text:
\section{Introduction}

In experiments on nematic liquid crystals, the director field can be aligned by many different physical mechanisms, including electric and magnetic fields, surface anchoring, and shear flow.  All of these mechanisms are useful for technological applications.  In liquid-crystal theory, there is an important difference between the theoretical approaches that are used to describe these alignment mechanisms.  If the alignment is induced by a static perturbation, it is modeled by adding appropriate terms to the free energy function, and then minimizing the free energy over all possible director fields.  By contrast, if the alignment is induced by shear flow, it is modeled by solving hydrodynamic equations~\cite{Ericksen1960,Ericksen1961,Leslie1966,Leslie1968,Beris1994}.  When we compare these approaches, it is natural to ask:  Is it possible to describe shear alignment by any type of minimization principle?  In other words, does the nematic director field evolve to minimize any effective potential?  If so, then we could develop an intuitive picture of shear alignment as motion toward some optimal state, by analogy with alignment by an applied field or other static perturbation.

To our knowledge, this kind of question has been considered at least three times in the liquid-crystal literature.  First, Olmsted and Goldbart developed a theory for the nonequilibrium isotropic-nematic transition under shear flow~\cite{Olmsted1990,Olmsted1992}.  This theory shows that shear flow has the same effect as an aligning field on the isotropic-nematic transition:  Weak shear flow raises the transition temperature, and sufficiently strong shear flow induces an isotropic-nematic critical point.  Because the theoretical approach involves solving hydrodynamic equations rather than minimizing any potential, it is easy for the theory to determine the limit of stability for each phase, but it is difficult for the theory to find the first-order transition temperature.  The first-order transition cannot be identified by searching for the minimum of any function; rather, it must be calculated by modeling the motion of the isotropic-nematic interface.

Later, Doi developed a general theory for the dynamics of soft matter, based on an Onsager-type variational approach~\cite{Doi2011,Doi2013}.  This theory is based on a single scalar function, called the Rayleighian, which combines the dissipation function with the generalized velocities and with derivatives of the energy function.  This approach is a variational theory, because it derives the equations of motion by setting certain derivatives of the Rayleighian equation to zero.  However, it is not exactly a minimization principle, because the system does not evolve toward the global minimum of any function.  This distinction will be discussed in Sec.~II below.

Most recently, Emer{\v{s}}i{\v{c}} \emph{et al}.\ developed theory and simulations to model the behavior of ``dowser'' and ``bowser'' domains in nematic liquid crystals confined in a narrow cell under Poiseuille flow~\cite{Emersic2019}.  Part of their work involves defining an effective potential or effective free energy for the dowser state, which includes the effects of flow as well as the elastic free energy.  In this case, the director field does evolve toward the minimum of the effective potential, and one can see that Poiseuille flow causes the dowser state to become more favorable than the bowser.

The purpose of this article is to introduce a unified theoretical formalism to address this issue.  We want to determine when liquid-crystal dynamics under shear flow can be described by an effective potential, such that the system moves toward the minimum of that potential.

In Sec.~II, we begin with a simple analogy in classical mechanics, in which we consider a particle moving in the wind.  In one dimension (1D), it is straightforward to define an effective potential for this particle, which includes the dissipative effects of the wind.  By comparison, in two dimensions (2D), this effective potential is only defined if the wind velocity field has zero curl, or if the motion is restricted to a 1D track on the 2D plane.

In Sec.~III, we apply this concept to a uniform liquid crystal under simple shear flow.  We show how the effects of shear flow can be represented by an effective potential.  In particular, the shape of the effective potential determines whether the director will tumble or align at the Leslie angle~\cite{Leslie1966,Leslie1968}.

In Sec.~IV, we extend the theory to a nonuniform liquid crystal with no defects.  In particular, we describe the dynamics of reverse tilt domains under simple shear flow, and demonstrate that the domain walls move in order to minimize an effective potential.

In Sec.~V, we generalize the theory to a nonuniform liquid crystal with defects.  In particular, we consider the disclination at the boundary between the dowser and bowser states in a narrow cell, and show that this disclination moves to minimize an effective potential.  For this problem, our results are consistent with the theory of Emer{\v{s}}i{\v{c}} \emph{et al}.~\cite{Emersic2019}; we show that their effective potential fits into the general framework presented here.

Finally, in Sec.~VI, we provide a general discussion of these examples.  We argue that the concept of minimizing an effective potential is a useful theoretical tool for describing liquid crystals under shear flow.  In the problems where it applies, the effective potential particularly helps to develop intuition for the effects of shear alignment.

\section{Classical mechanics analogy}

To introduce the concept of an effective potential for dissipative forces, we present a simple analogy in classical mechanics.  We first demonstrate this concept in 1D, and then show its limitations in higher dimensions.

\subsection{One dimension}

Consider the dynamics of a classical particle in the wind.  This particle experiences a conservative force from its potential energy, as well as a dissipative force from air drag against the wind.  The equation of motion can be written as
\begin{equation}
m\ddot{x}=F_\text{conservative}+F_\text{dissipative}
=-\frac{\partial U}{\partial x}-\frac{\partial D}{\partial\dot{x}},
\end{equation}
where $x(t)$ is the particle position, $m$ is the mass, $U$ is the potential energy, and $D$ is the Rayleigh dissipation function.  For overdamped motion, this equation simplifies to
\begin{equation}
0=-\frac{\partial U}{\partial x}-\frac{\partial D}{\partial\dot{x}}.
\label{overdamped}
\end{equation}
In steady state, we have $\dot{x}=0$, and hence the equation simplifies further to
\begin{equation}
0=-\frac{\partial U}{\partial x}-\left[\frac{\partial D}{\partial\dot{x}}\right]_{\dot{x}=0}.
\label{steadystate}
\end{equation}

For a simple model of the conservative force, suppose the potential energy is $U(x)=\frac{1}{2}k (x-x_0)^2$, so that $F_\text{conservative}=-k(x-x_0)$.  For a simple model of the dissipative force, suppose the wind velocity field is $v_\text{wind}(x)$.  In that case, the Rayleigh dissipation function is $D=\frac{1}{2}\gamma[\dot{x}-v_\text{wind}(x)]^2$, where $\gamma$ is the drag coefficient, and $F_\text{dissipative}=-\gamma[\dot{x}-v_\text{wind}(x)]$.  Hence, the overdamped equation of motion becomes
\begin{equation}
0=-k(x-x_0)-\gamma[\dot{x}-v_\text{wind}(x)],
\end{equation}
and the steady-state equation is
\begin{equation}
0=-k(x-x_0)+\gamma v_\text{wind}(x).
\end{equation}
Thus, we see that the wind shifts the steady-state position of the particle from $x_0$ to $x_0+(\gamma/k)v_\text{wind}(x)$.

To express the steady-state solution as a minimization principle, we would like to rewrite the steady-state equation (\ref{steadystate}) in the form
\begin{equation}
0=-\frac{\partial U_\text{eff}}{\partial x}.
\end{equation}
Hence, we must define the effective potential $U_\text{eff}(x)$ as
\begin{equation}
U_\text{eff}(x)=U(x)+\int dx \left[\frac{\partial D}{\partial\dot{x}}\right]_{\dot{x}=0}.
\end{equation}
For the simple example above, this construction gives
\begin{equation}
U_\text{eff}(x)=\frac{1}{2}k (x-x_0)^2 -\int dx \gamma v_\text{wind}(x).
\end{equation}
If the wind velocity is uniform, this effective potential is just $U_\text{eff}(x)=\frac{1}{2}k (x-x_0)^2 -\gamma v_\text{wind} x$.  We can easily see that the steady-state position found above is the minimum of this effective potential.

This example shows that the wind has the same effect as a linear contribution to the potential energy.  That statement agrees with the common intuition that moving downwind is like moving downhill, and moving upwind is like moving uphill.  More generally, the example also shows the procedure for calculating an effective potential:  First differentiate the Rayleigh dissipation function with respect to velocity, then set the velocity equal to zero, and then integrate with respect to the position.  In this article, we will apply that procedure to other generalized coordinates and generalized velocities in liquid-crystal physics.

Before going on, we should compare our analysis with the variational theory of Doi~\cite{Doi2011,Doi2013}.  Doi's theory also seeks to describe the behavior in terms of a single function.  That theory begins with the overdamped equation (\ref{overdamped}), and rewrites it in the form
\begin{equation}
0=-\frac{\partial R}{\partial\dot{x}},
\label{doi}
\end{equation}
where $R$ is a function that Doi calls the Rayleighian, defined by
\begin{equation}
R=\frac{\partial U}{\partial x}\dot{x}+D.
\end{equation}
Note that $R$ is different from $U_\text{eff}$, because $R$ is integrated with respect to $\dot{x}$ while $U_\text{eff}$ is integrated with respect to $x$.  For the simple example of a particle in the wind, we have
\begin{equation}
R=k(x-x_0)\dot{x}+\frac{1}{2}\gamma[\dot{x}-v_\text{wind}(x)]^2
\end{equation}
Equation~(\ref{doi}) then states that $R$ is minimized over velocity $\dot{x}$.  We emphasize that $R$ is \emph{not} minimized over position $x$.  Rather, minimization over $\dot{x}$ gives the equation of motion, and this equation must be solved to find the steady-state $x$.

As we understand it, Doi's theory is a useful way to derive equations of motion.  It is a variational theory in the sense that equations of motion are derived by differentiating $R$ with respect to velocity.  It is not actually a minimization theory, because the system does not move toward a minimum of $R$.  By contrast, the effective potential theory is a minimization theory in this stronger sense, because the system does move toward a minimum of $U_\text{eff}$.

\subsection{Two dimensions}

To see important limitations of the effective potential theory, consider 2D motion of a particle in the wind.  Suppose the particle position $\bm{r}(t)$, and the wind velocity field is $\bm{v}_\text{wind}(x,y)$, so that the Rayleigh dissipation function is $D=\frac{1}{2}\gamma|\dot{\bm{r}}-\bm{v}_\text{wind}(x,y)|^2$.  Following the same notation as above, the steady-equation of motion is
\begin{equation}
0=-\frac{\partial U}{\partial \bm{r}}-\left[\frac{\partial D}{\partial\dot{\bm{r}}}\right]_{\dot{\bm{r}}=0}
=-\frac{\partial U}{\partial \bm{r}}+\gamma\bm{v}_\text{wind}(x,y).
\end{equation}
We would like to rewrite that equation in the form
\begin{equation}
0=-\frac{\partial U_\text{eff}}{\partial \bm{r}},
\end{equation}
and hence we must define
\begin{align}
U_\text{eff}(x,y)&=U(x,y)+\int d\bm{r}\cdot\left[\frac{\partial D}{\partial\dot{\bm{r}}}\right]_{\dot{\bm{r}}=0}\nonumber\\
&=U(x,y)-\gamma\int d\bm{r}\cdot\bm{v}_\text{wind}(x,y).
\label{2dintegral}
\end{align}
We must now ask:  Does this integral have a single value, or does it depend on the integration path?  The answer depends on the curl of the wind velocity field.  If $\nabla\times\bm{v}_\text{wind}=0$, then the integral is independent of path, and hence the effective potential is a uniquely defined function.  By contrast, if $\nabla\times\bm{v}_\text{wind}\not=0$ (as in a hurricane), then the integral depends on the path, and the effective potential is not well defined.  This example demonstrates that the concept of an effective potential might or might not be useful in problems with more than one degree of freedom, depending on the generalized curl of the dissipative force.

