body,' the ICO said at the time.


Blackberry is a sinking ship which is currently hanging on just one support – BBM. Blackberry, it seems is trying to get back up again after hell of an year for the company by increasing its offerings on BBM. After announcing that BBM will come pre-loaded on LG phones, Blackberry has put a plan-in-action to popularise BBM in the coming year.
One of the best features that are going to pour in on BBM is BBM voice. Blackberry, starting next year, will offer free calling via this feature.
Along with this, BBM will also have new channels and a chat room like feature that will enable you to join groups based on hobbies and preferences. In addition to this, there will be added features such as easier and faster sharing of photos, location and other stuff along with 100 new emoticons.
Blackberry sure is trying its best to bounce back in the market and BBM is the right vehicle for doing so.


text:
Traverse Theatre announces Spring 2020 Season
Traverse Theatre announces Spring 2020 Season and launches £1 tickets for young people and those in receipt of a range of allowances.
TRAVERSE THEATRE ANNOUNCES SPRING 2020 SEASON (JANUARY-APRIL) AND LAUNCHES £1 TICKETS SCHEME FOR YOUNG PEOPLE AND THOSE IN RECEIPT OF ALLOWANCES
•	New £1 Tickets scheme makes theatre more accessible to under 25s and those in receipt of a range of allowances
•	Traverse Theatre Company present the world premiere production of Rona Munro's Donny's Brain
•	Award-winning sensation Mouthpiece returns for a limited run prior to worldwide touring
•	Extended eight-play season of lunchtime favourite A Play, A Pie and A Pint
•	Tickets on sale now
With a commitment to making theatre accessible to all, in 2020 we are launching a new £1 Tickets scheme. A new ticketing initiative, which was piloted throughout 2019, to welcome people from groups and communities who might not be aware of our work, or who may not otherwise have access to theatre – available to Under 25s and those receiving Job Seeker's Allowance, Employment Support Allowance, Universal Credit or Carer's Allowance. Tickets are available for all Traverse Theatre Company productions and co-productions (and most visiting company shows, too), across the entire run of a show. With that in mind, we look ahead to next year and reveal the full January-April 2020 season.
First up is Traverse Theatre Company's gripping hit about class, culture and appropriation – Mouthpiece (6-15 Feb), by Kieran Hurley – which returns following a sold-out run at Traverse Festival 2019, where it won the prestigious Carol Tambor Best of Edinburgh Award facilitating a New York transfer. It then goes on to tour to Tron Theatre, Glasgow (26-29 Feb); Adelaide Festival, Australia (6-14 Mar); and Auckland Arts Festival, New Zealand (19-28 Mar).
The ever-popular A Play, A Pie and A Pint, Òran Mór (presented by Traverse Theatre) season returns with an extended run of eight shows, taking in Infernal Serpent (31 Mar-4 Apr) by David Gerow; Celestial Body (7-11 Apr) by Morna Pearson; Rose (14-18 Apr) by Lorna Martin; The Storm (21-25 Apr) by Owen Whitelaw; Exquisite Corpse (28 Apr-2 May) by Conor O'Loughlin – which was presented script-in-hand at the Traverse's inaugural First Stages Festival of new talent in November 2019; Mary and Ada Set the World to Rights (5-9 May) by Jane Livingstone; Silver Superheroes (11-16 May) by Morna Young; and Milkshake (18-23 May) by Rob Drummond. Ticket price includes a pie and a drink.
Rounding off the season as a whole is the Traverse Theatre Company world premiere of Donny's Brain (14 Apr-2 May. Delving into the eternal mystery of the human brain, this dynamic and visually striking production follows Donny and Emma on a funny and moving journey as all they know about love and loss is thrown into question.
Visiting Company productions
The first visiting company production of the season is Mary Jane Wells and Scottish Theatre Producers' Heroine (30 Jan-1 Feb). Written and performed by Wells, it tells the true story of US soldier and survivor of military sexual trauma, Danna Davis, with grit, lyricism and necessary black humour. Both performances will be followed by a post-show discussion with a curated panel of military, legal and survivor advocate experts.
February opens on a comedic note with a one-night-only performance of Stephen Bailey's Can't Be Bothered (1 Feb), in which the comedian and renowned gossip takes in a bit of storytelling, some inappropriate anecdotes and more sincerity than he's ever dared before.
Next up, Tandem Writing Collective (7 Feb) playwrights Jennifer Adam, Amy Hawes and Mhairi Quinn present a taster of five topical new scripts and live music, performed script-in-hand by local actors, and featuring talented new directors.
Acclaimed theatre company LUNG (in association with Leeds Playhouse) present bold documentary theatre piece Trojan Horse (11 & 12 Feb), written by Helen Monks and Matt Woodhead (who also directs) – tackling a local story that hit the national press, of Muslim teachers and governors who were accused of plotting extremism in Birmingham schools, adapted from the real-life testimonies.
Shift Theatre Company return with another batch of Pride Plays (14 & 15 Feb), Scotland's first ever LGBTQI+ playwright festival – giving the stage to the voices of a community who still feel underrepresented in Scottish theatre. Part of LGBT History Month Scotland. Both performances will be followed by a post-show discussion.
Traverse regulars Scottish Dance Theatre return with Antigone, Interrupted (20-22 Feb) by Joan Clevillé – an intimate solo work marking Clevillé's first creation as Artistic Director of Scottish Dance Theatre. Together with performer Solène Weinachter, it re-imagines the classic story for a contemporary world through the body and voice of a single performer.
