text:
\section{Introduction}
\label{Intro}

The problem of flow of a fluid overlying a porous medium saturated by the same fluid is one which has attracted the attention of many
prominent scientists. A fundamental interface condition between the fluid and the porous medium was proposed by \citet{BeaversJoseph:1967}.
The first analysis of thermal convection in the situation where a fluid overlies a saturated porous medium is due to \citet{Nield:1977}
who succesfully employed the Beavers - Joseph boundary condition to derive a satisfactory model. A surprising result for the same thermal
convection problem was discovered by \citet{ChenChen:1988} who showed that the ratio of fluid depth, $d$, to porous layer depth, $d_m$,
defined by ${\hat d}=d/d_m$, is critical to determining the process for the onset of thermal convection in the two layer system. If ${\hat d}$
is below a critical value then convection commences in the porous layer whereas when ${\hat d}$ is above the critical value then convection
commences in the fluid. This class of problem was further investigated both experimentally and theoretically by \citet{ChenChen:1989,ChenChen:1992},
\citet{Chen:1991}, \citet{McKayStraughan:1993}, where the last mentioned article applies the theory to the problem of stone formation into regular
patterns at the bottom of a shallow lake.

The subject of thermal convection or generally flow in a two layer system has been studied in much detail with a review of the early work and
applications to various areas in industry or geophysics given in chapter 6 of \citet{Straughan:2008}. The intense interest in this class of problem
has been driven by the many applications to diverse areas such as heat pipe technology, renewable energy, see e.g. \citet{Straughan:2008},
contaminant dispersal in water ways, \citet{HibiTomigashi:2015}, \citet{Hibi:2020}, or even blood flow in arteries and veins in the human body,
see e.g. \citet{SharmaYadav:2017}, \citet{Tiwari:2020}, \citet{PonalagusamyManchi:2021}, \citet{WajihahSankar:2021}. Indeed, the last mentioned
article involves 5 layer flow comprising Darcy media, Brinkman media, plasma, core flow, and plug flow.

There are many recent stability analyses of fluid flow in the two layer fluid - porous configuration, see e.g.
\citet{CarrStraughan:2003}, \citet{Chang:2006},
\citet{HillStraughan:2008,HillStraughan:2009awr}, \citet{Chang:2017}, \citet{Samanta:2020}, \citet{Yin:2020}, \citet{Tsiberkin:2020}.
Particular analyses
involving the nonlinear theory and bifurcations are given by \citet{Han:2020}, \citet{McCurdy:2019}, \citet{LyuWang:2021},
and \citet{HillStraughan:2009}. In addition, mathematical analysis of the structural stability of the two layer system has been thoroughly
investigated, see e.g. \citet{Li:2018}, \citet{Li:2021}, \citet{Li:2021amo}, \citet{PayneStraughan:1998}.

In a separate development, there has been immense interest in thermal convection in a single layer of saturated porous material but when the porous
skeleton is of double porosity type. By double porosity we mean that the solid skeleton contains pores of a visible size known as macro pores, but
the skeleton itself contains cracks or fissures which give rise to much smaller micropores. Flow in such materials is additionally called
bidisperse or bidispersive.
The thermal convection problem in a bidisperse porous material was first developed by \citet{NieldKuznetsov:2006} who allowed for different velocities,
pressures and temperature fields in the macro and micro phases and
a critical review of the topic is given by \citet{GentileStraughan:2020}. There are many recent contributions
driven by the need to understand bidispersive convection in real life applications, cf. \citet{GentileStraughan:2020}, \citet{Straughan:2017},
chapter 13. Analyses of bidispersive thermal convection in isotropic, anisotropic, vertical layer, inclined layer, and with rotation effects are given
by \citet{BaddayHarfash:2021}, \citet{Capone:2020prsa}, \citet{Capone:2020mrc}, \citet{CaponeDeLuca:2020}, \citet{CaponeMassa:2021},
\citet{Capone:2021am}, \citet{Chaloob:2021}, \citet{Falsaperla:2016}, \citet{GentileStraughan:2017,GentileStraughan:2017prsa},
\citet{SaravananVigneshwaran:2020}, \citet{Straughan:2018prsa,Straughan:2019prsa,Straughan:2019abc}, and the structural stability aspect of the system
of equations is considered by \citet{Franchi:2017}.

The object of the current work is to present a model for thermal convection in an incompressible viscous fluid when that fluid overlies a
bidispersive porous medium saturated with the same fluid. We analyse the instability of thermal convection in this system and show there are definite
relations between the onset of convective motion and the respective depths of the fluid and porous layers, and of the properties of the macro and
micro pores. This is the first analysis we have seen of this problem and we believe it has much future application to diverse areas such as
blood flow, heat transfer, and renewable energy.

\section{Basic equations}
\label{equations}

We suppose a linearly viscous incompressible fluid is contained in the infinite layer $\mathbb{R}^2\times\{0<z<d\}$ and below this is a bidisperse
porous medium saturated with the same fluid and this occupies the infinite layer $\mathbb{R}^2\times\{-d_m<z<0\}$, with gravity acting in the
negative $z-$direction.

The equations for the fluid in the layer $\mathbb{R}^2\times\{0<z<d\}$ are then, cf. \citet{Chandrasekhar:1981},
\begin{equation}\label{E:FluidEqs}
\begin{aligned}
&V_{i,t}+V_jV_{i,j}=-\frac{1}{\rho_0}\,p_{,i}+\nu\Delta V_i+\gamma g k_i T,\\
&V_{i,i}=0,\\
&T_{,t}+V_iT_{,i}=\frac{k_f}{(\rho_0c_p)_f}\,\Delta T,
\end{aligned}
\end{equation}
where $V_i({\bf x},t)$ is the velocity field, $T({\bf x},t)$ is the temperature field, $p({\bf x},t)$ is the pressure field, ${\bf x}$ is the spatial
point in the layer, and $t$ is time.
We use indicial notation throughout in conjunction with the Einstein summation convention, so that, for example,
\begin{align*}
V_iT_{,i}\equiv \sum_{i=1}^3V_iT_{,i}&\equiv
V_1\frac{\partial T}{\partial x_1}
+V_2\frac{\partial T}{\partial x_2}
+V_3\frac{\partial T}{\partial x_3}\\
&\equiv
U\frac{\partial T}{\partial x}
+V\frac{\partial T}{\partial y}
+W\frac{\partial T}{\partial z}\,,
\end{align*}
where ${\bf V}=(V_1,V_2,V_3)\equiv (U,V,W)$. In equations \eqref{E:FluidEqs} $\gamma,g,\rho_0,k_f,\nu$ and $c_p$ are the thermal expansion
coefficient of the fluid, gravity, reference density, thermal conductivity of the fluid, kinematic viscosity of the fluid, and specific heat at
constant pressure of the fluid. The vector ${\bf k}=(0,0,1)$ and $\Delta$ is the Laplacian
\begin{equation*}
\Delta=\frac{\partial^2}{\partial x^2}
+\frac{\partial^2}{\partial y^2}
+\frac{\partial^2}{\partial z^2}\,.
\end{equation*}

For an isotropic bidisperse porous material we suppose the macro porosity is $\phi$, the micro porosity is $\epsilon$. If we denote
$(U^f_i,p^f)$ to be the pore averaged velocity and pressure in the macropores and
$(U^p_i,p^p)$ to be the pore averaged velocity and pressure in the micropores, then the governing equations of flow in the bidisperse porous
medium may be written, cf. \citet{GentileStraughan:2017}, \citet{Straughan:2018prsa},
\begin{equation}\label{E:PorEqs}
\begin{aligned}
&-\frac{\mu}{K_f}\,U^f_i-\zeta(U^f_i-U^p_i)-p^f_{,i}+\rho_0\gamma k_i g T^m=0,\\
&U^f_{i,i}=0,\\
&-\frac{\mu}{K_p}\,U^p_i-\zeta(U^p_i-U^f_i)-p^p_{,i}+\rho_0\gamma k_i g T^m=0,\\
&U^p_{i,i}=0,\\
&(\rho_0c)_mT^m_{,t}+(\rho_0c)_f(U^f_i+U^p_i)T^m_{,i}=k_m\Delta T^m,
\end{aligned}
\end{equation}
where $T^m({\bf x},t)$ is the temperature field of the fluid in the bidisperse porous medium.

Equations \eqref{E:FluidEqs} hold on the domain $\{(x,y)\in\mathbb{R}^2\}\times\{z\in(0,d)\}\times\{t>0\}$ while
\eqref{E:PorEqs} hold on the domain
$\{(x,y)\in\mathbb{R}^2\}\times\{z\in(-d_m,0)\}\times\{t>0\}$.
Equations \eqref{E:PorEqs} assume Darcy's law holds and a Boussinesq approximation is employed. The variable $\mu$ is the dynamic viscosity of the
fluid, $K_f$ and $K_p$ are the macro and micro permeabilities, $\zeta$ is an interaction coefficient which represents the momentum transfer
between the macro and micro phases, and $(\rho_0c)_m$, $k_m$ are given by
\begin{equation*}
(\rho_0c)_m=(1-\phi)(1-\epsilon)(\rho_0c)_s+\phi(\rho_0c)_f+\epsilon(1-\phi)(\rho_0c)_p\,,
\end{equation*}
and
\begin{equation*}
k_m=(1-\phi)(1-\epsilon)k_s+\phi k_f+\epsilon(1-\phi) k_p\,,
\end{equation*}
where $s,f$ and $p$ denote values in the solid skeleton, the fluid in the macropores, and the fluid in the micropores.

The boundary conditions at the top and bottom of the layer, $z=d$ and $z=-d_m$ are specified as follows
\begin{equation}\label{E:BCs1}
\begin{aligned}
& V_i=0,\quad T=T_U,\qquad {\rm on}\,\,z=d,\\
& U^f_3=0,\quad U^p_3=0,\quad T^m=T_L,\qquad {\rm on}\,\,z=-d_m\,,
\end{aligned}
\end{equation}
where $T_U,T_L$ are constants with $T_L>T_U>0$. Under these conditions \eqref{E:FluidEqs} and \eqref{E:PorEqs} admit a steady conduction
solution of form
\begin{equation}\label{E:SSoln}
\begin{aligned}
&{\bar U}^f_i=0,\qquad{\bar U}^p_i=0,\qquad {\bar V}_i=0,\\
&{\bar T}=T_0-(T_0-T_U)\,\frac{z}{d}\,,\qquad 0\le z\le d,\\
&{\bar T}^m=T_0-(T_L-T_0)\,\frac{z}{d_m}\,,\qquad -d_m\le z\le 0,
\end{aligned}
\end{equation}
where we have employed the fact that the temperature is continuous across the interface $z=0$. To determine the constant $T_0$ we require the
heat flux to be continuous across the interface $z=0$ and then
\begin{equation*}
k_m\,\frac{d{\bar T}^m}{dz}=k_f\frac{d{\bar T}}{dz}\,,\qquad {\rm at}\,\,z=0.
\end{equation*}
This yields $T_0$ as
\begin{equation}\label{E:T0val}
T_0=\frac{k_fT_Ud_m+k_mT_Ld}{dk_m+d_mk_f}\,.
\end{equation}