For one more variation on this problem, suppose that the particle is constrained to move on a 1D curve in 2D, like a train constrained to move on a railroad track.  If the curve is not closed, then there is only a single integration path from one point to another in Eq.~(\ref{2dintegral}), and hence the effective potential is uniquely defined as in 1D.  However, if the curve is a closed loop, then the integration path might go around the loop once or multiple times.  Hence, the effective potential becomes a multi-valued function, with a discrete set of possible values.  We can still work with it, but we need to be careful with branch cuts, so that we only compare the effective potential of states on the same branch.  Several examples of this phenomenon in liquid-crystal physics will be given in the following sections.

\section{Uniform liquid crystal under simple shear flow}

For an example of an effective potential in liquid-crystal physics, consider a nematic phase under simple shear flow.  For simplicity, we work in 2D, so that the director is $\hat{\bm{n}}(t)=(\cos\theta(t),\sin\theta(t))$.  We assume the phase is uniform, so that the director may depend on time but not on position.

In hydrodynamic theory, there are two modes that dissipate energy:  the strain rate tensor, $A_{ij}=\frac{1}{2}(\partial_i v_j +\partial_j v_i)$, and the director totation with respect to the background fluid vorticity, $N_i=\dot{n}_i-\frac{1}{2}(\partial_j v_i -\partial_i v_j)n_j$.  The most general quadratic dissipation function density is then~\cite{Stewart2004}
\begin{align}
\label{dissipationgeneral}
D=&\frac{1}{2}\alpha_4 A_{ij}A_{ij}+\frac{1}{2}(\alpha_5+\alpha_6)n_i A_{ij}A_{jk}n_k \\
&+\frac{1}{2}\alpha_1 (n_i A_{ij}n_j)^2 +\frac{1}{2}\gamma_1 N_i N_i +\gamma_2 N_i A_{ij} n_j,\nonumber
\end{align}
where the $\alpha$ coefficients are the Leslie viscosities for fluid flow, $\gamma_1$ is the rotational viscosity for director rotation with respect to background fluid vorticity, and $\gamma_2$ is the torsion coefficient, representing a dissipative coupling between strain rate and director rotation.

For simple shear flow, we consider the fluid flow velocity profile is $\bm{v}=(v'y,0)$.  Hence, the dissipative modes become
\begin{equation}
A_{ij}=
\begin{pmatrix}
0            & \frac{v'}{2} \\
\frac{v'}{2} & 0
\end{pmatrix},
\quad
N_i=
\begin{pmatrix}
-\sin\theta \\
\cos\theta
\end{pmatrix}
\left[\dot{\theta}+\frac{v'}{2}\right],
\end{equation}
and the dissipation function becomes
\begin{align}
D=&\frac{1}{8}(\alpha_4+\alpha_5+\alpha_6)v'^2 +\frac{1}{8}\alpha_1 v'^2 \sin^2 2\theta \\
&+\frac{1}{2}\gamma_1 \left[\dot{\theta}+\frac{v'}{2}\right]^2 +\frac{1}{2}\gamma_2 v'\left[\dot{\theta}+\frac{v'}{2}\right]\cos2\theta.\nonumber
\end{align}

To convert this dissipation function into an effective potential acting on the steady-state angle $\theta$, we follow the procedure developed in Sec.~II(A).  First, we calculate the dissipative force acting on $\theta$ by differentiating the dissipation function with respect to $\dot{\theta}$,
\begin{equation}
-\frac{\partial D}{\partial\dot{\theta}}=\gamma_1 \left[\dot{\theta}+\frac{v'}{2}\right] +\frac{1}{2}\gamma_2 v'\cos2\theta.
\end{equation}
Next, we go to the steady-state case by setting $\dot{\theta}=0$, and obtain
\begin{equation}
-\left[\frac{\partial D}{\partial\dot{\theta}}\right]_{\dot{\theta}=0}=\frac{1}{2}\gamma_1 v'+\frac{1}{2}\gamma_2 v'\cos2\theta.
\end{equation}
Finally, we integrate with respect to $\theta$, and find the effective potential
\begin{equation}
U_\text{eff}=\int d\theta\left[\frac{\partial D}{\partial\dot{\theta}}\right]_{\dot{\theta}=0}
=\frac{1}{2}\gamma_1 v'\theta+\frac{1}{4}\gamma_2 v'\sin2\theta.
\label{dissipationpotential}
\end{equation}

\begin{figure}
\includegraphics[width=\columnwidth]{fig1}
\caption{(Color online) Effective potential $U_\text{eff}(\theta)$ for shear alignment of a uniform nematic liquid crystal in the 2D plane.  If the viscosity ratio $|\gamma_2/\gamma_1|\leq1$ (as in the dashed red curve), the effective potential has no local minima, and the director tumbles.  If $|\gamma_2/\gamma_1|>1$ (as in the solid blue curve), the effective potential has local minima, and the director aligns at one of those minima.  The plot is drawn with $\gamma_1>0$, $\gamma_2<0$ (as in typical experimental materials), and $v'>0$.}
\end{figure}

This expression for $U_\text{eff}(\theta)$ is plotted in Fig.~1.  From this figure, we can see that the effective potential can have two possible shapes, depending on the viscosity ratio $|\gamma_2/\gamma_1|$.  If $|\gamma_2/\gamma_1|\leq1$, the effective potential is a monotonically increasing or decreasing function of $\theta$, with no local minima.  In that case, the director tumbles continuously toward lower values of $U_\text{eff}$.  The direction of tumbling depends on the sign of $v'$.  A positive shear flow $v'>0$ induces tumbling with $\dot{\theta}<0$, while $v'<0$ induces $\dot{\theta}>0$.  By contrast, if $|\gamma_2/\gamma_1|>1$, then the the effective potential has a series of local minima, and the director aligns at one of these minima.  To find the alignment orientation, we can solve $\partial U_\text{eff}/\partial\theta=0$, which gives
\begin{equation}
\theta=\frac{1}{2}\cos^{-1}\left[-\frac{\gamma_1}{\gamma_2}\right].
\label{leslieangle}
\end{equation}

Of course, the theory of shear alignment was developed and the alignment angle was calculated many years ago.  This calculation is normally expressed as a balance of stresses, rather than as the minimization of any function.  We suggest that the effective potential provides several insights into this classic calculation.  First, we can see that the magnitude of shear flow $v'$ does not affect the alignment angle, but it does determine the overall magnitude of $U_\text{eff}$.  Hence, a stronger shear flow gives a stronger alignment at the same angle.  Second, we can see that the arccosine in Eq.~(\ref{leslieangle}) has multiple values, and some of them are local minima of $U_\text{eff}$ while others are local maxima.  Reversing the sign of $v'$ reverses the sign of $U_\text{eff}$, and hences exchanges the minima and maxima.  Third, we can see how alignment by shear flow competes with other alignment mechanisms, such as alignment by an applied magnetic field.  The effective potential $U_\text{eff}$ derived from shear flow can simply be added to the magnetic free energy $-(\Delta\chi/2\mu_0)(\bm{H}\cdot\hat{\bm{n}})^2$, or to any other free energy terms, and the equilibrium director can be determined by minimization of the total effective free energy.

We note that the same physical state of the liquid crystal can be described by multiple angles ($\theta$, $\theta\pm\pi$, $\theta\pm2\pi$, \ldots), and hence the same physical state has multiple values of the effective potential.  This problem of a multi-valued effective potential is analogous to the problem of motion in a hurricane on a circular railroad track, as discussed in Sec.~II(B).  We can interpret the analogy by working in terms of the nematic director $\hat{\bm{n}}=(\cos\theta,\sin\theta)$.  The two components of $\hat{\bm{n}}$ are analogous to the 2D plane, and the constraint $|\hat{\bm{n}}|=1$ is analogous to the track that constrains the motion.  Alternatively, we can interpret the analogy by working in terms of the 2D nematic order tensor $Q_{ij}=S(2n_i n_j-\delta_{ij})$, where $S$ is the scalar order parameter.  Here, the two independent components $Q_{xx}=-Q_{yy}=S\cos2\theta$ and $Q_{xy}=Q_{yx}=S\sin2\theta$ are analogous to the 2D plane, and the thermal free energy that determines $S$ provides an approximate constraint on the motion, analogous to the track.  In either case, the effective potential is locally well-defined, under small rotations of the physical state.  However, there are different branches of the effective potential, depending on which branch of the angle $\theta$ is chosen, and it is not meaningful to compare different branches.

As we mentioned in the Introduction, previous theoretical research has studied the effects of shear flow on the isotropic-nematic transition~\cite{Olmsted1990,Olmsted1992}.  Near this transition, one must consider the two independent components of the nematic order tensor \emph{without} a strong constraint on the scalar order parameter $S$.  This problem is analogous to motion in the 2D plane without a track.  In that case, the effective potential involves an integral that is path-dependent, and hence is not even locally well-defined.  Thus, the concept of an effective potential may not be useful for that problem.

\section{Reverse tilt domains under simple shear flow}

In this section, we apply the concept of minimizing an effective potential to a nonuniform liquid crystal.  For a simple example of a nonuniform liquid crystal with no defects, we consider the dynamics of reverse tilt domains under shear flow.

\begin{figure}
\includegraphics[width=\columnwidth]{fig2}
\caption{Example of reverse tilt domains separated by a domain wall.  The top and bottom surfaces of the cell have strong planar anchoring, and an electric or magnetic field is applied across the thickness of the cell, in the $y$ direction.}
\end{figure}

The concept of reverse tilt domains is illustrated in Fig.~2.  When a nematic liquid crystal is confined to a narrow cell with strong anchoring conditions, and then subjected to an electric or magnetic field above the Fr\'eedericksz transition, the director field becomes nonuniform across the thickness of the cell.  It aligns with the anchoring direction near the walls, and tilts toward the field direction in the interior.  Ideally, it would tilt in the same orientation for all horizontal positions.  However, in typical experiments, the director tilts in a positive or negative orientation in different parts of the cell.  The regions of different tilt are called reverse tilt domains, and the narrow regions between these domains are domain walls~\cite{Shenoy1999,Lee2006,Wang2007}.

In the simple geometry of Fig.~2, there is a symmetry between the domains of positive and negative tilt on the left and right sides.  Because of that symmetry, the domains have equal free energy, and neither domain will grow or shrink.  In some cases, an experimenter might want to break the symmetry, in order to favor positive or negative tilt.  One method to break the symmetry is to prepare surfaces with a pretilt.  With modified anchoring conditions, the surface can induce the director field to have a slight tilt away from the planar orientation, in a positive or negative direction.  Another method is to tilt the applied electric or magnetic field.  This tilted field favors a the corresponding tilted domain, and disfavors the other.  These two methods for breaking the symmetry can certainly be described by a free energy.  With a specified surface pretilt or bulk tilted field, one can calculate the free energy difference between domains of positive and negative tilt.  Based on this free energy difference, one can predict how one domain grows and the other shrinks.