Another returning face (last here with Twa), Annie George presents Home is Not the Place (21 & 22 Feb) – contrasting the remarkable story of the short life and lost work of her grandfather, Kerala poet PM John shortly before India's independence, with her own, as an immigrant in the UK. Featuring music by Niroshini Thambar and visuals by Lorna Simpson and Jacqueline Matisse.
The Dynamite Club (in association with The Secret Actors Company) present Nan Shepherd: Howling at the Machine (26 & 27 Feb), written and directed by Erlend Clouston – an animated lecture on Nan Shepherd, the author of The Living Mountain. It features Fats Waller, Jefferson Airplane, Sigmund Freud, Mount Everest, and more, plus the voices of Björk, Tilda Swinton, Karine Polwart and Gerda Stevenson.
Northern Stage, in co-production with The Young'uns and Harbourfront Centre Toronto, present a musical celebration of northern working class activism, as Teesside folk trio The Young'uns perform a new, theatrical version of The Ballad of Johnny Longstaff (27-29 Feb), featuring songs from the original album alongside new material and animation.
Rounding off February, and making us thankful it's a leap year, is the Scottish premiere of W*ank Buddies (29 Feb), by Jake Jarratt and Cameron Sharp (in association with Live Theatre), which debuted to sell-out audiences at Elevator Festival 2019. Written and performed by Jarratt and Sharp, it touches on themes of identity, class, sexuality and masculinity to ask, what are boys really made of?
March opens with the world premiere of Scottish Ensemble and Untitled Projects' (in association with Perth Theatre, Horsecross) We Are In Time (3 & 4 Mar), written by Pamela Carter. It tells the extraordinary story of a transplanted heart, through song, words and a visionary new live score for strings and electronics by Icelandic composer Valgeir Sigurðsson.
Next up, In The Works present poet Ellen Renton's new spoken word theatre show – Within Sight (5 & 6 Mar) – a one-woman performance on disability, running and the Paralympics, confronting ableism within our society. In Traverse 1 the same week, acclaimed family theatre company Red Bridge Arts present a contemporary retelling of Frances Hodgson Burnett's literary favourite The Secret Garden (6 Mar), adapted and directed by Rosalind Sydney for everyone aged six-plus.
To be enjoyed individually, or as a trilogy, Tangram Theatre Company stage a takeover of the Songs of Friendship works by James Rowland – Team Viking (11 Mar); A Hundred Different Words for Love (12 Mar); Revelations (13 Mar), and as a trilogy (14 Mar). Written and performed by Rowland, they combine story, comedy, music and song in a revelatory storytelling cycle about love, life, friendship and death.
Ex-girlfriends Mary Higgins and Ell Potter asked women and trans people aged 11 to 97 what makes them sweat, flush and gush. They made a sweaty verbatim dance party out of the answers. Following a sell-out run at London's Soho Theatre, HOTTER Project and Ellie Keel Productions' HOTTER (12 & 13 Mar) launches arse-first in our direction.
A world premiere of breathtaking proportions, Theatre Gu Leòr with WHYTE (in association with Tron Theatre) present MAIM (17 & 18 Mar) Translated as 'Panic' in Gàidhlig, it is a call to arms, giving voice to the frustrations of the next generation who care deeply about the connection between their land and language.
March also features the Scottish premiere of Third Angel's co-production with Northern Stage (in association with Sheffield Theatres) – The Department of Distractions (19 & 20 Mar). Written by Third Angel Co-Artistic Director Alexander Kelly with Stacey Sampson and the Company, it promises a conspiracy-theory documentary-exposé detective story for the 21st century.
The producers of the critically-acclaimed good dog, tiata fahodzi, and Wrested Veil in association with Leeds Playhouse, Soho Theatre and Tara Finney Productions present seeds (20 & 21 Mar) – an exploration of the human story of a fatal stabbing, told through the eyes of those left behind. Shortlisted for the Alfred Fagon Award.
Rounding off March is the return of NT Connections (24-28 Mar) – a yearly celebration of young people, theatre-making and the importance of access to the arts, for which the National Theatre commission ten new plays for young people to perform.
Into April, Franz Kafka's influential, tragicomic novella The Metamorphosis (1-4 Apr) is brought to life in an international co-production between Vanishing Point, Emilia Romagna Teatro Fondazione and Tron Theatre. Adapted and directed by Matthew Lenton, it's the story of an ordinary man who wakes up to find he has been transformed into a giant insect.
Edinburgh College's Performing Arts Studio Scotland, the leading provider of performing arts education in Scotland, return to the Traverse with their end of year showcase – Pass Out 2020 (22 Apr) – this time creating new pieces on the theme of 'dirt'. And regular staple Soundhouse returns with its usual stellar calendar of acclaimed weekly Monday (and the occasional Sunday, and even one Friday!) gigs in the Traverse Bar Café (13 Jan-26 Apr).
Traverse Theatre, Edinburgh, EH1 2ED
Tickets on sale now: 0131 228 1404 and online at www.traverse.co.uk
Last Updated: 2 December 2019 11:14
Source: Traverse Theatre
Cure Blue Monday with a free milkshake at Hard Rock Cafe Edinburgh
Hard Rock Cafe Edinburgh are set to save the day this coming 'Blue Monday' (20th January 2020) by offering the first 50 people a FREE milkshake at the iconic Edinburgh venue.
Last Updated: 17th January 2020
GRAHAM kick starts partnership with Street League
Construction company, GRAHAM has agreed a partnership with Street League – the UK's leading 'sport for employment' charity which targets sports to engage with young people.
The Scottish Wedding Show returns for its February showcase
Scotland's largest wedding showcase will be returning to the SEC, Glasgow next month, offering brides and grooms-to-be everything they need to plan their perfect wedding, under one roof!
Book up to break away with Macdonald Resorts
Macdonald Resorts has unveiled its 2020 holiday offers and Winter Sale!
