text:
\section{Introduction}

When a heavy fluid is supported or accelerated by a light fluid, the physical phenomenon of small perturbations at the interface growing with time is called Rayleigh-Taylor (RT) instability. Because of the gravitational field, the light fluid rises as a bubble structure and the heavy fluid sinks as a spike structure. When the amplitude is equal to the wavelength, the disturbance begins to become asymmetric, and then grows nonlinearly, and finally enters the turbulent mixing stage\cite{Dimonte2004}. The RT instability is a typical and fundamental interfacial instability that plays an important role in many fields, such as inertial confinement fusion \cite{Ping2019, Lindl2004, Jacquemot2017}, supernova explosions \cite{Ribeyre2004, Fraschetti2010, Hillebrandt2013}, meteorology \cite{Agee1974, Jiang2013}, and geophysics \cite{Houseman1997, Kaus2007, Ghosh2020}. Therefore, the study of RT instability has important theoretical significance and application value, and has aroused considerable interest and been developed rapidly.

The study of RT instability began with the classical linear stability theory proposed by Rayleigh and Taylor, and they discovery that the amplitude of the disturbance in the early stage has exponential growth law\cite{Rayleigh1882, Taylor1950}. In the past few decades, scholars have proposed many numerical methods to study RT instability, including the monte carlo method \cite{Barber2006}, the direct numerical simulation method \cite{Cook2001,Liang2019}, the monotone integrated large eddy simulation \cite{Youngs2009}, the smooth particle hydrodynamics method \cite{Shadloo2013}, the parallel adaptive wavelet collocation method \cite{Reckinger2015}, the phase-field method \cite{Yang2021}, etc. The above methods provide an effective tool for the study of RT instability. By using these methods, authors studied the effects of different physical quantities on RT instability. Wang et al. studied the influence of interface width on the RT instability under weakly nonlinear conditions \cite{Wang2010}. Wei et al. studied the single-mode RT instability problem at low Atwood (At) numbers \cite{Wei2012}. Yang et al. studied the effect of side-wall boundary on RT instability \cite{Yang2021}. Bian et al. systematically analyzed the influence of the disturbed Reynolds number and At number on the late growth of RT instability \cite{Bian2020}.

The above research enriches our in-depth understanding of the RT instability, but at the same time, these conclusions are mainly focus on the macro level, and do not involve concrete thermodynamic non-equilibrium (TNE) information. In order to have a deeper understanding of the TNE evolution law of RT instability systems, we turn to the Boltzmann equation based on non-equilibrium statistical physics, which can not only provide macroscopic fluid dynamics information, but also mesoscopic non-equilibrium information. In the last three decades, the lattice Boltzmann method (LBM) develops rapidly and becomes an effective tool for researching complex dynamics and kinetic behavior, which is self-adaptive in physical description. The discrete Boltzmann method (DBM) is a variant of the standard LBM. Formally, both DBM and LBM use the discrete Boltzmann equation. But in most literature LBM is regarded as a new scheme to solve partial differential equations, while DBM is a coarse-grained physical model based on non-equilibrium statistical physics. It chooses a research perspective and selects a set of kinetic properties to study the system. Thus, it requires that the corresponding kinetic moments describing those properties to keep values in the model simplification \cite{Xu2012,XuAG2018,Xu2021,XuAG2021}. From the perspective of physical modeling, DBM which describes the TNE effect is approximately equivalent to a continuous fluid model and a coarse-grained model. In the region where the Navier-Stokes (NS) model is valid, it is equivalent to the NS equations plus a coarse-grained model of TNE. And in the case of the NS failure, it is equivalent to a modified NS equations plus a coarse-grained model of TNE \cite{Xu2012,Gan2015}. In recent ten years, DBM has been widely used in a variety of complex flow systems \cite{Xu2015,Lai2016,Lin2016,Chen2016,Lin2017,Xu2018,Chen2018,Zhangm2018,GAN2018,LiDM2018,Gan2019,Zhang2019,Ye2020,Chen2020,Lin2020}, and it provides an effective tool to study the non-equilibrium effects in RT instability. Lai et al. studied the influence of compressibility on RT instability, and found that compressibility inhibits the evolution of RT instability in the early stage, but promoted the development in the later stage. At the same time, the TNE also increases with the enhancement of compressibility \cite{Lai2016}. Chen et al. studied the effects of viscosity, heat conduction and Prandtl number on RT instability by using a multiple-relaxation-time DBM \cite{Chen2016}. Lin et al. studied the effect of Reynolds numbers on both global non-equilibrium manifestations and the growth rate of the entropy of mixing though the two-component DBM \cite{Lin2017}. Li et al. used the DBM
to simulate the multi-mode RT instability in a compressible fluid system and explore the evolutionary mechanism \cite{LiDM2018}. Ye et al. used the DBM to explore the influence of Knudsen number on the compressible RT instability, and found that the Knudsen number suppresses the development of RT instability, and also enhances both hydrodynamic non-equilibrium (HNE) and TNE strength \cite{Ye2020}. Chen et al. studied the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability system with the multi-relaxation-time DBM, and studied the complex fluid structure and dynamics process by introducing the morphological boundary length and TNE strength \cite{Chen2020}.

Furthermore, the specific heat ratio is one of the most important parameters to describe the thermodynamic properties of fluids, which is closely related to the compressibility of fluids. It is of great theoretical and application value to study the influence of the specific heat ratio on the evolution of complex fluid system. Bernstein et al. found that the evolution rate of RT instability decreases with the specific heat ratio increasing\cite{Bernstein1982}. Fraley et al. presented a solution for the perturbation growth of density discontinuity caused by shock waves at the material interface, and analyzed the interface asymptotic velocities at different specific heat ratios \cite{Fraley1986}. Livescu et al. found that when the specific heat ratios of the upper and lower fluids are different, the growth rate of RT instability is more sensitive to the change of the specific heat ratio of the lower fluid. However, when the At number is large, the growth rate is less affected by the specific heat ratio of the fluid, and then the equilibrium pressure at the interface becomes the main parameter that affects the compressibility of the system \cite{Livescu2004}. Lafay et al. proved that as the compressibility of the two fluids decreases, the linear growth rate increases, and when the compressibility of two fluids is equal, the linear and nonlinear behaviors are opposite \cite{Lafay2007}. He et al. studied the effect of the interface specific heat ratio on the growth rate of RT instability, and found that when the specific heat ratio of the upper heavy fluid is small, it would hinder the growth of RT instability. And the opposite effect will be achieved when the specific heat ratio of the lower fluid is relatively small \cite{He2008}. Xue et al. found that when the specific heat ratio decreases, the compressibility has a destabilizing effect \cite{Xue2010}. Wang et al. studied the evolution of RT instability related to the low specific heat ratio $(\gamma <5/3)$ in the remnants of the Type Ia supernovae \cite{Wang2011}. Hu et al. studied the impact of the specific heat ratio on the piston effect by simulating eight near-critical fluids \cite{Hu2016}. Zhao et al. studied the bubble growth in compressible RT and RM instabilities, and found that in the RT instability, the adiabatic index and density of the upper fluid increase the amplitude and velocity of the bubble, but reduce the radius of curvature in the early stage, while the influence of the adiabatic index and density of the lower fluid is exactly the opposite\cite{Zhao2020}. These studies have achieved fruitful results and improved our understanding of the physical laws of compressible RT instability.

However, the above research results mainly focus on the description of macroscopic HNE behaviors, and do not contain TNE effect at the intermediate scale. In this paper, the DBM is used to study the effects of the specific heat ratio on RT instability, and both TNE and HNE effects are discussed and analyzed. Furthermore, the non-equilibrium laws of mesoscopic dynamics are presented, which are helpful for us to understand the evolutionary process of multi-scale interface instability. The remaining structure of this paper is as follow: Section \ref{Methodology} introduces the DBM and the details of non-equilibrium quantity extraction. Section \ref{Numerical Simulations} displays the numerical simulation. The effects of the specific heat ratio on RT instability and its physical mechanism are analyzed in detail. Finally, a brief conclusion is given in Section \ref{Conclusions}.

\section{Discrete Boltzmann model}\label{Methodology}

In this work, the discrete Boltzmann equation with the Bhatnagar-Gross-Krook collision term \cite{Zhang2018, Tamura2011, Gan2013} can be described by:
\begin{equation}\label{e5}
\frac{{\partial {f_i}}}{{\partial t}} + {\textbf{v}_i}\cdot\frac{{\partial {f_i}}}{{\partial {\textbf{r}}}} - \frac{{{\textbf{a}}\cdot({\textbf{v}_i} - \textbf{u})}}{{T}}f_i^{eq} =  - \frac{1}{\tau }({f_i} - f_i^{eq}),
\end{equation}
where $f_i$ and $f_i^{eq}$ are the discrete forms of the velocity distribution function and the Maxwellian distribution function, respectively, $t$ is the time, $\textbf{v}_i$ the discrete velocity, $i (=1, 2, \cdots ,N)$ the discrete velocity direction, $\textbf{r}$ the space coordinates, $\textbf{a}$ the external force, $\textbf{u}$ the macroscopic velocity, $T$ the fluid temperature, and $\tau$ the relaxation time.