Now consider a third method to break the symmetry by applying a shear flow $\bm{v}=(v' y,0)$.  Under shear flow, one type of domain is closer to the favored shear alignment angle, and hence is compatible with the flow.  By comparison, the other type of domain is farther from the favored angle, and is less compatible with the flow.  The question is:  Can this method for breaking the symmetry be described by an effective potential?  Under shear flow, is there an effective potential difference between domains of positive and negative tilt, which determines how one domain grows and the other shrinks?

To answer that question, we extend the effective potential argument of the previous section to a nonuniform liquid crystal in a reverse tilt domain.  Suppose the director field is $\hat{\bm{n}}(y,t)=(\cos\theta(y,t),\sin\theta(y,t))$, and the applied electric field is $\bm{E}=(0,E)$.  The free energy density then becomes
\begin{equation}
F=\frac{1}{2}K\left(\frac{\partial\theta}{\partial y}\right)^2 - \frac{1}{2}\epsilon_0 \Delta\epsilon E^2 \sin^2 \theta,
\end{equation}
where $\Delta\epsilon$ is the dielectric anisotropy, and we assume a single Frank constant $K$.  Following the argument of Eqs.~(\ref{dissipationgeneral})--(\ref{dissipationpotential}), we construct the dissipation function, differentiate it with respect to $\dot{\theta}$ to find the dissipative force, and integrate it with respect to $\theta$ to find the dissipative part of the effective potential density,
\begin{equation}
\int d\theta\left[\frac{\delta D}{\delta\dot{\theta}}\right]_{\dot{\theta}=0}
=\frac{1}{2}\gamma_1 v'\theta+\frac{1}{4}\gamma_2 v'\sin2\theta.
\end{equation}
Combining the free energy and the dissipative terms gives the total effective potential density
\begin{align}
U_\text{eff}=&\frac{1}{2}K\left(\frac{\partial\theta}{\partial y}\right)^2 - \frac{1}{2}\epsilon_0 \Delta\epsilon E^2 \sin^2 \theta \nonumber\\
&+\frac{1}{2}\gamma_1 v'\theta+\frac{1}{4}\gamma_2 v'\sin2\theta.
\label{effectivepotentialRTD}
\end{align}

Now that we have derived the effective potential density, we can use it to calculate the steady-state director field, just as we are accustomed to using the free energy density to calculate the equilibrium director field.  In particular, we can construct the Euler-Lagrange equation
\begin{align}
0=&\frac{\delta U_\text{eff}}{\delta\theta}\\
=&-K\frac{\partial^2 \theta}{\partial y^2}-\frac{1}{2}\epsilon_0 \Delta\epsilon E^2 \sin2\theta+\frac{1}{2}\gamma_1 v'+\frac{1}{2}\gamma_2 v'\cos2\theta. \nonumber
\end{align}
This equation is equivalent to the Ericksen-Leslie equation for the steady-state director field in the Fr\'eedericksz transition under shear flow, and it is difficult to solve exactly.

As a simpler alternative, we make a variational ansatz for the steady-state director field $\theta(y)=\theta_0 \cos(\pi y/d)$, which satisfies the planar anchoring conditions at $y=\pm d/2$.  We insert this ansatz into the effective potential density~(\ref{effectivepotentialRTD}) and then average over the thickness of the cell to obtain
\begin{align}
U_\text{eff}^\text{average}=&\frac{\pi^2 K \theta_0^2}{4 d^2}+\frac{\epsilon_0 \Delta\epsilon E^2}{2}\left[J_0 (2\theta_0)-1\right]\nonumber\\
&+\frac{\gamma_1 v' \theta_0}{\pi}+\frac{\gamma_2 v'}{4} \bm{H}_0 (2\theta_0),
\end{align}
where $J_0$ and $\bm{H}_0$ are the Bessel and Struve functions, respectively.  Near the Fr\'eedericksz transition, for $\theta_0 \ll 1$, we can expand as a power series in $\theta_0$ to obtain
\begin{align}
U_\text{eff}^\text{average}=&\frac{(\gamma_1 + \gamma_2)v' \theta_0}{\pi}
+\frac{\epsilon_0 \Delta\epsilon(E_c^2-E^2)\theta_0^2}{2}\nonumber\\
&-\frac{4\gamma_2 v' \theta_0^3}{9\pi}
+\frac{\epsilon_0 \Delta\epsilon \theta_0^4}{8}+\cdots,
\end{align}
where $E_c=[(\pi^2 K)/(2\epsilon_0 \Delta\epsilon d^2)]^{1/2}$ is the critical field.  From this series, we can see how shear flow changes the Fr\'eedericksz transition.  In the absence of flow, for $v'=0$, the effective potential has an exact symmetry between positive and negative tilt $\theta_0$.  Above the critical field, there are two minima at $\theta_0 = \pm[2(1-E_c^2/E^2)]^{1/2}$, and these two minima have the same effective potential.  By contrast, for $v'\neq0$, the power series has odd terms that break the symmetry between positive and negative tilt.  The shear flow acts as an effective field that favors one sign of $\theta_0$.  Hence, the two minima are shifted, and one minimum becomes lower in effective potential than the other.  For that reason, the domain wall between neighboring domains in Fig.~2 will move, so that the domain with lower effective potential will grow, and the domain with higher effective potential will shrink.

We have performed numerical simulations of the dynamics of two reverse tilt domains separated by a wall, using the same $Q$ tensor method as in our previous article~\cite{Tang2019}.  These simulations confirm that the the domain of lower effective potential grows, and the domain of higher effective potential shrinks.  The velocity of the wall between these domains is proportional to the shear rate $v'$, and hence to the difference of effective potential between the two domains.  These results confirm that the effective potential provides a useful way to understand which domain is favored by the imposed shear flow.

\section{Dowser and bowser states under Poiseuille flow}

In this section, we consider the motion of a disclination between the dowser and bowser states in a narrow liquid-crystal cell.  This problem has already been studied using an effective potential concept by Emer{\v{s}}i{\v{c}} \emph{et al}.~\cite{Emersic2019}.  We show that their effective potential concept is consistent with the general approach presented in this article.

The dowser state has been found experimentally in several studies by Pieranski \emph{et al.}~\cite{Pieranski2016a,Pieranski2016b,Pieranski2017,Pieranski2019a,Pieranski2019b}.  It has the structure shown schematically in Fig.~3a.  Suppose that a liquid-crystal cell has strong homeotropic anchoring on both sides.  The simplest director configuration is just a uniform vertical alignment, shown in the right side of the figure.  However, under some circumstances, the director field might form a more complex state, shown in the left side of the figure, which Pieranski \emph{et al.}\ have called the dowser state.  In the dowser state, the director rotates through $180^\circ$ from the top to the bottom surface.  At any interface where the uniform and dowser states meet, the liquid crystal must have a disclination of topological charge $\pm1/2$, shown in the middle of the figure.

\begin{figure}
\includegraphics[width=\columnwidth]{fig3a}
\includegraphics[width=\columnwidth]{fig3b}
\caption{(Color online) (a)~Dowser and uniform states, separated by a disclination, in the absence of flow.  (b)~Dowser and bowser states, separated by a disclination, in the presence of Poiseuille flow (indicated by the red arrows).}
\end{figure}

In general, the dowser has a higher elastic free energy than the uniform state, because the dowser has director gradients while the uniform state does not.  In equilibrium, the dowser region shrinks and the uniform region grows, so that the liquid crystal can reduce its total free energy.  This process occurs by motion of the disclination at the interface.  In the example of Fig.~3a, the disclination moves to the left to reduce the dowser region and increase the uniform region.

In the experiments of Ref.~\cite{Emersic2019}, Emer{\v{s}}i{\v{c}} \emph{et al}.\ stabilize the dowser state by applying planar Poiseuille flow.  Poiseuille flow is a parabolic flow profile $\bm{v}=({v_\text{max}(1-4y^2/d^2)},0)$, so that the velocity is zero at the top and bottom surfaces $y=\pm d/2$, and is maximum in the middle of the cell, as shown in red in Fig.~3b.  Poiseuille flow includes shear flow $\partial v_x/\partial y$ with one sign in the upper half of the cell, and the opposite sign in the lower half of the cell.  This shear flow induces alignment of the director field with one sign in the upper half and the opposite sign in the lower half.  The profile of shear alignment angle across the thickness is similar to the director profile in the dowser state.  Hence, one might expect the dowser state to be compatible with Poiseuille flow.  By contrast, when the uniform state is exposed to Poiseuille flow, it deforms into the bow-like director profile on the right of Fig.~3b, which Emer{\v{s}}i{\v{c}} \emph{et al}.\ call the ``bowser'' state.  One might expect the bowser state to be less compatible than the dowser with Poiseuille flow.  Indeed, the experiments demonstrate that a large enough Poiseuille flow causes the dowser state to grow and the bowser state to shrink.

We would like to understand the stabilization of the dowser state through the same type of effective potential concept as in the previous sections.  In particular, we would like to see how the Poiseuille flow affects the effective potential of the dowser in comparison with the bowser state.

For this calculation, we repeat the argument of Sec.~IV with two small differences:  There is no applied electric field $E=0$, and the shear rate for Poiseuille flow is given by $v' = \partial v_x /\partial y = -8v_\text{max}y/d^2$.  Hence, the effective potential density becomes
\begin{align}
U_\text{eff}=&\frac{K}{2}\left(\frac{\partial\theta}{\partial y}\right)^2 -\frac{4\gamma_1 v_\text{max}y\,\theta}{d^2}-\frac{2\gamma_2 v_\text{max}y\sin2\theta}{d^2}.
\label{effectivepotentialbowserdowser}
\end{align}
We must integrate this density over the thickness of the cell for both bowser and dowser states.

For the bowser state, the simplest assumption for the director field is just the uniform $\theta(y)=\pi/2$.  By putting this assumption into the effective potential~(\ref{effectivepotentialbowserdowser}) and averaging over the thickness of the cell, we obtain just
\begin{equation}
U_\text{eff}^\text{bowser}=0.
\label{ueffbowser}
\end{equation}

For a more detailed model of the bowser, we could use the higher-order expression $\theta(y)=(\pi/2)+\theta_0 \sin(2\pi y/d)$, which is vertical at the top and bottom surfaces as well as in the center of the cell, and is tilted away from vertical in opposite senses in the upper and lower halves.  Putting this assumption into the effective potential, expanding as a power series for small $\theta_0$, and averaging over the cell thickness gives
\begin{equation}
U_\text{eff}^\text{average}=-\frac{2(\gamma_1-\gamma_2)v_\text{max}\theta_0}{\pi d}+\frac{\pi^2 K\theta_0^2}{d^2}
\end{equation}
Minimizing this expression over $\theta_0$ gives
\begin{equation}
\theta_0 = \frac{(\gamma_1-\gamma_2)v_\text{max}d}{\pi^3 K}.
\end{equation}
Hence, Poiseuille flow transforms the uniform state into a bowser with director variation $\theta_0$ proportional to $v_\text{max}$.  Putting that expression back into the effective potential gives corrections to Eq.~(\ref{ueffbowser}).  However, we will not need those corrections in the argument below.