Macdonald Houstoun House Hotel opens its venue to brides and grooms
To help budding brides and grooms organise their perfect day, Macdonald Houstoun House Hotel, near Livingston, will be hosting a special Wedding Open Day on Sunday 12 January.
Last Updated: 8th January 2020
Salvage Hunters on hunt for Scottish locations to feature on the upcoming series
Salvage Hunters, the well-loved and most watched Discovery Network show is on the hunt for locations to feature on the upcoming series.
National Theatre Live: Best of 2019 returns to Vue Edinburgh Omni
After a great year of live theatre on the big screen, Vue and National Theatre are bringing some of the biggest shows of 2019 back to the big screen in Edinburgh.
Last Updated: 29th December 2019
Photo Illusions Created by Homeless Young Scots go on Show
An exhibition of mind-bending photographic illusions created by young people who are homeless, or at risk of homelessness, opens in Edinburgh just before Christmas.
Macdonald Resorts to help spread Christmas cheer with Emergency Service Discount
To thank Emergency Service workers and help them relax after the festive season, Macdonald Resorts is offering an exclusive discount to be enjoyed after the big day.
Eat, Rock and Be Merry at Hard Rock Cafe Glasgow and Edinburgh this Christmas
Hard Rock Cafe® Glasgow and Edinburgh Serve Up Limited-Time, Multi-Course Menu Offerings and Breakfast with Santa for the Holidays.
Edinburgh International Childrens Festival 2020 commission announced
Imaginate is delighted to announce that its 2020 Festival commission will be 'Learning to Fly'a production by Barrowland Ballet.
Big Screen Christmas treats coming up at Vue Edinburgh Ocean and Vue Edinburgh Omni
This Christmas, visitors to Vue Edinburgh Ocean and Vue Edinburgh Omni can expect a festive array of screenings, including old classics, newly released films, live music and more.
Planning a festive proposal...
Macdonald Hotels & Resorts has marked the most romantic locations within its hotels with a velvet cushion designed to provide comfort to those getting down on one knee.
Mrs Browns Boys is Back!
The Award-Winning Brendan O'Carroll and Mrs. Brown's Boys have announced a live return to Edinburgh in 2020 with 'Mrs Brown D' Live Show.
Last Updated: 7th December 2019
Roland Gulliver to step down as Associate Director of Edinburgh International Book Festival
Roland Gulliver is to leave his role as Associate Director of Edinburgh International Book Festival in spring 2020 to take up an exciting new role which will be announced shortly.
Award winning 21 year old CEO, Chris Thomas, reveals the secrets of his success
21 year old Chris Thomas, the CEO of incovo, has just scooped the award for 'Business Growth' at the West Lothian Business Awards!
Scotch liqueur crowned king of the castle in Edinburgh
Scotland's leading Scotch malt whisky cream liqueur, Magnum, has been crowned one of the top selling products at Edinburgh Castle after smashing its annual sales target.
Edinburgh Gin Advert premieres with projection onto The Dome
Edinburgh Gin premieres its new advert on the streets of Edinburgh at 6pm tonight, with a special night-time projection on one of the city's most iconic buildings, The Dome.
Last Updated: 3rd December 2019
Festive fun for a good cause at Edinburgh care home
On Saturday 7th December, from 2pm-4pm, the Care UK team at Cairdean House, on Redford Road, will open the home's doors for a Christmas celebration in aid of the Bethany Christian Trust.
Last Updated: 2nd December 2019
Alasdair Gray wins the Inaugural Saltire Society Scottish Lifetime Achievement Award
In a ceremony presided over by BBC Presenter Cathy MacDonald, Alasdair Gray was awarded the inaugural Saltire Society Scottish Lifetime Achievement Award for his contribution to Scottish literature.
Last Updated: 1st December 2019
Get your hands on some of the hottest tickets in town this Black Friday
This Black Friday sees some amazing offers available on tickets for the biggest and best shows and gigs in Glasgow and Edinburgh!
Last Updated: 29th November 2019
Edinburgh care home set to celebrate first anniversary in style
Care UK's Murrayside, on South Beechwood is inviting the local community to help mark its first birthday, in true Scottish fashion.
Last Updated: 22nd November 2019
Lothians Schoolgirl crowned best home baker in Scotland
The Scottish Cafe & Restaurant at the Scottish National Gallery in Edinburgh has named 14-year-old Grace Warnock its champion home baker following its nationwide search earlier this year.
Last Updated: 21st November 2019
Family festivities begin at Vue Edinburgh Ocean and Omni with CBeebies Christmas Show: Hansel and Gretel
Once again, the family-friendly feast of festive fun that is the CBeebies Christmas Show is coming to Vue Edinburgh Ocean and Vue Edinburgh Omni.
Hard Rock Cafe Glasgow and Edinburgh will serve up a rockin meal for guests this Thanksgiving!
Hard Rock Cafe® Glasgow and Edinburgh will extend a warm holiday welcome to guests this Thanksgiving by serving up a limited-time turkey meal on Thursday, 28th November!
Edinburgh care home chef turns up the heat in national awards
Iain Young, head chef at Murrayside care home, at South Beechwood, has made it to the final stage in the 'Nutrition and eating well' category in the Scottish Care Home Awards 2019.
Cat Hepburn embarks on Scottish student tour as part of Book Week Scotland
The Scottish Book Trust has announced that award winning scriptwriter and spoken word artist Cat Hepburn will embark on a tour for Scottish students as part of Book Week Scotland.
Traverse Theatre announces new artistic leadership team and board appointments
The Traverse Theatre announces the successful candidates who will join the organisation's artistic and producing team following an extensive recruitment process.
Musical spectacular arrives at Vue Edinburgh Ocean and Vue Edinburgh Omni
Les Misérables, one of the world's most popular musicals, is coming to Vue Edinburgh Ocean and Vue Edinburgh Omni this December.