It can be easily proved that, by means of the Chapman-Enskog multi-scale expansion, the compressible NS equations can be recovered by this model in the hydrodynamic limit:
\begin{eqnarray}\label{e6}
\left\{
\begin{array}{ll}
\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0, &  \\[10pt]
\frac{\partial}{\partial t}(\rho \textbf{u}) + \nabla \cdot (\rho \textbf{u}\textbf{u} + p\textbf{I} + \textit{\textbf{P}}) = \rho \textbf{a}, &  \\[10pt]
\frac{\partial}{\partial t} \Big[\rho \Big(e + \frac{|\textbf{u}|^2}{2}\Big)\Big]+ \nabla \cdot \Big[\rho\textbf{u}\Big(e + T + \frac{|\textbf{u}|^2}{2} \Big) + \textit{\textbf{J}} + \textit{\textbf{P}} \cdot \textbf{u} \Big] \\[10pt]
= \rho \textbf{a} \cdot \textbf{u}, &
\end{array}
\right.
\end{eqnarray}
here, $\rho$ denotes the fluid density, $\textit{\textbf{P}}$ and $\textit{\textbf{J}}$ are quantities related to viscous stress and heat flux respectively, and the specific forms are:
\begin{equation}\label{e7}
\textit{\textbf{P}} = -\mu\Big[\nabla \textbf{u} + (\nabla \textbf{u})^T - \frac{2}{D+n}(\nabla \cdot \textbf{u})\textbf{I}\Big],
\end{equation}
\begin{equation}\label{e8}
\textit{\textbf{J}} = -\kappa \nabla T,
\end{equation}
and $e = [(D+n)/2]T$ is the internal energy per unit mass of the system, $\kappa = (D+n+2)\mu/2$ the thermal conductivity coefficient, $\mu = \tau\rho T = \tau p$ the dynamic viscosity coefficient, and $D$ the space dimension, $n$ the number of additional degrees of freedom introduced except translational freedom. In order to obtain a macroscopic result consistent with the compressible NS equations in the continuous limit condition, the local equilibrium distribution function in the discrete Boltzmann equation needs to satisfy the following seven kinetic moment relations:
\begin{eqnarray}\label{e9}
\sum\limits_{i}f_{i}=\sum\limits_{i}f_{i}^{eq}=\rho,
\end{eqnarray}%
\begin{eqnarray}\label{e10}
\sum\limits_{i}f_{i}\textbf{v}_i
=\sum\limits_{i}f_{i}^{eq}\textbf{v}_i=\rho \textbf{u},
\end{eqnarray}%
\begin{eqnarray}\label{e11}
\sum\limits_{i}f_{i}(\textbf{v}_{i} \cdot \textbf{v}_{i} + \eta_{i}^2)
=\sum\limits_{i}f_{i}^{eq}(\textbf{v}_{i} \cdot \textbf{v}_{i} + \eta_{i}^2)
=\rho \big[(D+n)T+\textbf{u} \cdot \textbf{u}\big],\nonumber\\
\end{eqnarray}%
\begin{eqnarray}\label{e12}
\sum\limits_{i}f_{i}^{eq}\textbf{v}_{i} \textbf{v}_{i}
=\rho (T\mathbf{I} +\textbf{u}\textbf{u}),
\end{eqnarray}%
\begin{eqnarray}\label{e13}
\sum\limits_{i}f_{i}^{eq}(\textbf{v}_{i} \cdot \textbf{v}_{i}+\eta_{i}^2)\textbf{v}_{i}
=\rho \textbf{u}\big[(D+n+2)T+\textbf{u} \cdot \textbf{u}\big],
\end{eqnarray}%
\begin{eqnarray} \label{e14}
\sum\limits_{i}f_{i}^{eq}\textbf{v}_{i}\textbf{v}_{i}\textbf{v}_{i}
=\rho\big[T(\textbf{u}_\alpha \textit{\textbf{e}}_\beta \textit{\textbf{e}}_\chi \delta_{\beta\chi}
+\textit{\textbf{e}}_\alpha\textbf{u}_\beta\textit{\textbf{e}}_\chi \delta_{\alpha\chi}
+\textit{\textbf{e}}_\alpha\textit{\textbf{e}}_\beta \delta_{\alpha\beta} \textbf{u}_\chi)\nonumber\\
+\textbf{u}\textbf{u}\textbf{u}\big],\qquad
\end{eqnarray}%
\begin{eqnarray}\label{e15}
\sum\limits_{i}f_{i}^{eq}(\textbf{v}_{i} \cdot \textbf{v}_{i}+\eta_{i}^2)\textbf{v}_{i}\textbf{v}_{i}
=\rho T \big[(D+n+2)T +\textbf{u} \cdot \textbf{u}\big]\textit{\textbf{e}}_\alpha\textit{\textbf{e}}_\beta \delta_{\alpha\beta}  \nonumber\\
+\rho \textbf{u}\textbf{u}\big[(D+n+4)T+\textbf{u}\cdot\textbf{u}\big].\qquad
\end{eqnarray}%
In fact, the above seven kinetic moment relations can be expressed in a matrix form as below:
\begin{equation}\label{e16}
\textbf{C} \cdot \textbf{f}^{eq} = \hat{\textbf{f}}^{eq},
\end{equation}
where
\begin{equation}\label{e17}
\textbf{f}^{eq} = [f_1^{eq}, f_2^{eq}, \cdots , f_N^{eq}]^{\rm{T}},
\end{equation}
\begin{equation}\label{e18}
\hat{\textbf{f}}^{eq} = [\hat{f}_1^{eq}, \hat{f}_2^{eq}, \cdots , \hat{f}_N^{eq}]^{\rm{T}},
\end{equation}
and $\textbf{C}$ is the coefficient matrix concerning the discrete velocity $\textbf{v}_i$ and the free parameter $\eta_i$. To solve $\textbf{f}^{eq}$ requires that the coefficient matrix should have at least $16\times16$ elements, namely, the velocity model should contain at least 16 discrete velocities. At this point, if $\textbf{C}$ is an invertible matrix, Eq. \ref{e16} leads to:
\begin{equation}\label{e19}
\textbf{f}^{eq} = \textbf{C}^{-1} \cdot \hat{\textbf{f}}^{eq}.
\end{equation}

In this work, 2-dimensional 16-velocity (D2V16) discrete velocity model is adopted\cite{Lin2016}, as shown in Fig. \ref{FIG01}. In the previous work \cite{Lai2016}, there is only one tunable parameter that controls all values of discrete velocities. In the current work, there are four tunable parameters which indicate magnitudes of four groups of discrete velocities. Compared with the former one, the latter discrete velocity model is more flexible in the selection of discrete velocities, and is beneficial to the robustness and accuracy of the DBM. And the discrete velocity value is obtained by these equations:
\begin{equation}\label{e20}
\textit{\textbf{v}}_i= \left\{
\begin{array}{ll}
v_a\Big[\cos\frac{(i-1)\pi}{2},\sin\frac{(i-1)\pi}{2}\Big], & i=1,\cdots,4, \\[10pt]
v_b\Big[\cos\frac{(2i-1)\pi}{4},\sin\frac{(2i-1)\pi}{4}\Big], & i=5,\cdots,8, \\[10pt]
v_c\Big[\cos\frac{(i-9)\pi}{2},\sin\frac{(i-9)\pi}{2}\Big], & i=9,\cdots,12,\\[10pt]
v_d\Big[\cos\frac{(2i-9)\pi}{4},\sin\frac{(2i-9)\pi}{4}\Big], & i=13,\cdots,16,
\end{array}
\right.
\end{equation}
meanwhile, $\eta_i=\eta_0$ when $i=1,\cdots,4$, and $\eta_i=0$ when $i=5,\cdots,16$.
\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.4]{FiG01.eps}
\caption{Sketch of discrete velocity model.}\label{FIG01}
\end{figure}

Both HNE and TNE effects play important roles in non-equilibrium fluid systems. In general, the non-equilibrium information is too complex to be described in detail. Fortunately, the DBM provides an effective tool for studying the non-equilibrium phenomena. Among the seven kinetic moment relations, Eqs. \ref{e9}-\ref{e11} represent the conservation of mass, momentum and energy, respectively, and remain unchanged when the system is moving toward or away from thermodynamic equilibrium. And the TNE information can be extracted from the deviation caused by the $f_{i}$ replacing $f_{i}^{eq}$ in the nonconserved kinetic moments Eqs. \ref{e12}-\ref{e15}.

According to the above ideas, we introduce the kinetic central moments $\textbf{M}_{m,n}^*$ of the velocity distribution function and the equilibrium distribution function \cite{Yan2013},
\begin{eqnarray}\label{e21}
\left\{
\begin{array}{ll}
\textbf{M}_{2}^*(f_i)=\sum\limits_i f_i \textbf{v}_{i}^*\textbf{v}_{i}^*,  \\[10pt]
\textbf{M}_{3}^*(f_i)=\sum\limits_i f_i \textbf{v}_{i}^* \textbf{v}_{i}^*\textbf{v}_{i}^*,\\[10pt]
\textbf{M}_{3,1}^*(f_i)=\sum\limits_i f_i[\textbf{v}_{i}^* \cdot \textbf{v}_{i}^*+\eta_{i}^2]\textbf{v}_{i}^*,\\[10pt]
\textbf{M}_{4,2}^*(f_i)=\sum\limits_i f_i[\textbf{v}_{i}^*\cdot \textbf{v}_{i}^*+\eta_{i}^2]\textbf{v}_{i}^*\textbf{v}_{i}^*,
\end{array}
\right.
\end{eqnarray}
and
\begin{eqnarray}\label{e22}
\left\{
\begin{array}{ll}
\textbf{M}_{2}^*(f_i^{eq})=\sum\limits_i f_i^{eq} \textbf{v}_{i}^*\textbf{v}_{i}^*,   \\[10pt]
\textbf{M}_{3}^*(f_i^{eq})=\sum\limits_i f_i^{eq} \textbf{v}_{i}^* \textbf{v}_{i}^*\textbf{v}_{i}^*,\\[10pt]
\textbf{M}_{3,1}^*(f_i^{eq})=\sum\limits_i f_i^{eq}[\textbf{v}_{i}^* \cdot \textbf{v}_{i}^*+\eta_{i}^2]\textbf{v}_{i}^*,\\[10pt]
\textbf{M}_{4,2}^*(f_i^{eq})=\sum\limits_i f_i^{eq}[\textbf{v}_{i}^*\cdot \textbf{v}_{i}^*+\eta_{i}^2]\textbf{v}_{i}^*\textbf{v}_{i}^*,
\end{array}
\right.
\end{eqnarray}
where $\textbf{v}_{i}^* = \textbf{v}_i - \textbf{u}$, the subscript ``$m, n$'' denotes the reduction of $m$-order tensor to $n$-order tensor. Then, the non-equilibrium quantity can be defined as follows:
\begin{eqnarray}\label{e23}
\boldsymbol{\Delta}_{m,n}^* &=&\textbf{M}_{m,n}^*(f_i)-\textbf{M}_{m,n}^*(f_i^{eq}),
\end{eqnarray}
which $\boldsymbol{\Delta}_{m,n}^*$ describes the information of the thermal fluctuations, including 12 components $\Delta_{2\alpha \beta}^*$, $\Delta_{3\alpha \beta \chi}^*$, $\Delta_{(3,1)\alpha}^*$, $\Delta_{(4,2)\alpha \beta}^*$, $\alpha, \beta, \chi = x$ or $y$. In order to qualitatively analyze the global TNE effect of the system, we define several specific TNE quantities:
\begin{eqnarray}\label{e24}
|\boldsymbol{\Delta}_{2}^*| = |\Delta_{2xx}^*| + |\Delta_{2xy}^*| + |\Delta_{2yy}^*|,
\end{eqnarray}
\begin{eqnarray}\label{e25}
|\boldsymbol{\Delta}_{3,1}^*| = |\Delta_{3,1x}^*| + |\Delta_{3,1y}^*|,
\end{eqnarray}
\begin{eqnarray}\label{e26}
|\boldsymbol{\Delta}_{4,2}^*| = |\Delta_{4,2xx}^*| + |\Delta_{4,2xy}^*| + |\Delta_{4,2yy}^*|,
\end{eqnarray}
\begin{eqnarray}\label{e27}
|\boldsymbol{\Delta}_{3}^*| = |\Delta_{3xxx}^*| + |\Delta_{3xxy}^*| + |\Delta_{3xyy}^*| + |\Delta_{3yyy}^*|.
\end{eqnarray}
And the total TNE quantity can describe the degree of deviation from the equilibrium of the fluid system:
\begin{eqnarray}\label{e28}
|\boldsymbol{\Delta}^*| = |\boldsymbol{\Delta}_{2}^*| + |\boldsymbol{\Delta}_{3,1}^*| + |\boldsymbol{\Delta}_{4,2}^*| + |\boldsymbol{\Delta}_{3}^*|.
\end{eqnarray}

Moreover, the global average TNE strength in the system is defined as:
\begin{eqnarray}\label{e29}
\overline{D} = \frac{1}{L_xL_y}\int_0^{L_x}\int_0^{L_y} |\boldsymbol{\Delta}^*| dxdy,
\end{eqnarray}
the global average viscous stress tensor strength in the system is defined as:
\begin{eqnarray}\label{e30}
\overline{D}_{2} = \frac{1}{L_xL_y}\int_0^{L_x}\int_0^{L_y} |\boldsymbol\Delta_{2}^*| dxdy,
\end{eqnarray}
and the global average heat flux strength in the system is defined as:
\begin{eqnarray}\label{e31}
\overline{D}_{3,1} = \frac{1}{L_xL_y}\int_0^{L_x}\int_0^{L_y} |\boldsymbol\Delta_{3,1}^*| dxdy,
\end{eqnarray}
where $L$ represents the boundary length of the simulation region.