For the dowser state, we must be careful to choose the appropriate quadrant for the angle $\theta$.  In choosing the quadrant, we use the following physical argument:  Suppose that the disclination moves to the right, so that the bowser is transformed into the dowser.  In the upper half of the cell, the director rotates counter-clockwise to $\theta>\pi/2$.  In the bottom half of the cell, the director rotates clockwise to $\theta<\pi/2$.  Hence, the simplest assumption for the director field is
\begin{equation}
\theta(y)=
\begin{cases}
\pi(1-y/d), & \text{for } 0<y<d/2,\\
-\pi y/d, & \text{for } -d/2<y<0.
\end{cases}
\label{dowseransatz}
\end{equation}
In other words, we must put a branch cut for $\theta$ at $y=0$, the same height as the disclination.  This choice of quadrant corresponds to the issue discussed in Sec.~II(B) for the effective potential of a particle  that is constrained to move on a closed loop.  The effective potential is a multi-valued function, and our choice of the branch must be consistent to compare the bowser and dowser states.

By putting assumption~(\ref{dowseransatz}) for the director field into the effective potential~(\ref{effectivepotentialbowserdowser}) and averaging over the cell thickness, we obtain
\begin{equation}
U_\text{eff}^\text{dowser}=\frac{\pi^2 K}{2d^2}-\frac{v_\text{max}}{d}\left(\frac{\pi\gamma_1}{6}-\frac{\gamma_2}{\pi}\right).
\label{ueffdowser}
\end{equation}
In typical experimental materials, we have $\gamma_2<0$, and hence the term in parentheses is positive.

We can now compare the effective potentials of the bowser and the dowser in Eqs.~(\ref{ueffbowser}) and~(\ref{ueffdowser}), respectively.  When the Poiseuille flow velocity $v_\text{max}$ is low, the unfavorable elastic term dominates the effective potential for the dowser, and hence $U_\text{eff}^\text{bowser}<U_\text{eff}^\text{dowser}$.  By contrast, when $v_\text{max}$ is high, the favorable dissipative term dominates the effective potential for the dowser, and hence $U_\text{eff}^\text{bowser}>U_\text{eff}^\text{dowser}$.  The two effective potentials are equal at the velocity
\begin{equation}
v_\text{max}^*
=\frac{\pi^2 K}{2d}\left(\frac{\pi\gamma_1}{6}-\frac{\gamma_2}{\pi}\right)^{-1}.
\end{equation}
Hence, the effective potential concept shows quantitatively that the bowser is preferred for $v_\text{max}<v_\text{max}^*$ and the dowser for $v_\text{max}>v_\text{max}^*$.

We can extend this concept to model the motion of the disclination driven by a difference of effective potential.  If the disclination moves to the right by a distance $\delta x$, then an area $d\,\delta x$ is transformed from bowser to dowser, so the total effective potential changes by $d\,\delta x(U_\text{eff}^\text{dowser}-U_\text{eff}^\text{bowser})$.  Hence, the effective potential generates a force of $F_\text{potential}=-d(U_\text{eff}^\text{dowser}-U_\text{eff}^\text{bowser})$ acting on the disclination.  In addition, the motion of the disclination with velocity $u$, with respect to the Poiseuille flow with velocity $v_\text{max}$, generates a drag force of $F_\text{drag}=-\eta(u-v_\text{max})$, where $\eta$ is the drag coefficient for the disclination.  A classic result for this drag coefficient~\cite{Imura1973}, discussed in our previous paper~\cite{Tang2019}, is $\eta=(\pi\gamma_1/4)\log[d/(2r_\text{core})]$, where $r_\text{core}$ is the disclination core radius.  (This minimal model assumes equal Frank constants, flow viscosity $\alpha_4$ much greater than rotational viscosity $\gamma_1$, and all other viscosities equal to zero.)  When the drag force cancels the effective potential force, the disclination moves at the steady-state velocity
\begin{align}
\label{dowservelocityplanar}
u&=v_\text{max}-\frac{d}{\eta}(U_\text{eff}^\text{dowser}-U_\text{eff}^\text{bowser})\\
&=v_\text{max}+\frac{2v_\text{max}[1-(6\gamma_2)/(\pi^2\gamma_1)]-(6\pi K)/(d\gamma_1)}{3\log[d/(2r_\text{core})]}.\nonumber
\end{align}
In this result, the first term shows that the disclination is carried along by the Poiseuille flow, and the second term shows the extra (positive or negative) motion induced by the difference of effective potential between bowser and dowser.

\begin{figure}
\includegraphics[width=\columnwidth]{fig4}
\caption{(Color online) Three-dimensional (3D) geometry of dowser and bowser states, separated by a twisted disclination, in the presence of Poiseuille flow (indicated by the red arrows).}
\end{figure}

The 2D geometry of a disclination between bowser and dowser necessarily shows both motion carried along by the Poiseuille flow and motion induced by the effective potential difference.  As a conceptual exercise, one might want to separate these two effects, and see only motion induced by the effective potential difference.  For that reason, we consider the 3D system shown in Fig.~4.  In this geometry, the Poiseuille flow is in the $x$ direction, the director field is in the $(x,z)$ plane, and the boundary between dowser and bowser occurs at $y=0$.  Hence, the disclination runs along the $x$-axis, and the director around the disclination has a 3D twisted structure.  Hence, the Poiseuille flow carries the disclination along its own length, in the $x$ direction.  By contrast, the effective potential difference pushes the disclination in the $y$ direction, so that the bowser grows and the dowser shrinks, or vice versa.  The force from the effective potential is the same as in the previous case, while the drag force is $F_\text{drag}=-\eta u$.  Hence, the forces balance when the disclination moves at the steady-state velocity
\begin{equation}
u=\frac{2v_\text{max}[1-(6\gamma_2)/(\pi^2\gamma_1)]-(6\pi K)/(d\gamma_1)}{3\log[d/(2r_\text{core})]}
\label{dowservelocitytwisted}
\end{equation}
in the $y$ direction.

To test the effective potential approach, we perform numerical simulations of a moving disclination between bowser and dowser states, under imposed Poiseuille flow.  We use the same $Q$ tensor method as in our previous article~\cite{Tang2019}.  In this method, the free energy density is
\begin{equation}
F=-\frac{1}{4}a Q_{ij}Q_{ij} + \frac{1}{16} b (Q_{ij}Q_{ij})^2 + \frac{1}{16}L(\partial_k Q_{ij})(\partial_k Q_{ij}),
\end{equation}
and the dissipation function density is
\begin{equation}
D=\frac{1}{16}\Gamma_1 B_{ij}B_{ij} + \frac{1}{4}\Gamma_2 B_{ij}A_{ij} + \frac{1}{2}\alpha_4 A_{ij}A_{ij},
\end{equation}
where
\begin{align}
B_{ij}&=\dot{Q}_{ij} - \omega_m (\epsilon_{mlj}Q_{il}+\epsilon_{mli}Q_{lj}),\nonumber\\
A_{ij}&=\frac{1}{2}(\partial_i v_j + \partial_j v_i),\nonumber\\
\bm{\omega}&=\bm{\nabla}\times\bm{v},
\end{align}
and $\epsilon_{ijk}$ is the Levi-Civita symbol.  The coefficients in this tensor representation are related to the coefficients in the director representation by $K = L S^2$, $\gamma_1 = \Gamma_1 S^2$, and $\gamma_2 = \Gamma_2 S$, where $S$ is the scalar order parameter.  For the simulations, we use parameters $d=2$ $\mu$m, $K=10$ pN, $\gamma_1 = 0.08$ Pa s, $\gamma_2 = -0.09$ Pa s, similar to the liquid crystal 5CB.  We choose $a$ and $b$ so that $S_\text{bulk}=(a/b)^{1/2}=1$ and $r_\text{core}=(K/a)^{1/2}=0.2$ $\mu$m.  (The core radius $r_\text{core}$ must be exaggerated for the numerical algorithm, but the results are not very sensitive to this value.)  We impose the Poiseuille flow profile, and then solve the hydrodynamic equation for the director field to find the steady-state velocity of the disclination.

\begin{figure}
\includegraphics[width=\columnwidth]{fig5}
\caption{(Color online) Simulation results for the disclination velocity $u$ as a function of Poiseuille flow velocity $v_\text{max}$, in comparison with the predictions of the effective potential theory, which are in Eq.~(\ref{dowservelocityplanar}) for the planar disclination and Eq.~(\ref{dowservelocitytwisted}) for the twisted disclination.  Numerical parameters are given in the text.}
\end{figure}

In Fig.~5, the black circles show the simulation results for the disclination velocity $u$ as a function of the Poiseuille flow velocity $v_\text{max}$.  By comparison, the black solid line shows the effective potential prediction of Eq.~(\ref{dowservelocityplanar}).  These two calculations show consistent behavior.  When $v_\text{max}=0$, the disclination moves to the left, with $u<0$.  The dowser shrinks and the bowser grows, so that the system can reduce its elastic free energy.  By comparison, when $v_\text{max}$ becomes large enough in the positive direction, the dowser is stabilized, and then the disclination moves to the right, with $u>0$, so that the dowser grows and the bowser shrinks.  We can regard this change as driven by the dissipative part of the effective potential.  Although the simulations and theory agree very well for small $v_\text{max}$, there are some discrepancies for larger $v_\text{max}$.  To address these discrepancies, we can add corrections to the effective potential calculation by allowing the director field to respond to the Poiseuille flow, but we do not present those results here.

We also perform numerical simulations of the twisted disclination between bowser and dowser.  These simulations use the same procedure as for the planar disclination, except that the Poiseuille flow is in the $x$ direction and the $Q$ tensor is in the $(x,z)$ plane.  The simulation results are shown by the red squares in Fig.~5, while the effective potential prediction of Eq.~(\ref{dowservelocitytwisted}) is shown by the red dashed line.  Again, the simulations and theory agree very well for small $v_\text{max}$, although there are some discrepancies for larger $v_\text{max}$.  We can see that the slope of $u$ as a function of $v_\text{max}$ is smaller for the twisted disclination than for the planar disclination, because the twisted disclination moves in response to effective potential differences but is not carried by Poiseuille flow.

Our effective potential theory for the motion of the disclination between bowser and dowser is equivalent to the theory developed by Emer{\v{s}}i{\v{c}} \emph{et al}.~\cite{Emersic2019}.  The significance of our work is to show how this theory fits into the general formalism for an effective potential that includes dissipative contributions.  In particular, we can see that this concept is the same effective potential that enters into shear alignment at the Leslie angle, and into the motion of reverse tilt domains.