\section{Perturbation equations}
\label{pert}

As our goal is to study instability of the base solution \eqref{E:SSoln} we now introduce perturbations to the variables
$V_i,T,p^f,U^f_i,U^p_i,T^m,p^p$
as
$u_i,\theta,\pi^f,u_i^f,u_i^p,\theta^m$
and
$\pi^p$.
We derive the perturbation equations for these variables from equations \eqref{E:FluidEqs} and \eqref{E:PorEqs}. However, it is convenient to present these
in non-dimensional form with length scales
$d,d_m$
in the fluid and bidisperse porous layers, and with corresponding velocity scales
$U$ and $U^m$,
although we here select
$U=U^m$.
The time scales are
$\mathcal{T}$ and $\mathcal{T}^m$
where
$\mathcal{T}=d^2/\nu$,
with
$\nu=\mu/\rho_0$
and we pick
$\mathcal{T}=\mathcal{T}^m$.
The pressure scale is
$P=\mu U/d$.
The temperature scales are
\begin{equation*}
T^{\sharp}=\frac{U(T_0-T_U)d(\rho_0c_p)_f}{k_f}
\end{equation*}
and
\begin{equation*}
T^{\sharp}_m=U^m(T_L-T_0)\frac{d_m(\rho_0c_p)_f}{k_m}
\end{equation*}
and thus one finds
\begin{equation*}
\frac{T^{\sharp}}{T^{\sharp}_m}=\Bigl(\frac{k_m}{k_f}\Bigr)^2{\hat d}^2\,,\qquad
\frac{T_0-T_U}{T_L-T_0}=\frac{k_m}{k_f}\,{\hat d}
\end{equation*}
where
${\hat d}=d/d_m$.
It is convenient to introduce the notation
\begin{equation*}
{\hat k}=\frac{k_f}{k_m}\,,\qquad{\hat\kappa}=\frac{(\rho_0c)_m}{(\rho_0c)_f}\,{\hat k}\,,
\end{equation*}
and to define the Prandtl number, $Pr$, and the porous Prandtl number, $Pr_m$, by
\begin{equation*}
Pr=\frac{\nu}{\kappa}=\frac{\mu}{\rho_0}\,\frac{(\rho_0c_p)_f}{k_f}\,,\qquad
Pr_m=\frac{\mu}{\rho_0}\,\frac{(\rho_0c)_m}{k_m}
\end{equation*}
from which one may show
$Pr_m={\hat\kappa}Pr$.

The fluid and porous Rayleigh numbers $Ra$ and $Ra^m$ are defined by
\begin{equation}\label{E:RaDef}
Ra=\frac{\gamma gd^4}{\kappa_f\nu}\,\frac{(T_0-T_U)}{d}\,,
\end{equation}
where
$\kappa_f=k_f/(\rho_0c_p)_f$,
and
\begin{equation}\label{E:RamDef}
Ra_m=\gamma gK^f\frac{(T_L-T_0)}{d_m}\,\frac{d_m^2}{[k_m/(\rho_0c)_f]\nu}\,,
\end{equation}
from which one shows
\begin{equation*}
Ra=\Bigl(\frac{{\hat d}}{{\hat k}}\Bigr)^2\,\frac{Ra_m}{Da}
\end{equation*}
where $Da$ is the Darcy number defined here as
\begin{equation*}
Da=\frac{K_f}{d^2}\,.
\end{equation*}
The relative permeability $K_r$ is defined by $K_r=K_f/K_p$, and another useful non-dimensional variable is
$\delta=\sqrt{K_p}/d_m$,
from which we may see that
$Da=K_r\delta^2/{\hat d}^2$.

With the above non-dimensionalization one may show that the linearized fluid perturbation equations have form
\begin{equation}\label{E:FluidPert}
\begin{aligned}
&u_{i,t}=-\pi_{,i}+\Delta u_i+Rak_i\theta,\\
&u_{i,i}=0,\\
&Pr\theta_{,t}=w+\Delta\theta
\end{aligned}
\end{equation}
where $w=u_3$ and these equations hold on $\mathbb{R}^2\times\{z\in(0,1)\}\times\{t>0\}$
while the linearized bidispersive porous media equations have form
\begin{equation}\label{E:PorPert}
\begin{aligned}
&-u^f_i-\xi(u_i^f-u_i^p)-\pi^f_{,i}+Ra^mk_i\theta^m=0,\\
&u^f_{i,i}=0,\\
&-K_ru^p_i-\xi(u_i^p-u_i^f)-\pi^p_{,i}+Ra^mk_i\theta^m=0,\\
&u^p_{i,i}=0,\\
&\frac{Pr^m}{{\hat d}^2}\,\theta^m_{,t}=w^f+w^p+\Delta\theta_m
\end{aligned}
\end{equation}
where
$w^f=u_3^f,w^p=u_3^p$ and equations \eqref{E:PorPert} hold on
$\mathcal{R}^2\times\{z_m\in(-1,0)\}\times\{t>0\}$. The non-dimensional momentum transfer interaction coefficient $\xi$ is defined by
$\xi=\zeta K_f/\mu$.

Equations \eqref{E:FluidPert} and \eqref{E:PorPert} when reduced to the thermal convection instability problem essentially represent a twelth order system
of equations. We thus require twelve boundary conditions. In this work we employ a normal mode instability analysis and it is sufficient to require the
following conditions
\begin{equation*}
w=w^{\prime}=\theta=0,\qquad {\rm on}\,\,z=1,
\end{equation*}
where $w^{\prime}=\partial w/\partial z$. This corresponds to a fixed upper surface. Also,
\begin{equation*}
w^f=w^p=\theta^m=0,\qquad {\rm on}\,\,z=-1.
\end{equation*}
The remaining six boundary conditions come from considerations on the interface $z=0$.
At the micoscopic level the velocity $W$ in the fluid should be continuous across the interface with the actual velocity $W^f$ in a macro pore
and with the actual velocity $W^p$ in a micro pore. In dimensional form this requires at $z=0$,
\begin{equation*}
W=\frac{W^f}{\phi},\qquad{\rm and}\qquad W=\frac{W^p}{\epsilon(1-\phi)}\,,
\end{equation*}
where $w^f$ and $w^p$ are the pore averaged values. Likewise the dimensional temperatures are continuous so
\begin{equation*}
\theta=\theta_m,\qquad{\rm at}\qquad z=0.
\end{equation*}
In addition the normal component of heat flux ${\bf q}\cdot{\bf n}$ is continuous across $z=0$. Two further conditions are needed and these arise by
requiring continuity of normal stress, and by appealing to a combination of appropriate forms of the experimentally verified \citet{BeaversJoseph:1967}
condition. Details of these boundary conditions are amplified below.

\section{Instability analysis}
\label{instab}

The next step is to remove the pressure terms $\pi,\pi^f$ and $\pi^p$ from \eqref{E:FluidPert} and \eqref{E:PorPert}
and this we do by taking curl curl of equations \eqref{E:FluidPert}$_1$ and \eqref{E:PorPert}$_{1,3}$
and retaining the third component. This results in the
system of equations
\begin{equation}\label{E:Lin1}
\begin{aligned}
&\sigma\Delta w=\Delta^2w+Ra\Delta^*\theta,\\
&\sigma Pr\theta=w+\Delta\theta,
\end{aligned}
\end{equation}
and
\begin{equation}\label{E:Lin2}
\begin{aligned}
&(1+\xi)\Delta w^f-\xi\Delta w^p-Ra^m\Delta^*\theta^m=0,\\
&(K_r+\xi)\Delta w^p-\xi\Delta w^f-Ra^m\Delta^*\theta^m=0,\\
&\frac{\sigma_m Pr_m}{{\hat d}^2}\,\theta^m=w^f+w^p+\Delta\theta^m,
\end{aligned}
\end{equation}
where we have represented time by $e^{\sigma t}$ in the fluid equations and by $\exp(\sigma_mt)$ in the bidispersive porous equations. The symbol
$\Delta^*$ is the horizontal Laplacian. Equations \eqref{E:Lin1} hold on
$\mathbb{R}^2\times(0,1)$
while \eqref{E:Lin2} hold on
$\mathbb{R}^2\times(-1,0)$.

We next solve \eqref{E:Lin2}$_{1,2}$ in terms of $\Delta w^f$ and $\Delta w^p$. We represent $w$ and $\theta$ as
$w=W(z)h(x,y)$,
$\theta=\Theta(z)h(x,y)$,
and
$w^f=W^f(z)h^m(x,y)$,
$w^p=W^p(z)h^m(x,y)$,
$\theta_m=\Theta_m(z)h^m(x,y)$,
where $h$ and $h_m$ are plan forms which tile the plane, cf. \citet{Chandrasekhar:1981}, pp. 43-52,
and are typical of the hexagonal convection cell forms found in  real life. The functions $h$ and $h_m$ satisfy the relations $\Delta^*h=-a^2h$
and
$\Delta^*h_m=-a_m^2h_m$,
for wavenumbers $a$ and $a_m$.
We reduce \eqref{E:Lin1}$_1$ to two second order equations by setting $\Delta w=\chi$, and then we arrive at the following coupled system of equations
to solve for the growth rate (eigenvalues)
$\sigma,\sigma_m$,
\begin{equation}\label{E:Lin3}
\begin{aligned}
&(D^2-a^2)W-\chi=0,\\
&(D^2-a^2)\chi-Ra\,a^2\Theta=\sigma\chi,\\
&(D^2-a^2)\Theta+W=Pr\,\sigma\,\Theta,
\end{aligned}
\end{equation}
on $z\in(0,1)$, where $D=d/dz$, and
\begin{equation}\label{E:Lin4}
\begin{aligned}
&(D^2-a^2_m)W^f+Ra_m\,a_m^2\,\frac{(K_r+2\xi)}{(K_r+\xi+\xi K_r)}\,\Theta_m=0,\\
&(D^2-a^2_m)W^p+Ra_m\,a_m^2\,\frac{(1+2\xi)}{(K_r+\xi+\xi K_r)}\,\Theta_m=0,\\
&(D^2-a^2_m)\Theta_m+W^f+W^p=\frac{Pr_m}{{\hat d}^2}\,\sigma_m\,\Theta_m,
\end{aligned}
\end{equation}
on $z_m\in(-1,0)$.

The non-dimensional boundary conditions are
\begin{equation}\label{E:BCs1A}
\begin{aligned}
&W=W^{\prime}=\Theta=0,\qquad z=1,\\
&W^f=W^p=\Theta^m=0,\qquad z=-1,
\end{aligned}
\end{equation}
together with the non-dimensional interface conditions
\begin{equation}\label{E:BCs2}
\begin{aligned}
&W=\frac{W^p}{\epsilon(1-\phi)}\,,\qquad\frac{W=W^f}{\phi}\,,\qquad z=0,\\
&\theta_m=\theta\Bigl(\frac{k_m}{k_f}\Bigr)^2\,{\hat d}^2,\qquad
\frac{d\theta_m}{dz_m}=\frac{d\theta}{dz}\,{\hat d}\,\frac{k_m}{k_f}\,,\qquad z=0,
\end{aligned}
\end{equation}
where the latter two arise due to continuity of temperature, and continuity of heat flux.

For the remaining interface conditions we argue as follows.

