text:
\section{Introduction}

In spite of several decades of intense studies, the problem of the
connection between the physics of the inner parts of the solar
atmosphere and the solar wind remains incompletely understood. There
is a general consensus that the mechanisms of coronal heating are
somehow related to the mechanisms responsible for the acceleration
of the solar wind. The so-called ``basal" coronal heating (at $r <
1.5\;R_{\bigodot}$) is usually attributed to a mixture of processes,
e.g.\ wave dissipation (by phase mixing and/or resonant absorption),
magnetic reconnection, turbulence and plasma instabilities
\citep{cra02,cra04}. In `open' magnetic flux tubes which are feeding
the fast solar wind at $r > 2\;R_{\bigodot}$ where the solar plasma
is largely collision-less, however, additional heating seems to take
place. This conclusion follows from a number of \emph{bona fide}
observational signatures, viz.\ (a)~low electron temperatures
($T_e<1.5 \times 10^6 \;{\rm K}$) in coronal holes, (b)~\emph{in
situ} observations of the temperature anisotropy $T_p
> T_e$ at 1~AU, (c)~low radial gradients of these temperatures
throughout the solar wind. These signatures unequivocally indicate
at a gradual, temporally and spatially extended addition of energy
\citep{cb03} to the solar wind (the so-called ``extended coronal
heating") at a wide range of heliocentric distances.

Presumably, propagating perturbations -- magnetohydrodynamic (MHD)
waves, vortices, shocks, turbulent eddies -- are the best
candidates for the transmission of energy from the inner to the
outer parts of the solar atmosphere and further into the solar
wind. In particular, Alfv\'en waves are believed to play a
significant role in the coronal heating and the subsequent
acceleration of the solar wind \citep{cb05}. They are also
considered as important diagnostic tools of the various physical
processes occurring in solar plasmas.

The presence of these efficient ``energy-transmitters" is currently
quite convincingly established. Even though previous observational
studies only emphasized the appearance of Alfv\'en waves in the
solar atmosphere, in the modern era of satellite-based solar studies
it became increasingly clear that the solar atmosphere hosts all
three basic MHD wave modes, i.e.\ Alfv\'en waves and both slow and
fast magneto-acoustic waves. Many different sets of observations
contributed to this ever growing evidence: in coronal loops the
evidence came from the Extreme Ultra Violet (EUV) data from the
TRACE satellite; in coronal plumes (slow magneto-acoustic waves)
from the EIT instrument on-board SOHO; in the solar wind
(propagating Alfv\'en waves) from \emph{in-situ} Helios and Ulysses
spacecraft measurements \citep{cra02}. Therefore, both the
observational data and the current theoretical studies are strongly
in favor of the presence of a causal bond between the heating of the
solar corona and the acceleration of the solar wind and some,
probably significant, role of the MHD waves in the functioning of
this bond. However, it is still unknown up to what extent the fluxes
of the solar wind's mass, momentum, and energy are driven by
``classic", Parker-type gas pressure gradients, and what is the
relative share of wave-flow (wave-particle) interactions and/or
turbulence \citep{cra04}.

It is widely believed that one of the main mechanisms responsible
for the heating of the solar wind, is the turbulent cascade of
Alfv\'enic fluctuations. The advantage of this heating model is that
it can also explain the above-mentioned relatively high proton
temperatures at 1~AU \citep{grm95}. Remarkably, it was also shown
\citep{gr99} that the turbulent cascade in the solar wind seems to
evolve most rapidly in areas with a formidable velocity shear. At
the same time, the measurements of significant density fluctuations
($\delta\rho/\rho\sim 0.1$) in the solar wind \citep{grm95} are
usually interpreted as evidence for the presence of magneto-acoustic
waves not only in the corona but also in the solar wind. On the
other hand, both slow and fast magneto-acoustic modes are expected
to be strongly damped by Landau damping for solar wind parameter
values \citep{bar79}. Therefore, there is a very scarce, if any,
chance for their undamped propagation from the solar corona up to
the outer wind regions. This logically leads to the following
presumable solution of this puzzle: the magneto-acoustic waves in
the solar wind should have a local origin.

It has been suggested that three- and/or four-wave resonant
processes may be of a considerable importance in the solar wind
\citep{lm80,bn01,c05}. However, after studying the nonlinear
interaction of oblique fast magneto-acoustic waves with Alfv\'en
waves in the solar wind, Lacombe and Mangeney came to the conclusion
that ``this non-linear process is not very efficient in the solar
wind, so that Alfv\'en waves can be considered as decoupled from
compressive waves in the major part of the m.h.d. spectral range"
\citep[see][Abstract]{lm80}. Another argument against this scenario
is that, if one of the modes is strongly damped, three- and/or
four-wave resonant processes transform into the induced scattering
of the involved waves by plasma particles \citep{bzm73} and, hence,
they do not lead to the reappearance of the damped wave mode. In
addition, there are observational arguments against the multi-wave
scenario. It is known \citep{bis03} that in the slow solar wind the
fluctuation amplitudes are smaller then in the fast solar wind. If
nonlinear multi-wave resonant processes were responsible for the
generation of compressive fluctuations, then one should expect a
much higher level of density fluctuations in the fast wind than in
the slow wind. However, observations show that the slow solar wind
is usually much more compressional then the fast solar wind
\citep{bb91,bpb04}. Consequently, the local generation of
magneto-acoustic waves could hardly be explained by multi-wave
resonant processes.

Hence, the gradual appearance of locally-produced magneto-acoustic
waves throughout the solar wind seems to be an observationally
confirmed fact, but still solicits for an adequate explanation. In
the present paper, we argue that the velocity-shear-induced linear
mode conversion of Alfv\'en waves into fast and slow
magneto-acoustic waves represents an efficient mechanism for the
generation of the observed magneto-acoustic waves within the solar
wind. It is also argued that the velocity shear could have an
important contribution in the gradual ``energization" of the solar
wind via the generation of fast and slow magneto-acoustic MHD waves,
that are eventually strongly damped by Landau damping. Our analysis
shows that the linear mode conversion of Alfv\'en waves into
magneto-acoustic waves is especially efficient for the low-frequency
Alfv\'en waves from the energy containing interval. Afterwards,
these perturbations can cascade to the smaller scales \citep{mbm87}
by turbulence.