\section{Discussion}

From the classical mechanics analogy in Sec.~II, we can see that the effective potential concept does not always apply.  The main issue that determines whether it works is the number of degrees of freedom.  If there is only one degree of freedom, the effective potential can be defined unambiguously.  If there is more than one degree of freedom, the effective potential might or might not be a uniquely defined quantity, depending on whether the dissipative force has a nonzero curl.  In an intermediate case, a system might have a closed path within a space with more than one degree of freedom, like a train on a circular track.  In that case, the effective potential is a multi-valued function, which still might be useful provided that one is careful with branches of the function.

A 2D nematic liquid crystal has both a magnitude $S$ and a direction $\theta$ of orientational order.  For that reason, it really is a system with more than degree of freedom.  However, in many cases, the magnitude is approximately fixed, and only the direction can vary.  In that sense, it is analogous to a train on a circular track of allowed states.  Hence, the effective potential is a multi-valued function, which depends on which branch of the angle $\theta$ is chosen.  Indeed, the multi-valued nature can be seen because the effective potential depends on $\theta$, not just on $\sin2\theta$ and $\cos2\theta$.

This multi-valued nature of the effective potential might or might not be important, depending on the problem.  For shear alignment in a uniform system, the multi-valued nature is not important as long as the director remains near a specific angle.  However, it becomes important if the director can tumble through a full circle.  For the reverse tilt domain problem, the surface anchoring constrains the director near a specific angle.  Hence, all physical states are on a single branch of the $\theta$ function, and the multi-valued nature of the effective potential is not important.  For the dowser and bowser, there is a disclination at the interface between the two states, and hence we cannot work consistently with a single branch of the $\theta$ function.  Even so, we can still compare the effective potentials of dowser and bowser, provided that we choose the quadrant of angle in a consistent way that matches the physical motion of the disclination.

In conclusion, this article has shown that the effective potential concept is a useful way to think about shear alignment of liquid crystals.  Using the effective potential, we can see that one state is more favorable than another in the presence of imposed shear flow.  Hence, the effects of shear flow can be understood as minimization of effective potential, just as the effects of applied fields or surface alignment can be understood as minimization of the free energy.  This type of argument is more intuitive than just solving the hydrodynamic equations, and we expect that it will be useful for a range of nonequilibrium alignment problems.

\acknowledgments

We would like to thank S. \v{C}opar, P.~D. Olmsted, and U. Tkalec for helpful discussions.  This work was supported by National Science Foundation Grant DMR-1409658.

redpajama_set_name: RedPajamaArXiv


Finished my Pyttipanna Shawl, using my new Summer Colors hand painted by www.lavendersheep.comThe body colorway is "Copper Kettle"
The lace edge colorway is "Brosa"This yarn is hard to sell, I have a overwhelming urge to hoard it for myself. Love this stuff! Limited supply at my local yarn store in Hoodriver, OR. "Knot Another Hat"