In terms of the fluid and pore averaged velocities at the microscopic level, the \citet{BeaversJoseph:1967} condition may be applied separately to the macro
and micro components to yield in dimensionless form
\begin{equation}\label{E:BJf}
\frac{1}{d}\,\frac{\partial u_{\beta}}{\partial z}=\frac{\alpha_1}{\sqrt{K_f}}\,(u_{\beta}-u^f_{\beta})\,,\qquad\beta=1,2,
\end{equation}
and
\begin{equation}\label{E:BJp}
\frac{1}{d}\,\frac{\partial u_{\beta}}{\partial z}=\frac{\alpha_2}{\sqrt{K_p}}\,(u_{\beta}-u^p_{\beta})\,,\qquad\beta=1,2,
\end{equation}
where $\alpha_1$ and $\alpha_2$
are experimentally determined constants. For a single porosity material \citet{BeaversJoseph:1967} write that ``{\sl $\alpha$ is a dimensionless
quantity depending on the material parameters which characterize the structure of permeable material within the boundary region}".
Our first approach is to take an averaged value of each of the conditions \eqref{E:BJf} and \eqref{E:BJp} and propose at the interface $z=0$,
\begin{equation}\label{E:BJ1}
\frac{\partial u_{\beta}}{\partial z}=(A_1+A_2)u_{\beta}-A_1u^f_{\beta}-A_2u^p_{\beta}\,,\qquad\beta=1,2,
\end{equation}
where
\begin{equation}\label{E:BJA1A2}
A_1=\frac{\alpha_1d}{2\sqrt{K_f}}\,\qquad A_2=\frac{\alpha_2d}{2\sqrt{K_p}}\,.
\end{equation}
We next differentiate \eqref{E:BJ1} and employ the incompressibility conditions to derive the interface condition
\begin{equation}\label{E:BJ11}
w_{zz}=(A_1+A_2)w_z-A_1{\hat d}w^f_{z_m}-A_2{\hat d}w^p_{z_m}
\end{equation}
where the derivatives are with respect to $z,z_m$ non-dimensional, $0\le z\le 1$, $-1\le z_m\le 0$.

We also consider an alternative procedure whereby we combine the \citet{BeaversJoseph:1967} conditions \eqref{E:BJf} and \eqref{E:BJp} in a manner which
reflects the macro and micro contributions.
Thus, define the constants
$c_1$ and $c_2$ by
\begin{equation*}
c_1=\frac{\phi}{\phi+\epsilon(1-\phi)}\,,\qquad c_2=\frac{\epsilon(1-\phi)}{\phi+\epsilon(1-\phi)}\,.
\end{equation*}
We now produce an equation of form \eqref{E:BJ1} but where now
\begin{equation}\label{E:A1A2def}
A_1=c_1\alpha_1d/\sqrt{K_f}\qquad
A_2=c_2\alpha_2d/\sqrt{K_p}\,.
\end{equation}
We thus derive an equation of form \eqref{E:BJ11} but with $A_1$ and $A_2$
as given here. The differences in employing \eqref{E:BJ11} and the pore weighted version just discussed are considered in the numerical results section.
For ease in understanding the numerical results where the effect of parameter variation upon the solution is considered we specifically write the two
versions of \eqref{E:BJ11} here as, equal splitting,
\begin{equation}\label{E:BJes}
w_{zz}=\Bigl(\frac{\alpha_1d}{2\sqrt{K_f}}+\frac{\alpha_2d}{2\sqrt{K_p}}\Bigr)w_z-\frac{\alpha_1d}{2\sqrt{K_f}}\,{\hat d}\,w^f_{z_m}
-\frac{\alpha_2d}{2\sqrt{K_p}}\,{\hat d}\,w^p_{z_m}
\end{equation}
and pore weighted
\begin{equation}\label{E:BJpw}
w_{zz}=\Bigl(\frac{c_1\alpha_1d}{\sqrt{K_f}}+\frac{c_2\alpha_2d}{\sqrt{K_p}}\Bigr)w_z-\frac{c_1\alpha_1d}{\sqrt{K_f}}\,{\hat d}\,w^f_{z_m}
-\frac{c_2\alpha_2d}{\sqrt{K_p}}\,{\hat d}\,w^p_{z_m}\,.
\end{equation}

At the microscopic level, continuity of normal stress at the interface $z=0$ requires
\begin{equation*}
\pi^f=\pi-2\mu w_z,\qquad {\rm for}\,\,{\rm a}\,\,{\rm macropore},
\end{equation*}
and
\begin{equation*}
\pi^p=\pi-2\mu w_z,\qquad {\rm for}\,\,{\rm a}\,\,{\rm micropore}.
\end{equation*}
Our first continuity of normal stress interface condition is
\begin{equation}\label{E:CtyNS}
\frac{\pi^f+\pi^p}{2}=\pi-2\mu w_z,\qquad {\rm on}\,\,z=0.
\end{equation}
Equation \eqref{E:CtyNS} is differentiated with respect to $x_{\alpha}$, $\alpha=1,2$,
and one then employs the differential equations \eqref{E:FluidPert}$_{1,2}$ and \eqref{E:PorPert}$_{1-4}$ in the forms
\begin{equation}\label{E:Int}
\begin{aligned}
&\pi_{,\alpha}=\Delta u_{\alpha}-\sigma u_{\alpha}\,,\qquad u_{\alpha,\alpha}+w_{,z}=0,\\
&\pi^f_{,\alpha}=-u^f_{\alpha}-\xi(u^f_{\alpha}-u^p_{\alpha})\,,\qquad u^f_{\alpha,\alpha}+w^f_{,z}=0,\\
&\pi^p_{,\alpha}=-K_r u^p_{\alpha}-\xi(u^p_{\alpha}-u^f_{\alpha})\,,\qquad u^p_{\alpha,\alpha}+w^p_{,z}=0,
\end{aligned}
\end{equation}
to eliminate the pressure terms. The differentiated form of \eqref{E:CtyNS} is rewritten using \eqref{E:Int} as
\begin{equation}\label{E:Int2}
\frac{1}{2}\bigl(-u^f_{\alpha}-\xi[u^f_{\alpha}-u^p_{\alpha}]-K_ru^p_{\alpha}-\xi[u^p_{\alpha}-u^f_{\alpha}]\bigr)
=\Delta u_{\alpha}-\sigma u_{\alpha}-2\mu w_{,z\alpha}\,,
\end{equation}
where $\alpha=1,2$.
Note that in this case the $\xi$
terms disappear.
Now differentiate \eqref{E:Int2} for $\alpha=1$ with respect to $x$ and for $\alpha=2$ with respect to $y$. This yields after summation to
\begin{equation*}
\frac{1}{2}(-u^f_{\alpha,\alpha}-K_r u^p_{\alpha,\alpha})=\Delta u_{\alpha,\alpha}-\sigma u_{\alpha,\alpha}-2\mu w_{,z\alpha\alpha}\,.
\end{equation*}
Then use the incompressibility conditions to find
\begin{equation}\label{E:Int3}
\frac{1}{2}(w^f_{,z}+K_rw^p_{,z})=-\Delta w_{,z}+\sigma w_{,z}-2\mu\Delta^*w_{,z}
\end{equation}
where $\Delta^*=\partial^2/\partial x^2+\partial^2/\partial y^2$.
Equation \eqref{E:Int}$_3$ allows one to determine the following non-dimensional interface condition
\begin{equation}\label{E:CtyNS2}
\frac{1}{2}(D_mw^f+KrD_mw^p)=\frac{Da}{{\hat d}}\,(\sigma Dw-D^3w-3\Delta^*Dw),
\end{equation}
where $D=d/dz,z\in(0,1)$,
$D_m=d/dz_m,z_m\in(-1,0)$.

Alternatively, one may employ a weighted form of \eqref{E:CtyNS} where we write
\begin{equation*}
c_1\pi^f+c_2\pi^p=\pi-2\mu w_z\,.
\end{equation*}
This then leads to a weighted form of \eqref{E:CtyNS2}. In deriving the weighted form the interaction terms involving $\xi$ do not vanish. The precise forms
are given in the next section.

Thus, the complete set of boundary conditions are \eqref{E:BCs1A}, \eqref{E:BCs2}, together with \eqref{E:BJ11} and \eqref{E:CtyNS2}, or the
weighted equivalents of these latter two equations.

\section{Numerical method}
\label{nummeth}

We solve equations \eqref{E:Lin3} and \eqref{E:Lin4} by a Chebyshev tau method, cf. \citet{Dongarra:1996}, coupled with the $QZ$ algorithm for a generalized
matrix eigenvalue problem, cf. \citet{MolerStewart:1971}.
Equations \eqref{E:Lin3} are transformed into the Chebyshev domain $(-1,1)$ and equations \eqref{E:Lin4} are likewise transformed into the same domain with
the interface now being $z=-1$. The variables
$W,\chi,\Theta,W^f,W^p$ and $\Theta^m$ are written as finite series of Chebyshev polynomials, e.g.
\begin{equation*}
W=\sum_{i=0}^N W_iT_i(z)\,,
\end{equation*}
for Fourier coefficients $W_i$. This yields a block matrix generalized eigenvalue problem of form
$A{\bf x}=\sigma B{\bf x}$
for $6N\times 6N$
matrices $A,B$ with $B$ singular, where
\begin{equation*}
{\bf x}=({\tilde W},{\tilde\chi},{\tilde\Theta},{\tilde W^f},{\tilde W^p},{\tilde\Theta^m})
\end{equation*}
${\tilde W}$ etc., being the truncated versions of $W$, etc., i.e.
\begin{equation*}
{\tilde W}=(W_0,\cdots,W_N),\cdots,{\tilde\Theta^m}=(\Theta^m_0,\cdots,\Theta^m_N).
\end{equation*}
The boundary conditions are likewise expanded in Chebyshev polynomials and added as rows of the
matrices $A$ and $B$ via a similar procedure to that explained in \citet{Dongarra:1996}.

The complete set of boundary conditions on $z=1$ or $z=-1$ are now
\begin{equation}\label{E:BCsCD}
\begin{aligned}
&W=0,\,\,DW=0,\,\,\Theta=0,\,\,W^f=0,\,\,W^p=0,\,\,\Theta_m=0,\quad z=1,\\
&W=\frac{W^f}{\phi}\,,\quad W=\frac{W^p}{\epsilon(1-\phi)}\,,\quad z=-1,\\
&\Theta_m=\Theta\,\frac{{\hat d}^2}{{\hat k}^2}\,,\quad D_m\Theta_m+\frac{{\hat d}}{{\hat k}}\,D\Theta=0,\quad z=-1,\\
&A+a^2W-2(A_1+A_2)DW\\
&\qquad -2A_2{\hat d}D_mW^p-2A_1{\hat d}D_mW^f=0,\quad z=-1,
\end{aligned}
\end{equation}
and
\begin{equation}\label{E:BCcns}
2DA-4a^2DW-\frac{{\hat d}}{Da}\,D_mW^f-\frac{K_r{\hat d}}{Da}\,D_mW^p=2\sigma DW,\quad z=-1.
\end{equation}
This is for the case \eqref{E:CtyNS} and \eqref{E:BJ11} with $A_1$ and $A_2$ given by \eqref{E:BJA1A2}. When the weighted version of the Beavers - Joseph
and continuity of normal stress conditions are employed then \eqref{E:BCsCD}$_3$ holds but with $A_1$ and $A_2$ given by \eqref{E:A1A2def}.
However, in the weighted case \eqref{E:BCcns} should be replaced by
\begin{equation}\label{E:BCWtd}
\begin{aligned}
2DA&-4a^2DW-\frac{2{\hat d}}{Da}\,[c_1+\xi(c_1-c_2)]D_mW^f\\
&-\frac{2{\hat d}}{Da}[K_rc_2+\xi(c_2-c_1)]D_mW^p=2\sigma DW,
\end{aligned}
\end{equation}
where it is to be observed that the interaction terms involving $\xi$ are present.

\section{Numerical results}
\label{num}

This section reports on numercial results for the critical Rayleigh number and critical wavenumber for the equations for thermal convection in a
linearly viscous fluid overlying a bidisperse porous material. We choose parameter values appropriate to water being the working fluid and a bidisperse
porous material being based upon a glass bead skeleton.