It is well-known \citep{rgmg92,gr99} that velocity shear is one of
the most important ingredients in the solar wind dynamics. Recent
studies, based on in situ observations, showed that the fast/slow
wind interface in the interplanetary space has two parts: a smoothly
varying ``boundary layer" flow that separates the fast wind from the
coronal holes, and a sharper discontinuity between the slow and the
intermediate solar wind \citep{s05}. A relatively high velocity
shear was observed by \emph{Ulysses} over its first orbit in the
transition area between the fast and slow solar winds at
$13^\circ-20^\circ$ latitudes. The analysis of the data
\citep{mrgbf98} showed that the transition area between the two
winds consisted of two regions, the first one with a width $\Delta
l_1\approx 2~10^7~{\rm km}$ and a velocity change $\Delta V_1
\approx 200~{\rm km \, s^{-1}}$, and the second one with $\Delta
l_2\approx 8~10^7~ {\rm km}$ and $\Delta V_2 \approx 100~{\rm km \,
s^{-1}}$. However, during \emph{Ulysses'} second orbit, the global
solar wind structure was remarkably different from that observed
during its first orbit \citep{m01,m03}. Overall, the solar wind was
the slowest seen thus far in the satellite's ten-year journey (~270
km s$^{-1}$). The wind was highly irregular, with less pronounced
periodic stream interaction regions, more frequent coronal mass
ejections, and only a single, short interval of fast solar wind. The
complicated solar wind structure obviously was related with a higher
complexity of the solar corona around the solar activity maximum,
e.g.\ with the disappearance of large polar coronal holes and with
the presence of smaller-scale coronal holes, frequent CMEs and
coronal streamers.

Originally, the idea of (velocity-)Shear-induced Wave
Transformations (SWTs) in the solar wind was proposed by
\citet{prm98}. However, the model of these authors was based on a
phase-space analysis of the temporal evolution of individual
fluctuation harmonics in the ideal (viscosity- and resistivity-less)
limits, and it was only of a qualitative nature. Since then,
considerable progress has been made in three important directions:
(i)~real (physical) space numerical simulations have been performed
and it has been shown that SWTs occur in a well-pronounced way and
they lead to easily recognizable collective phenomena in MHD plasma
flows \citep{bprr01}; (ii)~the role of the dissipation has been
analyzed and the concept of shear-induced \emph{self-heating} was
introduced \citep{rog04} and it was found that compressible wave
modes (e.g., sound waves in hydrodynamic flows and fast
magneto-acoustic waves in MHD flows) grow non-exponentially and
undergo subsequent viscous and/or resistive damping leading to the
heating of the ambient flow by ``inborn" waves; (iii)~a noteworthy
quantum-mechanical (QM) analogy has been disclosed that helped to
apply efficient mathematical tools from the scattering matrix theory
of QM to the SWT studies which helped to give a quantitative rigor
to this theory and to calculate directly the efficiency of different
wave transformation channels by determining the corresponding
transformation coefficients.

The aim of the present paper is to apply the latter method to the
study of MHD wave transformations in the solar wind and to give a
fully quantified description of the coupling efficiency by
calculating the corresponding transformation coefficients. The
mathematical methods used in this paper are similar to the ones that
originally were developed in the 1930s for quantum mechanical
problems \citep{stu32,zen32,lan32}. More recently, similar
asymptotic methods have been successfully applied to various other
problems including the interaction of plasma waves in inhomogeneous
media \citep{swa98,gcsl04,RG05}.

The present paper has the following structure: the main mathematical
consideration is presented in the next section. Different regimes of
wave transformations, depending on the value of the plasma-$\beta$,
are studied in the third section. A brief discussion and the
conclusions are given in the final section.

\section{Basic Formalism}

In this section, we give a brief synopsis of the basic shear flow
model that was studied by \citet{prm98}. In this vein, we consider a
plane-parallel, compressible, magnetized, unbounded shear flow with
uniform values of the equilibrium plasma density $(\rho_0)$ and
pressure $(P_0)$. The equilibrium magnetic field $\bf B_0$ is
considered to be uniform as well and is assumed to be directed
parallel to the flow velocity which, in turn, is spatially
inhomogeneous and oriented in the $z$-direction:
$$
{\bf U}_0=(0,0,A x), \eqno(1)
$$
with the shear parameter $A>0$ being defined as a positive constant.

The linearized ideal MHD equations governing the evolution of the
perturbations of the plasma density $(\rho^{\prime})$, pressure
$(p^{\prime})$, velocity field $(\bf{u^{\prime}})$ and magnetic
field $(\bf {b^{\prime}})$ in this flow are [with the notation
${\cal D}_t \equiv
\partial_t + {\bf U}_0 \cdot {\bf \nabla}$]:
$$
{\cal D}_t \rho^{\prime} + {\rho_0} {\bf \nabla} \cdot
{\bf{u^{\prime}}} = 0, \eqno(2)
$$
$$
{\rho_0}[{\cal D}_t{\bf{u^{\prime}}} + ({\bf u^{\prime}} \cdot
{\bf \nabla}) {\bf U}_0] =- {\bf \nabla} p^{\prime} -
\frac{1}{4\pi} {\bf B}_0 \times ({\bf \nabla} \times
{\bf{b^{\prime}}}),  \eqno(3)
$$
$$
{\cal D}_t{\bf{b^{\prime}}} - ({\bf B}_0 \cdot {\bf \nabla}
){\bf{u^{\prime}}} + {\bf B}_0 ({\bf \nabla} \cdot
{\bf{u^{\prime}}})= 0, \eqno(4)
$$
$$
{\bf \nabla} \cdot {\bf{b^{\prime}}} = 0. \eqno(5)
$$

The standard technique of the so-called ``shearing-sheet
approximation" \citep{gl65} implies that it is convenient to expand
the perturbations as follows:
$$
\mbox{\boldmath $\Phi$}^\prime({\bf x},t) = \mbox{\boldmath
$\Phi$}^\prime ({\bf k},t) \exp \left[ i(k_x(t)x + k_yy+k_zz)
\right], \eqno(6)
$$
where the state vector $\mbox{\boldmath $\Phi$}^\prime \equiv [{\bf
u}^{\prime}, {\bf b}^{\prime}, \rho^\prime, p^\prime]$, while
$k_x(t) \equiv k_x(0) - k_z A t$, and $k_x(0)$, $k_y$, and $k_z$ are
the initial ($t=0$) values of the components of the wave number
vector ${\bf k}(t)$. Remarkably, this ansatz reduces the
mathematical part of the task to the solution of a closed set of
ordinary differential equations (ODEs) in time: a solvable initial
value problem. Note that $k_x(t)$ varies in time and this fact is
usually referred to as the ``drift" of the Spatial Fourier Harmonics
(SFH) in the phase ${\bf k}$-space \citep{crt96,prm98}.