redpajama_set_name: RedPajamaCommonCrawl


Need help planning your vacations for this summer? Plan your next trip to a dope music festival. I've done the research to make sure Ja Rule isn't behind any of these, we do not want another FYRE situation. Here are all the festivals with amazing lineups waiting to take your coins.
Broccoli Con and Broccoli City Festival really is a festival for the people. A week long of conferences, workshops, art installations, games, and more ending the week with 2-stage festival right in the United State's capital. The prices are fairly reasonable however they even have layaway plans if you need a little help budgeting it out.
As soon as I saw the lineup, I knew what it was! As long as Curren$y and Wiz perform How Fly, I am good. This is the festival's second year and with all your favorite smokers in one place this is bound to be a peaceful environment and from my festival experience that is RARE. This one is April 28, almost two months away, so you need to jump into planning it quickly. They still have a few early bird tickets available for $150 and you can purchase them here. Single Day Passes are available also.
This is one of America's longest running festivals and this is their 43rd edition. I included this festival because $155 for three days and $55 for one day is insane! It has a good mixture of artists and is not limited to hip hop. I have never been to Tennessee but this festival has 4 stages and is 3 days, looks lit for the price. You can purchase tickets here.
JMBLYA is a popular traveling festival in Texas that started in 2013. This is a great deal to see some pretty big names for one day. Plan a trip to Texas and make sure to include one of these shows in your trip itinerary. You can purchases your tickets here.
Described as "a hip-hop head's Disney World" by XXL Mag, this 3-day festival has one the best rap lineups I have seen for this year. They were offering payment plans but I did not see that option anymore. Anyway, even though tickets are pricey and can be purchased here it is 3 days with the best line up, something to think about.
This would be a fun trip! Goldenvoice, the company behind Coachella, has announced Blurry Vision Festival. It will take place May 12-13 at Middle Harbor Shoreline in Oakland, California. The line up has a quite a few of my favorite artists and some I've been dying to see, like Alina Baraz. You have enough time to plan and it's not too far away! The tickets are affordable, $185 for a 2-day pass or $99 for a day pass. You will be able to purchase tickets March 2 at 1 p.m. ET on the festival's official website.
Looking for somewhere to go or something to do Memorial Day weekend. Everyone is going to the beach, head up to Minnesota where they have this dope 1-day festival. It's the 25th Anniversary of "Enter the Wu-Tang 36 Chambers" so they will be in attendance alongside artists like Jaden Smith, Migos, Erykah Badu and more. Tickets go on sale today and you can get them here at 1pm.
I could not create this list without including the Governors Ball. I've heard great things about this festival, It has a good mixture of different types of artists but the 2nd and 3rd-day lineups look the best. You can totally just buy a single day pass here if you are not interested in the other shows, which is what I may do.
Have yall seen Dave Chappelle's movie Block Party? Go watch it then tell me you don't wanna be at this year's Roots Festival. I have to be there. This event looks so lit and the fact that they are offering so much more than just concerts like the Lifestyle and Podcast Stages make me want to go EVEN MORE! Check out the lineup, buy your ticket here and plan a summer road trip to Philly!
A few friends and I plan on traveling across the big pond this year, why not see how they do festival while we are at itt? Last year Solange and Frank Ocean headlined this festival, and this year I was excited when I saw N.E.R.D headlining beside some other dope names. The prices for the Lovebox festival are fairly reasonable, £115.00($158.73) for a 2-day pass,£59.50($82.13) for a Friday Pass, and £69.50 ($95.93). They also have a ton of artists I haven't seen yet that rarely go on tour so I have my eye on this one! If you have your passport and this one looks interesting to you, you can purchase tickets here.
Afropunk has not announced their line up but they have announced that they are doing BOGO tickets! When you purchase one general admission weekend ticket Afropunk gives one general admission pass to youth in the area. DOPE RIGHT?! Afropunk is a traveling festival also with shows in Atlanta, Paris, Johannesburg, and London but they have not released date for these. You can purchase tickets and keep up with Afropunk festival here.