As this is the first calculation for this problem we restrict attention to $\alpha_1=\alpha_2=\alpha$ for the Beavers - Joseph constant. Since there are many
parameters we believe this is justified. For numerical values of the many parameters we refer to \citet{GentileStraughan:2020} who employed tabulated
experimental values of \citet{Hooman:2015}, \citet{ImaniHooman:2017}, \citet{Chen:1991}, \citet{Rees:2009,Rees:2010} and \citet{Nield:2000}.

\citet{BeaversJoseph:1967} reported values of $\alpha$ for a single porosity material in the range 0.1 to 4. These values are for a granular aloxite
material and for man made porous foams. In this work we concentrate on more granular materials and choose $\alpha$ values close to 0.1. The values reported
in \citet{GentileStraughan:2020} suggest we take relative permeabilities of
\begin{equation*}
K_r=25,151.7,263.16
\end{equation*}
and values for the non-dimensional momentum transfer coefficient in the group
\begin{equation*}
\xi=1.515\times 10^{-2},2.347\times 10^{-2},2.987\times 10^{-2},0.1316.
\end{equation*}

We here choose to investigate the behaviour of the critical $Ra_m$ and $a_m$ values upon
$K_r,\alpha,\xi,\phi,\epsilon$, and upon the equal splitting interface conditions of Beavers and Joseph
and continuity of normal stress together with the analogous pore weighted interface conditions.

For core values using glass beads and water the thermal conductivities, densities and specific heats are taken from the internet version of
Engineering Toolbox to yield $k_m,k_f,(\rho c)_m$ and $(\rho c)_f$. We also employ the parameter ranges in \citet{GentileStraughan:2020} to find
values for $\xi,K_r$ and $\delta$.
In this way we obtain
$Pr=6,Pr_m=0.75828,$ $Da=0.161278\times 10^{-2}$, $\delta=0.3279\times 10^{-2},$ ${\hat k}=0.16736$, $\phi=0.3,\epsilon=0.3$, $\alpha=0.1$,
$\xi=0.02987$, ${\hat\kappa}=0.12638$, $K_r=25$, although specific values will be varied at appropriate points in our discussion.
The nature of the onset of convective motion in all cases depends on ${\hat d}$, the depth of fluid layer to depth of porous layer.
There is a critical value of ${\hat d}$ such that when ${\hat d}$ is below this value then convective motion commences in the porous layer
whereas such motion is initiated in the fluid layer when ${\hat d}$ is above the critical value. The critical ${\hat d}$ value also depends
strongly on the other parameters in the problem and this variation is examined in detail here.

The bimodal behaviour of the neutral curves is displayed in figures \ref{fig:fig1} and \ref{fig:fig2}. Figure \ref{fig:fig1} shows that
when ${\hat d}=0.12$ the lowest minimum for $Ra_m$ is at $a_m=2.1$ and this corresponds to convection initiating in the porous layer, whereas
when ${\hat d}=0.13$ the lowest minimum for $Ra_m$ is at $a_m=17.0$ and this corresponds to convective motion initiating in the fluid layer. From table
\ref{Ta:Ta1} we see that the critical value for ${\hat d}$ corresponding to figure \ref{fig:fig1} is when ${\hat d}_{crit}\in(0.1260,0.1261)$.
Observe that from table \ref{Ta:Ta1} the wavenumber jumps from $a_m=2.1$ to $a_m=17.7$ as the initiation of convection switches from the porous layer
to the fluid layer. Since $a_m$ is inversely proportional to the aspect ratio of the convection cell this means that for a non-dimensional depth of
porous layer of 1 the width of the cell changes from $2\pi/2.1$ to $2\pi/17.7$, i.e. from 2.99 to 0.355, or from wide cells in the porous layer
to cells 8.42 times smaller in the fluid layer. Of course, the aspect ratio also depends on other parameters in the bidispersive porous medium.
Figure \ref{fig:fig2} also displays a switch from convection in the porous layer to convection in the fluid layer, but now when ${\hat d}$
is fixed. In this case the switch of convection is due to the macro porosity changing.

It is noticeable that the minima associated to the fluid are widely separated in figure \ref{fig:fig1} whereas in \ref{fig:fig2} it is the minima
associated to the porous medium which display the greater variation. Since figure \ref{fig:fig2}
is displaying changes in the porosity the larger variation in the ``porous minimum" is to be expected.

Table \ref{Ta:Ta1} displays how the critical values of the porous Rayleigh number $Ra_m$ and the critical values of the porous wavenumber $a_m$ change as
$K_r$ is varied. Since we are effectively fixing $K^f$ in our computations changing $K_r$ corresponds to changing $1/K^p$. As $K_r$ increases in
table \ref{Ta:Ta1} from values of 1.5 through to 263.16 we see that $Ra_m$ increases, both for the porous and fluid minima. This corresponds to the
layered system becoming less easy to convect as $\Delta T=T_L-T_U$ increases. Since $K_r$ increasing corresponds to $K^p$ decreasing this means it is more
difficult for the fluid to move in the micro pores and so we expect the system to be more stable. It is worth observing that in all our computations we have
found that at criticality the growth rate $\sigma$ is real.

From table \ref{Ta:Ta1} the porous wavenumber $a_m$ increases by a factor of approximately 2.5 over the range of variation of $K_r$ but the wavenumber
corresponding to the fluid decreases from 24.4 or 26.1 to 9.3 or 8.3, respectively, depending on the value of ${\hat d}$. Thus, at the onset of convection when the
motion is initiated in the porous layer increasing $K_r$ decreases the cell aspect ratio whereas the opposite is true when the convective motion is initiated
in the fluid layer. The quantitative value of this effect does demonstrate that the presence of the bidisperse layer is significant in both cell aspect
ratio and whether convection will occur.

Table \ref{Ta:Ta2} displays how $Ra_m$ and $a_m$ change at criticality with variation in the Beavers - Joseph interface parameter. We find that increasing
$\alpha$ decreases the value of $Ra_m$ and also that of $a_m$. Since the coefficient $\alpha$ multiplies $u_{\alpha}-u^{f,p}_{\alpha}$ increasing
its value has the effect of increasing the shear flow term $\partial u_{\alpha}/\partial z$ which is making the system more stable and increasing the
convection cell aspect ratio.

Table \ref{Ta:Ta3} displays the effect of changing the momentum transfer coefficient $\xi$ upon $Ra_m$ and $a_m$. It is seen that a relative change of
over 4 in $\xi$ reduces both $Ra_m$ and $a_m$, although the change is relatively small.

Table \ref{Ta:Ta4} demonstrates how the critical values of $Ra_m$ and $a_m$ are affected by changing the macro porosity $\phi$ and the micro porosity
$\epsilon$. For a fixed value of $\phi$ increasing $\epsilon$ leads to an increase in $Ra_m$ and $a_m$ for the convection initiation in the porous
medium, while the values associated to initiation in the fluid part of the layer show little variation. This indicates that increasing $\epsilon$ for fixed $\phi$
helps to stabilize the fluid layer. This could be an important factor in any application which requires the fluid/porous layer to not convect.

Increasing $\phi$ for fixed $\epsilon$ decreases both $Ra_m$ and $a_m$ as might be expected since a larger macro porosity should mean convective motion is
easier to commence. However, care must be taken in interpretation. The Rayleigh number $Ra_m$ as defined in \eqref{E:RamDef} may be rewritten as
\begin{equation}\label{E:RamDef2}
Ra_m=\frac{\gamma g(T_L-T_U)d_md^2}{\kappa_m\nu}\,\frac{Da}{(1+{\hat d}/{\hat k})}\,\frac{(\rho c)_f}{(\rho c)_m}\,.
\end{equation}
Clearly $Ra_m$ has the correct structure but since $Da=K_f/d^2$ there is a direct dependence on the macro permeability $K^f$ and it is widely believed that
$K^f$ depends strongly on $\phi$. For example, for glass spheres \citet{Chen:1991} uses the Carmen - Kozeny relation
\begin{equation*}
K^f=\frac{d_s^2}{172.8}\,\frac{\phi^3}{(1-\phi)^2}
\end{equation*}
where $d_s$ is the diameter of the glass beads. It is clear that $Ra_m$ in \eqref{E:RamDef2} would then depend strongly on $\phi$ and in any application this
would need to be taken into account.

We have calculated the necessary values of $a_m$ even though they are not displayed in table \ref{Ta:Ta4}. For the first set of values where
$\phi=0.5$ and $\epsilon=0.2,\cdots,0.6$,
convection always initiates in the porous zone, and $a_m$
takes values 1.4, 1.8, 2.0, 2.1 and 2.2, respectively, while
$a_m^{(2)}$
has values 18.6 and 18.7 four times. This means lowering the micro porosity increases the width of the convection cells. It is useful to compare this
with the case of a single porosity material as studied in \citet{Straughan:2002ijnamg}. Figure 7 and table VII of that work are appropriate as $\phi=0.5$
there. However, it is difficult to compare directly since the meaning of terms is different, for example, here
$\delta=\sqrt{K_p}/d_m$
whereas in \citet{Straughan:2002ijnamg},
$\delta=\sqrt{K}/d_m$ with $K$
being the permeability in the single porosity medium. Nevertheless, the case in \citet{Straughan:2002ijnamg} demonstrates convection initiates
strongly in the porous region. The single porosity case is formally achieved for equations \eqref{E:FluidPert} and \eqref{E:PorPert} by taking
$\xi=0$ and $K_r=1$,
although this is a formal calculation since $\epsilon\to 0$
needs a careful treatment of interface conditions. Although if we take $\xi=0$
and $K_r=1$
and compute $a_m,Ra_m,a_m^{(2)}$ and $Ra_m^{(2)}$
we find for ${\hat d}=0.08$,
$a_m=1.0,Ra_m=3.183,a_m^{(2)}=27.6,Ra_m^{(2)}=5.124$
whereas when ${\hat d}=0.09$,
$a_m=0.7,Ra_m=2.695,a_m^{(2)}=23.6,Ra_m^{(2)}=3.080$.
If these values are compared with corresponding values in table \ref{Ta:Ta1}, for $K_r=1.5$
and table \ref{Ta:Ta4}
then we see that as $\epsilon$
decreases $Ra_m$ decreases and the layer system becomes less stable. This is important because for some applications one requires the layer to
not convect and so the presence of a bidisperse porous medium is highly beneficial. For example, in experiments with a solar pond \citet{Wang:2015}
found that the presence of a porous layer stabilizes the pond and increases efficiency, but, additionally the presence of a bidisperse porous material
further stabilizes and increases efficiency. Of course, our model does not describe a solar pond where one must also account for a salt distribution
and different boundary conditions due to solar radiation heating. However, we do believe it is very interesting that our model does predict
the presence of a bidisperse porous layer could be very beneficial in applications.

Finally tables \ref{Ta:Ta5} and \ref{Ta:Ta6} show the variation in the values of $Ra_m$ depending on whether the Beavers - Joseph and continuity of normal
stress conditions employ the equally split (ES) value of 0.5 or the pore weighted (PW) values. For the $K_r$ and $\alpha$ values selected here the
variation is relatively small, but not totally insignificant. It would be useful to have experimental results to compare with in order to assess which
class of interface conditions is preferable.

\section{Conclusions}

We have formulated equations for thermal convection in a fluid layer which overlies a layer of bidisperse (or double porosity) porous medium
saturated by the same fluid. The macro and micro porosities $\phi$ and $\epsilon$ and the analogous macro and micro permeabilities $K^f$ and $K^p$ are explicitly
included and play a major role in the model along with the depth of the fluid layer $d$ and the depth of the porous layer $d_m$. The interface conditions
between the fluid and porous medium are very important and we have adopted two approaches. One is to adopt an equal weighting to both the macro and micro phases
while the other approach employs a pore weighted average reflecting the relative porosities $\phi$ and $\epsilon$.