\section{Numerical Simulations}\label{Numerical Simulations}

In this section, numerical simulations are carried out in a two-dimensional rectangular region $\Omega = [-d/2, d/2] \times [-2d, 2d]$. The system with upper and lower layers of fluid is placed in a gravitational field with constant gravitational acceleration, and a cosine disturbance $y_c(x) = y_0\cos(kx)$ is applied at the interface between the two fluids, where $y_0 = 0.05d$, $k = 2\pi/\lambda$ denotes wave number, and $\lambda = d$ the perturbance wavelength. At the initial moment, the system satisfies the static equilibrium condition:
\begin{eqnarray}\label{e32}
\partial_y p_0(y) = -g\rho_0(y),
\end{eqnarray}
where $g$ indicates the magnitude of gravitational acceleration. And the initial conditions of the unstable system are:
\begin{equation}\label{e33}
\left\{
\begin{array}{l}
T_0(y)=T_u,~\rho_0(y)=\frac{p_0}{T_u}\exp{\big[\frac{g}{T_u}\big(2d-y\big)\big]},~y>y_c(x), \\[8pt]
T_0(y)=T_b,~\rho_0(y)=\frac{p_0}{T_b}\exp\big[\frac{g}{T_u}\big(2d-y_c(x)\big)
\\[8pt]
-\frac{g}{T_b}\big(y-y_c(x)\big)\big],~y<y_c(x),
\end{array}
\right.
\end{equation}
where $p_0$ represents the pressure at the top of the system, $T_u$ and $T_p$ express the initial temperatures of the upper and lower fluid, respectively. At the same time, the pressure beside the interface of the two fluids should be consistent, which can be known from the equation of state of ideal gas:
\begin{equation}\label{e34}
\rho_u T_u=\rho_b T_b,
\end{equation}
where $\rho_u$ and $\rho_b$ are the densities of the upper and lower fluids near the interface, respectively.

In the simulation process, a computing grid $N_x \times N_y = 256 \times 1024$ is used. The top and bottom boundaries are dealt with solid wall boundary conditions, and the left and right boundaries are dealt with periodic boundary conditions, the time and space steps are $\Delta t = 2 \times 10^{-5}$, and $\Delta x = \Delta y = 5\times10^{-4}$, respectively. The initial pressure at the top of the system is $p_0 = 1.0$, and the relaxation time $\tau = 4 \times 10^{-5}$. The temperatures at the upper and lower parts are $T_u = 1.0$ and $T_p = 4.0$, respectively. And the other parameters are $(v_a, v_b, v_c, v_d) = (0.9, 0.9, 4.2, 4.2)$, $\eta_0 = 15$, $a_x = 0.0$, $a_y = -g = -1.0$.

Next, we will focus on the influence of the specific heat ratio $\gamma$ on the RT instability. The specific heat ratio is one of the most important parameters to describe the thermodynamic properties of gases. And the expression of $\gamma$ is as follows:
\begin{eqnarray}\label{e35}
\gamma = \frac{n+4}{n+2}.
\end{eqnarray}

\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.17]{FIG02.eps}
\caption{Temperature contours at different time instants (from left to right) $t$ = 0.8, 1.6, 2, 2.14, 2.68, and 3, respectively.}\label{FIG02}
\end{figure}

\begin{figure*}
\begin{center}
\includegraphics[bbllx=200pt,bblly=0pt,bburx=592pt,bbury=477pt,width=0.4\textwidth]{FIG03.eps}
\end{center}
\caption{Evolution of global average temperature gradients with various specific heat ratios: (a) the global average temperature gradient in the $x$ direction, (b) the global average temperature gradient in the $y$ direction, (c) the global average temperature gradient, (d) the relationship between the gradient value at $t=1.6$ and the specific heat ratio.}\label{FIG03}
\end{figure*}

In order to study the effect of $\gamma$, we adjust the number of extra degrees of freedom $n$ to change $\gamma$. Here, we choose $n=0,1,2,\cdots,8$, correspondingly $\gamma =2$, 5/3, 3/2, 7/5, 4/3, 9/7, 5/4, 11/9, 6/5. In order to observe the changes of interface length and width more clearly, the spatial distribution diagram of temperature is presented with $\gamma =7/5$, as shown in Fig. \ref{FIG02}. Firstly, the global average temperature gradients in fluid system are discussed. The formula for calculating the global average temperature gradients are shown below:
\begin{equation}\label{e33}
\overline{T_x}=\frac{1}{L_x L_y} \int_0^{L_x}\int_0^{L_y}|\nabla_x T|dxdy,
\end{equation}
\begin{equation}\label{e33}
\overline{T_y}=\frac{1}{L_x L_y}\int_0^{L_x}\int_0^{L_y} |\nabla_y T|dxdy,
\end{equation}
\begin{equation}\label{e33}
\overline{T}=\frac{1}{L_x L_y}\int_0^{L_x}\int_0^{L_y} |\nabla T|dxdy.
\end{equation}

Figures \ref{FIG03} (a)-(b) delineate the evolution of the global average temperature gradients in $x$ and $y$ directions, respectively, and Fig. \ref{FIG03} (c) illustrates the global average temperature gradient of the fluid system over time. It can be seen from Fig. \ref{FIG03} (a) that the global average temperature gradients in $x$ direction corresponding to different $\gamma$ values have roughly the same changing trend. Take the case with $\gamma = 7/5$, $\overline{T_x}$ gradually rises and presents an exponential growth state, and at $t = 2.06$, the $\overline{T_x}$ no longer increases and then shows a downward trend. At $t = 2.68$, $\overline{T_x}$ shows a short-term upward trend, and this state continues until $t = 3$, after that $\overline{T_x}$ starts decreasing all the way down.

The physical reason for this phenomenon is that, at the initial stage, the distance between the bubble and the spike increases exponentially, and the change of the temperature in the $x$ direction is concentrated in the middle range between the spike and the bubble, so the temperature gradient shows an exponential growth trend in the early stage, at this time, a large number of high-temperature and low-density fluids at the bottom have risen to low-temperature and high-density flow fields, which reduces the temperature at the bottom and increases the temperature at the top. In the $x$ direction, the temperature at the bottom generally presents a state of high temperature fluid on both sides and low temperature fluid in the middle. When the spike is about to touch the bottom, the mixing of two fluids further increases and even tends to be saturated, this makes the temperature in the system tend to be consistent, leading to the decrease in the global average temperature gradient. At the same time, with the increase of $\gamma$, the values of $\overline{T_x}$ are roughly the same, but there is a big difference near the peak value. Due to the disordered development of the system, the physical mechanism becomes more complex in the latter stage.

However, the change of the global average temperature gradient in the $y$ direction is completely different from the one in the $x$ direction. As can be seen from Fig. \ref{FIG03} (b), $\overline{T_y}$ keeps constant from $t = 0$ to $t = 0.85$, and increases from $t = 0.85$ to $t = 1.6$. After $t = 1.6$, $\overline{T_y}$ begins to show a downward trend until the spike arrive at the bottom. Then, the RT system enters into the chaotic stage, and the evolution of $\overline{T_y}$ becomes more complex. Throughout the evolution, an interesting phenomenon can be observed: $\overline{T_y}$ always keeps constant during the initial period. This is because, in the early stage, the change of the temperature is concentrated in the front of the spike and bubble, and the change is uniform, while in other regions, the change of the temperature are negligible, which makes $\overline{T_y}$ maintain constant in the early stage. As the system evolves, some small vortex structures appear due to the shear stress in the fluid system, and the temperature no longer varies monotonously in the vertical direction, which leads to the gradual increase of $\overline{T_y}$. Therefore, the moment when $\overline{T_y}$ is out of the fixed value can be taken as the criterion to judge the formation of the vortex structure. Fig. \ref{FIG03} (c) illustrates the change curve of the temperature gradient of the fluid system. It can be observed that the maximum of $\overline{T_x}$ is twice that of $\overline{T_y}$. The integral absolute value of temperature gradient in the $x$ direction ($y$ direction) is associated with the changing trend of temperature gradient along the $x$ direction ($y$ direction) and the vertical (horizontal) length of the computational region. On the one hand, within the mixing area between the hot and cold media, the value of temperature gradient first decreases then increase in the $x$ direction, and the value of temperature gradient reduces monotonously in the $y$ direction. On the other hand, the vertical length $L_y$ is greater than the horizontal length $L_x$. In other words, the area where the temperature gradient in the $x$ direction ($y$ direction) deviates from zero is larger (smaller). Consequently, the maximum of temperature gradient in the $x$ direction is larger than that in the $y$ direction. Moreover, with the increase of $\gamma$, the global average temperature gradient shows an decreasing trend. This is because for a larger specific ratio, the morphological structure of the fluid becomes more complex, and the temperature field has larger spatial changes. Furthermore, it can be found that the value of $\overline{T}$ at $t = 1.6$ and $\gamma$ have the following functional relationship: $\overline{T}_{t=1.6} = 39.94-1.07\gamma$.

\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.18]{FIG04.eps}
\caption{Schematic diagram of the ways that the specific heat ratio effects affect the global TNE intensity.}\label{FIG04}
\end{figure}

Next the TNE behaviors of the RT instability are investigated, and then the change of different TNE quantities are analyzed. The ways the specific heat ratio effects affect the global TNE intensity are shown in Fig. \ref{FIG04}. Figure \ref{FIG05} shows the evolution of the global average intensity $\overline{D}_2$ of the non-equilibrium quantity $\Delta_{2\alpha \beta}^*$ over time. It can be found that, $\overline{D}_2$ increases first and then decreases. Furthermore, $\overline{D}_2$ increases with the decrease of $\gamma$. To explain the trend of $\overline{D}_2$ in detail, we take $\gamma =7/5$ as an example, it can be found that $\overline{D}_2$ increases rapidly at the early period, and with the spike reaches bottom at $t = 2.14$, $\overline{D}_2$ first shows a down trend and then gradually increases, and at $t = 5.8$, it reaches the peak, after that $\overline{D}_2$ starts to oscillate less. Next, the effect of $\gamma$ on $\overline{D}_2$ is analyzed. When $t < 2.14$, there is no significant difference in fluid structure between different examples. At this point, with the increase of $\gamma$, the compressibility decreases and the TNE strength decreases, which is consistent with our previous work. At $t > 2.14$, the morphological structure of the system generates great difference, and the complexity of the morphological structure makes the evolution of $\overline{D}_2$ have no obvious rule.