From the set of Eqs.~(2)--(5), considering adiabatic perturbations
$p^\prime = {c_s}^2 \rho^\prime$, where $c_s$ is the sound speed,
and introducing the following non-dimensional parameters and
variables $R \equiv A/(V_A k_z)$, $\tau \equiv k_z V_At$, $\beta
\equiv c_s^2/V_A^2$, $K_y \equiv k_y/k_z$, $K_x(\tau) \equiv
k_x/k_z-R \tau$, $K^2(\tau)=K_x^2(\tau)+K_y^2 + 1$, $\rho({\bf
k},\tau)\equiv i {\rho^{\prime}({\bf k},\tau)}/{\rho_0}$, ${\bf
b}({\bf k},\tau) \equiv i{{\bf b}^{\prime}({\bf k},\tau)}/{B_0}$,
${\bf v}({\bf k}, \tau) \equiv {\bf u}^{\prime}({\bf k},\tau)/V_A$,
$\psi \equiv \rho + K_x(\tau)b_x + K_yb_y =\rho - b_z$, ($V_A \equiv
B_0/ \sqrt{4 \pi \rho_0}$ is the Alfv\'en speed), one can derive the
following set of ODEs \citep{prm98} [$F^{(n)}\equiv\partial^n_tF$]:
$$
\psi^{(2)} + {\cal C}_{11}\psi + {\cal C}_{12}(\tau)b_x+{\cal
C}_{13}b_y = 0, \eqno(7)
$$
$$
b^{(2)}_x + {\cal C}_{22} (\tau) b_x +{\cal
C}_{21}(\tau)\psi+{\cal C}_{23}(\tau)b_y=0, \eqno(8)
$$
$$
b^{(2)}_y + {\cal C}_{33} b_y + {\cal C}_{31}\psi+{\cal
C}_{32}(\tau)b_x=0, \eqno(9)
$$
where $||{\cal C}||$ is a $3 \times 3$ symmetric matrix defined
as:
$$
||{\cal C}|| = {\left(\matrix{\beta& - \beta K_x(\tau) & -\beta
K_y \cr - \beta K_x(\tau) & 1+(1+\beta)K_x^2(\tau) & (1+\beta)
K_x(\tau) K_y \cr - \beta K_y  & (1+\beta) K_x(\tau) K_y  &
1+(1+\beta)K_y^2 \cr}\right)}.\eqno(10)
$$

The total energy of the perturbations, in the non-dimensional
form, can be defined as the sum of the kinetic, the magnetic and
the compressional energies. It can be written down in the
following way:
$$
E({\bf k},\tau) \equiv {1 \over 2}{\biggl[|\textbf{v}|^2 +
|\textbf{b}|^2+ \beta \rho^2\biggr]}. \eqno(11)
$$

From Eqs.~(7)--(9) it is easy to see that in the absence of the
shear in the flow (i.e.\ for $R=0$, and thus $A=0$), these equations
describe independent oscillations with the fundamental
eigenfrequencies \citep{prm98}:
$$
{\Omega^2_{s,f}}=\frac{1}{2}(1+\beta) K^2 \left[1 \pm
\sqrt{1-\frac{4\beta}{(1+\beta)^2 K^2}} ~\right],  \eqno(12a)
$$
$$
{\Omega^2_A}=1, \eqno(12b)
$$
that can be easily identified as fast and slow magneto-acoustic
waves (FMW and SMW) and Alfv\'en waves (AW), respectively. For the
eigenfunctions, $\Psi_i$, corresponding to the above-defined
$\Omega_i$ eigenvalues, we find \citep{gcsl04}:
$$
\Psi_f = \frac{(\Omega_S^2 - \beta)\rho + \Omega_S^2 (K_x b_x +
K_y b_y )}{\sqrt{(\Omega_S^2 - \beta)^2+\beta^2 K_\perp^2}}, \eqno(13a)
$$
$$
\Psi_s = \frac{\beta {K_\perp^2} \rho + (\Omega_S^2 - \beta K^2
)(K_x b_x + K_y b_y )}{K_\perp \sqrt{(\Omega_S^2 -
\beta)^2+\beta^2 K_\perp^2}}, \eqno(13b)
$$
$$
\Psi_A = \frac{K_y b_x - K_x b_y}{\sqrt{K_\perp^2}}. \eqno(13c)
$$
where $ K_\perp^2 \equiv K_y^2+K_x^2$.

Notice than, when the flows are only weakly sheared (i.e.\ when $R
\ll 1$), the coefficients in Eqs.~(7)--(9) vary only slowly or
adiabatically. This implies that the expressions for the fundamental
eigenfrequencies, given by Eq.~(12), and the corresponding
eigenfunctions, given by Eq.~(13), are still useful for a
qualitative description of the shear-induced dynamics of the wave
modes and their coupling/conversion properties \citep{crt96,prm98}.

\section{Transformation regimes: the transition matrix method}

As will be shown in the next section, the characteristic values of
the normalized velocity shear rate in the solar wind plasma always
satisfy the condition $R \ll 1$. This necessarily implies that the
coefficients in Eqs.~(7)--(9) are only slowly varying functions of
$\tau$ and, therefore, the adiabatic (WKB) approximation holds
everywhere except in the immediate vicinity of the turning
[$\Omega_i(\tau_t)=0$] and the resonant
[$\Omega_1(\tau_r)=\Omega_2(\tau_r)$] points. Using Eq.~(12) one can
evaluate that the condition:
$$
\dot{\Omega}_i \ll {\Omega}_i^2, \eqno(14)
$$
is satisfied for all the MHD wave modes at any moment of time, or
equivalently, none of the turning points are located near the real
$\tau$-axis. From a physical point of view, this means that there
are no (over-)reflection phenomena \citep{gcsl04} and resonant
coupling can only occur between different waves modes with the same
sign of the phase velocity.

A careful analysis of the system yields that the resonant coupling
takes place in the vicinity of the point $\tau_\ast$ where
$K_x(\tau_\ast)=0$ \citep{prm98}. According to the general theory of
such systems, the timescale of the resonant coupling $\Delta \tau$
is of the order of $\Delta \tau \sim R^{-n/(n+1)}$ \citep{gcsl04},
where $n$ indicates the order of the resonant point \footnote{The
resonant point is said to be of the order $n$ when
$(\Omega_1^2-\Omega_2^2) \sim (\tau - \tau_{r})^{n/2}$ in the
neighborhood of $\tau_{r}$}, and, therefore, the evolution of the
waves is adiabatic when
$$
|K_x(\tau)| \gg R^{1/(n+1)}. \eqno(15)
$$

If this condition is satisfied, the temporal evolution of the waves
is described by the standard WKB solutions:
$$
\Psi_i^\pm = \frac{D_i^\pm}{\sqrt {\Omega_i(\tau)}}e^{\pm i \int
\Omega_i(\tau)d\tau}, \eqno(16)
$$
where the $D_i^\pm$ denote the WKB amplitudes of the wave modes with
positive and negative phase velocity along the $z$-axis,
respectively. All the physical quantities can be readily found by
combining the Eqs.~(7)--(9). The energies of the involved wave modes
satisfy the standard adiabatic evolution condition \citep{prm98}:
$$
E_i = \Omega_i(\tau) (|{D_i^+}|^2 + |{D_i^-}|^2). \eqno(17)
$$
From this equation it follows that $|{D_i^\pm}|^2$ can be
interpreted as the number of `wave particles' (the so-called
`plasmons'), in analogy with quantum mechanics.