We suggest a variant of the \citet{BeaversJoseph:1967} interface condition which holds when the porous medium is one of bidispersive type. In general,
this allows for two Beavers - Joseph interface coefficients $\alpha_1$ and $\alpha_2$ corresponding to the macro and micro phases. In our numerical
results we assume $\alpha_1=\alpha_2$ although in specific applications $\alpha_1$ may need to be different from $\alpha_2$ and our model allows for this.

Our numerical results show that the bidisperse porous medium is very different from the single porous medium case in that the coefficients of the double
porosity material do have a strong effect on convective instability. Since the two layer convection problem with a fluid overlying a bidisperse porous
medium does have serious application to renewable energy generation, see e.g. \citet{Wang:2015,Wang:2018}, we believe the current work is very useful. Of course, two layer
convection with a single porosity medium already has many parameters, see e.g. \citet{Chen:1991}, \citet{ChenChen:1988,ChenChen:1989,ChenChen:1992},
\citet{Straughan:2001jcp,Straughan:2002ijnamg}, while convection in a single
bidisperse layer likewise involves many parameters. The combined problem is necessarily complicated and, therefore, involves a lot of parameters. Future work will
apply this theory to specific renewable energy situations.

\vskip12pt

\noindent{\bf Conflict of interest statement}. This work does not have any conflicts of interest.

\vskip12pt

\noindent{\bf Funding}. The work of BS was supported by an Emeritus Fellowship of the Leverhulme Trust, EM-2019-022/9. PD acknowledges partial support by the DFG through project 441523275/SPP225.

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


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This page was last edited on 8 April 2018, at 01:51.


Private student loans are vilified. Subprime mortgage loans are slowly being eradicated. But there is another loan product readily available to borrowers that could do even more damage: PLUS loans.
As a part of the student funding program offered by the Department of Education, PLUS loans fill in the large gaps left by limited federal options like Perkins Loans and federal grants.
In August of this year, President Obama passed a law decreasing the interest rate on federal student loans. Although a lower rate of 6.41 percent helped to reduce interest charges for PLUS loans, large problems, such as non-existent loan limits and lax underwriting, were left unchanged.
Loans.org investigated how this oversight can cause sweeping problems for both borrowers and their families.
Patrick Kandianis, co-founder of SimpleTuition, said that part of the limited lending rules comes from legacy issues. Originally, the PLUS loan program was viewed as supplemental to other aid and not borrowed in large amounts. As the cost of college increased, these norms disappeared.
Parents and graduate students can utilize PLUS loans and borrow the remaining cost of college if necessary. This can stretch into tens of thousands of dollars per year.
The problems do not stop there. Not only are parents able to borrower limitless amounts of student loans for their children, they qualify even when they have no means to repay the debt. The Parents PLUS loan program, coupled with the Grad PLUS loan program which works in a similar fashion for graduate students, only runs a simple credit report to see if a delinquency has occurred in the past 90 days, if the borrower has a tax lien against them, or if they have faced a recent repossession or bankruptcy.
It does not require a detailed employment or asset account and it does not require borrowers or co-signers to detail how they will pay off the student loans. The lack of rules creates an unstable environment for both the borrowers and the federal government — a situation akin to what we saw during the recent mortgage crisis.
This high level of risk is simply a part of the PLUS loan program, according to Navah Fuchs, chief education officer for Angel Ed.
She said if underwriters denied the federal loans based on the risky nature of the borrowers, it would be counterintuitive to the specific loan purpose.
"All federal student loans operate on the premise of making capital available to those who otherwise would not be able to afford their educational pursuits," she said.
Despite a generally lax underwriting policy, each borrower's experience is different. For 26-year-old college graduate Daniella DiMartino, the loan process for her father was extremely long-winded when he applied in late 2010.
For the $13,000 that DiMartino's father borrowed on her behalf, he was required to provide information about employment, taxes, pensions, savings and other financial documents proving that he was fit to repay.
He was hesitant to take out the loan for her due to low post-grad employment rates. He also knew that he was legally liable for all of the debt. Even two years later, after securing an account executive position with a public relations firm and faithfully paying her monthly dues, her father remains concerned. She understands why. Each time her father needs to prove his financial history, such as when buying a car or applying for a credit card, the student loan debt is present.
"When he goes to look for anything, it is there," she said.
It is commonly thought that borrowing from federal lenders is safer than from private lenders, but the government's overarching power of retrieving loans makes it nearly impossible for borrowers to hide from their debts. Borrowers can lose significant amounts of their wages, Social Security checks, and tax returns if they do not repay the federal loans on time.
In comparison to credit card companies who have retrieval rates in the single digits, federal student lenders have a phenomenal recovery rate, according to Mark Kantrowitz, senior vice president and publisher of Edvisors.com. The federal government nets between 80 to 85 percent of the money it lends, while the gross rate, before paying collection agencies, is over 100 percent.
DiMartino and her father can count themselves among the lucky who have not faced the brazen retrieval methods of the government. But as the PLUS loan program grows, so will those affected by it.
In 2011, the government approved $10.6 billion in Parent PLUS loans to fewer than one million borrowers. For PLUS loans originating in the 2011 fiscal year, it expects about 9.4 percent will default in the next 20 years. This figure is only for budgetary purposes because the real default figure will likely be higher.
Even on a shorter time period, federal student loan default rates are higher. The DOE found that 14.7 percent of federal student loans defaulted during a three-year time period.
This increasing rate has caused many private lenders, such as Sallie Mae and JP Morgan, to limit or stop their student loan programs.
As the options for borrowers diminish, it is likely that the large PLUS loan figure will increase.
Although it complicated the borrowing process, DiMartino was lucky that the federal government required financial documents from her father.
Kantrowitz said the DOE should create more rational loan limits. He said students are borrowing loans based on how much the college is charging and not how much they can realistically repay.
A common lending rule states that borrowers should not take on more debt throughout their education than they can earn during one year post graduation. So if a future social worker faces an average income of $35,000, this borrower should not request more than that figure, whereas lawyer that will likely earn over $100,000 can increase the debt limitations for his or her education.
Advisers recommend these equations, but they are not followed by either lenders or borrowers.
"It's not really well designed to give signals to what is a reasonable amount of debt," Kantrowitz said.
Instead, he said borrowers are "chasing a dream" regardless of the long-term cost.
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Unless the data is requested from Congress, the government will not begin analyzing it. He has personally requested financial data from the DOE and been turned away.
Kantrowitz said there is a "distinct lack of awareness of the nature of the problem" facing borrowers and their families because this data is absent.
Time and time again, experts promote a simple suggestion that could have a sweeping impact on the debt issue: education. If borrowers are educated about how student loans work, how much will be repaid over the course of a loan, and how default could impact their future life, borrowers would treat the lending process more seriously thereby improving the student loan system.
Without necessary data like university-specific default rates, financial education is much more difficult. Furthermore, without this information, Kantrowitz said it is impossible to make claims about the value of an education.
"How can you say that debt makes college more affordable?" he questioned.
Fuchs does not denounce the importance of a college education, but she does question the amount of money invested in various outlets. Most universities, whether prestigious or not, devote thousands to millions of dollars per year on positive public relations, such as landing on eco-friendly lists.
This same dedication is not transmitted to more beneficial outlets, such as job placement and career counseling sessions for students.
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Student loan debt has been labeled as another potential economic crisis, similar to the housing crash that plagued the United States in 2008 and subsequent years.
Whether or not student loans have the power to deface a country's economy is uncertain. If the loans do have that power, there is simply not enough protection or limitation for borrowers.
To prevent another housing crisis, the Consumer Financial Protection Bureau has created and passed several mortgage lending rules which make subprime lending nearly impossible. Although the CFPB has created an educational platform for student borrowers, rules governing educational funding is significantly less impactful.
Kandianis said this is because the CFPB is charged at overseeing private, bank-driven lenders even though federal lenders originate about 85 percent of student loans.
The Bureau is a significant force in consumer lending. But students do not need studies about debt, they need laws for protection.
Fuchs believes the solution lies more within the context of how students view themselves and their value in the working economy. She said student loans should be under the same regulation as businesses. Almost all startups are denied standard business loans because the risk of failure is too high. Once the business proves itself, the possibility of funding is expanded.
In this way, only the most dedicated businesses, and the owners with the most realistic ideas about their need within a community or economic sector, survive. This same idea could transfer to students in a positive way.
College students across the country have deluded ideals about their economic value. This is repeated semester after semester. For example, it is present for the philosophy graduate who leaves higher education with $80,000 in debt but is facing job offers of $30,000 per year.
Each student can make a meaningful impact on society, but not every student has the potential to make six figures per year.
If lenders were willing to view students in the same light as startups, writing a check to the borrower and expecting interest back, the process should be the same. Fuchs said that going to college is the same thing and students should gain the resources and knowledge to become a marketable entity. In the end, college is a startup of oneself.
"If you can't hold the same accountability, the same regulations, as the entrepreneur, you are doing a disservice to that student," Fuchs said.


text:
The Future of Stationary Energy Storage is Led by Policy and Renewables, Reports IDTechEx
BOSTON, Jan. 11, 2021
BOSTON, Jan. 11, 2021 /PRNewswire/ -- Electricity generation from renewable energies is growing on a daily basis and, to integrate their variable nature, energy storage systems are growing in parallel. IDTechEx have investigated the evolution of the energy storage market, forecasting its growth in the next ten years, in the new report: "Batteries for Stationary Energy Storage 2021-2031".
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The services provided by the batteries are similar most of the time, although on a different scale.
The report "Batteries for Stationary Energy Storage 2021-2031" aims to provide the reader with a clear picture of the current status of the development of these two branches in the main countries currently adopting battery storage systems.
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The result of this analysis shows a similar but different scenario among the investigated countries. The renewable energy target, with the current status of the grid infrastructure, in consideration of the different types of energy sources adopted by the country, defined a specific scenario for every country. As well as the differences, a clear point has been identified: the stationary storage market is only in its early stages, from both technical and policy aspects.
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About IDTechEx
IDTechEx guides your strategic business decisions through its Research, Subscription and Consultancy products, helping you profit from emerging technologies. For more information, contact research@IDTechEx.com or visit www.IDTechEx.com.
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redpajama_set_name: RedPajamaCommonCrawl


text:
Жупар Бактибеківна Габдулліна ( 15 січня 1978, Аягузький район, Семипалатинська область, Казахська РСР) — казахстанська оперна співачка (сопрано), Заслужений діяч Республіки Казахстан (2016), провідна солістка Державного театру опери та балету «Astana Opera» (2013).

Біографія

 Жупар Бактибеківна Габдулліна народилася 15 січня 1978 року в Семипалатинській області, Аягозькому районі, в селі Тарбагатай.
 1992 року закінчила 9 клас Жовтневої середньої школи.
 1996 році закінчила музичний коледж імені М.Толебаєва.
 1996 році вступила в Казахську національну консерваторію імені Курмангазы за спеціальністю «Сольний спів» (клас доцента Р. А. Смаїлової) закінчила в 2003 році. Навчалася в аспірантурі там же у класі професора, Заслуженого артиста РК, лауреат держпремії РК, професор Шахимардан Абілова (2003—2005).
 2007—2013 р. солістка Казахського театру опери та балету імені Абая
 З 2013 року — провідна солістка опери Astana Opera.