text:
arXiv Vanity renders academic papers from arXiv as responsive web pages so you don't have to squint at a PDF
View this paper on arXiv
Chaos in resonant-tunneling superlattices
O. M. Bulashenko [†] and L. L. Bonilla Universidad Carlos III de Madrid, Escuela Politécnica Superior, Butarque 15, 28911 Leganés, Spain
Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.
PACS numbers: 73.20.Dx, 73.40.Gk, 47.52.+j, 47.53.+n
Nonlinear oscillations and chaos have been predicted in systems where a predominantly quantum dynamics is corrected by mean-field nonlinear terms due to collective interactions (Hartree) [2] or to interactions with classical subsystems having a widely different time scale. [3] These phenomena are different from quantum chaos, [4] i.e., the behavior of quantum systems whose classical counterpart is chaotic. So far chaotic oscillations have been predicted for systems with few degrees of freedom and experimental evidence is scarce. In this paper we predict chaotic behavior with loss of spatial coherence in a system with many degrees of freedom for which the main transport mechanism is resonant tunneling: a weakly-coupled multiquantum well superlattice (SL). As far as we know these are the first results on chaotic behavior in SLs. In contrast to unbiased triple-well heterostructure, [2] our SL is subject to external dc+ac bias, as it was the case with the two-level system of Ref. 2.
Very recently time-dependent oscillations of the current on GaAs/AlAs SLs subject to dc voltage bias have been found. [5] The oscillations are damped for undoped photoexcited SLs and undamped for doped SLs without photoexcitation. [6] For large values of the photoexcitation or the doping, there is stable formation of stationary electric field domains leading to the well-known oscillatory I-V characteristic. [7, 8, 9] According to a discrete drift model, [10] the current oscillations are caused by the creation, motion and recycling of domain walls separating two electric field domains. [11] This situation is reminiscent of that found in bulk semiconductor devices with negative differential resistance (NDR), where dc voltage bias gives rise to high-field domain dynamics and the well-known Gunn oscillations. [12, 13] A significant difference is that the space charge waves are dipoles in the Gunn oscillations and charge monopoles in the SL current oscillations. Another is that the Gunn waves are generated close to the injecting contact whereas the domain walls appear clearly inside the SL. [11]
Having found a system with a natural oscillation due to traveling-wave motion, it is natural to ask whether harmonic forcing would lead to chaos with spatial structure. The answer is affirmative. This is also the case for the periodically driven Gunn diode studied by Mosekilde et al. [14] Experimental studies have been carried out by Kahn et al. [15] on ultrapure p-Ge, where the NDR is caused by negative differential impurity impact ionization, [16] and the transition to a chaotic attractor with loss of spatial coherence has been observed.
We consider a set of weakly interacting quantum wells (QWs) characterized by average values of the electric field Ei(t), and the electron density ni(t), with i=1,…,N denoting the QW index. This mean-field-like approach is often justified because the relevant time scale for the oscillations (∼0.1 μs) is much larger than those for the tunneling process between adjacent QWs (∼1 ns) and the relaxation from excited levels to the ground state within each QW (∼1 ps). [10] The one-dimensional equations governing the dynamics of the system are the Poisson equation averaged over one SL period l, Ampère's equation for the balance of current density and the voltage bias condition:
1l(Ei−Ei−1)=eϵ(ni−ND) (1)
ϵdEidt+eniv(Ei)=J (2)
lN∑i=1Ei=V(t). (3)
Here ϵ, e, and ND are the average permittivity, the electron charge, and the average doping density, respectively. [17] The total current density J(t) is the sum of the displacement current and the electron flux due to sequential resonant tunneling eniv(Ei). The effective electron velocity v(E) exhibits maxima at the resonant fields for which the adjacent levels of neighboring QWs are aligned, [18] as shown in the inset of Fig. 1. The voltage V(t) in (3) is the sum of a dc voltage Vb and an ac microwave signal of relative amplitude A and driving frequency fd: V(t)=Vb{1+Asin(2πfdt)}. The boundary condition ϵ(E1−E0)/(el)=n1−ND=δ allows for a small negative charge accumulation in the first well, which is taken to be δ∼10−3×ND. The physical origin of δ is that the n-doped SL is typically sandwiched between two n-doped layers with an excess of electrons, thereby forming a n+-n-n+ diode. [6] Then some charge will be transferred from the contact to the first QW creating a small dipole field that will cancel the electron flow caused by the different concentration of electrons at each side of the first barrier.
To study our equations, it is convenient to render them dimensionless, using the characteristic physical quantities. As the unit of the electric field E=E/E1−2 we adopt the typical electric field strength needed to align the first and the second electron subbands of the nearest QWs E1−2. The dimensionless velocity v(E) is obtained normalizing v(E) by its value at E=E1−2, where it has a local maximum due to resonance in tunneling (see inset of Fig. 1). The others dimensionless quantities are defined as follows: the donor concentration ν=elND/ϵE1−2; the time τ=t/ttun where ttun=l/v(E1−2) is the characteristic tunneling time; the dc bias V=Vb/E1−2lN; the ac bias amplitude a=AV; the driving frequency ω=2πfdttun. By time-differentiating (3) and using Ampère's law (2), one can express the current density as
J(t)=ϵlNdVdt+eNN∑j=1njv(Ej), (4)
and after its substitution into (2) we obtain a system of N equations for the electric field profiles:
dEidτ= 1NN∑j=1v(Ej)[Ej−Ej−1+ν] (5)
−v(Ei)[Ei−Ei−1+ν]+aωcos(ωτ),