\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.28]{FIG05.eps}
\caption{Evolution of the global average strength $\overline{D}_2$.}\label{FIG05}
\end{figure}

\begin{figure*}[tbp]
\begin{center}
\includegraphics[bbllx=200pt,bblly=0pt,bburx=592pt,bbury=477pt,width=0.4\textwidth]{FIG06.eps}
\end{center}
\caption{TNE quantities $\overline{D}_{3,1x}$, $\overline{D}_{3,1y}$ and $\overline{D}_{3,1}(=|\overline{D}_{3,1x}|+|\overline{D}_{3,1y}|)$ versus time under different specific heat ratios. (d) the fitting curve of the value of $\overline{D}_{3,1}$ at $t=1.6$ and $\gamma$ as: $\overline{D}_{3,1,t=1.6} = 0.01+14.21
\times\exp(-5.67\gamma)$.}\label{FIG06}
\end{figure*}
Figure \ref{FIG06} shows the evolution of the average intensity and global average intensity of each component of $\Delta_{3,1\alpha}^*$ with time. It can be found from the three subgraphs that $\overline{D}_{3,1x}$, $\overline{D}_{3,1y}$ and $\overline{D}_{3,1}$ all decrease with the increase of $\gamma$. To explain this physical phenomena, we resort to Eq. \ref{e8}. It can be seen that both $\kappa$ and $\nabla T$ vary with $\gamma$ in Eq. \ref{e8}, however, as shown in Fig. \ref{FIG03}, the temperature gradients in different cases are similar, so the change of $\textit{\textbf{J}}$ is mainly controlled by $\kappa$. Therefore, the absolute value of $\textit{\textbf{J}}$ decrease with the increase of $\gamma$, which explains the relationship between each non-equilibrium quantity and $\gamma$. In addition, Fig. \ref{FIG06} (a) shows that when $\gamma =7/5$, $\overline{D}_{3,1x}$ rapidly increases to the maximum at the beginning, and then declines. There are two main physical mechanisms in the whole evolution process: one is the growth rate of the mixing area between hot and cold fluids, and the other is the heat conduction caused by the change of temperature gradients. The increase of the area of contact between two fluids causes the increase of the area of heat exchange. And the increase of the temperature gradients also lead to the increase of the heat exchange. In the early stage, the area of contact between two fluids is increasing and the total temperature gradient is also increasing, so the heat exchange is also increasing. After the spike touches the bottom, $\overline{T_x}$ decreases rapidly. Although the contact area is still increasing, the growth rate becomes slower. At this moment, the change of temperature gradient is dominant. For $t = 2.68-3$, the temperature gradient rises again, so $\overline{D}_{3,1x}$ increases. Later, the contact area between the two fluids does not increase with the development of evolution, and the temperature gradient always plays a decisive role, so $\overline{D}_{3,1x}$ will gradually decrease and remain near a fixed value.

From Fig. \ref{FIG06} (b), it can be observed that $\overline{D}_{3,1y}$ maintains constant from $t =0$ to $t =0.85$. This is because the total temperature gradient in $y$ direction keeps constant, while the contact area grows slowly. Therefore, the temperature gradient plays a greater role at this period. When $t = 0.85-1.6$,  the contact area of the two fluids increase due to the appearance of the vortex structure, and the total temperature gradient is also rising. As a result, the combined action of the temperature gradient and the increase of the area of contact leads to the increase of $\overline{D}_{3,1y}$. And when $t > 1.6$, $\overline{D}_{3,1y}$ shows a downward trend. With the spike arrives at the bottom, the RT system enters into the chaotic stage, and the evolution of $\overline{D}_{3,1y}$ becomes more complex. Interestingly, as $\gamma$ decreases, $\overline{T_y}$ does not change much, just only a slight difference, but the interaction between the contact area and the temperature gradient has a great influence on the numerical change of $\overline{D}_{3,1y}$. Furthermore, in the later stage, the evolution of $\overline{T_y}$ and $\overline{D}_{3,1y}$ under different $\gamma$ has no obvious rule. In order to explain the inherent physical mechanism, the temperature contour map at $t = 4$ is given by Fig. \ref{FIG07}. It can be observed that there is a great difference in the temperature contour under different $\gamma$ conditions. Therefore, it can be known that the difference in the morphology and structure of the flow field is the main reason for the occurrence of this phenomenon.

\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.2]{FIG07.eps}
\caption{Temperature contours corresponding to $\gamma$= 2, 3/2, 4/3, 5/4, 6/5 from left to right with the same time $t = 4$. The color from blue to red indicates the increase of values.}\label{FIG07}
\end{figure}

The global average TNE intensity is closely related to the macroscopic physical gradients (including temperature, density and velocity gradient) and the area of the non-equilibrium region. The numerical study shows that in the early stage of RT instability, the local physical gradients decrease, such as the local temperature gradient, so the local TNE intensity decreases. However, with the development of RT instability, the increasing area of non-equilibrium region makes the global TNE strength increasingly stronger. That is, the effect of the macroscopic physical gradient and the effect of the non-equilibrium area are competing with each other. In order to facilitate the analysis of the evolution law of global non-equilibrium, the proportion of the non-equilibrium region $S_r$ (i.e., the ratio of non-equilibrium area to total area) is defined. Here, we use the following method to calculate it. Namely, to count the number of points which non-equilibrium intensity is greater than the given threshold and then to compare them with the total number of points to get $S_r$.

Figure \ref{FIG08} shows the evolution of $S_r$, from which it can be seen that the proportion of the non-equilibrium region increases at first and then decreases. At the beginning, both the non-equilibrium intensity at each point and the non-equilibrium area increase, so that the $S_r$ has an exponential growth trend in the previous period. As time evolves, the fluid system tends to be more balanced, the non-equilibrium strength decreases, and the area of the non-equilibrium region tends to be saturated, which makes $S_r$ gradually decrease. It is further found that there is a relationship between the non-equilibrium area and the specific heat ratio as follows: $S_{r,t=1.6}=0.29+1.59\times\exp(-2.37\gamma)$.

\begin{figure*}[tbp]
\begin{center}
\includegraphics[bbllx=200pt,bblly=0pt,bburx=592pt,bbury=477pt,width=0.5\textwidth]{FIG08.eps}
\end{center}
\caption{(a) evolution of the proportion of the non-equilibrium region $S_r$, (b) relationship between the value of the proportion of the non-equilibrium region $S_r$ at $t=1.6$ and the specific heat ratio $\gamma$.}\label{FIG08}
\end{figure*}

\begin{figure}[tbp]
\center\includegraphics*%
[scale=0.17]{FIG09.eps}
\caption{Spatial profiles of the global TNE quantity with $\gamma=7/5$ at different time instants (from left to right) $t$ = 0.8, 1.6, 2, 2.14, 2.68, and 3, respectively. The color from blue to red indicates the increase of values. The values of the global TNE quantity is high at the interface, while it is almost zero away from the interface.}\label{FIG09}
\end{figure}

Furthermore, the global TNE quantity are shown in Fig. \ref{FIG09}, which can help us to get the spatial distributions of the non-equilibrium region. It can be seen that the TNE intensity which near the front end of the bubble and spike is the highest, this is because the physical gradients near the interface is sharpest. With the evolution of RT instability, the mixing layer gradually elongates, and many small structures appear in the system, leading to the increasing area of the non-equilibrium region. Finally, we discuss the evolution law of the global average TNE intensity $\overline{D}$. Figure \ref{FIG10} shows the evolution of $\overline{D}$ over time. The global average TNE intensity is numerically determined by $\overline{D}_2$, $\overline{D}_{3,1}$, $\overline{D}_3$ and $\overline{D}_{4,2}$, and its intrinsic evolution rules are determined by the physical gradients and the non-equilibrium area of the system. The numerical results show that $\overline{D}$ increases rapidly in the beginning. During this process, the proportion of the non-equilibrium region plays a leading role. In addition, the non-equilibrium area increases with the disturbance amplitude increasing, which leads to the global TNE intensity shows an exponential growth trend. At the time $t = 2.14$, $\overline{D}$ stops growing and starts to decline slowly. This is because the non-equilibrium area shows a downward trend at this time, thus the global non-equilibrium intensity decreases. Meanwhile, it can be seen from Fig. \ref{FIG10} (b) that there is an exponential relationship between the global average non-equilibrium intensity $\overline{D}$ at $t = 1.6$ and the specific heat ratio $\gamma$ as follows: $\overline{D}_{t=1.6} = 0.04+128.40\times\exp(-6.76\gamma)$. Although this work focus on two-dimensional case, the model with flexible specific heat ratio can be applied to pick up information from three-dimensional physical fields. And the non-equilibrium information of three-dimensional RT instability in compressible flows deviating far away from thermodynamic equilibrium deserve further study. But on the other hand, the two-dimensional model does not take into account the geometric effects of the three-dimensional system.

\begin{figure*}[tbp]
\begin{center}
\includegraphics[bbllx=200pt,bblly=0pt,bburx=592pt,bbury=477pt,width=0.5\textwidth]{FIG10.eps}
\end{center}
\caption{(a) the global average TNE intensity $\overline{D}$ evolves with time under different specific heat ratios, (b) the fitting curve of the global average TNE intensity $\overline{D}$ at $t=1.6$ and $\gamma$ as: $\overline{D} = 0.04+128.40
\times\exp(-6.76\gamma)$.}\label{FIG10}
\end{figure*}

\section{Conclusions}\label{Conclusions}

The DBM has been applied to study the effects of the specific heat ratio on the compressible RT instability. Firstly, two kinds of non-equilibrium quantities related to the viscous stress and heat flux are investigated. It is found that with the increase of the specific heat ratio, the global average strength of the non-equilibrium quantity $\Delta_{2\alpha \beta}^*$ related to the viscous stress decreases, and the overall trend is first increasing and then decreasing. Secondly, with the increase of the specific heat ratio, the total average intensity of the non-equilibrium quantity $\Delta_{3,1\alpha}^*$ related to the heat flux will decrease, and the overall performance is first increases and then decreases. There are two main factors contributing to this phenomenon, i.e., (i) the increasing temperature gradient increases the non-equilibrium strength, (ii) the increase of the area of contact between the two fluids promotes the heat exchange, thus enhancing the non-equilibrium strength. These two factors compete with each other and jointly determine the overall average intensity. Furthermore, the global average thermodynamic non-equilibrium strength $\overline{D}$ is discussed. The numerical simulation results reveal that $\overline{D}$ also increases first and then decreases, and $\overline{D}$ also increases with the decrease of the specific heat ratio. This is because the increasing non-equilibrium area enhances the global non-equilibrium effects, and the decreasing physical gradients weakens the local TNEs. The combined action of the two factors determine the global non-equilibrium strength of the system. These results of the macro and mesoscopic non-equilibrium information contribute to a deeper understanding of the physical mechanisms of the compressible RT instability.