Творчість

 Стажувалася в Академії театру Ла Скала (Італія, 2014).
 На сцені Маріїнки-2 виступила в партії Одабелли в опері Дж. Верді «Аттіла» під керівництвом Валерія Гергієва (Санкт-Петербург, 2014) і в концертному виконанні партії Одабеллы на сцені Опери Бастилія, диригент Алан Бурибаев (Франція, 2014).
 Виконала партію Аїди в однойменній опері Дж. Верді в Румунському національному театрі опери та балету, диригент Фрідріх Пфайфер (Бухарест, 2014) і Красноярському державному театрі опери та балету, диригент А. Чепурний (2014).
 На сцені Стамбульського оперного театру і Театру опери імені Лейли Генджер (Анкара) виконала партію Сари в опері М. Тулебаева «Біржан — Сара» (2014).
 Виступила на сценах Carnegie Hall (Нью-Йорк), Sony Centre (Торонто), в залі Stadsschouwburg (Антверпен), в концертному залі De Doelen (Роттердам), в Ханойском національному театрі опери та балету (В'єтнам).

Репертуар

 Аїда («Аїда» Дж. Верді)
 Леонора («Трубадур» Дж. Верді)
 Одабелла («Аттіла» Дж. Верді)
 Амелія («Бал-маскарад» Дж. Верді)
 Турандот («Турандот» Дж. Пуччіні)
 Туга («Тоска» Дж. Пуччіні)
 Недда («Паяци» Р. Леонкавалло)
 Ліза («Пікова дама» П. Чайковського)
 Сара, Алтынай («Біржан — Сара» М. Тулебаєва)
 Ажар («Абай» А. Жубанова, Л. Хаміді)
 Дана («Ер Таргын» Е. Брусиловського)
 Нігяр («Кероглу» У. Гаджибекова)

Досягнення
Нагороди вокальних конкурсів:

 2002 р. Дипломант XII Республіканського конкурсу вокалістів ім. К. Байсеїтової (Астана)
 2003 р. Лауреат I премії Республіканського конкурсу вокалістів Е. Хасангалієва (Сімей)
 2005 р. Лауреат I премії Республіканського конкурсу ім. Р. Жубанової (Астана)
 2007 р. Лауреат III премії III Міжнародного конкурсу вокалістів Б. Тулегенової
 2009 р. Почесна грамота "За участь у II турі Міжнародного конкурсу вокалістів ім. М. Глінки (Москва)
 2009 р. Учасник міжнародного проекту оперних співаків «Турандот» Дж. Пуччіні в Італії (Верона)
 2010 р. Гран-прі Міжнародного конкурсу вокалістів «Мистецтво XXI століття» (Київ, Україна)
 2013 р. Гран-прі Республіканського конкурсу імені Н. Тлендієва (Астана)
 З 2009 року володар гранту Фонду Першого Президента КАЗАХСТАНУ — Лідера Нації

Державні нагороди

 2012 — Лауреат Державної молодіжної премії «Дарин»
 2014 — Лауреат Премії Фонду Першого Президента Республіки Казахстан — Лідера нації (Премія за внесок у розвиток музичного мистецтва)
 2015 — Лауреат Державної стипендії в галузі культури Республіки Казахстан.
 2016 — Присвоєно почесне звання «Заслужений діяч Республіки Казахстан» (за заслуги у галузі казахського театрального і музичного мистецтва)

Примітки

Вікіпедія:Статті з іншим значенням на Вікіданих
Заслужені діячі Казахстану
Оперні співаки XXI століття
Персоналії за алфавітом
Випускники Казахської національної консерваторії

redpajama_set_name: RedPajamaWikipedia


In preparing these monographs for inclusion into Virtual Commons, the conversion from Microsoft Works to Microsoft Word caused changes in pagination. Therefore, footnotes within these monographs referring to specific pages in other titles in the series may be incorrect. Because of the changes in pagination, the Tables of Contents presented in the printed versions of these monographs have not been included.
Spence, Benjamin A. (2010). Fire Service in Bridgewater, Massachusetts, 1844-1910. In Bridgewater, Massachusetts: A Town in Transition. Monograph 7.