Let us assume that initially $K_x(0) \gg R^{1/(n+1)}$. Due to the
linear drift in the ${\bf k}$-space, $K_x(\tau)$ decreases and when
the mode enters the ``degeneracy area" \citep{prm98}, the mode
dynamics becomes non-adiabatic due to the resonant coupling between
the modes. Afterwards, when $K_x(\tau) \ll-R^{1/(n+1)}$, the
evolution becomes adiabatic again. Denoting the WKB amplitudes of
the wave modes before and after the coupling region by
${D_{i,B}^\pm}$ and ${D_{i,A}^\pm}$, respectively, and by employing
the formal analogy with the $S$-matrix of the scattering theory
\citep{kop95}, one can connect ${D_{i,A}^\pm}$ with ${D_{i,B}^\pm}$
via the so-called transition matrix:
$$
{\bf D}^+_{A} = {\bf T} {\bf D}^+_{B}, ~~~{\bf D}^-_{A} = {\bf
T}^{\ast} {\bf D}^-_{B}, \eqno(18)
$$
where ${\bf T}$ and its Hermitian conjugated matrix ${\bf T}^\ast$
are $3\times3$ matrices. Note, that none of the turning points are
located near the real $\tau$-axis and, therefore, there is no
transition between the modes with opposite signs of the phase
velocity along the $z$-axis \citep{gcsl04}.

Notice that all the coefficients in the governing equations are
real. Moreover, the matrix given by Eq.~(10) is symmetric. As a
consequence \citep{kop95,fed83}, the transition matrix ${\bf T}$ is
unitary \footnote{A matrix ${\bf U}$ is {\it unitary} if its
conjugate transpose, ${\bf U}^{H}$ is equal to the inverse matrix
${\bf U}^{-1}$.}, and
$$
\sum_j |T_{ij}|^2 =1. \eqno(19)
$$
Generally speaking, this equation represents the conservation of the
wave action. When $R \ll 1$, it transcribes  into the energy
conservation throughout the resonant coupling of the wave modes
\citep{gcsl04}. Energetically this means that a transformed wave
mode is generated solely on the expense of the energy of the
incident wave mode.

The crucial physical importance of this matrix follows from the fact
that the value of the quantity $|T_{ij}|^2$ represents a part of the
energy transformed via the resonant coupling of the modes. That is
why the absolute values of the transition matrix components
$|T_{ij}|$ are called the `transformation coefficients' of the
corresponding wave modes. For the resonant interaction of two wave
modes, e.g.\ $i$ and $j$, the unitarity of the matrix ${\bf T}$
guarantees an important property of the transition matrix, viz.\
$T_{ij}=T_{ji}$. This symmetry property holds for the resonant
interaction of two wave modes only. If, in the same time interval,
there is an effective coupling of more then two wave modes, then the
symmetry property fails.

In earlier studies, a lot of attention was usually paid to the
resonant points of the first order \citep{ll77,fed83}. In this case,
only the dispersion equations of the waves are needed to derive the
transformation coefficients with accuracy $O(R^{1/2})$. For the
second and/or higher order resonant points, analytical expressions
for transformation coefficients can be derived only in the case of
weak interactions ($ T_{ij}\ll 1,~~ i \neq j$). As a matter of fact,
if the resonant points are not close to the real $\tau$ axis, in the
sense that
$$
\phi_{ij} = \left| {\rm Im}
\int_{\tau_0}^{\tau_{r}}(\Omega_i-\Omega_j)d\tau \right|\gg 1,
\eqno(20)
$$
then the transformation coefficient is just equal to:
$$
T_{ij} \approx \frac{\pi}{2} \exp\left(- \phi_{ij} \right).
\eqno(21)
$$
Here, and hereafter, the signs of the absolute magnitude for
transformation coefficients are omitted, i.e., from now on the
notation $T_{ij}$  means $|T_{ij}|$.

In the context of the {\em linear} problem that we are studying in
this paper, viz.\ the velocity-shear-induced coupling of MHD waves,
all the resonant points are of the second order, as will be shown
later.

In the following subsections, we will study in detail the coupling
of MHD wave modes (AW, FMW, and SMW) for different regimes of the
plasma-$\beta$ that are interesting in the solar wind context. For
the earlier, detailed, but only qualitative analysis of the same
regimes see \citet{RPM00}.

\subsection{The case $\beta \ll 1$}

It is well-known that the magnetic field dominates the plasma
($\beta \ll 1$) throughout most of the solar corona, especially at
lower altitudes and within the so-called `active' regions, as well
as in the innermost regions of the solar wind. For the MHD waves in
this regime, the frequency of the SMW is far smaller then the
frequencies of the FMW and the AW. Therefore, the coupling of the
SMW with the other two MHD modes is exponentially small with respect
to the large parameter $1/R$ and can be neglected. Consequently, in
the set of the governing equations Eqs.~(7)--(9), the equation for
the variable $\psi$ decouples from the other equations, and the
equations for $b_x $ and $b_y$ describe the evolution of the coupled
AW and FMW:
$$
{\ddot b}_x  + \left[ 1+ K_x^2(\tau) \right] b_x = -K_x(\tau) K_y
b_y, \eqno(22)
$$
$$
{\ddot b}_y + \left[ 1 + K_y^2 \right] b_y = -K_x(\tau) K_y b_x.
\eqno(23)
$$

The normalized frequencies of the coupled wave modes are:
$\Omega_f^2(\tau) = 1 + K_y^2 + K_x^2(\tau),~\Omega_A^2 = 1$.
Therefore, there are two, complex conjugated, second order
resonant points:
$$
K_x(\tau_{fA}) = i K_y,~~~K_x(\tau_{fA}^\ast) = -i
K_y. \eqno(24)
$$

The condition (15) then implies that the evolution of the waves is
adiabatic if
$$
\delta \equiv |K_y^3|/R \gg 1, \eqno(25)
$$
and if this condition is satisfied, Eq.~(21) yields:
$$
T_{fA} = \frac{\pi}{2} \exp\left( -\frac{\delta^3}{3} \right).
\eqno(26)
$$

An analytical expression for the transformation coefficients can
also be derived in the opposite limit, $\delta \ll 1$. In this
case \citep{gcsl04}:
$$
T_{fA} \approx \frac{2^{2/3}\pi}{3^{1/3}\Gamma \left(
\frac{1}{3}\right)} \delta \left( 1 - \frac{\Gamma\left(
\frac{1}{3}\right)}{2^{7/4} 3^{1/3} \Gamma \left(
\frac{2}{3}\right)} \delta^4 \right). \eqno(27)
$$

Results of the numerical solution of the initial set of equations
(7)--(9) (solid line) as well as of the analytical expressions given
by Eqs.~(26) (dash-dotted line) and (27) (dashed line) are presented
in Fig.~1. This plot shows that the transformation coefficient
attains its maximal value $(T_{fA}^2)_{max} = 1/2$ at $\delta^{cr}
\approx 0.89$.