which we solved numerically by the fourth-order Runge-Kutta method with the boundary condition E0=E1−νδ and initial conditions Ei(0)=V,∀i. As an example, we consider a GaAs/AlAs SL at T=5 K with N=40, l=13 nm, E1−2≈105 V/cm, ND≈1.15×1017cm−3, for which undamped time-dependent oscillations of the current were first observed. [6] One get ν≈0.1, ttun≈ 2.7 ns, and we take V=1.2 (corresponding to Vb≈7.8 V). The main features of our numerical results are as follows.
For the dc case (a=0) undamped time-periodic current oscillations of frequency f0≈9 MHz, (in excellent agreement with the observed value [6] ) set in after a transient period. The electric field and charge profiles corresponding to one period of the current oscillation are similar to those found in the undoped case (cf. Figure 9 in Ref. 9). During each period a domain wall (charge monopole) is formed inside the SL. It then moves towards the corresponding contact. Depending on the applied voltage, it may or may not reach the end of the SL before it dissolves and a new monopole is formed starting a new period of the oscillation. Since in a 40-period SL the wall moves only a few QWs, it may be hard to distinguish this monopole recycling from a true spatial oscillation of a single monopole. Simulations of longer SLs (N≥100), however, clearly show monopole recycling with two monopoles coexisting during some part of one current oscillation period. The frequency of the oscillation is mainly determined by the number of QWs the monopole moves across (which increases with N) and by the average drift velocity. [11]
Now consider the ac case. We start with a uniform initial field profile and solve the equations for dc bias. After a short transient, the self-sustained oscillations set in and we switch on the ac part of the bias. Our main result is that the competition between the natural oscillation due to monopole dynamics and the forcing gives rise to narrow windows of spatio-temporal chaos for appropriate values of V, a and ω, and that the size and richness of these windows increases with N. Let us fix the ratio between the natural frequency f0 and the driving frequency fd at the golden mean (√5−1)/2. To detect and visualize the chaotic regions in parameter space, we need to define a Poincaré mapping. The current is a good measure of the amplitude (norm) of the solutions which is illustrated by the use of current vs voltage characteristics as bifurcation diagrams. [13] Denoting the period of the ac bias Td=2π/ω, we adopt as Poincaré mapping (for each value of a) the current at times τm=mTd, m=0,1,… (after waiting enough time for the transients to have decayed). The result is the bifurcation diagram in Fig.1. Notice the period-doubling sequences that point to the existence of chaos near their accumulation points. There we have computed the largest Lyapunov exponent and found it positive, which confirms chaos within the windows marked by arrows in Fig.1. The chaotic regions are interspersed with locking to periodic and quasiperiodic regimes. Quasiperiodic routes to chaos have been found at the first and last windows marked with arrows in Fig.1. Notice that the period-2 orbits span the widest parameter region from the narrow chaotic band around a≈0.01 up to the next chaotic region at a≈0.09. For a≥0.145 the solution is attracted to the period-1 orbit with the driving frequency fd.
More insight into the transition between chaotic and non-chaotic regions of the bifurcation diagram can be obtained by sweeping-down through it, as follows. We set a0=0.16 (the leftmost value in Fig. 1, where there is period-1 locking) and take an initial field profile {Ei}=V. We now solve the problem (5), compute Jm=J(mTd) and find out when the solution is periodic within a 10−5 accuracy. At that time, we stop the simulation, depict all Jm correspondent to the period, store the resulting electric field profile, and use it as initial condition for another simulation with a=a0−Δa, Δa=2×10−4. By repeating this process, we arrive at chaotic or quasiperiodic regions of a, where the integration is stopped at a much larger time mTd, with m=2000, and only the last 1000 points are depicted, thereby eliminating transients. Fig.1 is the result of such a sweep-down run. The transition points between different regions in the bifurcation diagram are found to be different when a sweep-up run is made, demonstrating thus hysteresis.
To illustrate the spatially chaotic nature of the solutions we pick arbitrarily two far-away QWs and depict the simultaneous values of the electric field at them after each period of the driving force Td. The resultant attractors for several amplitudes a are presented in Fig. 2. The first example [Fig. 2(a)] shows a chaotic attractor with layered structure and variation in the density of points. The chaotic attractor of Fig. 2(b) has several separate branches almost continuously filled. Finally Fig. 2(c) corresponds to a value of a on the quasiperiodic region. The closed loop with periodic pattern [see Fig. 2(d)] indicates quasiperiodicity: the orbit fills the attractor (torus), never closing on itself. The points in the chaotic attractors cluster with varying density on different regions, which means that they can be characterized by their multifractal dimension Dq (calculated by the method of Ref. 18). We have found that for the particular case of Fig. 2(a), Dq decreases from D−∞≈ 1.57 to D+∞≈ 0.72, going through the capacity dimension D0≈1.18.
Loss of spatial coherence in the chaotic regime is easily found in long SLs. Density plots for the electron concentration (dark regions mean high electron density) in a 200-period SL with natural frequency ≈ 1.9 MHz are shown in Fig. 3. The density plots show the transition from periodic [Fig. 3(a)] to chaotic domain wall dynamics with loss of spatial coherence [Fig. 3(b)]. Under dc+ac driving with golden mean frequency ratio, nucleation of monopole wavefronts occurs more frequently: in addition to long-living waves travelling over almost the whole SL, there are short-living waves. The two types of waves are distributed chaotically in space and nucleated both at the beginning and deep inside the SL. Detailed calculations show coexistence of up to three monopoles connecting four electric field domains during certain time intervals. We thus have that the loss of spatial coherence is due to chaotic domain-wall dynamics, as seen in Fig. 3(b).