text:
Paul Murray's Blog
Everyone needs a blog. This is mine.
Exchristian Stuff
iCal Home
iCal Work
My work stuff has been moved
SIck, sick, sick
Sooo sick. It's been like a series of four or five different diseases, each with different symptoms. At the moment, a cough – throat raw and painful, and that tickle that precedes a coughing bout, and worst of all, for some reason the particular spot where I am feeling the itch to cough isn't scratched by the coughing. Everything else is beat to shit, flaps of tender, irritated pharyngeal flesh flayed freshly raw with each bout of helpless hacking, but that one spot somewhere in my throat, that one complaining nerve untouched.
Tonsils hurt. Hurt, hurt, hurt. For a week now. I imagine them half full of blood and pus, ready to burst. I dread swallowing. Hot coffee seems to soothe them, but never for long. Yeah, I've gargled with salt water. Yeah, I've taken zinc. Went to the chemist – just about every painkiller is ibuprofen based, which is exactly what I don't want, the tissue in my throat more relaxed to flap around painfully when I cough. I found some paracetamol and some asprin. Asprin – the first wonder drug. Sadly underrated, but I'm a fan. When I was a child, I knew a woman who was addicted, "taking a powder" a few times a day. Way to get bleeding stomach ulcers.
Nights are the worst, of course. Cold, cold, cold. It's snowing at the ANU, and I live in a shitty uninsulated flat. So cheap! No shit it's cheap. Can't sleep. The air is icy razors, and when I relax to sleep, it's cough time. I'm pulling the sheet over my head to rebreathe warm, humidified air. I'm wearing layers of clothing. I'm running a ceramic blow heater, freshly bought. I have had an oil column heater for ages. It does nothing. Cold runs down the walls, it cascades in a torrent from the window, an invisible, icy cataract. I have fitted a layer of plastic inside the window, making my place look like a drug den, to try to hold back the cold. It does nothing.
Mum died around this time of year.
I suppose a lot of people living alone must do. I lie in bed, waiting for the next coughing fit, my feet still cold in socks under the blankets and wonder if I am going to die like a homeless person, sick and killed by exposure while laying in my own bed in a flat that I rent. If not this year, maybe next year. I'll be fifty, you know.
It's been shit, guys.
2 Comments	| Uncategorized	| Permalink
Posted by Paul Murray
On the Crimean (repost)
This is reposted from here: http://www.smirkingchimp.com/thread/paul-murray/54826/on-the-current-kerfuffle-in-the-crimea . Smirkingchimp is always threatening to run out of money, so in case it goes dark here is this piece on my blog. It's not currently in the news, but the topic is perennial.
I think I might weigh in on the topic of the recent kerfuffle in the Crimean peninsula.
But before I do, I am going to talk about Panama.
CAVEAT: I am not a defence person, I know nothing about these topics other than general knowledge and access to Google maps.
The USA is and always has been a naval power. It's simple. To the west, over the Pacific Ocean, is Asia and civilisation. To the east, over the Atlantic Ocean, is Europe and civilisation. While europeans can fight with each other using land armies, the only way the USA can make war is over the ocean. The USA, in fact, has an entire corps of armed servicemen alongside the navy, army, and air force whose entire reason for being is "soldiers who go to places on ships".
The USA has two coastal frontages – east and west. There are four ways to get a navy from one side of the USA to the other.
First, put the ships on rollers and haul them down the interstate. Good luck with that.
Second, and just as impractical, sail them through north around Canada through the arctic sea, which only recently has not been icebound in summer.
Third, sail them around the tip of south america – a quarter of the circumference of the world away – and through the Southern Ocean.
Fourthly, the ditch. The Panama Canal.
The military importance of the ditch to the USA cannot be overstated. I mean literally – try overstating it, try coming up with a form of words that is maybe a bit much. Can't do it, right? The permits the USA to threaten both China and also Europe/Africa/The middle east with the full force of its naval power. The USA can field all of its carriers, all of its subs, all of its marines against the enemy du jour in either hemisphere in a matter of days. Without the ditch, the USA would have to run two navies, or only be able to field half a navy to each.
The USA will never, never, never cede control over the ditch to anyone. Ever. Oh, it may be technically in the hands of a foreign power, Panama may be a whole 'nother country to the USA, but you know and I know and everyone in the world knows that that's bullshit. It's a US asset. And the USA would, if it had to, fight WWIII over it.
I am not exaggerating.
What do you think the Cuban Missile Crisis was really about? Nukes striking the American mainland? Pfft. A nuke will take out several square miles of a city – but there's plenty of those. It will kill a bunch of people – there's millions more. It will destroy an ammo dump (Dr Strangelove reference there) or a military base. So what? Miami is simply not a military target. Military targets (missile silos, airfields, command centers) are dispersed all over the US exactly in order to make the US military capability more nuke-proof.
But nuking the ditch would be a serious and unacceptable game-changer. It would not only maim the Navy, it would throw the armed forces into chaos for days. No freaking way will the USA permit it, or even the possibility that it might be done. Kennedy would have pressed the button over it.
At this point, dial up google maps, zoom out, and have a look at Russia.
Actually – this is really the main point that this post is trying to make. None of this makes sense unless you look at a freaking map and get an idea of where everything is. It's all about geography. Look at a goddamn map – not opinion pieces about gay rights, not comparisons of Putin to Hitler, not blatherings about ethnic russians – you need to look at the damn map. That's what it's all about. People are talking about the Crimean business like it's a battle of words and ideas, probably because that's what they mainly know about. The Crimean Kerfuffle is not about words and ideas. It's about ships and troops.
Russia has three naval frontages. In the east, access to the Pacific. In the north and west, access to the Arctic Ocean. Good luck sailing out of that in winter – although I suppose its ok for submarines (and this is why subs are important to Russia).
The third naval frontage is access to the Black Sea. The Black Sea is connected to the Agean Sea and the Mediterranean via the Bosphorus, and from there to the Atlantic Ocean to the west and the Suez canal to the south east.
As you can see because you are looking at the map, Russia has a fair bit of the coast of the Black Sea on the east. But you can see that it's all mountains – the Caucasus I think. Useless. The land is inhabited by wild, hairy tribes of barbarous inbred wogs, many of whom don't much like Russians (with, admittedly, excellent reason). You can't build a road there, and if you could you couldn't march troops down it to the transports.
At the north of the Black Sea is a booger of land about a hundred miles across. This is the Crimean Peninsula. And at the southern tip of it, on the west coast, a little place called Seavastopol. This place was put there by the Tsars to serve as Russia's port and access to the Mediterranean. The Crimean Peninsula is Russia's Panama, and that port is Russia's panama canal. Thanks to some stuff that went down late last century, that booger of land is technically part of a whole 'nother country called "The Ukraine". But you know and I know and everyone in the world who pays attention knows that that's bullshit. It is a Russian asset.
The kerfuffle in the Crimea has go nothing to do with gays, or ethnic russians (although obviously the Crimea is as full of them as Panama is full of americans), or even Putin. It is 100% about The Great Game. There is no way in hell that Russia will lose control of that port. No freaking way. They will fight WWIII over it, if they have to. They would rather not, but like Kennedy and Panama, Putin will press the button rather than lose that asset.
And that's what this is about.
Perhaps the main question remaining is: why is this blowing up now? That is a whole new topic, and the answer is probably (as in: you know and I know and everybody else in the world knows) that the Pentagon and the security state of the USA are fomenting trouble there in response to the budget squeeze at home. It's a fund-raiser.
And a lunatic dangerous one. Russia will not, will not, will not lose control of Svestapol without a fight, and they will escalate as far as it takes, whatever it takes. They are not bluffing. They still have nukes. If they have to, they will march the Red Army south right through the middle of the Ukraine, and to hell with anyone who gets in the way. If Kiev doesn't like it, fuck them. If anyone wants to help out Kiev, fuck them too.
And it's all down to the pentagon having a hissy-fit over their trillion-dollar budget taking a haircut, the military establishment wanting to remind the world that warmaking is still relevant.
1 Comment	| politics	| Tagged: Crimea, realpolitik, Russia, USA	| Permalink
Just a simple soldier
I have missed so many weeks blogging, I am not even going to attempt to do a catch-up post.
Ok – briefly:
we stumbled into the woods looking for Edmund the Marked.
Found orcs and trolls. Wound up in a three-way fight. Beat eveyone up.
Elves came out, looking for Tarry. Some centaur important druid person want him.
Got taken to some other part of the world. A woodhenge.
Centaur is dead. Everyone is dead. Smells like orcs.
Tracks led thataway. We followed.
Came to a ship in the river. Hold full of dead orcs.
While investigating, we were attacked by an adventuring team of some sort.
The sorcerer got away. One left alive – the boss. We questioned him.
We questioned our prisoner, who appeared to be the leader of the gang. I Charmed him, but he told me little but that they had been hired by a man in a white hat. Some of us suspected Captain Colonel, but I doubt that he could or would have anything do do with either murdering an envoy of the high druid or sending men to hunt us down several days south into the woods.
We did not learn anything from him about the orcs in the hold of the ship, or the ship itself. He offered to tell us more for an extravagant sum of gold, but we decided that he was almost certainly lying, and tossed him bound into the hold of the ship.
We elected to pursue the remaining member of the gang. Misthanar returned to the ship to speak to him again, buy he had already slipped his bonds and escaped.
Andy's way of telling Jez "Dude, that whole scene of the play is over. Move on.". It's like herding cats, honestly, without an actual cat-herder.
The sorcerer's tracks led to a cave opening. Shieldglider and Toasten, naturally, took the lead and led us underground.
… meanwhile …
Our NPC "Derrick the Cleric" is now being played by the new guy. Andrew got him up to speed with how to play, a process much, much easier in 13th Age than in Pathfinder. Derrick had lost our horses, was wandering about. He found a cave.
Derrick's backstory is that he has been bumbling around on the fringes of the group, holding the horses, being a bit of a pest. He tried being a cleric, then he tried being a rogue. Andrew had the new guy play him – he kept away from the mooks, fired his bow. So the ruling is "ok, Derrek seems to be using his bow, so we'll make him a ranger", which is just a great way to make that kind of decision with a new player that hasn't got definite ideas on what he wants to play. And we don't have a ranged combatant, really, so is all good. Other thing is that Derrek rolled a couple of 1s and shot Misthanar, to cries around the table of "Fucking Derrek! God, he's useless!" It was a fun moment. Role-playing games are not about winning, they are about having a good time.
Goblin attack, underground cave, Wild Woods 4 days SSE of Chancer's hope
Terrain, etc
Our group entered a cave on the trail of a mage (probably sorcerer) who was part of the group that attacked us at the orc ship.
Below was a large chamber with a throne of some sort built into the stone.
The chamber had two exits – a door and a passageway.
The passageway was intersected by a narrow (10′-15′) chasm of unknown depth.
Unknown to us at the time, Derrek had also found this same cave by another entrance.
What are the odds, eh?
A number (approx 12-20) of goblins emerged fro the chasm and attacked.
One of their number appeared to be a shaman or other spellcaster, who remained behind the line and the chasm.
Course of battle
Shieldglider advanced to block the passageway.
Misthanar advanced further into the cave and beyond line of sight, to assist Derrek whom he had heard.
I ordered Tarry to spike the door so that we would not be flanked. Tarry dissappeared into shadow.
Tarry did not spike the door, but advanced to attack the spellcaster.
I moved forward to Shieldglider's position to fully block the passage.
With a line at the front and spellcasters to the rear, we killed about 5 to 10 goblins within a few seconds.
The spellcaster then summoned a rust monster from the chasm.
Our casters concentrated fire on the rust monster.
Shieldglider concentrated on the goblins.
Misthanar at this time was surrounded by goblins and fell to them and to friendly fire from Derrek.
As the numbers of the goblins had been thinned, Lashley moved forward through them and was able to revive Misthanar.
I moved forward to get a better view of the situation.
I judged that our casters (Elsbeth, particularly) had the rust monster in hand, and so I deployed a Color Spray against the goblins surrounding Misthanar and Derrek.
The rust monster was killed, and we moved forward to mop up the remaining goblins. Shieldglider's armour is beyond repair.
The caster, whom we had not dealt with, commenced to summon more Rust monsters.
At which point, Edmund of the Council of Four intervened and magically dealt with the remaining foe.
Notes, evaluation
Tarry's action was reasonable. I am not in command of this group, and dealing with the caster was a reasonable thing to do. It transpired that that door was blocked on the other side, and so spiking it would have accomplished nothing.
That's in-character, of course. In character, James is the only one who's an actual soldier and officer, apart from maybe Sheildglider, so the tries to throw orders around. Sometimes, people listen (especially when the order is "Try Again!" 🙂 ). He might occasionally pout a little, but this is the situation he's been thrown into and he'll do the best he can. Its a heroic campaign, so he is not butthurt and negative about not being the boss.
I have mentioned before that Misthanar will get himself killed if he continues to separate himself from the group. That nearly happened this time.
A glass cannon cannot run around the corner where no-one can see him into a mob of bad guys, even if the are mooks. Mind you – the reason for it was that Derrek was right in the middle of it all.
We needed to have dealt with the goblin spellcaster more promptly. None of us but Lashley and Elsbeth are able to engage a foe at range. Derrek will be a valuable asset if he can be trained to shoot straight.
As I mentioned – he rolled a couple of 1s. It happens.
Edmund led us to a clearing with a "house" at which lived a blind gypsy woman. She read the cards for us – it is always unwise to completely trust or completely discount such things. The trick is knowing what to trust and what to discount, but if you had such a trick then – why – you yourself would have to be able to see the future.
Edmund sent me into the house to fetch his cloak. Quite a lovely thing – very fine, an amazing blue. It wrapped itself around my arm and across my shoulders when I picked it up. Edmund seemed to find this amusing. "So!", he said, "The Archmage will be most displeased!"
I have no idea why. It seems that there is no escape from Horizon politics, although what I am embroiled in, I cannot say. The cloak is clearly magical, but what its magics might be, I can only guess. One does not prefer to be a target of the Archmage's displeasure, obviously, but it's many leagues between here and Horizon.
Unknown to James, he has a two-die "conflicted" relationship with The Archmage.
In 13th Age, magic items are meant to be special and unique, and Andy has been handing out a signature item to each character. At present, they have no special powers. So far as we know.
I'm pleased with mine, I think it's awesome, and I made this eye-bleeding background to celebrate. W00T!
Leave a Comment »	| 11 - James Mallard	| Tagged: 13thAge	| Permalink
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· HE IHEATItE "If cf!? A I $, O: #J '. 'I ' NICH[ VO T HE trouble with "The Prum- ise," a Russian importation by Aleksei Arbuzov at the Henry Miller, is tha t-a t least in translation (by Ariadne Nicolaeff)-it all too often sounds like one of those satiric routines with which Mike Nichols and Elaine May used to entertain us, and SInce the play is supposed to be deadly serious, this unintended comicality hurts. There are three characters involved here, and at the outset-the scene being Lenin- grad under siege in 1942-they are presented as adolescents, ranging in age from fifteen to seventeen. \Vhatever their other attractions, the members of the cast-Eileen Atkins, Ian McKellen, and Ian McShane-are hardly in their teens, and their decidedly English ac- cen ts are of no help in inducing us to believe that they are bona-fide Russians. The implau- sibility uf the drama, the plot of which I'll get around to in a min- ute, is compounded by the direction of Frank Hauser, who seldom permits his actors to have a quiet moment, and there IS not much help to be had from the set, by vVilIiam RItman-a room in a Leningrad apart- ment, where the only indication of a city close to destructIon is the absence of sheets on a mattress. Nor did vague offstage rUl1l- blings convince me that I was getting a true pic t u r e of th e way things were in I.Jenin- grad in those days. The title of the pLty has to do with the ob- ligation of the surVIvors of the Second World \Var to make sure that their dead have not die d in va in. Th e heroine is a doctor's daughter who aspires to become a kind of Flor- ence Nightingale. (It is X l, .. 4 t ft ^.,' "'-,., - t , .' þ . ' . "" ", , '''"',- . "- , \ ,l. _. "; \\ :'.b-. - 1 ,' p/ '" . . . t ..... \ . when she talks about her dreams of a splendid medical future that she sounds most lIke ElaIne May, who, you may remember, once wanted to be a dental assistant in a leper colony.) As played by Miss Atkins, she is something less than compelling, and Mr. McShane and Mr. McKellen, as the two men in her life, struck me as rather dull. Mr. :Y1c- Shane portrays a I11endacious, blustering resident of Leningrad, who inflates a scratch on his arm into a major wound, which he clainls to have suffered while capturing a German parachutist. De- spite, or because of, hIs hoasting, he eventually achieves high rank in the Soviet Army. Mr. McKe]]en, on the other hand, is shy, modest, and poetic, and Miss L\tkins' dilemma, w hlch takes /' I \ f ----- .....' ....':..... : ^ V"""'i j ... , , J <> :':I i \ ' f } \: [" (it \ i l t ., , 1 J \I " $ . 'il \. . .. to .. ....... __ .:f " - .. 11># ... I' ,/ 7' ", ' , / ^..,' , - ><>-= J'. <> .... .J'. ... . 0" . ",,,,:tIIV; :-::::' "'" " '" . . . do ....;. .. ......;. '.... , .. /'. . .... ....: - -- /' ,t} ../ 149 a hell of a long time to resolve-the last act brings LlS up to 195 9-is whether to go for the Army big wheel or for her gentle chum, who has un- deniably lost an arm in comhat. Noth- ing really enthralling develops as this triangle sorts itself out, but I suppose it's a guod thing to have a modern Russian play, however inferior, on view hereahouts. I wish my welcome could be I110re cordial. A N EGRO cast has taken over "Hello, Dony! ," at the St. J ames, and [ must say that a lot of bounce has been added to a show that has been running since the McKinley Administration. Particularly meritori- ous is Pearl Bailey-the Dony on this oc- casion-who is, of course, an entertainer impossible to fault. Also on hand is Cab Calloway, who can still strut with the best of them. 1 he production has been exuberantly restaged by Lucia \Tictor, and Freddy \Vittop has supplied sonle da7zhng costumes. The ubIquitous Oli- ver Sll1ith created the settings, which are admirable. - JOHN MCCARTEN c::::::...... lVN'....'V v..c .., .Æ '> ,. ...ø / , f' /'. " 'It 'it: .01 ! f i I I :' , ,I í : - 1 ...- "'. "" '" ,/ , , i" f ! ,,! 1 · J rU , , ;, ', , , ,"" ' f, . , . w ; . :N. j;1 ;1 r' t '" . , . . h , ..W l ' . .. . ' . ',. ,Wf . ," A.. ^ .... J . . " " .... ........ . .. ... . . :.:. .. celt seems like only yesterday 7))e had her bootzes bronzed"