In the case of first-order resonant points, the transformation
coefficient monotonically tends to unity when the resonant points
tend to the real axis \citep{ll77,fed83} and, therefore, the total
conversion of one wave mode into another wave mode is possible.
Here, in the case of second-order resonant points, existing for the
FMW-AW coupling in a low-$\beta$ plasma, $({T_{fA}}^2)_{max} = 1/2$.
This leads to the following important astrophysical conclusion: in
those regions of the solar wind where $\beta \ll 1$, even under the
most favorable conditions, at most half of the energy of the AWs can
be transformed into FMWs and vice versa!

Yet another important aspect of the coupling in this case is that,
if the resonant point tends to the real $\tau$ axis (i.e., $K_y
\rightarrow 0$), the transformation coefficient tends to zero.

\subsection{The case $\beta \gg 1$}

In the high-$\beta$ case, $\Omega_s,\Omega_A \ll \Omega_f$.
Therefore, only the coupling between the AW and the SMW can be
important in this regime. From the expressions for the fundamental
frequencies [see Eq.~(12)] one can easily deduce that, for the
AW-SMW coupling, there are two complex conjugated, second-order
resonant points, that are given by Eq.~(24). The condition (20) in
this case has the following form:
$$
\frac{1}{\beta R}\left| K_y -\frac {\mbox{arcsinh} \left( K_y
\right) }{\sqrt {1+K_y^2}} \right| \gg 1. \eqno(28)
$$

If this condition is satisfied, and in addition $K_y \ll 1$, we can
derive from Eq.~(21) the following formula for the transformation
coefficient:
$$
T_{sA} \approx \frac{\pi}{2} \exp\left( -\frac{|K_y|^3}{3\beta R}
\right). \eqno(29)
$$

Unlike in the low-$\beta$ case, now there is no unique parameter,
like the parameter $\delta$, which would give a complete description
of the transformation process. Instead, in this limit, there are two
``governing" parameters, viz.\ $K_y$ and $\beta R$.

Let us first consider the case $ \beta R \ll 1$. In this case,
Eq.~(28) reduces to $\delta_1 \equiv |K_y|/(\beta R)^{1/3} \gg 1$,
and the properties of the wave transformation are essentially the
same as in the case of the transformation of the AW to the FMW and
vice versa. As a matter of fact, if $\delta_1 \ll 1$, then the
leading term of the asymptotic expressions of the transformation
coefficient is given by Eq.~(27), with $\delta$ replaced by
$\delta_1$. At $ \beta R\ll 1$, the transformation coefficient
reaches its maximum $(T_{sA}^2)_{max} =1/2$ at $\delta_1^{cr}$ that
coincides with $\delta^{cr}$.

The dependence of the transformation coefficient on $K_y$, on the
other hand, provides some very interesting and new details, compared
with the low-$\beta$ case. On Fig.~2, we display the numerical
solution of the initial set of equations (7)--(9) for the cases
$\beta R = 0.025 $ and $\beta R = 1 $. This numerical inspection
shows a remarkable fact: when $\beta R$ is not small the properties
of the transformation process are quite different (see Fig.~2). As a
matter of fact, when $K_y \ll 1$, it turns out that the
transformation coefficient $T_{sA}$ does not depend on $\beta R $ at
all and is given by the formula $T_{sA} \approx 2.05 K_y$. Besides,
as it can be seen clearly from Fig.~2, $(T_{sA})_{max}=1$, i.e.\
now, unlike the low-$\beta$ situation, a total transformation of one
wave mode into another wave mode is possible!

\subsection{The $\beta \sim 1$ case}

The $\beta \sim 1$ case is the most interesting but also the most
complicated case of velocity-shear-induced MHD wave transformations.
The frequencies of all three modes are of the same order in this
case and a simplification or reduction of the set of Eqs.~(7)--(9)
is not possible. However, the analysis of Eq.~(12) enables us to see
that there is a pair of complex conjugated first-order resonant
points:
$$
{K_x}(\tau_{1,2}) = \pm i \sqrt{ K_y^2+\left(
\frac{\beta-1}{\beta+1} \right)^2}, \eqno(30)
$$
and another pair of complex conjugated resonant points of the second
order:
$$
{K_x}(\tau_{3,4}) = \pm i K_y.  \eqno(31)
$$

The essential complexity of this case stems from the fact that the
transition matrix method does not allow one to derive analytic
expressions for the transformation coefficients when more than two
wave modes are effectively coupled. However, the numerical study of
the problem shows (see for details \citet{gcsl04}) that the
qualitative character of the wave transformation processes in this
case is mainly similar to the cases described in the previous
subsections.

\section{Discussion and conclusions}

Several years ago, \citet{prm98} argued that velocity-shear-induced
MHD wave transformations could be an important ingredient of the
wave dynamics in the solar wind, contributing to its acceleration
and heating. It was further argued \citep{prm99,RPM00} that SWTs can
contribute to the transmission of the waves from the chromosphere,
through the transition layer to the corona and further into the
solar wind. Besides, it was speculated that ``self-heating" of the
solar plasma flows \citep{rog04,srp04,spp06}, via the agency of
mutually coupled wave modes, might be one of the reasons for the
coronal heating (both ``basal" and ``extended") and the acceleration
of the solar wind.

Up to now, the scenario of the linear coupling and the mutual
transformations of the MHD wave modes in the solar wind was outlined
only qualitatively. Clearly, this merely qualitative picture lacked
quantitative strength and rigor, since it was not clear how
efficient the SWTs could be in the solar wind context. In this
paper, we solved this problem and we provided a systematic,
quantitative description of SWTs in terms of the recently developed
transition matrix method (originally developed in the 1930s for
quantum mechanical applications) and transformation coefficients.

In particular, we have demonstrated that the dynamics of the MHD
wave conversions is determined by three key parameters: the flow
velocity shearing rate $R$, the plasma $\beta$ and the ratio
$K_y=k_y/k_z$. Since the aim of this paper is to verify whether the
SWTs are well-pronounced in the solar wind, it is necessary to
analyze whether these parameters within the solar wind really have
values which favor efficient mode transformation processes or not.