\section*{Acknowledgments}
This work was supported by National Natural Science Foundation of China (under Grant Nos. 51806116, 11875001), Natural Science Foundation of Fujian Provinces (under Grant Nos. 2018J01654).

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I was told the CWU would be demo-ing outside the High Court's Rolls Building in support of the JFSA and claimant Subpostmasters from 9.30am. What I didn't realise is that they'd be done by 10am. I rocked up (phrase of the day - see below) at 10.05am to find a few CWU members lurking outside, but no placards.
Thankfully, efficient people took photographs and forwarded them on.
There was a definite buzz around, both inside and outside the Rolls Building. Court 26 was the fullest I've seen it. At least a dozen claimants were in attendance, including Seema Misra, Jo Hamilton, Sue Knight, Lee Castleton and Pam Stubbs.
Ron Warmington from Second Sight was also there, as were many of the CWU reps who had been stationed outside early doors (including National Organiser Andy Furey and Postmaster Mark Baker - the latter singled out by the judge in the Common Issues trial judgment for his "redoubtable" Freedom of Information campaigning).
On the hack front, Karl Flinders from Computer Weekly put in a shift, as did Jane Croft from the Financial Times. It was great to see Joshua Rozenburg wander in, too. He is a legend in legal journalism and I remember watching him on telly as a kid. When he came over to say hello I didn't tell him that, but I wanted to.
The court was so full a couple of claimant supporters arrived late and saw the only chairs available were on the solicitors' benches. Not knowing any better they plonked themselves down and became the only members of the public to have their own personal court documentation screen. The solicitors were either too polite or worried about disrupting proceedings to tell the visitors to push off, so they stayed there.
After lunch the same supporters came back and sat in exactly the same spot without anyone batting an eyelid.
So what did everyone witness today? Why were we there?
It is possible to ask a judge to recuse (sack) him or herself of grounds of apparent or actual bias. The Post Office believes that J Fraser, in his Common Issues trial judgment has displayed apparent bias against the Post Office.
It is an objective test. A recusal application will succeed "if a fair-minded and informed observer, having considered the facts, would conclude that there was a real possibility that the judge was biased"
The "fair-minded and informed observer" took on almost mythical proportions as the day progressed. It is s/he who will tell the judge if he is biased. Unfortunately s/he doesn't exist.
It was a day of two halves, Brian. In the morning, Lord Grabiner QC for the Post Office took the judge to pieces by isolating specific parts of his judgment and pointing out that any reasonable person could not impute anything other than apparent bias. In the afternoon, Patrick Green QC for the claimants built the context around those specific parts of J Fraser's judgment and argued his comments were entirely justified.
In fact you could almost draw parallels with the Brexit situation.
Post Office: How could we possibly lose? You've done it all wrong!
Claimants: You lost. Get over it.
1. The Post Office will appeal the common issues trial judgment.
2. The decision to apply for the recusal was made at Post Office board level.
3. The judge has reserved his decision on recusal until Tuesday 9 April at 2pm at the earliest.
4. If the recusal is successful the Post Office wants the Horizon trial to be stayed and restarted.
Bearing in mind we are three years and £20m into this litigation, if the Post Office is successful, we will almost be back where we started. Which is, of course, exactly what the Post Office wants - a big reset to regain the initiative, and a ramping up of the costs to make everything as expensive as possible. That way the claimants will hopefully run out of money and throw in the towel.
In litigation, no one said you had to play nice.
To be fair, the Post Office is bossing things right now. It has successfully seized the initiative from the claimants after the Common Issues trial judgment. Anyone who reads even a few hundred words of that judgment can see the pasting the Post Office got. Factually, legally, reputationally and culturally the Post Office was massively exposed by the judge's findings.
For an organisation which is obsessed with its public image and shrouded by a cult of "excessive secrecy", this must have been a shock. On 15 March, when the judgment was handed down, the Post Office was not just on the ropes, it was floored. Yet within a week it was back. Off the canvas and swinging like a champion.
A recusal application is still a massive call, though. To switch metaphors, aiming to sack a senior judge because you don't like some of the things he's said is the legal equivalent of going all in on a pair of tens. You have to be feeling lucky.
But as every gambler knows, it isn't just about the cards, it's about the player.
On the evidence of today, m'learned friend could stroll into any long-running, hotly-contested™ litigation and own it. He has a presence and charisma which might persuade a casual observer that everything which happened in the litigation before he got involved didn't really matter.
This is a man who presumably doesn't take instruction unless he is being paid several thousand pounds an hour, or knows he's going to win. Or both.
wasn't necessary for the purposes of the Common Issues.
viewed by an objective observer."
"Well, I mean, your Lordship can imagine what I would be saying about that, but my submission is that the passage speaks for itself.
It was quite something to behold.
J Fraser would mention that Lord Grabiner had omitted his qualifying statements and caveats and Lord Grabiner would acknowledge this, but add he was coming to it later.
ahead and made those findings."
You can read the transcript here and my unrolled live tweets here. It must be hard to hear one's professional integrity being taken apart in such an eloquent and public way. But the judge took it on the chin. And after lunch, he turned to Patrick Green QC for the claimants.
specifically on a misapprehension as to the proper judicial assessment of the proceedings."
having regard to the judgment as a whole."
observer knows about the trial as it was presented to your Lordship.
about the trial. So "informed" I would underline in relation to the approach of the informed observer test.
And he was off. The main two points he made were that the Post Office was not once saying that any of the judge's findings were wrong, just that they were irrelevant. His second point was that in the context of the trial, the proceedings preceding the trial and litigation as a whole... actually they really were very relevant.
Mr Green said in the context of someone who has been through all the pre-trial shenanigans, and the framing of the way proceedings happened, the judge was justified in what he wrote in his the Common Issues trial judgment. Yet according to Mr Green, the judge was not just expected to take into account what was happening in his courtroom, he was, by case law, required to make findings on it.
MR JUSTICE FRASER: I am not sure "rocking up" is right.
MR GREEN: I might have put that a bit lightly.
seriousness. Evidence-in-chief was given orally.
in advance of arriving at court and listening to what they were going to say."
"They have adopted internally inconsistent positions in relation to the relevance of evidence and essentially tried to ride two horses going off in completely different directions, and your Lordship has had to try and manage the consequence of that, and clarify it, where possible, on credibility, still leaving an extremely unsatisfactory position, make findings in the light of the litigation as it was presented before court, and then be accused of apparent bias for having done so."
I have spoken to a number of senior people since the hearing finished, some of whom were legally qualified. They broadly agreed there is a minuscule chance the judge will recuse himself and an even smaller chance the Court of Appeal will make the decision for him.
I'm not so sure. Grabiner was good.


Tetsro – shaving in Japan with Philip's shaver – did you ask Philip before you borrowed it?
Published January 19, 2016 at 2000 × 1500 in 327. The LEP Photo Competition – Please check out the photos and vote.