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Coaching Packages For Wellness Meet Melesha Wellness Education Testimonials Contact Check out the Newest Offer Login
Stress, Mental Fatigue, and PTSD Can Traumatize Your Health
How Current Events & Mental Fatigue Can Traumatize Your Health
Events are moving rapidly every day that feels like we are experiencing whiplash. Daily news, social media, and newspapers are exposing us to images of death, protest, riots, bigotry, racism, unrest, and a health crisis on steroids. These are traumatic events that are dramatically affecting bodies and minds.
A traumatic event is an incident that causes physical, emotional, spiritual, or psychological harm. Many are feeling threatened, anxious, or frightened that's taking a toll both mentally and physically. Those feelings of uneasiness take many forms that may be hard to explain verbally. Feelings of hopelessness to situations that are out of control; that's how trauma is manifest.
Racism, unequal health care, police brutality is rearing its ugly head, and there's no escape this time! We see it constantly, and it's permeating deep in our souls. Those images are ingrained in our minds, and they are affecting our health. It can feel and show up as PTSD.
Research has linked racism to a host of problems, including serious psychological distress, physical health problems, depression, anxiety, binge drinking, and eating disorders, according to Monica T. Williams of Psychology Today. The results can be irritability, anger, difficultly concentrating, fear, headache, nausea, withdrawal, and isolation. When you add the stress of dealing with COVID-19 makes the problems even more difficult
The wave of these ongoing traumatic current events is having a profound effect on People of Color with underlying chronic health conditions such as Diabetes, Heart Disease, Arthritis, Respiratory issues, and Digestive Problems. These events are impacting our ability to manage these conditions, and the body becomes exasperated while working to process and balance a healthy lifestyle and mental fatigue.
So, how do we manage these stressful situations before they cause adverse effects on our health?
Talk to someone or write in a journal.
Be gentle with yourself and work not to internalize situations that you have no control over.
Find a support group or seek professional help.
Give yourself a break from social media.
Eat a balanced diet, exercise, stay hydrated, and get plenty of rest.
Decrease alcohol consumption
Maintain a positive daily routine with structured activities
Pursue hobbies like gardening, reading, taking care not to overdo it
It's common for people with signs of trauma to withdraw from friends and family or swing to the opposite of withdrawal to rage and anger. It's important to respect their boundaries. Comfort and support can help the person overcome feelings of helplessness, grief, and despair. Trauma experts believe that face-to-face support from others is an essential factor in recovery and the ability to move forward.
Take notice when you or someone you know show symptoms of being withdrawn, sullen, angry, or show signs of depression. Sometimes all that is needed is for someone to listen and show concern.
Here are some tips on how to approach someone that is demonstrating prolong signs of mental trauma:
Don't pressure someone to talk- Be a good listener.
Do normal activities together.
Let them take the lead instead of you telling them what or what not to do.
Be sure to manage your stress.
The world is changing fast, and the need to be consciously aware of what's going on can leave you or someone you know feeling traumatized and mentally fatigued. Stay mindful and prayerful, and let nothing keep you down long.
Join my private Facebook group For Women Only as we address this issue and more. Love 4 Life Private Facebook Group.
If you feel you need someone to talk to about stress and your health, I do a FREE consultation to talk about you! Contact me. Make an appointment for a FREE consultation. See you soon!
Your Sister in the Journey,
Melesha
© 2021 Love 4 Life Wellness, LLC
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Upon your request for a FREE consultation you will be contacted to set a 45 minute appointment to talk about your concerns.


The March-April 2017 issue of Copy WatchTime is on newsstands now (and also available in our online shop), featuring reviews of the Tudor Black Bay Bronze, Omega Seamaster Planet Ocean Chronograph, and TAG Heuer Monza; a tour of Grand Seiko's watchmaking studios; a pilots' watch face-off between IWC and Breitling, and more.
Tudor added a new bronze model to its Heritage Black Bay collection in 2016. Like its predecessors, this dive watch dips into history with a material that appeals to contemporary tastes. In our cover story, "Modern Heritage," Martina Richter conducts an extensive test of this popular replica watch (with an additional wrist review from yours truly), which features original photos by OK-Photography.
In 1976, TAG Heuer introduced its Monza model, named for the world famous Italian Formula 1 racetrack. Forty years later, the Monza Calibre 17 recalls the glory days of racing while offering a great deal more than retro design. Alexander Krupp goes under the hood of this "Retro Racer" in this in-depth fake watch test featuring more original photos from OK-Photography.
In "Seiko's Grand Tour," Roger Ruegger journeys to Japan to visit to Seiko's watch studios in Shizukuishi and Shiojiri, the two watch-producing facilities within the Seiko Group responsible for the manufacturing of Grand Seiko watches. He also interviews Shinji Hattori, president and CEO of Seiko Watch Corporation, about the future of Credor, Grand Seiko, the newly launched Presage collection — and his own favorite watch.
In "Flight Fight," two watch brands strongly associated with aviation, IWC and Breitling, duel for horological supremacy in the air. Writer Jens Koch looks at icons such as cheap copy iwc original big pilot watch and Breitling's Navitimer, as well as modern classics like the Big Pilots's Watch Annual Calendar "Le Petit Prince" and Breitling Avenger Hurricane.
« 5 Major Trends Of Counterfeit Watches At Sihh 2017: Will Baselworld Follow Suit?


About 15 years ago, I came across this article on how to develop the skill of being lucky. I immediately related it to the skills we learn in the Alexander Technique.
"Findings have revealed that the thoughts and behavior of unlucky people are responsible for much of their misfortune," according to research by Richard Wiseman. What are the traits associated with being lucky? Being more aware, less tense, and less anxious. These are all skills we develop in the Alexander Technique.
The article says that unlucky people are so focused on a particular activity or task that they don't notice opportunities. Lucky people see what's in front of them, not just what they're looking for. In the Alexander Technique we practice using a "unified field of awareness," which is being aware of what's going on inside yourself as well as what's going on outside. Unlucky people practice tunnel vision. As your awareness opens up to include things that aren't your immediate goal (i.e., unified field of awareness), you more easily notice chance opportunities that would otherwise have slipped by you.
Unlucky people tend to be creatures of routine, according to the article. Being able to escape from the pull of habit is a trait we develop in the Alexander Technique. The process we use encourages people to stop themselves before going down the path of habit and then consciously choosing how they'd like to respond to a situation.
Lucky people are more aware of their intuition. Many times, people react so quickly and automatically to a situation that they're already in action before they're aware of what their intuition is telling them. The article says that lucky people, "are interested in how they both think and feel about the various options..." In the Alexander Technique, we make it a practice to pause before reacting so we can have time to think through the options and choose the best course of action. That gives us time to listen to our intuition. Granted, some situations require a quick response, and, in time, this pause prior to action can become instantaneous.
Wiseman states that lucky people create lucky situations with particular skills. We develop some of these same skills in the Alexander Technique. Maybe learning the Alexander Technique could make you luckier.
The Alexander Technique (AT) is the work of opening doors and windows and tiny cracks in people's habit patterns so they can experience something new. When you experience something outside of your automatic, stereotyped behavior, you can start the work of change - of figuring out what you want and moving toward it. Until you can step outside your habitual pattern for a moment, there's very little real ability to change.
AT is about bringing to light our habit patterns so we can avoid activating them. Only then can we start to have access to something new and different. One of the wonderful things about this work is that you can't quite imagine what the new thing you'll have access to is. It's at the far side of a leap of faith. Alexander referred to this as "going from the known to the unknown." You can't know ahead of time what it will be like to have a new experience.
I think of acupuncture as the same work in a different form. I use needles, non-insertive tools, cups, gua sha tools, and moxa to make small changes that add up to a new experience of one's self. Once you have a new experience, you can begin the work of nurturing the conditions which allow this new sense of self to flourish.


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The idea of Calculated Intrinsic Value
18 Juli 2022 20 Juli 2022 Cua Suwar 0 Komentar
You've probably heard of the concept of estimated intrinsic value. But what would it really mean? How do you determine it? What are the different types of factors that go into determining intrinsic benefit? Here are some of the most important types to consider. And remember, not all values are comparable. Actually some people maintain a thinking that certain everything is incommensurable with others. You're probably thinking about how to apply this concept to your own purchase portfolio.
Beardsley's position is that everything has a extrinsic value, not an innate one. This kind of is what has intrinsic value may also experience extrinsic benefit. In fact , a lot of things with extrinsic value have neutral intrinsic benefit. Therefore , Beardsley argues that extrinsic benefit is the more important. In other words, all of us can't just ignore extrinsic value.
The idea of basic innate worth is also significant. Feldman claims that says that do not have proper parts have no innate value. Or in other words, a negative condition has no inbuilt value. This kind of idea may be used to justify the presence of the concept of inbuilt value. Nonetheless there's even more to the concept than that. In addition to two major concepts, intrinsic value can be used to assess other things. Although how can you determine whether something is intrinsically valuable?
A few philosophers have got argued that the principle of organic unities is valid and valuable, but that the concept of measured intrinsic value is merely not a sound one. There are several people https://conglomerationdeal.com/why-uniting-in-corporate-headquarters-conglomeration who decline the rationale and expectation that anything more methodical will come along. But they concur with that it may exist. Yes and no that there is such a thing since intrinsic benefit. In the meantime, we ought to use different methods to measure it. Consequently we can understand it better.
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Joss Whedon Pushed for 'Daredevil' to Be a Movie
Posted on Wednesday, April 29th, 2015 by Russ Fischer
Daredevil, the first of five Marvel Netflix series, has arrived to stream, and many of you have probably already devoured the entire series. There's even a second-series order in place, and dreams on the part of star Charlie Cox of appearing in one of the big-screen Marvel adventures.
But if Avengers mastermind Joss Whedon had his way, we would have seen a new Daredevil movie go straight to the theater. He pushed for a film rather than a TV series, and in a way, it's all about Batman. Because it's always about Batman.
IGN talked to Whedon, who said,
I fought for Daredevil to be a film instead of a TV show… If the show's working, the show's working. Comic books are serialized entertainment and a lot of them lend themselves to TV shows as much or more than they do to movies.
I like him because he's basically Marvel's Batman, thanks to Frank Miller basically. So for me I didn't think they'd be able to sustain that sort of mood on TV but TV has changed so much. It's come up so much that I think it might just be the right place.
Funny that one of the people whose work helped bring American TV to the point it's at now would initially be thinking of a character like Daredevil as a better fit for the big screen. In the end, I think Daredevil is great for television, even if I have issues with this first season. There's every reason to hope that the second season will iron out some of the things that didn't always go well in the first thirteen hours.
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Comic Book/Superhero, Marvel Studios, Daredevil, Joss-Whedon


Leave a Comment on Living Room Becoming Lifeless? Get Your Artistic Cap On!
Light plays a very important role in your living room.
This is why a living room should be full of windows. But there is one more thing that actually makes your living room worth being lived and laughed in. Colours immediately attract attention. They fill a room with lots of good vibes and when you blend in some good vibes with vibrant colours in your living room, you are bound to spend more time in that area than in any other part of your room.
To make your living room attractive, you need not have all your upholstery changed. Even if you have a very basic seating arrangement with classic colours like white or brown, you can easily pump up the happy quotient of the room by adding a colourful table to it.
There are a variety of options available, from carved ethnic tables, like the one shown in the image above, to simpler designs coloured in pastels. Bringing in a coloured table to your living room will cut sharply through the boredom and add that extra oomph to it.
While simply designed tables do the job while staying in the corner, a more complex design, like a horse or a fish carved on the table, might as well be used for decorative purposes other than just keeping stuff over it as a table.
It is amazing to see how a simple piece of furniture if thrown into a dull room after colouring, creates a totally different environment altogether. If you are thinking of making your living area more lively, get a beautifully painted table for it or just show your artistic side with some acrylic paint and a paintbrush. Paint it up!