For the dimensionless shearing parameter $R$ we have
$$
R=\frac{\Delta V}{\Delta l}\frac{1}{\Omega_a}. \eqno(32)
$$
Using for $\Delta V$ and $\Delta l$ the values presented in the
Introduction, we found that even for very low frequency Alfv\'en
waves (with $\Omega_a > 10^{-4}~{\rm s^{-1}}$), the dimensionless
shear parameter satisfies the condition $R \ll 1$, for both regions
of the transition area between the fast and slow solar winds.
Bearing also in mind that the plasma $\beta \sim 1$ in the solar
wind, we obtain that $R \beta \ll 1$, and according to the
considerations in the previous section, the coupling of the AWs with
both the fast and slow magneto-acoustic waves has the same
qualitative character. As a matter of fact, Eq.~(25) gives us the
necessary condition for an effective coupling
$$
K_y \lesssim R^{1/3}, \eqno(33)
$$
showing that an effective coupling between the Alfv\'en mode and the
fast and slow magneto-acoustic modes takes place for the low
frequency Alfv\'en waves from the energy containing interval.
Indeed, using for the frequency of the AWs, $\Omega_a=2\pi/T_a
\approx 6\times10^{-4}~{\rm s^{-1}}$, and using for $\Delta V$ and
$\Delta l$ the values presented in the Introduction, we found that
$R_1\approx 1.6\times10^{-2}$ and $R_2\approx 2\times10^{-3}$ for
the two regions of transition between the fast and slow solar winds.
Equation~(33) then yields for the perpendicular wave numbers of the
waves, $k_y \lesssim 0.25 k_z$ for the first transition region and
$k_y \lesssim 0.13 k_z$ for second transition region, respectively.
Noting that in the energy containing range, the turbulent
fluctuations are nearly isotropic \citep{bbgv06}, we can expect that
for the typical turbulent fluctuations in this range parallel and
perpendicular wave numbers of the same order ($k_y \sim k_z$).
Consequently, the linear transformations of Alfv\'en waves to fast
and slow magneto-acoustic waves are quite likely to take place in
this frequency band.

On the other hand, the linear transformation of Alfv\'en waves to
magneto-acoustic waves seems to be inefficient in the high frequency
band, including the inertial interval of solar wind fluctuations. As
a matter of fact, Eqs.~(32) and (33) yield that the modes which
could be effectively transformed should satisfy $k_y \ll k_z$.
However, theoretical research of MHD turbulence as well as numerical
simulations and analysis of the solar wind data
\citep{smm83,gs95,cv00,mbg03,bis03,om05,g06} all indicate that the
energy cascade in the inertial interval proceeds much more
effectively in the direction perpendicular to the mean magnetic
field and, therefore, for high-frequency modes one usually has $k_y
\gg k_z$. Consequently, the condition (33) could be hardly fulfilled
for typical parameters of high-frequency Alfv\'en waves in the solar
wind.

Although the performed analysis allows us to make quite definite
predictions about the efficiency of linear conversion of AWs into
FMWs and SMWs, direct quantitative comparison with the observations
is difficult since the compressive part of the velocity field can
not be isolated by single spacecraft observations \citep{bis03}.
Consequently, it is difficult to associate the observed density
fluctuations to specific mode characteristics, such as fast or slow
magneto-acoustic modes.

Nevertheless, on the qualitative level, the predictions of the study
presented here are in good agreement with the observations. As a
matter of fact, (i)~in the regions with strong velocity shear,
Alfv\'enic correlations are reduced and a high level of density
perturbations are observed \citep{gr99}; (ii)~the spectrum of
density fluctuations in the inertial interval of the solar wind
fluctuations follows the Kolmogorov scaling $\rho^\prime \sim
k^{-5/3}$ \citep{mt90}. This agrees with the model developed by
\citet{mbm87}, where it has been shown that in the weakly
compressible limit, the density perturbations behave like a passive
scalar, i.e., they follow the scaling of the magnetic field
perturbations. The findings of the present paper supplement this
model and offer an efficient mechanism for the generation of the
density perturbations in the energy containing interval, which
afterwards are cascaded to the smaller scales.

Another interesting and not completely understood problem is the
spatial aspect of the velocity-shear-induced wave transformations in
the solar wind. If the largest values of the flow shearing rates
appear in the relatively narrow ``transition zones" between the slow
and the fast solar wind, one may wonder whether the
velocity-shear-induced mode conversions are confined to these
regions or whether they tend to occupy a wider volume of the wind
plasma!? Evidently only real-space numerical simulations, taking
into account physical characteristics of the solar wind, may answer
this question. Direct numerical simulations, performed in the
general context of SWTs, have shown \citep{bprr01} that when the
Alfv\'en waves get transformed into the fast magneto-sonic waves,
the latter tend to leave their ``birthplace" and propagate quite
rapidly due to their high velocities. We suppose that the
observational signature of the waves generated by means of this
mechanism would be their appearance throughout both the sheared and
the non-sheared wind volume with the maximal probability of their
detection in the vicinity of the strongly sheared transition
regions.

In the near future, we would like to take into account the effect of
the kinematic complexity \citep{MR99} and verify whether the
transition matrix method can lead to a quantitative description of
the SWTs not only for the solar wind, but also for solar jet-like
flows with a more complicated geometry and complicated kinematics.

\acknowledgments
Andria Rogava wishes to thank the \emph{Katholieke Universiteit
Leuven} (Leuven, Belgium) and the \emph{Abdus Salam International
Centre for Theoretical Physics }(Trieste, Italy) for supporting him,
in part, through a Senior Postdoctoral Fellowship and a Senior
Associate Membership Award, respectively. The research of Andria
Rogava and Grigol Gogoberidze was supported in part by the Georgian
National Science Foundation grant GNSF/ST06/4-096. The research of
Grigol Gogoberidze was supported in part by INTAS grant
06-1000017-9258. Andria Rogava and Grigol Gogoberidze are grateful
for the hospitality to the Abdus Salam International Centre for
Theoretical Physics, where a part of the work was done during their
visits to the ICTP, in 2005, as a Senior Associate and a Young
Collaborator, respectively. These results were obtained in the
framework of the projects GOA 2004/01 (K.U.Leuven), G.0304.07
(FWO-Vlaanderen) and C~90203 (ESA Prodex 8).