text:
4th Global Food Security, Food Safety & Sustainability Conference, April 19-20 , 2019 Montreal, Canada
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Montreal is the most populous municipality in the province of Quebec and the second-most populous in Canada. Originally called Ville-Marie, or "City of Mary", it is named after Mount Royal, the triple-peaked hill in the heart of the city. In 2017 the city had a population of 1,709,994. French is the city's official language and is the language spoken at home by 49.8% of the population of the city, followed by English at 22.8% and 18.3% other languages. The agglomeration Montreal is one of the most bilingual cities in Quebec and Canada with over 59% of the population able to speak both English and French. Montreal is the second-largest primarily French-speaking city in the world, after Paris.
Historically the commercial capital of Canada, it was surpassed in population and economic strength by Toronto in the 1970s. It remains an important centre of commerce, aerospace, finance, pharmaceuticals, technology, design, education, culture, tourism, gaming, film and world affairs. Being the location of the headquarters of the International Civil Aviation Organization, Montreal is one of three North American cities home to organizations of the United Nations and also has the 2nd-highest number of consulates in the continent. Montreal was also named a UNESCO City of Design. In 2009 Montreal was named North America's leading host city for international association events, according to the 2009 preliminary rankings of the International Congress and Convention Association (ICCA).The 2017 edition of QS Best Student Cities ranked Montreal as the best city in the world to be a university student. According to the 2015 Global Liveability Ranking by the Economist Intelligence Unit, Montreal ranked 14th out of 140 cities.
Montreal has hosted multiple international conferences and events throughout its history, including the 1967 International and Universal Exposition and the 1976 Summer Olympic Games. It is the only Canadian city to have held the Summer Olympics. Currently, the city hosts the Canadian Grand Prix of Formula One, the Montreal International Jazz Festival and the Just for Laughs festival. In 2012, Montreal was ranked as a Beta+ world city.
Holiday Inn EXPRESS, 10888
Chemin de la Côte-de-Liesse, Lachine,
QC H8T 1A6, Canada.
Venu
4th Global Food Security, Food Safety & Sustainability Conference
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text:
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text:
Last edited by Shalkree
Tuesday, August 4, 2020 | History
6 edition of Tolkien"s modern Middle Ages found in the catalog.
Tolkien"s modern Middle Ages
by Jane Chance
Published 2005 by Palgrave Macmillan in New York .
Tolkien, J. R. R. 1892-1973 -- Criticism and interpretation,
Tolkien, J. R. R. 1892-1973 -- Knowledge -- History,
Literature and history -- England -- History -- 20th century,
Fantasy fiction, English -- History and criticism,
Medievalism -- England -- History -- 20th century,
Postmodernism (Literature) -- England,
Middle Earth (Imaginary place),
Middle Ages in literature,
History in literature
Includes bibliographical references (p. ) and index.
Statement by Jane Chance.
Series New Middle Ages, New Middle Ages (Palgrave Macmillan (Firm))
LC Classifications PR6039.O32 Z6224 2005
Pagination p. cm.
None of them can be said to be 'about' the history of the Second Age. The closest you will find is The Silmarillion. It has two chapters at the end which deal with Numenor and the creation of the Rings of Power. Unfinished Tales also has small pas. Here are my top 10 rewritings of medieval tales and traditions, each making strategic use of the middle ages to think about how people are living their lives now. 1. Hamlet by William Shakespeare.
"Tolkien: Medieval and Modern"Ap at PM. I like very much the distinction you make here between more static (non-performative) forms of art like painting and sculpture and the dynamic demands placed on the performers and audience by music. The Early Middle Ages, which marked the end of the Roman Empire and the creation of the kingdoms of Western Europe, was a period central to the formation of modern Europe. This period has often been drawn into a series of discourses that are more concerned with the eighteenth, nineteenth, and twentieth centuries than with the distant past.4/5(5).
Buy a cheap copy of The Maps of Tolkien's Middle-earth book by Brian Sibley. Best-selling Tolkien expert Brian Sibley (The Lord of the Rings: The Making of the Movie Trilogy and The Lord of the Rings Official Movie Guide) presents a Free shipping over $/5(5). Tolkien's Modern Sources: Middle-earth Beyond the Middle Ages. by Holly Ordway Tolkien is widely regarded as a man steeped in medieval literature and language; this is indeed true, but his Phone: ()
true and exact particulars and inventories of all lands, tenements, hereditaments, goods, chattels, debts, and personal estate whatsoever, of Arthur Ingram, Esq late director of the South Sea Company
Responding to low dairy prices
Experiencing the Spirit
progressive process firm
Compositions of John Flaxman, sculptor
Making the race, stating the case: thinking about racism,identity and social change
history of Polybivs the Magalopolitan
Mouse mess
The Woman Who Toils
Strange toys.
Ranch and Modern Homes
World cement production.
Theatre and film in exile
Airborne windshear detection and warning systems
Aging-face surgery with emphasis on face-lift
Race, Sex, and National Origin
Undocumented immigrants and higher education
Living with the law
Tolkien"s modern Middle Ages by Jane Chance Download PDF EPUB FB2
The "Modern Middle Ages" serves the reader much as the "Tolkien Studies" series does. If you buy this, take advantage of the toofa and read Marjorie Burns' excellent book 4/5(1). Tolkien delved into the Middle Ages to create a critique of the modern world in his fantasy, yet did so in a form of modernist literature with postmodern implications and huge commercial : J.
Chance. About this book J.R.R. Tolkien Tolkiens modern Middle Ages book into the Middle Ages to create a critique of the modern world in his fantasy, yet did so in a form of modernist literature with postmodern implications and huge commercial success.
Tolkien's Modern Middle Ages by Jane Chance,available at Book Depository with free delivery worldwide/5(24). Tolkien delved into the Middle Ages to create a critique of the modern world in his fantasy, yet did so in a form of modernist literature with postmodern.
Tolkien's Modern Middle Ages is a collection of essays edited by Jane Chance and Alfred K. Siewers. [] From the PublisheJ.R.R. Tolkien delved into the Middle Ages to create a critique of the modern world in his fantasy, yet did so in a form of modernist literature with postmodern implications and huge commercial success.
These essays examine that paradox. The essays in Tolkien's Modern Middle Ages look to Tolkien's fascination with the medieval world, its languages and peoples, and his inclusion of motifs, language, imagery, and cultural values of this period in his literary works. These studies cover a.
The "Modern Middle Ages" serves the reader much as the "Tolkien Studies" series does. If you buy this, take advantage of the toofa and read Marjorie Burns' excellent book Reviews: 1.
The essays in Tolkien's Modern Middle Ages look to Tolkien's fascination with the medieval world, its languages and peoples, and his inclusion of motifs, language, imagery, and cultural values of this period in his literary works.
These studies cover a wide array of topics and questions. Tolkien's Modern Middle Ages, edited by Jane Chance and Alfred K. York: Palgrave Macmillan, xiv, pp.
$ (hardcover) ISBN Summary: "J. R.R. Tolkien delved into the Middle Ages to create a critique of the modern world in his fantasy. Yet he did so in a form of modernist literature with postmodern implications and huge commercial success.
Description J.R.R. Tolkien delved into the Middle Ages to create a critique of the modern world in his fantasy, yet did so in a form of modernist literature with postmodern implications and huge commercial by: Books cover huge amounts of mythological ground, so to use "Unfinished Tales" as an example, it encompasses the 1st, 2nd, and 3rd ages of Middle Earth.
If you really wanted to do this chronologically, you'd have to jump between books. This is a list of the writings of the English writer and philologist J.
Tolkien. The Homecoming of Beorhtnoth Beorhthelm's Son (a play written in alliterative verse), published with the accompanying essays Beorhtnoth's Death and Ofermod, in Essays and Studies by members of the English Association, volume 6.
Romantic poems from the Middle Ages?). But the overwhelming influence of J.R.R. Tolkien on the genre remains a fundamental certainty.
"What Tolkien does in that book. Tolkien - Literary Criticism: Books. 1 - 11 of 11 results. Grid View Grid. List View List. Add to Wishlist. Read an excerpt of this book. Quickview. The Monsters and the Critics. by J. R Tolkien's Modern Middle Ages. by J. Chance.
Tolkien's Women: The Medieval Modern in The Lord of the Rings by 1 J.R.R. Tolkien, "On Fairy-Stories," The Tolkien Reader, New York: Ballantine Books,33, Print.
purity reigned in the earlier ages of Middle-earth, echoing Tolkien's own obsessive nostalgia forFile Size: KB. Similarly, Rebekah Long within her chapter titled "Fantastic Medievalism and the Great War in J.R.R. Tolkien's The Lord of the Rings", which can be found in a book titled Tolkien's Modern Middle Ages, follows a similar argument as Garth.
Within Long's chapter, she specifically focuses on post-war soldiers and their writing, most. However, the term "Middle-earth" is not found in Tolkien's earliest writings about the subject, dating from the early s and published in The Book of Lost Tales (–84). Nor is the term used in The Hobbit ().Created by: J.
Tolkien. Valar make war on Melkor in the War for Sake of the Elves. The earth is shaken. The shores of Beleriand are formed and bays are created on the North. Over the next two years Melkor is defeated, and retreats into Utumno. The Siege of Utumno begins. North is desolated and the Sea widened.
The Siege of Utumno ends, as the Valar storm the final. Tolkien's Middle-Earth, true History? by T.S. Caladan Is it possible that the world J.R.R. Tolkien so elegantly defined for us in 'Lord of the Rings' has a ring of historical truth? Could elements of the 'Hobbit' and the following 'Trilogy' be his interpretations of actual events?.
Jay Weidner's work (see 'Kubrick' article on W-M) inspired this writer with a mention of. "Tolkien: Medieval and Modern" J.R.R. Tolkien's The Lord of the Rings is one of the most popular works of imaginative literature of the twentieth century. This course seeks to understand its appeal by situating Tolkien's creation within the context of Tolkien's own work as both artist and scholar alongside its medieval sources and modern.TOLKIEN: MEDIEVAL AND MODERN.
Now we must praise the Guardian of Heaven, the might of the Lord and His purpose of mind, the work of the Glorious Father; for He, God Eternal, established each wonder, He, Holy Creator, first fashioned heaven as a roof for the sons of men. Then the Guardian of Mankind adorned this middle-earth below, the world.
sunshinesteaming.com - Tolkiens modern Middle Ages book © 2020


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Stephen Baldwin Has Revealed What He Thinks About His Daughter Dating Justin Bieber
The fact Bieber is still alive says it all really.
We told you a couple of weeks ago that Justin Bieber was dating Stephen Baldwin's daughter Hailey and today TMZ have finally caught up with Stephen to find out his opinion on the young man.
Stephen is pretty complimentary about Bieber as he's being bothered walking through an LA airport after a long flight by an annoying reporter – but he also crucially says that the two of them aren't actually dating and are 'just friends'. Check out the footage below:
Well there you have it – what a revelation. Seriously though what is the reporter talking about at the end? It sounds like he's really struggling for questions when he's all like 'would Justin have to go all old fashioned and ask you for her hand?' – I mean I know a lot of people are going to say who even cares what Stephen Baldwin thinks about Justin Bieber, but honestly nobody cares if he's going to have to go all 'old fashioned' if he wants to marry his daughter.
Maybe Stephen should have a word with Justin about getting his Instagram followers to track down girls he fancies though, because that isn't exactly that cool when you've got a girlfriend.
Related Items:annoying, Bothered, Complimentary, Fathers, Hailey Baldwin, instagram, Just Friends, JUSTIN BIEBER, LA, old fashioned, reporter, stephen baldwin, TMZ, weird
Man Has Just Two More Attempts At Lost Password For Bitcoin Account Worth $220 Million
This Guy Will Lose His Licence If He's Caught Driving Without A Colander On His Head
Kanye West Is Planning A David Bowie Tribute Album As He Feels That "The Torch Has Been Passed On To Him"


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redpajama_set_name: RedPajamaGithub


After a long and arduous winter, the first signs of spring are appearing – lighter evenings, warmer temperatures and blooming flowers. But the changing season can bring challenges which we all need to be aware of to ensure we keep operating safely as spring approaches.
With the sun sitting lower in the sky during the spring months, it is vital that your field of vision is as clear as possible. Around 3,900 people are injured in accidents caused by the blinding effects of the sun each year, according to data from the Department for Transport. Make sure your dashboard is totally clear – no coffee cups, maps, delivery notes or anything else should be on there to get in the way of your view out of the cab. Make sure the glass is clean, inside and out, before setting off, and keep a pair of sunglasses in the cab, as the low angle of the sun can be difficult to deal with at this time of year.
Always use indicators when turning, to ensure that other vehicles are aware of your intentions. Keep alert to other road users too – vulnerable road users like cyclists and motorcyclists can be more difficult to spot when the light is failing, so take extra time to check before pulling out or across traffic. And be aware that reflective road surfaces, combined with damp or wet driving conditions, can make it very difficult to see things clearly, particularly at multi-point junctions or away from main roads with good lighting. Check and check again before manoeuvring to ensure that all road users can keep moving as safely as possible.
When you picture an athlete, what comes to mind? Perhaps you conjure up images of a runner or a rugby player, but athletes come in all forms and it is easy to overlook the physical challenges more everyday jobs can bring. For example, informal research by FTA found parcel delivery operators walk nearly 40 miles and carry over 1.5 tons of parcels on average per week!
To recognise the physical and mental demands that often come from driving professionally, the theme of FTA's 2019 Van Excellence Operational Briefings is the industrial athlete. The three briefings, held in Edinburgh, Derby and London from 26 March to 2 April, will equip operators with the tools and techniques they need to help strengthen their drivers' physical and mental health.
Caring for drivers is one of the best ways for employers to improve the safety record of their businesses; operators of all fleet sizes will be able to pick up hints and tips on changing the health of their workforce at the sessions.
A recent survey found that more than 75% of drivers deliberately restrict fluid intake during the day, to reduce the need for stops in a busy working day. This, of course, can easily affect cognitive skills and risk perception; even mild dehydration can have the same impact on driver errors as drink driving, according to a study by Leasing Options. The British Dietetic Association will speak on the importance of proper diet and hydration.
Driving while drowsy is suspected to be a primary cause in more than 20% of road fatalities, according to the Transport Accident Commission. The Third Pillar of Health will look at the impact of fatigue on the working day and share sleep management strategies.
Stress and setbacks can wreak havoc on our mental health; successful motor racing driver and mental attitude coach, Andy Neale, will share techniques on how to become resilient and develop "bouncebackability".
Organisations must embed good wellbeing practices into their day to day operations; Transport Research Laboratory will provide suggestions of supportive mental wellbeing strategies for workplaces to adopt.
The police recognise the importance of effectively managing wellbeing and health issues in the workplace; representatives from the police will explain how this leads to safer driving and more comprehensive risk management.
Ex-international rugby player and fleet manager, John Dalziel, will draw on his wide-ranging experience to explain the parallels in preparation, mindset and performance between professional drivers and top-level athletes. And finally, Campaign Against Living Miserably (CALM) will discuss the charity's work to raise awareness around male suicide and how Van Excellence is supporting it through its CALMVan initiative.
The Operational Briefings are sponsored by Van Excellence Platinum Partner, Mercedes-Benz Vans, and Gold Partners Bott, Brigade Electronics, Hertz, Quartix and Lex Autolease.
While daily pre-use van checks are not required by law, this is no reason to believe they are not an essential activity. The safety of the driver and other road users is reliant upon all of us operating a vehicle that's roadworthy and fit to drive. Tyres, lights, steering, brakes and mirrors – among many other features – should be checked before departure.
A recent survey by Mercedes-Benz Vans found 20% of van drivers avoid drinking fluids during the day so they do not have to stop for a relief break. While the pressures of the job often mean relief breaks are not always possible, proper hydration plays a crucial role in maintaining good health and staying safe; motorists who are dehydrated make twice as many mistakes, according to research by Loughborough University. Dehydration can have a significant effect on the way we work – in fact a 1% dehydration level causes a 10% drop in performance: something we should all bear in mind when operating on Britain's busy roads.
All van drivers and operators should try to achieve the highest standards of compliance and safety at all times. While this is easier said than done, Van Excellence is here to help. Whether it's by aspiring to achieve its Van Excellence Code, attending its briefings, or taking part in a training course, there are plenty of resources available to ensure that your van fleet is operated to the highest possible standards.