text:
Category: Willis Trophy 2020
Bob Willis Trophy 2020 ~ Final ~ Somerset v Essex ~ A Herculean Struggle
8th Oct 2020 24th Jan 2021 'farmer white'
All Bob Willis Trophy matches were played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching the ECB's enhanced live stream of the match, without which this report would not have been possible. The stream was watched with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live.
Bob Willis Trophy Final. Somerset v Essex. 23rd, 24th, 25th, 26th and 27th September 2020. Lord's.
Somerset. B.F.G. Green, T.A. Lammonby, T.B. Abell (c), E.J. Byrom, G.A. Bartlett, S.M. Davies (w), L. Gregory, C. Overton, J.H. Davey, M.J. Leach, J.A. Brooks.
Essex. N.L.J. Browne, Sir Alistair Cook, T. Westley (c), D.W. Lawrence, P.I. Walter, R.N. ten Doeschate, A.J.A. Wheater, S.R. Harmer, A.P. Beard, S.J. Cook, J.A. Porter.
Overnight. Somerset 301 and 227 for 7. Essex 337 for 8 inns closed. Somerset lead by 191 runs with three second innings wickets standing.
Final day – A Herculean struggle
This was another day of push and counter-push between two sides who had given their all in this match in pursuit of the Bob Willis Trophy. The day had begun with half an hour of cricket rather akin to a concert support act before the main event. Interesting and competitive in itself, but never likely to rival what was to follow. That is not to decry the batting of Overton and Davey who played well enough in lifting the Essex target ahead of the anticipated declaration; or the bowling of Harmer and Porter, who bowled tightly to limit the target and perhaps reduce the length of time their batsmen would have to bat. But the main issue of the day, irrespective of whether Essex made an attempt on the target, would be: could Somerset take ten wickets? Any other outcome would see Essex winning the trophy.
Bob Willis Trophy Final 2020 ~ Somerset v Essex ~ Fourth Day ~ Lammonby keeps the trophy room door open for Somerset
2nd Oct 2020 24th Jan 2021 'farmer white'
All Bob Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching the ECB's enhanced live stream of the match, without which this report would not have been possible. The stream was watched with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live.
Overnight. Somerset 301. Essex 271 for 6. Essex trail by 30 runs.
Fourth day. 26th Sept. – Lammonby keeps the trophy room door open
Another glorious century for Tom Lammonby lit up the afternoon of another day of dimpsy autumnal weather. But whilst Lammonby shone brightly for Somerset, it was Essex who gained the high ground in the match by taking a first innings lead. From that moment, under the tie-breaker rules for the final, Somerset had to force victory to win the Bob Willis Trophy. For Essex, a draw would suffice. The start was not auspicious for Somerset. With Essex needing 31 runs for the lead, Somerset's normally disciplined bowlers took a few overs to find their lines and strayed too often onto leg stump. Two balls deflected off the pads to fine leg, each for four leg byes, and a leg glance for four from Adam Wheater the result. A boundary driven to the Nursery End off Overton by the nightwatchman, Porter, added to the pressure on Somerset. A no ball from Lewis Gregory and the four byes which finally took Essex into the lead completed a dispiriting start for Somerset's screen-watching supporters.
Bob Willis Trophy Final 2020 ~ Somerset v Essex ~ Third day ~ Alistair Cook ~ A class above
27th Sep 2020 24th Jan 2021 'farmer white'
Third day. 25th September – Alistair Cook – a class above
I once saw Robert Stephens, subsequently a theatrical knight, play King Lear at Stratford, co-incidentally in the same year that Marcus Trescothick first played for Somerset. I have, over a lifetime, seen most of Shakespeare's plays. Most of the individual performances, enjoyed in the moment, have since merged into a lifetime of theatrical experience. Some still stand out, but Robert Stephens' performance stands out above all. It was the most complete and compelling individual theatrical performance I have ever seen. So compelling, the entire cast joined in the applause, a rare occurrence in the theatre.
Bob Willis Trophy Final 2020 ~ Somerset v Essex ~ Second Day ~ "Come on! Run, the ball!"
Overnight. Somerset 119 for 4.
Second day. 24th September – "Come on! Run, the ball!"
"Come on! Run, the ball!" I heard myself shouting at my laptop. I am not normally inclined to shout at my laptop, except perhaps after the latest update designed to 'improve' something that had worked perfectly well up to that point. Craig Overton had just driven Aaron Beard straight along the ground towards the Pavilion boundary. An Essex fielder was in hot pursuit and the ball was running a little more slowly than the fielder. Somerset were 184 for 5 and Overton and Byrom were building a partnership that was pulling Somerset out of the indeterminate first innings marshlands of 139 for 5 towards the more solid ground beyond 200. The involuntary shout was indicative of the gnawing tension inherent in a closely fought match on which hangs a trophy.
Bob Willis Trophy Final 2020 ~ Somerset v Essex ~ First day ~ A dimpsy day
Essex. N.L.J. Browne, Sir Alistair Cook, T. Westley (c), D.W. Lawrence, P.I. Walter, R.N. ten Doeschate, A.J.A. Wheater, S.R. Harmer, A.P.Beard, S.J. Cook, J.A. Porter.
Toss. Essex. Elected to field.
First day. 23rd September – A dimpsy day
Somerset have been here before. In 2008, 2010, 2016 and again in 2019 they began the final match of the season with the possibility of winning their first County Championship. In the end of course, the trophy went elsewhere. 2020 is different. This is not the County Championship. The Bob Willis Trophy is a much-truncated affair in comparison with the County Championship. Six matches instead of fourteen. Not all the stronger teams have played each other, and no team has played another on a home and away basis. And so, instead of in a league of the strongest teams, the domestic first-class trophy is to be decided in a five-day grand final played at Lord's.
Bob Willis Trophy ~ Worcestershire v Somerset ~ Final Day ~ 9th September ~ Through to the final
All Bob Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching Worcestershire CCC's live stream of the match without which the report would not have been possible. The stream was watched throughout with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live; and to enable him to form his own view of the play.
Bob Willis Trophy. Central Group. Worcestershire v Somerset 6th, 7th, 8th and 9th September 2020. Worcester.
Somerset. B.G.F. Green, T.A. Lammonby, T.B. Abell (c), G.A. Bartlett, E.J. Byrom, S.M. Davies (w), C. Overton, L. Gregory, J.H. Davey. M.J. Leach, J.A. Brooks.
Worcestershire. D.H.K. Mitchell, J.D. Libby, T.C Fell, J.A. Haynes, B.L. D`Oliveira, M.H. Wessels, O.B. Cox (w), E.G. Barnard, J. Leach (c), J.C. Tongue, D.Y. Pennington.
Overnight. Somerset 251 and 193. Worcestershire 200 and 58 for 2. Worcestershire need 187 runs to win with eight wickets standing.
Final day. 9th September – Through to the final
In the end, on the final day, Somerset pushed over their wall. Worcestershire resisted in phases, and at times raised the level of anxiety in Somerset supporters' minds more than is comfortable. At one point the Worcestershire batsmen made a dash for the line, but throughout the innings no partnership lasted long enough to apply the persistent pressure to Somerset necessary to force a win. At the crunch, the Somerset bowling proved too strong for the Worcestershire batsmen on a pitch on which each innings total was lower than the one before. It was a day of greater tension than the end result or the cold facts of the result portray. Throughout the final day Worcestershire were under the greater pressure, but only at the very end did the task seem beyond them. Until then, however regularly Somerset took wickets, Worcestershire's target always seemed within range of an exceptional innings or a determined partnership.
Bob Willis Trophy ~ Worcesterhire v Somerset ~ Third day ~ 8th September ~ Lammonby's student masterclass
9th Sep 2020 24th Jan 2021 'farmer white'
Third day. 8th September – Lammonby's student masterclass
"I think we might have found a batsman," said the incoming text even before Tom Lammonby had reached his century. In the end, Lammonby carried his bat at the age of 20 with Somerset under the most intense pressure, and with a place in the final of this competition at stake. It was a performance to rank with some of the best Somerset innings the author has witnessed in over six decades of watching Somerset play cricket.
Bob Willis Trophy 2020 ~ Worcestershire v Somerset ~ 8th September ~ Second day ~ Irresistable
Overnight. Somerset 251. Worcestershire 14 for 0. Worcestershire trail by 237 runs.
Second day. 7th September – Irresistible
The first hour looked like it might put Somerset's first innings total into a worrying perspective, at least from a Somerset point of view. Somerset resumed with Davey and Overton beneath an autumnal sky. The distant, narrow bands of cloud which lined the horizon beyond the Basil D'Oliveira Stand were marble smooth and white with a tinge of grey. Across the sky, between the bands, were the narrowest strips of blue. It set a relaxed mood which the Worcestershire batting seemed to pick up as it faced Somerset bowling unable to derive much by way of help from the pitch or the overhead conditions.
Bob Willis Trophy ~ Worcestershire v Somerset ~ First Day ~ 6th September 2020 ~ Zeitgeist of an earlier age
Toss. Somerset. Elected to bat.
First day. 6th September – Zeitgeist of an earlier age
The cricket on the first day of this match was a universe away from the frenetic boundary clearing and wide line bowling of the T20 match these two teams had fought out less than a week before. Nearly 450 runs in that match in what, in the Bob Willis Trophy, would be less than half a day's cricket. The T20 was played in the modern high-sided stadium that is Edgbaston, although the R.E.S Wyatt Stand at the Birmingham End retains all the character of an earlier age. This match was played in front of the majestic Worcester cathedral on the other side of the Severn. The ground itself retains virtually all the character of old, including a small area of trees just beyond the boundary to the left of the Ladies Pavilion. I have taken shelter from a searing sun under those trees on more than one visit to Worcester. T20 has caught the sporting zeitgeist of the modern age, the huge and more diverse nature of its crowds is testimony to that. The Bob Willis Trophy brings with it the zeitgeist of an earlier age.
Bob Willis Trophy ~ Somerset v Gloucestershire ~ Final Day ~ The final reckoning
25th Aug 2020 24th Jan 2021 'farmer white'
All Bob Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching Somerset CCC's excellent multi-camera live stream of the match without which the report would not have been possible. The stream was watched throughout with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live; and to enable him to form his own view of the play.
Bob Willis Trophy. Central Group. Somerset v Gloucestershire. 22nd, 23rd, 24th and 25th August 2020. Taunton.
Somerset. E.J. Byrom, T.A. Lammonby, T.B. Abell (c), J.C. Hildreth, G.A. Bartlett, S.M. Davies (w), C. Overton, R.E. van der Merwe, J. Overton, J.H. Davey. J.A. Brooks.
Gloucestershire. C.D.J Dent, B.G. Charlesworth, G.L. van Buuren, T.C. Lace, G.T. Hankins, R.F. Higgins, G.H. Roderick, G.F.B. Scott, D.A. Payne, J. Shaw, M.D. Taylor.
Overnight. Somerset 237 and 223 for 1 dec. Gloucestershire 76 and 63 for 8. Gloucestershire need another 322 runs to win with two second innings wickets standing.
Final day. 25th August – The final reckoning
Even the rain could not stop Somerset this time. It blew through with such force that the damp it left behind was blown away by the wind that brought it, with a little help from some sun. The rain had gone by breakfast time, the ground dried out quickly enough for the cricketers to take an early lunch, and the match was over in time for your correspondent to enjoy an afternoon ice cream on a bench overlooking the Blackdowns. It is not quite the same as enjoying one whilst watching the cricket from in front of the Garner Gates, but the victory over Gloucestershire was more than enough compensation for that.
Bob Willis Trophy 2020 ~ Somerset v Gloucestershire ~ Third day ~ Deja vu
Overnight. Somerset 237 and 223 for 1 dec. Gloucestershire 76 and 14 for 3. Gloucestershire need another 371 runs to win with seven second innings wickets standing.
Third day. 24th August – In the hands of Damocles
"Only Somerset could declare their second innings on 223 for 1 on the second day and then draw the match with the opposition on 97 for 9," said the incoming text an hour into what would have been the afternoon session of the third day. It is to be hoped that the person who sent the text is not a prophet, for of the still possible results that is one of them. It was a curious sight, watching the covers on the live stream. Curious because the stands beyond them were devoid of people. Not that stands devoid of people are in any way out of the ordinary in these strange times. It was more that, in the past, if you were at a match when it rained heavily, most people headed for the nearest cover, or bar. But not everyone. There were always one or two people who sat it out in the stands, waterproofs on and umbrella up, if only to keep their seats dry. It was the absence of those people, who always seemed to be there, that struck home. Strange times indeed.
Bob Willis Trophy 2020 ~ Somerset v Gloucestershire ~ Second Day ~ "Most Satisfactory"
Overnight. Somerset 237. Gloucestershire 13 for 4. Gloucestershire trail by 224 runs with six first innings wickets standing.
Second day. 23rd August – "Most satisfactory"
This was another day of stunning Somerset success. In the first three matches of this competition the opposition has been overwhelmed. It might have stood against Somerset early in a match but by the end it had been, in cricketing terms, devastated. There is still cricket to be played in this match, Gloucestershire still have seven wickets standing, but they are 371 runs short of victory in a competition in which no team has thus far scored more than 166 in an innings against Somerset. Only two opposition batsmen have passed 50, whereas six centuries have been scored by Somerset batsmen. On the basis of those statistics there will be many bruised arms in Somerset and beyond as supporters repeatedly pinch themselves to seek reassurance that they are actually awake.
Bob Willis Trophy 2020 ~ Somerset v Gloucestershire ~ First day ~ "That'll do"
23rd Aug 2020 24th Jan 2021 'farmer white'
Toss. Gloucestershire. Elected to field.
First day. 22nd August – "That'll do"
In the first match of the Bob Willis Trophy George Bartlett received a sickening blow on the helmet from Marchant de Lange. It stopped play for a considerable amount of time whilst he was ministered to and the required concussion tests were carried out. He carried on, but to my eye showed less fluency after the blow. He did not have quite the same composure he had shown before it. He was checked twice more and doggedly continued for some time before he was out. He has missed the two intervening matches under the ECB concussion regulations. You would not have known it on the first day of this match. He played an innings of sheer joy, at least for the watching Somerset supporter. It was an innings too of crucial importance for his team. He came to the wicket at 44 for 3, was still there at 176 for 9 and left undefeated on 100 after he and Jack Brooks had extended Somerset's total to 237. Applause would have resounded around the ground in other times. All that could stand would have been on their feet, hands clapping above their heads as he jumped a celebratory jig in the middle of his 100th run. And again, a ball later, as the players walked off. It was a transformation to warm the cockles of a Somerset heart.
Bob Willis Trophy 2020 ~ Warwickshire v Somerset ~ Final day ~ "That was cruel"
All Bob Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching Warwickshire CCC's live stream of the match without which it would not have been possible. The stream was watched throughout with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live; and to enable him to form his own view of the play.
A different type of take on a frustrating day:—
Bob Willis Trophy. Central Group. Warwickshire v Somerset. 15th, 16th, 17th, and 18th August 2020. Edgbaston.
Warwickshire. R.M.Yates, R.M.H. Rhodes (c), S.R. Hain, I.R. Bell, M.J. Lamb, M.G.K. Burgess (w), T.T. Bresnan, A.T. Thomson, H.J.H. Brookes, C.N. Miles, O.H. Hannon-Dalby.
Somerset. E.J. Byrom, T.A. Lammonby, T.B. Abell (c), J.C. Hildreth, T. Banton, S.M. Davies (w), L. Gregory, C. Overton, R.E. van der Merwe, J.Overton, J.H. Davey.
Overnight. Warwickshire 121 and 104 for 6. Somerset 413 for 9 dec. Warwickshire trail by 188 runs with four second innings wickets standing.
Final day. 18th August – "That was cruel"
"That was cruel," said the incoming text seconds after the match was abandoned. And it was, at least in cricketing terms. And long drawn out cruelty at that. So much potentially hung on the outcome of this match. The points position at the top of the three groups was so tight, winning or drawing might make the eventual difference between qualifying for the final and not.
Bob Willis Trophy 2020 ~ Warwickshire v Somerset ~ Third day ~ The broadsword and the rapier
Overnight. Warwickshire 121. Somerset 214 for 6. Somerset lead by 93 runs with four first innings wickets standing.
Third day. 17th August – The broadsword and the rapier
Batsmen not out overnight are always vulnerable first thing in the morning, either to a good ball or to a lapse in concentration. At least, anecdotally to my mind, it has seemed that way over the years. It was Hildreth on the second day here, Gregory on the third. In the second over, Bresnan bowled an innocuous-looking ball wide of off stump, Gregory essayed what had all the appearance of a speculative drive and the ball, from the direction in which the players looked across the screen, was caught at mid-off. Somerset 215 for 7. Van der Merwe joined Davies and drove a straight ball from Hannon-Dalby off the back foot through point for four. He attempted to steer the next ball to third man, the ball cut away off the pitch and the faint edge carried straight to Burgess behind the stumps. Somerset 226 for 8, a lead 105, and the previous evening's hopes of a score of 300 were receding.
Bob Willis Trophy 2020 ~ Warwickshire v Somerset ~ Day two ~ Glowering skies – Glorious cricket
Overnight. Warwickshire 121. Somerset 80 for 2. Somerset trail by 41 runs with eight first innings wickets standing.
Second day. 16th August – Glowering skies – glorious cricket
A glowering sky presented itself when the live stream woke up on the second morning of this match. Then, the dreaded words presented themselves. "Start delayed. Wet outfield. Rain." The wide-angle camera located in the Pavilion presented its view of the Birmingham skyline. A skyline that was doing battle with those clouds. Half-buildings with their heads in the clouds. I could almost feel the dank atmosphere. The sullen-looking outfield didn't help. Neither did the Blackdowns, for they looked depressed and expectant of rain. Perhaps, like me, they knew of the importance of Somerset getting enough time on the field in this match to force a win. It is the halfway point of a five-match competition in which only two of the three group winners can progress to the final. Even five wins might not guarantee a place. Weather could be a crucial factor in determining the outcome, and the forecast for the final three days of this match is poor. The players will have had their own view, but the supporter dreamt of them only having to bat once, perhaps, dream of dreams, of reaching 300 and then letting slip the … Well, not exactly the dogs of war, but you get my drift after the Somerset bowling performance in the first Warwickshire innings.
Bob Willis Trophy 2020 ~ Warwickshire v Somerset ~ First day ~ Oh, to be in Birmingham …
Toss. Warwickshire. Elected to bat.
First day. 15th August – Oh, to be in Birmingham
The picture on the Somerset CCC website brought an immediate flood of memories. It was taken from the upper reaches of the five-storey Pavilion at Edgbaston. Beyond the far end of the ground can be seen the Birmingham skyline. If you know where to look you can pick out the iconic structure of the ultra-modern library. It is a view I have taken in from the packed members lounge on many an occasion on my annual visits to Edgbaston for Somerset's Championship match there. I have had many an enjoyable chat in that lounge with Somerset and Warwickshire supporters both. Not today. Today, as the camera scans the empty stands it is another stark cricketing reminder of the times through which we are passing. The sun is shining, and the shadows of the players are clear on the pitch. It looks a perfect day for cricket. A perfect day to sit in my usual haunt at Edgbaston, square of the wicket in the Hollies Stand, where last year I and two or three other Somerset supporters formed an informal Somerset cricket symposium for the day. Not today. As it is, with the sun shining in Birmingham, I am ensconced in an armchair watching the Edgbaston live stream on an elderly laptop with a rain-filled sky obliterating my treasured view of the Blackdowns.
Bob Willis Trophy 2020 ~ Northamptonshire v Somerset ~ Final day ~ Making a difference – Craig and Jamie Overton
All Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching Northamptonshire CCC's live stream of the match. The stream was watched with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live.
Bob Willis Trophy. Central Group. Northamptonshire v Somerset. 8th and 9th August 2020. Northampton.
Northamptonshire. E.N. Gay, B.J. Curran, R. Vasconcelos, R.I Keogh, C.O. Thurston, L.A Procter, A.M. Rossington (c) (w), G.K. Berg, Blessing Muzarabani, B.D. Glover, B.W. Sanderson.
Somerset. E.J. Byrom, T.A. Lammonby, T.B. Abell (c), J.C. Hildreth, T. Banton, S.M. Davies (w), C. Overton, R.E. van der Merwe, J.Overton, J.H. Davey, J.A. Brooks.
Overnight. Somerset 166 and 15 for 1. Northamptonshire 67. Somerset lead by 114 runs with nine second innings wickets standing.
Final day. 9th August – Making a difference – Craig and Jamie Overton
One of the things that is supposed to give most satisfaction in life is to make a difference. There is no doubt about who made the difference in this match. I am sure there would be only one answer from a bruised Northamptonshire. Somerset won by 167 runs. Together Craig and Jamie Overton scored a total of 148 runs over the two innings. Nineteen short to be sure. But perhaps the nine wickets and five catches they took between them might make up for that. Batting and bowling, it was an outstanding performance by all the Somerset bowlers, but the Overton brothers were, as they say, up front and central to it.
Willis Tropy 2020. Northamptonshire v Somerset. First day. A madcap day at the cricket.
9th Aug 2020 24th Jan 2021 'farmer white'
Bob Willis Trophy. Central Group. Northamptonshire v Somerset. 8th, 9th, 10th, and 11th August 2020. Northampton.
First day. 8th August – A madcap day at the cricket
The journey to my armchair is somewhat shorter than the one from home or a hotel to the cricket used to be, but the anticipation builds up just the same as the early part of the morning wears on. There is nothing quite like the first morning of a first-class cricket match. I was once asked if I would be travelling to a particular match. "Yes," I answered, "but I can only get the time to go to one day. I will probably gauge which day to go to from the score." The questioner looked at me in horror. "First day!" he said, almost ordering me to comply. He had a point. By the start of the subsequent days the match is part shaped. On the first morning the anticipation is boundless. After that, it is bounded by what has gone before. The only time I have had a feeling quite like the one I have on the morning of a four-day Championship match was on the mornings of those great set-piece battles that were the acutely anticipated quarter and semi-finals of the Gillette Cup in its heyday. The prospect of glory or elimination, so near the prize, concentrated the mind wonderfully.
Wonderful ~ Bob Willis Trophy ~ Somerset v Glamorgan ~ Final day
All Willis Trophy matches are being played behind closed doors due to the coronavirus restrictions in place. This report was therefore written following a day watching Somerset CCC's live stream of the match. The stream was watched with the commentary muted and with notes being taken to enable the author to replicate as far as possible his experience of watching matches live. He would like to pay tribute to the excellence of the Somerset CCC's multi-camera live stream without which the writing of this report would not have been possible.
Bob Willis Trophy. Central Group. Somerset v Glamorgan. 1st, 2nd, 3rd, and 4th August 2020. Taunton.
Somerset. E.J. Byrom, T.A. Lammonby, T.B. Abell (c), J.C. Hildreth, G.A. Bartlett/B.G.F. Green*, S.M. Davies (w), C. Overton, R.E. van der Merwe, J.Overton, J.H. Davey, J.A. Brooks.
*B.G.F. Green played on the final two days as a concussion replacement for G.A. Bartlett.
Glamorgan. N. J. Selman, C.R. Hemphrey, W.T. Root, C.B. Cooke (c) (w), D.A. Douthwaite, G.G. Wagg, K.A. Bull, K.S. Carlson, M. de Lange, M.G. Hogan, R.A.J. Smith,
Final day. 4th August – Wonderful
Somerset finished this match off with a near-clinical performance in just over an hour. To the fore was Jamie Overton in a longer spell than he might normally bowl. He will leave Somerset at the end of this season, but no-one watching the live stream could question his commitment to Somerset's cause in this match. He has celebrated as one with the team on the field, and when the ball was in his hands, bowled with focus, determination, and no little skill. The ball with which he removed Kieran Bull just before the end was one to place in the display cabinet of the memory bank. It was essentially the same ball with which he removed Nick Selman, lbw, with the third ball of the innings on the previous evening. On this occasion no pad intervened, and the off stump was spectacularly uprooted. Unforgettable.