In conclusion, spatio-temporal chaos is expected to occur in weakly-coupled semiconductor superlattices (with sequential resonant tunneling as the main transport mechanism) under appropriate dc+ac voltage bias. This prediction should be experimentally testable in currently available n-doped GaAs/AlAs samples forming n+-n-n+ diodes. [6]
We thank J. M. Vega and C. Martel for valuable discussions. O. M. B. has been supported by the Ministerio de Educación y Ciencia of Spain. This work has been supported by the DGICYT grant PB92-0248, and by the EC Human Capital and Mobility Programme contract ERBCHRXCT930413.
[†] On leave from Institute of Semiconductor Physics, National Academy of Sciences, Pr Nauki 45, 252650 Kiev, Ukraine.
[2] G. Jona-Lasinio, C. Presilla, and F. Capasso, Phys. Rev. Lett. 68, 2269 (1992).
[3] L. L. Bonilla and F. Guinea, Phys. Rev. A 45, 7718 (1992).
[4] F. Haake, Quantum signatures of chaos (Springer, Berlin, 1991).
[5] S.H. Kwok, T.B. Norris, L.L. Bonilla, J. Galán, J.A. Cuesta, F.C. Martínez, J. Molera, H.T. Grahn, K. Ploog, and R. Merlin, Phys. Rev. B 51, 10171 (1995).
[6] J. Kastrup, R. Klann, H.T. Grahn, K. Ploog, L.L. Bonilla, J. Galán, M. Kindelan, M. Moscoso, and R. Merlin, (1994), unpublished.
[7] H. T. Grahn, R. J. Haug, W. Müller, and K. Ploog, Phys. Rev. Lett. 67, 1618 (1991).
[8] D. Miller and B. Laikhtman, Phys. Rev. B 50, 18426 (1994).
[9] F. Prengel, A. Wacker, and E. Schöll, Phys. Rev. B 50, 1705 (1994).
[10] L. L. Bonilla, J. Galán, J. Cuesta, F. C. Martínez, and J. M. Molera, Phys. Rev. B 50, 8644 (1994).
[11] L. L. Bonilla, in Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices, edited by F.-J. Niedernostheide (Springer Verlag, Berlin, 1995), Chap.1.
[12] M. P. Shaw, V. V. Mitin, E. Schöll, and H. L. Grubin, The Physics of Instabilities in Solid State Electron Devices (Plenum, New York, 1992).
[13] L. L. Bonilla and F. J. Higuera, Physica D 52, 458 (1991); F. J. Higuera and L. L. Bonilla, Physica D 57, 161 (1992); I. R. Cantalapiedra, L. L. Bonilla, M. J. Bergmann, and S. W. Teitsworth, Phys. Rev. B 48, 12278 (1993).
[14] E. Mosekilde, R. Feldberg, C. Knudsen, and M. Hindsholm, Phys. Rev. B 41, 2298 (1990); E. Mosekilde, J. S. Thomsen, C. Knudsen, and R. Feldberg, Physica D 66, 143 (1993).
[15] A. M. Kahn, D. J. Mar, and R. M. Westervelt, Phys. Rev. Lett. 68, 369 (1992).
[16] L. L. Bonilla and S. W. Teitsworth, Physica D 50, 545 (1991).
[17] The doping density ND has been incorporated into the equations of Ref. 9, and the hole density has been set equal to zero, as we do not include photoexcitation due to laser illumination in this paper.
[18] In our calculations we use the curve v(E) obtained from the experimental current-voltage characteristics of Ref. 5, as explained in Ref. 4.
[19] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Phys. Rev. A 33, 1141 (1986).
Figure 1: Bifurcation diagram of the current at times mTd (for sufficiently large m) versus the driving-force amplitude, for a 40-period SL and the golden-mean ratio between natural and driving frequencies. Windows of chaotic solutions are marked by arrows. Inset: Dimensionless velocity as a function of the electric field. The point indicates the electric-field value corresponding to the dc bias V=1.2 used in the calculations.
Figure 2: Electric field values E5 and E36 (at two different QWs of the 40-period SL) measured at times mTd for: (a) a=0.088; (b) a=0.101; (c) a=0.14. (d) is a blow-up of the small region inside the rectangle in (c). 104 successive points have been used to depict each attractor.
Figure 3: Density plots for the electron concentration in a 200-period SL for: (a) pure dc bias; and (b) dc+ac bias with a=0.112. x- and y-axes correspond to time (in units of 16 ttun) and QW index respectively. Darker regions indicate high electron density and mark the location of the domain boundary for each time.
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Initial prognosis on Chargers G Forrest Lamp is torn ACL. Sending off MRI for second opinion.
Preseason hasn't even started and Chargers OL are already going down.
Yea, RaiderX wins. We can all just top acting like this is a matter of opinion. MY GOD.
So their 1st and 2nd round pick out for the season?
No other team can complain about injuries.
Only the 2nd rounder at this point. However, if I had a choice, I would rather have lost the 1st rounder for the season than the 2nd rounder. Rivers can make mediocre receivers look good if he had protection. Which at this point doesn't look as good.
Didnt I hear something about Mike Williams being out too?
There's conflicting reports about that. All I know is that MW was running at practice even though he did not directly participate in training camp.
Just when I begin to think the Ravens might have them beat on the injury front.
Will it be Feeney replacing him? It's not like he was miles behind Lamp as a prospect.
I was under the impression Lamp and Feeney would be their starting guards. Maybe they will move Matt Slausen back to guard and have Max Tuerk and Spencer Pulley compete for the starting job at center?
The Chargers have the worst luck with injuries. To bad too as they were looking like playoff contenders.
Yep, Slauson from the time the new staff got here was our LG, and they had Pulley slotted in at C. Feeney was rotating in with the 1s at both RG and C, and I assumed that he was planning on playing the backup IOL role, so they had someone they were comfortable with at either OG or C so they could keep 7 OL active on gamedays.
I'm not sure what's going on with Tuerk, he has struggled snapping the ball, and hasn't been worked in at all with the 1's. I'd be surprised if they give him a crack at the starting spot at this point. Something has to be going on with him though.
So this injury hurts us more for depth purposes than anything else. While Lamp was really good, Feeney isn't THAT far behind him IMO, and both had similar profiles as OG's, so I'm pretty confident in Feeney's ability to step in and start right away, but depth is an issue now unless Tuerk really steps up.