Your approach might not get you the results you want.
You might be experiencing some business issues that you've never seen before. Maybe your team isn't performing like it used to with results that match that performance. Signs of challenge – like turnover or a lack of engagement – might be starting to become more evident.
Is this a temporary blip or a larger trend? Is it worth exploring alternate paths?
*If this hasn't been your experience, perhaps you didn't give yourself enough credit as you were answering the questions. You're welcome to try again.
Organizations like yours tend to start to see an increase in turnover, usually concentrated among newer employees. Perhaps you've heard (or said) statements like, "as soon as we train them and they get any good, they leave." You might also be hearing (or thinking) that it's the employee's fault for being frustrated or leaving.
Our experience shows that people leave people, not organizations. Is there a logjam preventing movement within your organization? Are a few people holding all of the knowledge and decision making? We recommend doing a deep dive into how your organization sees its workforce and their role in your ability to be successful.
Are you missing sales goals or not replacing your customers as quickly as before?
Is there more and more work being put into hiring and training new employees?
Have you been actively developing your talent or taking a wait-and-see approach?
Our complimentary 5-Day Next Leader Boot Camp gives you the best advice we give to our clients. Once you've completed the boot camp, you'll have plenty of the information you need to ensure that your team is ready now and in the future.
Get the consulting advice we give to our clients with the 5-Day Next Leader Boot Camp. We'll cover the five key developmental priorities for your Next Leaders and how to prepare them to become the executive-level decision makers you need.
You have successfully joined the 5-Day Next Leader Boot Camp. We're looking forward to working with you over the next 5 days!


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Laura Linney Puts the Comedy in Cancer
There's an interesting cover story on the actress Laura Linney by Frank Bruni in the current New York Times Magazine. Linney's had a remarkable career in movies, television and Broadway, but it didn't begin taking off until she was 35. Now she's one of the small number of actresses over 40 getting meaty roles. After losing close friend Natasha Richardson last year in a fluke accident that occurred on a ski trip, Linney's taken the lead role in the mortality-themed The Big C, a Showtime ... (read more)
The Heavy: David Letterman Likes Them Now
On Jan. 18, the British band The Heavy impressed David Letterman so much with their song "How You Like Me Now?" that he did something he's never done before in the history of his program -- he asked for an encore. The YouTube video is the televised broadcast -- which edits out most of the encore -- but you can see it in full in high quality on Letterman's web site. Paul Shaffer and Letterman even perform part of the encore. There have been some great live performances on Letterman, including TV ... (read more)
Meet Sarah Killen, Conan O'Brien's Favorite Twit
Since joining Twitter on Feb. 24, Conan O'Brien has amassed more than 534,000 followers and posted 10 tweets. Contractually exiled from late night television until September, O'Brien has embraced the new medium, sharing inane personal details of his life, airing petty grievances and even posting a Twitpic of how many people it takes for him to compose each tweet. Friday afternoon, O'Brien announced that he has taken his first follower: I've decided to follow someone at random. She likes ... (read more)
Parenthood: So Heart-Warming It Hurts
I posted a review on Mister Television of NBC's new drama Parenthood: The Parenthood pilot on NBC was the most exhausting television I've endured this season. The show begins with Peter Krause jogging down a Berkeley, Calif., street. The jog has left him wheezing for air, in spite of the fact that Krause is physically fit and doesn't appear to have an ounce of fat on him. (I make this observation in an entirely heterosexual way.) He's sitting on his taut buttocks (OK, that was a little gay) ... (read more)
CBS News Whores for Cheap Hits from Google
Yesterday, the CBS News web site ran a five-paragraph story on the fact that Susan Dey was absent from a Partridge Family reunion: The Partridge Family cast was one member short when they reunited on television Tuesday morning. The cast of the popular '70s sitcom appeared on the Today Show as part of their "Great TV Families Reunited" series, but actress Susan Dey, who played eldest daughter Laurie Partridge, was not in attendance. Danny Bonaduce, who in the years after his child stardom faced ... (read more)
The Car for the Man Who Hates His Wife
Here's an interesting message for 100 million Super Bowl viewers: If you hate your hectoring shrew of a wife ... ... you'll love a Dodge Ram Charger! ... (read more)
Human Target's Opening Credits Hit the Mark
The new Fox series Human Target has amazing opening credits: I caught the pilot during a special preview Sunday night sandwiched between episodes of 24. Regular airings begin Wednesday. The show, based on a DC comic book from the '70s, was a light escapist romp. Mark Valley, who was great a few years ago in a similar role as Keen Eddie, plays an out-of-his-mind bodyguard for hire who manages to get shot, stabbed, blown up and trapped on a runaway bullet train in a single episode. The great ... (read more)
Is Miss Farrell Crazy on Mad Men?
I've become an obsessed viewer of Mad Men this season, catching each episode on its first Sunday night airing and hitting the web afterwards to read reactions. The best place to do this is the blog of New Jersey Star-Ledger television critic Alan Sepinwall, who posts an extremely long critique of each episode that attracts hundreds of interesting comments. For several weeks, Sepinwall's readers have been increasingly critical of Suzanne Farrell, the outspoken young teacher who is Don ... (read more)
Last Day to Enter Television Death Pool
Today's the last day to enter the Ted Marshall Open Television Death Pool, a contest to predict the shows most likely to be cancelled during the fall TV season. To play, you must predict 10 comedies, dramas, games shows or news programs on the five major networks -- ABC, CBS, CW, FOX and NBC -- that will be cancelled by Aug. 31, 2010. Last year I finished in a tie for 24th place by picking eight shows that went to their doom: ER (NBC) 90210 (CW) Opportunity Knocks (ABC) The Mentalist (CBS) Life ... (read more)
Richard Corliss Makes Excuses for Michael Jackson
Before Michael Jackson's death Friday, I wasn't aware that I had any affection left for the King of Pop. Like millions of others, I grew up watching Jackson and the rest of his family grow up. Janet Jackson's my age, and when she played Penny as a 10-year-old on the sitcom Good Times, I was in love. I decided to save myself for her -- not that she appreciated it -- until I finally gave up at age 18. I'm not the only one who still had some affection for Jackson, but the extent of the tonguebath ... (read more)
Read More Entries


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About WCR FM
WCR Shows
Here's what you can hear on 101.8 WCR FM. Sometimes programmes might change at short notice: we'll try and keep you as up to date as possible.
What's On Today - Monday
1:00 am: Through The Night
5:00 am: Andy Swift's Early Show
6:00 am: Dicky Dodd at Breakfast sponsored by Tile Choice
10:00 am: Susan Vickers in the Morning
12:00 pm: Wolverhampton Today with Jason Forrest
3:00 pm: Stu Hickman drives Wolverhampton home
7:00 pm: Music and Memories with Austin Powell
9:00 pm: Paul Newman Music into the Night
10:00 pm: Late Night Rosie Kendrick
Full Weekly schedule
12:00 am - 1:00 am: Saturday Night Mix with Lyndon Edwards
1:00 am - 3:00 am: Global Warmup with Judge Jules
3:00 am - 4:00 am: Future Disco with Carly Foxx
4:00 am - 6:00 am: The Chillout Zone
6:00 am - 8:00 am: Stretch on Sunday including the Golden Hour after 7
8:00 am - 10:00 am: Chris Allen's Sunday Show
10:00 am - 12:00 pm: Taste Wolverhampton with David King
12:00 pm - 2:00 pm: Sunday Lunch with Andy Swift
2:00 pm - 4:00 pm: Mick Wright in the Afternoon
4:00 pm - 5:00 pm: Mike Zeller's Album Show
5:00 pm - 6:00 pm: Inside Tracks with Pete Whitehouse
6:00 pm - 8:00 pm: Supergold Sunday with Chris Harper
8:00 pm - 10:00 pm: Soul Kitchen with Steve Welch.
10:00 pm - 1:00 am: Pillow Talk with Robin the Vinyl Junkie
1:00 am - 5:00 am: Through The Night
5:00 am - 6:00 am: Andy Swift's Early Show
6:00 am - 10:00 am: Dicky Dodd at Breakfast sponsored by Tile Choice
10:00 am - 12:00 pm: Susan Vickers in the Morning
12:00 pm - 3:00 pm: Wolverhampton Today with Jason Forrest
3:00 pm - 7:00 pm: Stu Hickman drives Wolverhampton home
7:00 pm - 9:00 pm: Music and Memories with Austin Powell
9:00 pm - 10:00 pm: Paul Newman Music into the Night
10:00 pm - 12:00 am: Late Night Rosie Kendrick
12:00 am - 1:00 am: Mike Hardacre's Milestones & All That Jazz
7:00 pm - 9:00 pm: Tuesday Takeover with Amber
9:00 pm - 10:00 pm: Acceptable in the 00's
10:00 pm - 12:00 am: Unchained Music Club with Garry Foster
12:00 am - 1:00 am: Jack Haywood
6:30 pm - 7:00 pm: Drivetime Extra with Chris Allen
7:00 pm - 9:00 pm: Alex's Real Recognise Real Show
12:00 am - 1:00 am: Inside Tracks (repeat from Sunday)
6:30 pm - 7:00 pm: WCR Sport Non-League Football with Skye Stewart
7:00 pm - 9:00 pm: Wolverhampton Country with Jim Duncan
9:00 pm - 10:00 pm: Susan Vickers Live Night
10:00 pm - 12:00 am: Prog Rock Files with Garry Foster
12:00 am - 2:00 am: Susan Vickers Soulnation
10:00 am - 12:00 pm: The Friday Briefing with Chris Allen
6:00 pm - 7:00 pm: The Milk Bar with Jason Forrest
7:00 pm - 8:00 pm: The Friday Feeling with Lyndon Edwards
8:00 pm - 10:00 pm: N-R-G with Stu Haycock
10:00 pm - 12:00 am: Friday Night Dance Party with Niel Jackson
12:00 am - 2:00 am: Roger Sanchez - Release Yourself
2:00 am - 3:00 am: Sister Bliss in Session
3:00 am - 4:00 am: Candypants Radio Show with Just Daniel
4:00 am - 6:00 am: The Chill Out Zone
6:00 am - 8:00 am: Alan Nicklin's Guilty Pleasures
8:00 am - 10:00 am: Saturday Sixties with Les Ross
10:00 am - 12:00 pm: Saturday Sport with Skye Stewart
12:00 pm - 2:00 pm: Andy Swift
2:00 pm - 4:00 pm: Chris Weaving
4:00 pm - 6:00 pm: Shaun Baxter
6:00 pm - 8:00 pm: Out On The Floor with Hitsville Chalky
8:00 pm - 10:00 pm: Groove Indicator with Andy Walters
10:00 pm - 11:59 pm: Saturday Night Mix with Lyndon Edwards
© WCR FM 2021