redpajama_set_name: RedPajamaCommonCrawl


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Q: MS bot framework, identify connected client support Card Actions and Hero Card How can identify that connected client supports Card Action and Hero Card? If there is any way I can use Card Action against channel specific API call.
This feature is specially required to identify request is coming from Skype or Skype Web (Developer version)?

A: There is no way to distinguish between the Skype desktop client and the web client but they should have feature parity with the new release.

redpajama_set_name: RedPajamaStackExchange


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Жорж дьо Режибюс () е швейцарски спортист и учител по физкултура. Режибюс е човекът, положил основите на футбола в България, след като донася първата футболна топка в страната през 1894 г. Преподава в Мъжката гимназия във Варна в продължение на две години.

Биография
Роден е в градчето Епаланж, в близост до Лозана. Син е на италианеца Пиер дьо Режибюс, родом от Болоня. През 1889 г. се премества в Ивердон ле Бен, където работи в Швейцарската железница.

Спортна кариера
Режибюс се занимава с няколко вида спорт. Той е гимнастик, боксьор, борец и футболист. По време на футболната си кариера играе като вратар за Грасхопър. Освен това е дипломиран инструктор по гимнастика. Описван е като "среден на ръст, с широк гръден кош, с подходяща за спортист физика".

В България
През 1894 г. Режибюс и още няколко швейцарски учители по физическо възпитание (сред които Шарл Шампо и Луи Айер) са поканени от министъра на образованието на Княжество България Георги Живков, за да спомогнат за развитието на спорта в страната. Жорж става преподавател във Варненската мъжка гимназия, където на 14 май 1894 г. е проведен първият български футболен мач.

Режибюс се превръща в организатор и рефер на училищните футболни двубои, а понякога участва и като играч. Мачовете се провеждат на различни места във Варна, като един от терените е бил на мястото на днешната Морска градина. Един от учениците, практикуващи футбол под ръководството на Режибюс, е бъдещият премиер на България Васил Коларов.

Режибюс преподава в България в продължение на 2 години и напуска страната на 12 юли 1896 г.

Късна дейност
След като се завръща в Швейцария, Режибюс отваря собствено кафене. По-късно заминава за Египет, където преподава в продъление на две десетилетия. В края на Първата световна война отново се връща в Швейцария, прекарвайки остатъка от живота си в Лозана.

Памет
На 14 май 2016 г. във Варна се провежда възстановка на първия футболен мач в България. В ролята на Режибюс се превъплъщава футболистът Божидар Искренов.

Източници

Швейцарски футболисти
Швейцарски гимнастици
Швейцарци в България
Швейцарски учители
Швейцарски треньори по футбол
Швейцарски треньори по гимнастика
Починали в Лозана

redpajama_set_name: RedPajamaWikipedia


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No Reality Show for LeAnn Rimes, Eddie Cibrian
No go on the reality show for LeAnn and Eddie.
By Michael Preston
Published Mar 10, 2011 at 1:51 AM | Updated at 2:00 AM EST on Mar 10, 2011
Singer LeAnn Rimes arrives at 2011 MusiCares Person of the Year Tribute to Barbra Streisand at Los Angeles Convention Center on February 11, 2011 in Los Angeles, California.
Despite rumors the contrary, LeAnn Rimes and fiance Eddie Cibrian won't be coming in for the celebrity reality treatment any time soon.
Though a source told US Magazine that a "deal is nearly done" on March 9, Rimes took to her Twitter account to refute the story, reports PopEater.
"I don't know how many times I have to say Eddie and I would never do a reality show about our lives," she wrote on the social media site.
Rimes' publicist also strongly denied any notion that the couple would be participating in a show, calling the idea "absolutely untrue."
Celebrity Hookups: David Foster, Katharine McPhee Marry
Allen Berezovsky/Getty Images
"There has never been, nor are there, any plans for LeAnn and Eddie to do a reality show," the publicist added.
Rimes and Cibrian were engaged in December 2010 after each left their former spouses due to a relationship they started while filming a Lifetime movie in 2008.
Selected Reading: PopEater, US Weekly, People
Top Entertainment Photos


text:
Politics Trudeau switches targets in bid to cut Mulcair's momentum in polls
Trudeau switches targets in bid to cut Mulcair's momentum in polls
Campbell Clark
Published July 21, 2015 Updated May 15, 2018
The dynamics have changed. Where once Justin Trudeau shrugged off the NDP, insisting his opponent was Stephen Harper, the Liberal Leader has made the telltale decision to switch targets.
Now, the Liberals are campaigning like the third-place party, attacking Thomas Mulcair and the New Democrats rather than keeping their guns trained solely on Mr. Harper and the Conservatives.
That is driven by the reversal of fortunes for the two opposition parties in which the NDP has taken the lead in many polls, with the Liberals in third. But many Liberals are also feeling that the fall election is shaping up as a referendum on whether Mr. Harper and the Conservatives stay or go – and that those in the latter camp will coalesce behind whichever party seems mostly likely to displace them.
And if that is the case, they fear, Mr. Trudeau cannot afford to go into the official campaign too far behind Mr. Mulcair. So they are trying to knock him back in the weeks before the writ is dropped.
On Monday, while Mr. Mulcair was launching a tour of southern Ontario ridings that have mostly been unthinkable long-shots for New Democrats, the Liberals sent out Adam Vaughan, a left-leaning downtown Toronto MP, to attack the NDP for policies that he said would help the wealthy, not the middle-class.
The party put out a press release in which Mr. Vaughan cited a collage of complaints, starting with the fact that the NDP opposes Mr. Trudeau's proposal for middle-class tax breaks aimed at low- and middle-income families, and that it opposes the Liberals' plan to hike taxes for more affluent Canadians. But it was rounded out with charges that Mr. Mulcair would re-open the Constitution (to try to abolish the Senate) and make it easier for Quebec to separate (by setting the threshold at 50 per cent plus one.)
Many Liberal candidates think it is about time for such a move. They have been watching the party's poll numbers darken, along with some of their own election prospects. It is time "to raise questions" about Mr. Mulcair and the NDP, one said, such as whether their policies are really progressive, and what the party leader thinks of free trade. "Who would be their finance minister?" another candidate asked rhetorically. Expect Mr. Trudeau to be "increasingly feisty" in making these points.
Liberal ranks have experienced a loss of confidence. Some have also lost faith in the people around Mr. Trudeau, saying they should have done more to consolidate their gains when he was enjoying a wave of popularity, and questioning whether they have a clear plan to reverse the decline. Others see the drop in polls as the inevitable result of the non-stop barrage of Conservative attack ads that say Mr. Trudeau is not ready – and they think the real test will come when the campaign really heats up.
But many Liberals have another reason for wanting to hit the NDP now: the idea that Liberal and NDP voters are part of a pool that wants change and will turn to whomever they think can provide it.
Some Liberal candidates said they feel a palpable desire for change – not necessarily that Mr. Harper's supporters have turned against him, but that those who were not really his supporters are more fed up. But that sentiment is more about Mr. Harper than the alternatives.
Of course, the goal of the Conservatives is to make those alternatives seem less palatable to voters.
For now, they are still mostly focused on Mr. Trudeau's Liberals, who, after all, were historically the alternative, and are more centrist. But they have a plan: If that succeeds, they will attack the NDP as risky, too.
It is the Liberals who cannot afford to wait. Mr. Trudeau now leads a nervous party. It fears what the NDP long feared: being out of the race before a campaign officially begins. The Liberals have to try to cut Mr. Mulcair's momentum back. And in doing so, they are underlining how much things have changed.
Mulcair defends Quebec policy as he launches Ontario tour
NDP eager to shed big-spender image as party crafts social policies
Trudeau vows Liberal environment plan will 'be putting a price on carbon'
Follow Campbell Clark on Twitter @camrclark