redpajama_set_name: RedPajamaArXiv


In addition to providing advice and counsel to businesses and individuals, I am a trial lawyer. Good trial skills are earned through training and experience. Great trial skills are acquired by learning from the best lawyers - first in the classroom, then in the courtroom. I have been fortunate to learn from some of the best lawyers in the country. One important thing I have learned is that great lawyers come in all shapes and sizes. Some come from large firms, some from solo practices. Some are public defenders and civil rights advocates - and some routinely handle bet the company litigation for major corporations. During my career, I've gone to trial against lawyers from some very large and well-respected law firms, including: Baker Hostetler, Ice Miller, Vorys Sater, Barnes and Thornburgh, The Ohio Attorney General, and Dinsmore and Shohl. I have also litigated hundreds of cases short of trial against lawyers from some of the largest law firms in the country, including: Littler Mendelson, Winston Strawn, Seyfarth Shaw, Morgan Lewis, Squire Patton - just to name a few. Many of the lawyers I've faced at these firms were very talented - many were not. The lesson is, you can never judge a trial lawyer by the name of the firm under his/her signature or the law school he/she went to. This is especially true at trial. Once jury selection begins, those things simply don't matter - the lawyer's talent and skill does.
In addition to actual first, second and third chair trial experience, I have received extensive training in trial techniques from many of the best lawyers in the country. I have attended the following well-regarded programs taught by the National Institute of Trial Advocacy (NITA): NITA 9-day National Session Trial Skills Seminar (Boulder, CO), NITA Advanced Trial Skills Seminar (District of Columbia). I have also attended numerous trial skills courses taught by the American Association for Justice at conventions in the following cities: Montreal, Palm Springs and Boca Raton. Because of my practical trial experience and training, I have been sought out by other lawyers in Ohio and elsewhere to co-counsel complex employment and commercial litigation cases.
Jury Verdict for Former Employee. After a five-day disability discrimination trial, the jury returned a verdict for my client. The judgment, attorneys' fees and costs after the verdict total in excess of $500,000.
Jury Verdict for Former Employee - $423,000. After a three-day disability discrimination trial, the jury returned a verdict for my client, awarding him $73,900 in back pay and $350,000 in compensatory damages. The employer had made no settlement offer prior to trial. Brian Williams v. Sims Bros., Inc., 3:11-CV-00332 (Northern District of Ohio).
Settlement before trial - This was a disability discrimination case for a former long-term warehouse supervisor. The case settled for $147,000 shortly before trial.
Settlement before trial - This was a disability discrimination case for a former long-term health-care worker. The case settled the day before trial for $205,000.
Settlement before trial - This was a disability discrimination case for a former factory worker. The case settled a few weeks before trial for $175,000.
Arbitration Award for Former Employee - $476,176. After a five-day sexual harassment arbitration, the Arbitrator found in favor of my client, awarding the client back pay, front pay, pecuniary damages, emotional distress damages and attorneys' fees. The employer's last settlement offer before arbitration was less than $150,000.
Settlement during trial - After the start of an age discrimination trial, the employer agreed to pay my client over $200,000 in a confidential settlement agreement. The employer's last offer before trial was approximately $50,000.
Settlement before trial - Early in the case, I obtained a settlement of $105,000 for my client, an advertising executive.
Settlement during trial - After the start of a gender discrimination trial, the employer agreed to pay my client in excess of $75,000. The employer's last offer before trial was $1,500.
I successfully settled a case for a family-owned, Columbus health care supply company that was sued for pregnancy discrimination. After representing the company before the Ohio Civil Rights Commission, I was able to settle the claims on terms very favorable for the company.
ERISA Class Action Settlement - My firm filed a lawsuit against the fiduciaries of a self-insured health care plan to force the fiduciaries to pay unpaid medical bills. After the plan stopped making payments, the medical providers began collection proceedings against plan beneficiaries. As a result of the lawsuit brought by my firm, the fiduciaries personally guaranteed payment and eventually paid or settled every medical claim. The total amount of medical bills paid as a result of the class action settlement exceeded $600,000. Furthermore, the plan beneficiaries never had to pay a dime for legal services as the Defendants agreed to pay the class member's attorneys' fees.
After taking over for another firm, I successfully defended a family owned transportation company in a lawsuit brought by an agency of the State of Ohio for medical claims totaling approximately $1,000,000. The company had been fraudulently induced to pay for stop-loss insurance that didn't exist. I pursued the company's former insurance broker for negligence and obtained enough money to satisfy the debt to the State of Ohio.
COBRA case - My client's former employer refused to pay for over $125,000 in health care claims after my client retired, as required by COBRA. I pursued the employer in court and forced it to pay all of the medical bills. Not only did this save my client financially, but the hospital benefitted by obtaining payment it otherwise never would have received.
Long-Term Disability Case - A major disability insurance company refused to pay my client her long-term disability benefits claiming that she wasn't disabled. Early in the case, I obtained a settlement for my client of $125,000.
Before the United States Sixth Circuit Court of Appeals, I argued an appeal in an ERISA class action case involving a major uranium enrichment contractor that was represented by a major Washington, D.C. law firm.
Jury Verdict for Former Employee - $549,000. This was a race discrimination case tried in Franklin County, Ohio. The trial team consisted of Greg Mansell, Derek Walden and Danny Caudill. After a four-day trial, the jury returned a verdict for our client. $200,000 of the award was for punitive damages. Don O. Smith v. Superior Production LLC, 11CV-015815 (Franklin County Common Pleas Court).
I defended an Ohio non-profit company in a race discrimination charge filed with the Ohio Civil Rights Commission by a former employee. I was able to achieve a settlement that was very favorable for my client at a minimal cost.
I successfully defended a non-profit, charitable organization in a lawsuit alleging religious discrimination. The court judgment dismissing the case was upheld in the appeals court.
I successfully defended an Ohio company and its owner, who were sued for alleged tortious interference with contract, theft of trade secrets and breach of a non-compete agreement. Although a TRO had been issued against my client prior to my involvement, I was able to mount a defense that resulted in a settlement whereby my client was able to retain the very customers he was accused of stealing.
I successfully defended an Ohio company in a breach of non-compete agreement case brought in Jacksonville, Florida by a Florida transportation company. The Plaintiff in the case attempted to use the lawsuit to discover my client's entire book of business, which would have given the Plaintiff an unfair competitive advantage. I achieved the client's goal of settling the case, without ever permitting the Plaintiff to obtain any of my client's customer information.
I successfully prosecuted a preemptive declaratory judgment action in a California court on behalf of my client against a national transportation logistics company.
I successfully defended a Texas businessman, who was sued in an Ohio court for breach of a non-compete agreement and tortious interference with contract. Taking over the case from a large, regional law firm, I was able to achieve the settlement my client desired at a much lower cost than his former firm would have had to charge.
I cannot guarantee any particular result in any case. The cases above are merely examples of verdicts, judgments and settlements I have obtained for clients in the past. Every case is different.


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text:
Florence City Center Walking Tour
The Best of Florence - A stroll through the City Center
Enjoy an orientation tour from your accommodation in Florence and cover the most famous highlights of the historical center
Spot the best picture-perfect areas where to create lovely memories to bring home. Florence is just like a painting come to life!
Learn about the amazing history of the city from the time it was the capital of Renaissance to the time it became the capital of early unified Italy
No entrance tickets are needed! Enjoy your tour!
There is a moderate amount of walking involved so please wear comfortable shoes!
Meet&Greet your Guide at your Hotel/Accommodation in Florence
Transfer to Florence from Rome or any transfers required for hotels located outside Florence's historical center
Entrance tickets to any desired sites
Baptistery of Saint John
Florence Duomo
A medieval stone bridge that is known around the world for its beautify and uniqueness Locals still work and operate on the unique bridge still to this day and is part of the mysterious "Corridoio Vasariano" - The Ponte Vecchio (Old Bridge) was the only bridge spared by Hitler's strict orders while retreating from his opposition during World War 2. Locals say his decision was to save its beauty, as many building were destroyed either end of the bridge to block the enemy passing.
Characterized by the white Carrara and green Prato marble, it is one of the most ancient churches in Florence and gently marks the square of the city Cathedral. Its fascinating past, combining faith, history and art, has given scholars much food for thought with regard to its meaning and connection to the Renaissance era.
The main symbol of Florence is its impressive and imposing Duomo, named Santa Maria del Fiore. Famously designed by Arnolfo di Cambio six hundred years ago, it is still the third largest in the world! The outer colours and facade strongly follow the local traditions in Florence, holding the medieval rivalry again Siena within its design. Having a guided tour lets you understand the history full facade as well as the beautiful frescoed ceiling that is waiting for you inside.
Discover the highlights of Florence and follow an expert and entertaining guide to the most significant places. Start your experience touring around the religious center of the city: admire the Duomo, whose impressive Dome was designed by Brunelleschi, and the Baptistery of Saint John.
From the religious center we will walk to the political center, and enjoy a pleasant stroll through Piazza della Signoria, surrounded by ancient places and by the Loggia, up to the medieval bridge on the Arno River: the stunning Ponte Vecchio.
Add headsets to your tour to improve your party's comfort.