Best video ever ..finally no ads!
I'm not emo but I like the emo haircut it makes you look mysterious.
I liked because you DIDN'T plug anyone.!!!
Id say swap out the emo hair and replace it with balding combover. Unlike the other styles listed, there is an entire subculture with style behind it. It's just a small accessory to a bigger package. That being said I both share and respect your opinion, but only addressing a small aspect without addressing anything else makes it incomplete. You would have to address the rest of your opinions on that style in a separate video.
So a mullet is alright?
Dolph Lundgren can rock a flat top.
breking necks, that was funny.
So my mullet is okay?
That was a close one Jose, I was panicking since the video was about to end and you didn't promote anything.
I've never felt good about my face. I naturally have no eyebrows, a major deviated septum on my nose that I won't be able to fix until I'm 18, a big over bite, and a mole on the right side of my face. On top of this, I have the "Justin Bieber Cut" and get made fun of and called his name at school for it. I want to change my haircut, but I'm afraid I'll get made fun of even more, because it will look stupid, and show how bad my eyebrows are. I don't know what to do, I'm starting 8th grade and all my friends have a girlfriend or have at least been asked out by one, and I'm the only one who hasn't. If someone has advice on what I should do please tell me, I'm going through a bad time right now, because of how much I'm being made fun of. No matter how good my style is I'm still ugly, and I'm tired of it.
Hoze where u from man 👱😁?
Forgot to mention the worst haircut: The Undercut Like looking like Hitler youth? Like looking like every other guy and being lost in a crowd of basic? Like people knowing you walked into a salon looked at the front cover of a magazine and said "give me that"? Then the undercut is right for you.
I wanna grow my hair so i can tie it on a bun how do you deal with the akward stage?
Hi Teachingmensfashion , how bout baldhead?
Like and reply if you agree the bowl haircut is very ugly, goofy, and kind of annoying.
1:47 the man in the middle is Polanreff!!!
What is your hairstyle in this video?


text:
import EventEmitter from 'events';

class HistoryListItem {
  constructor(text) {
    this.id = Date.now();
    this.text = text;
    this.preview = text.split('\n')[0];
  }
}

class HistoryList extends EventEmitter {
  static EVENT_UPDATED = 'updated';

  constructor(clipboardManager, maxItems = 50) {
    super();

    this.cm = clipboardManager;

    this.list = [];
    this.setMaxItems(maxItems);

    this.addListeners();
  }

  addListeners() {
    this.cm.on(this.cm.EVENT_CHANGED, text => {
      this.list.unshift(new HistoryListItem(text));
      this.list = this.list.slice(0, this.maxItems);

      this.emit(HistoryList.EVENT_UPDATED, this.list);
    });
  }

  setMaxItems(maxItems) {
    this.maxItems = maxItems;
  }

  getList() {
    return this.list;
  }

  destroy() {
    this.cm = null;
    this.list.length = 0;
  }
}

export default HistoryList;

redpajama_set_name: RedPajamaGithub