Renowned bariatric surgeon and advocate of plant-based eating Garth Davis, M.D. has partnered with Memorial Hermann Memorial City Medical Center and the Rawfully Organic Co-Op to open Houston's first hospital-based organic produce stand.
What does it take to make a brand?


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Landscape (5 of 5): ‹ Prev‹ Previous ArtistAll Artists
WADE HOEFER
Wade Hoefer Biography
The painter Wade Hoefer was born in Long Beach, California and studied Fine Art at California College of Art and Craft in Oakland. Hoefer, who has become an influential figure in the vast realm of Western landscape painting, has exposed throughout the U.S. in major museums and prominent collections.
Wade Hoefer was born in 1948 in Long Beach, CA. In 1972 he earned an M.F.A. at California College of Art and Craft in Oakland, CA.
1997 "Trio of Landscape Artists: Katherine Bowling, April Gornik, Wade Hoefer," David Floria Gallery, Aspen, CO
1996 "American Landscape Painting in the 90's." Harn Museum, Gainesville, FL
1995 Monique Knowlton Gallery, NY, NY California Center for the Arts Museum, Escondido Beach, CA
Anne Reed Gallery, Ketchum, ID
Los Angeles Municipal Art Gallery, Los Angeles, CA
1994 Olga Dollar Gallery, San Francisco, CA
Thomas Babeor & Co., La Jolla, CA
1994 Aurobora Press, San Francisco, CA
1993 Edith Caldwell Gallery, San Francisco, CA
Miller/Block Gallery, Boston, MA
1992 Elizabeth Leach Gallery, Portland, OR
1991 Patricia Faure Gallery, Los Angeles, CA
1990 Gibbs Museum of Art, Charleston, SC
Little Rock Museum of Contemporary Art, Little Rock, AK
1989 Cheney Cowles Museum of Art, Spokane, WA
University of New Mexico, Las Cruces, NM
Palm Springs Museum of Art, Palm Springs, CA
1987 Janet Steinberg Gallery, San Francisco, CA
Patricia Faure Gallery, Los Angeles, CA
San Francisco Art Institute, San Francisco, CA
1986 Richmond Art Center, Richmond, CA
1985 Gabriella Cardazza, Venice, Italy
1981 Tom Luttrell Gallery, San Francisco, CA
1978 Oakland Museum, Oakland, CA
1975 National Gallery of Art, Washington, D.C.
SELECTED COLLECTIONS
The Estee Lauder Companies, Inc.
Microsoft Corporation, Los Angeles, CA
Bank of America, World Headquarters, San Francisco, CA
Frederick R. Weisman Foundation, Los Angeles, CA
J.P. Morgan, Los Angeles, CA
Twigg-Smith Foundation, Honolulu, HI
Thurston Twigg-Smith, Honolulu, HI
Oakland Museum, Oakland, CA
University Art Museum Berkeley, CA
San Diego Museum of Art, San Diego, CA
San Francisco Arts Commission, S.F. International Airport, CA
Philip Morris Companies, Inc., New York, NY
General Electric Company, New York, NY
General Electric Company, Fairfield, CT
University Art Museum at Berkeley, CA
Fidelity Investors, Boston, MA
Samuel P. Harn Museum of Art, Gainesville, FL
Mason Phelps, La Jolla, CA
Frederick Weisman, Los Angeles, CA
Edgar Bronfman Sr., Sun Valley, ID
Budd Bishop, Director, Samuel P. Harn Museum of Art, Gainesville, FL
Stephanie French and Amory Houghton III, New York, NY
Jim Hedges, H.H.L. Global Investments, Naples, FL
Goldie Hawn, Los Angeles, CA
Nicolas Cage, Los Angeles, CA
Tommy Chong, Santa Monica, CA
Robert Bergman and Marie Krane Bergman, Chicago, IL
Dyersbyrg Corporation, New York, NY
The Aspen Times, "Trio of Landscape Artists at David Floria Gallery:
Katherine Bowling, April Gornik, Wade Hoefer," Karrie Click, Feb. 8, 1997
Art in America, "Wade Hoefer at Monique Kowlton,"
Gerrit Henry, February 1996, p. 89
Los Angeles Times, "Wade Hoefer," Susan Kandel, September 27, 1991
Art in America, "Wade Hoefer at Modernism," Gay Morris, December, 1992
The San Diego Union Tribune, "Contemporary Artist Envisions Imaginary Worlds," Robert L. Pincus, November 4, 1993
The Washington Post, "This Land is Your Land," Ferdinand Protzman, October 31, 1995
1997 Artist in Residence, Tamarind Institute, Albuquerque, NM
1992 Artist in Residence, Experimental Workshop, San Francisco, CA
2006 Susan Street Fine Art Gallery, Solano Beach, CA
2005 Elins Eagles Smith Gallery, San Francisco, CA
2004 Lisa Kurts Gallery, Nashville, TN
Patricia Faure Gallery,
Santa Monica Gallery Camino Real, Boca Raton, FL
Galerie de Bellefeuille, Montreal, Canada
2003 Flanders Contemporary Art, Minneapolis, MN
"Wade Hoefer – Manuel Neri", Anne Reed Gallery, Ketchum, ID
Michael Dunev Art Projects, Torroella de Montgri (Spain)
Galerie Janos, Paris
2002 Miller Block Gallery, Boston, MA
Gallery Camino Real, Boca Raton, FL
Ron Judish Gallery, Denver, CA
David Floria Gallery, Aspen, CO
Hemphill Fine Arts, Washington, DC
Hidell Brooks Gallery, Charlotte NC
Lisa Kurts Gallery, Nashville, TN
2000 Michael Dunev Art Projects, Torroella de Montgri', Spain
David Beitzel Gallery, New York
Hemphill Fine Arts, Washington DC
John Berggruen Gallery, San Francisco, CA
Lisa Kurts Gallery, Memphis TN
Miller/Block Gallery, Boston MA
Flanders Contemporary Art, Minneapolis, MN
Patricia Faure Gallery, Santa Monica, CA
1998 Patricia Faure Gallery, Santa Monica, CA
Aurobora Press, San Francisco, CA
1997 "New Monotypes," Monique Knowlton Gallery, NY, NY
Jean-Pierre Prebet, Roanne
Franca Monique Knowlton Gallery, NY
1996 "Multi-panel Landscape Paintings, " Monique Knowlton Gallery
1995 Monique Knowlton Gallery, NY, NY
Modernism, San Francisco, CA
Jacques Kaplan, Kent, CT
Hemphill Fine Arts, Washington, D.C.
Galerie Janos, Paris, France
1994 Miller/Block Gallery, Boston, MA
1993 Soma Gallery, San Diego, CA
1992 Modernism, San Francisco, CA
1991 Patricia Faure, Los Angeles, CA
1990 Haines Gallery, San Francisco, CA
Gallery Paule Anglim, San Francisco, CA
1985 Portland Museum of Art, Portland, OR
Richmond Art Center, Richmond, CA
Acme Art, San Francisco, CA
Gabriella Cardazza, Venice, Italy
1983 Grapestake Gallery, San Francisco, CA
1976 Eliane Ganz, San Francisco, CA


text:
Simon Stijl, né le  à Harlingen et mort dans cette ville le , est un homme politique et un poète néerlandais.

Biographie
Stijl fait ses études de médecine dans les universités de Franeker et de Leyde, où il pratique la médecine. Diplômé en 1754, il rentre à Harlingen, dans la province de Frise et s'installe comme médecin. De 1761 à 1766, il préside la société médicale . Passionné de théâtre et d'histoire, il écrit fréquemment des poèmes en parallèle à son activité. En 1762, il fonde un théâtre et dirige une troupe d'amateurs. Il écrit quelques pièces et interprète souvent le premier rôle.

Membre du comité révolutionnaire de Harlingen, sa réputation lui vaut d'être élule , au début de la Révolution batave, à l'assemblée provisoire de la Frise, puis représentant de la province aux États généraux des Provinces-Unies le . En juin, il rentre en Frise et devient président de l'assemblée des représentants du peuple de Frise. En , il est élu, contre sa volonté, député du district de Sneek à la première Assemblée nationale batave et est nommé à la commission chargée de rédiger la constitution de la République batave. Cependant, il ne se rend à La Haye qu'à partir du mois de juillet. Il s'y signale en prenant position en faveur d'une constitution fédérale. Le , le comité rend son rapport, un projet de compromis entre les idées unitaristes et fédéralistes et Simon Stijl prononce un discours pour le présenter. Le projet, modifié et amendé jusqu'au mois de , est rejeté par référendum le . Au même moment a lieu le renouvellement de l'Assemblée et n'est pas réélu, à sa grande satisfaction. Il se retire de la vie politique et reprend son activité de médecin.

Publications
 De torenbouw van het vlek Brikkekiks in het landschap Batrachia
 De vryer na de kunst
 Krispyn filozoof (1768)
 De Mityleners (1768)
 De opkomst en bloei der Vereenigde Nederlanden (1774)
 Het leven van Jan Punt (1781)

Bibliographie

Liens externes

  Sa fiche sur parlement.com
  Présentation sur la Bibliothèque numérique de la littérature néerlandaise (DBNL)

Député de l'Assemblée nationale batave
Poète néerlandais du XVIIIe siècle
Poète néerlandais du XIXe siècle
Médecin néerlandais du XVIIIe siècle
Médecin néerlandais du XIXe siècle
Naissance en février 1731
Décès en mai 1804
Décès à 73 ans


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