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Fócio - patriarca bizantino de Constantinopla;
  - patriarca grego de Constantinopla;
 Fócio (Emirado de Creta) - renegado bizantino;

redpajama_set_name: RedPajamaWikipedia


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Sehore district
Budni tehsil
Khidiya Kurmi
Khidiya Kurmi Population, Caste, Working Data Sehore, Madhya Pradesh - Census 2011
Khidiya Kurmi is a village situated in Budni tehsil of Sehore district in Madhya Pradesh. As per the Population Census 2011, there are total 124 families residing in the village Khidiya Kurmi. The total population of Khidiya Kurmi is 716 out of which 383 are males and 333 are females thus the Average Sex Ratio of Khidiya Kurmi is 869.
The population of Children of age 0-6 years in Khidiya Kurmi village is 104 which is 15% of the total population. There are 66 male children and 38 female children between the age 0-6 years. Thus as per the Census 2011 the Child Sex Ratio of Khidiya Kurmi is 576 which is less than Average Sex Ratio (869) of Khidiya Kurmi village.
As per the Census 2011, the literacy rate of Khidiya Kurmi is 67.6%. Thus Khidiya Kurmi village has higher literacy rate compared to 59.5% of Sehore district. The male literacy rate is 79.5% and the female literacy rate is 54.92% in Khidiya Kurmi village.
As per constitution of India and Panchyati Raaj Act (Amendment 1998), Khidiya Kurmi village is administrated by Sarpanch (Head of Village) who is elected representative of the village.
Khidiya Kurmi Data as per Census 2011
As per the Population Census 2011 data, following are some quick facts about Khidiya Kurmi village.
Children 104 66 38
Literacy 67.65% 79.5% 54.92%
Scheduled Caste 103 57 46
Scheduled Tribe 178 94 84
Schedule Caste (SC) constitutes 14.4% while Schedule Tribe (ST) were 24.9% of total population in Khidiya Kurmi village.
In Khidiya Kurmi village out of total population, 456 were engaged in work activities. 97.4% of workers describe their work as Main Work (Employment or Earning more than 6 Months) while 2.6% were involved in Marginal activity providing livelihood for less than 6 months. Of 456 workers engaged in Main Work, 139 were cultivators (owner or co-owner) while 297 were Agricultural labourer.
Cultivators 139 72 67
Other Workers 8 6 2
Marginal Workers 12 11 1
Map of Khidiya Kurmi, Sehore, Madhya Pradesh
Nearby Villages to Khidiya Kurmi, Budni
Below are the list of villages near Khidiya Kurmi village in Budni.
Chikli 675
Chandla Kalan 233
Karitalai 148
Hoda 305
Richhoda 517
Isharpur 386
Bans Gehan 506
Gadar 967
Khabada 964
Khoha 1,045
Khidiya Kurmi, Sehore, Madhya Pradesh - Wikipedia


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in: 1840 in the United States, Decennial federal censuses of the United States, United States government stubs, United States history stubs
1840 United States Census
The United States Census of 1840 was the sixth census of the United States. Conducted by the Bureau of the Census on June 1, 1840, it determined the resident population of the United States to be 17,069,453 — an increase of 32.7 percent over the 12,866,020 persons enumerated during the 1830 Census. The total population included 2,487,355 slaves. In 1840, the center of population was about 260 miles (418 km) west of Washington, near Weston, West Virginia.
2 Census questions
3 Data availability
Politics[]
One notable effect of the published census results on the political debates of the time was that the percentage of "insane negroes" seemed to increase the further North one went, reaching catastrophic proportions in Massachusetts and Maine. Pro-slavery advocates pointed to this as evidence of the beneficial effects of slavery. These statistics were later revealed to be false, but no formal correction to the census results was ever published, partly due to John C. Calhoun being Secretary of State in 1844.[1] The statistical problems were detailed in an 1844 publication of the American Statistical Association entitled Memorial of the American Statistical Association Praying the Adoption of Measures for the Correction of Errors in the Census Detailing Certain Errors in the Sixth Census, Including too many Mentally Ill African Americans.[2] This report was presented to Congress by John Quincy Adams who notes that it demonstrates "a multitude of gross and important errors in the printed census of 1840."[3]
Census questions[]
The 1840 census asked these questions[4]:
Name of head of family
Number of free white males and females
in five-year age groups to age 20
in 10-year age groups from 20 to 100
100 years and older
number of slaves and free colored persons in six age groups
number of deaf and dumb
number of blind
number of insane and idiotic in public or private charge
number of persons in each family employed in seven classes of occupation
number of schools and number of scholars
number of white persons over 20 who could not read and write
number of pensioners for Revolutionary or military service
Data availability[]
No microdata from the 1840 population census are available, but aggregate data for small areas, together with compatible cartographic boundary files, can be downloaded from the National Historical Geographic Information System.
Historical census data
Census Records, 1790-1840
^ Tenzer, Lawrence R. (October/November 2000). "Racial Theory & The Pre-Civil War Census". Archived from the original on 2008-03-28. http://web.archive.org/web/20080328222623/http://multiracial.com/site/content/view/458/27/. Retrieved 2009-10-19.
^ Edward Jarvis, William Brigham and John Wingate Thornton, Memorial of the American Statistical Association Praying the Adoption of Measures for the Correction of Errors in the Census Detailing Certain Errors in the Sixth Census, Including too many Mentally Ill African Americans, 1844
^ Adams, Charles Francis, ed. Memoirs of John Quincy Adams,: Comprising Portions of His Diary from 1795 to 1848, Philadelphia, Penn.: J. B. Lippincott & Co., 1877, Vol. 12, p. 61
^ "Library Bibliography Bulletin 88, New York State Census Records, 1790-1925". New York State Library. 1981. http://purl.org/net/nysl/nysdocs/9643270.
United States Censuses (Census Bureau)
1790 • 1800 • 1810 • 1820 • 1830 • 1840 • 1850 • 1860 • 1870 • 1880 • 1890
1900 • 1910 • 1920 • 1930 • 1940 • 1950 • 1960 • 1970 • 1980 • 1990 • 2000 • 2010
This United States government-related article is a stub. You can help by expanding it.
This article relating to the history of the United States is a stub. You can help by expanding it.
This page uses content from the English language Wikipedia. The original content was at 1840 United States Census. The list of authors can be seen in the page history. As with this Familypedia wiki, the content of Wikipedia is available under the Creative Commons License.
1840 in the United States
Decennial federal censuses of the United States
United States government stubs
United States history stubs


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Orlando Gunman's Father Praised the Taliban as "Our Warrior Brothers"on Television
The Orlando terrorist's father claims he had no idea his son was planning the horrific Orlando club shooting that killed 50 civilians. He told members of the press:
"We are apologizing for the whole incident. We weren't aware of any action he is taking, we are in shock like the whole country. This had nothing to do with religion."
Now, video is surfacing that shows the terrorist's father on a fringe Afghan political show praising the Taliban.
Mashable reports:
The father of Omar Mateen, who has been identified as the gunman who killed 50 people at a gay nightclub in Orlando on Sunday, ranted against the Pakistan government and Afghan president Ashraf Ghani in several appearances on a US-based Afghan satellite channel. Dozen of videos of Seddique Mateen talking on a fringe political show – the "Durand Jirga Show" – hosted on the California-based Payam-e-Afghan channel can be found on YouTube.
In one video, Mateen seems to entrust the Afghan Taliban – called "our warrior brothers" – to solve the issue of the disputed Durand Line, the border between Afghanistan and Pakistan which was demarcated by the British in 1893.
"Our brothers in Waziristan, our warrior brothers in [the] Taliban movement and national Afghan Taliban are rising up," he said in Dari, a dialect of Persian spoken in northern Afghanistan, according to a Washington Post translation. "Inshallah the Durand Line issue will be solved soon."
The owner of the channel told Reuters Mateen took part to the show "three or four times a year". "He'd talk for about two to three hours," Khatab said. "He'd buy his own time and come here and broadcast and leave within a day."
Clearly, this family has been radicalized and deranged for a very long time.
Islamic extremism


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Q: Creating two expandable menus Android Java I've created two expandable menus in my application but seem to have messed up somewhere. Each menu displays duplicate content when they should each have their own list content.
Here's my code:
MainActivity.java
String names[] = Constant.name;
String subNames[] = Constant.subNameRecoveryTools =
Constant.subNameAdmissions;

private List<TitleMenu> getList() {
    List<TitleMenu> list = new ArrayList<>();
    for (int i = 0; i < names.length; i++) {
        List<SubTitle> subTitles = new ArrayList<>();
        for (int j = 0; j < subNames.length; j++) {
            SubTitle subTitle = new SubTitle(subNames[j]);
            subTitles.add(subTitle);
        }
        TitleMenu model = new TitleMenu(names[i], subTitles, null);
        list.add(model);
    }
    return list;
}

Constant.java
public class Constant {

public static String [] name = {"Recovery Tools", "Admissions"};
public static String [] subNameRecoveryTools = {"Withdrawal Scales", "Shame Scale", "Drinking Limits", "Worksheets", "eBooks"};
public static String [] subNameAdmissions = {"Pre_Screen", "Intake Paperwork", "Client Handbook", "Meet your Therapist"};

}

A: Go throught this link. Hope it helps you.
https://www.androidhive.info/2013/07/android-expandable-list-view-tutorial/