redpajama_set_name: RedPajamaCommonCrawl


text:
nations / italy / tier 3 / M16/43 Sahariano
M16/43 SaharianoTier 3, Medium tank★ Premium tank
At the end of 1940, the Italian Army encountered the British Cruiser Tank Mk. IV for the first time, and Italian engineers were interested in the concept of a high-speed tank. Initially, the plan was to create a low vehicle with a maximum armor thickness of 30 mm, a maximum weight of 13 tons, and armaments typical for Italian vehicles. Its 250 h.p. engine was supposed to provide a top speed of 55 km/h. The tank's weight and length gradually increased, and, as a result, it was a low-silhouette vehicle with a height of 2 meters. However, the vehicle did not pass full-fledged testing. By mid-1942, the 30 mm armor was not enough, and the project was discontinued.
Marks of Excellence requirements for M16/43 Sahariano: beta
100%N/A
Mastery badges for M16/43 Sahariano - base XP needed:
Target damage WN8 for M16/43 Sahariano:
Cannone da 47/40 bis (damage per shot: 50):
AMX 38
Sexton II
M4-85
Vickers Medium Mk. III
Progetto CC55 mod. 54
KV-2 (R)


Georges-Pierre Seurat (December 1859 – 29 March 1891) was a French post-Impressionist painter and draftsman. He is noted for his innovative use of drawing media and for devising the painting techniques known as chromoluminarism and pointillism.
A Sunday on a La Grande Jatte Georges-Pierre Seurat. Made in the USA by Peaceful Wooden Jigsaw Puzzles. Unique puzzle pieces with no two pieces alike. Puzzles features creative and fun whimsy pieces.


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text:
Packers Foundation awards $250,000 impact grants
Grants announced Tuesday at Annual Meeting of Shareholders
The Green Bay Packers Foundation has awarded $250,000 impact grants to both the Medical College of Wisconsin (MCW)-Green Bay and the American Foundation of Counseling Services (AFCS), the organization announced Tuesday at the Annual Meeting of Shareholders.
The grants are matching grants, requiring each organization to raise an additional $250,000 in order to secure the donation from the Packers Foundation.
The recipient of the Packers Foundation's Staff Impact Grant, MCW-Green Bay, is the Green Bay campus of the Medical College of Wisconsin, one of two medical schools in Wisconsin.
MCW-Green Bay works in partnership with the best academic and medical institutions in the region to bring students contemporary classroom technology and labs, first-class clinical education experience and personalized learning. Featuring a three-year Discovery curriculum, the college utilizes a calendar-efficient schedule spanning 134 weeks to allow students to complete medical school in only three years.
The organization will use the Staff Impact Grant for funding student scholarships.
The recipient of the Packers Foundation's Impact Grant, AFCS, provides counseling for individuals and families, foster care programs, and organizational development services, including support for clergy and congregations throughout the Green Bay area.
AFCS will use the Impact Grant for the Resident Training Program to support AFCS's overall efforts to increase access to mental health care within the community, as well as to develop community partnerships to improve the system of mental health care in Green Bay and Northeast Wisconsin.
"The Packers Foundation and the Packers are proud to be able to support two organizations that work so hard to improve the health and wellbeing of our community, from educating doctors to increasing access to mental health care," said Packers President/CEO Mark Murphy. "With these grants, MCW-Green Bay and AFCS can each have a direct and lasting impact on Northeast Wisconsin and beyond."
Check presentations for each organization will take place at a later date. To learn more about each organization, visit MCW-Green Bay at www.mcw.edu/Medical-School/Green-Bay-Campus-Discovery-Curriculum.htm, and AFCS at www.afcscounseling.org.
The Packers Foundation now has distributed more than $4 million for charitable purposes since it was established in 1986 by Judge Robert J. Parins, then-president of the Packers Corporation, "as a vehicle to assure continued contributions to charity." The Foundation awarded 225 grants in 2014 totaling $1.1 million.
The Green Bay Packers Foundation Trustees include Charlie Lieb (chairman), Tom Arndt, Valerie Daniels-Carter, Rick Chernick, Ricardo Diaz, Terry Fulwiler, Jerry Ganoni, Mark McMullen, Tom Olson and John Zakowski. Bobbi Jo Eisenreich is the secretary of the Foundation.
A component of the Green Bay Packers Give Back program, the grants, combined with other Green Bay Packers charity endeavors, contributes to a comprehensive Packers charity impact that was in excess of $7 million in the past year.


text:
Eyes On the Dog Run
By Glenn McAnanama
Talk about "eyes on the street," there is a group of New York City residents who patrol the city's streets and parks at all hours of the day and night, everyday. They are the city's dog owners and dog walkers. And they are under attack.
The boom in New York dog ownership owes itself in large part to an informal agreement that allows dog owners to take their dogs into parks between 9 pm and 9 am on any day of the week and let their dogs romp and roam parks unleashed.
Urban dog owners, like this one, know that their dogs are more well behaved when they have the chance to get a lot of exercise and socialize with other dogs and people. Where I grew up in suburban Staten Island, dogs were more territorial because, off the leash, they occupied only one small yard their entire lives, rarely interacting with other people and other dogs.
There is currently a lawsuit that would put an end to off-leash hours in city parks. Despite a 60 percent decline in the number of dogs bites in city parks over the past two decades, a Queens man wants the Parks Department and NYPD to enforce the city law mandating that dogs must be on leashes at all times in public.
That would be a bad enforcement policy. If the court rules that it must be enforced, many dog owners may be forced to leave the city for the suburbs. It also may encourage the return of criminals, drug dealers and anti-social behavior in park spaces that are currently well-used thanks to dogs and their owners.
The city's enforcement policy should continue to respect the current 9 pm to 9 am off-leash policy. The vast majority of dog owners realize that it is a privilege to let their pets roam free in the city parks and are good at self-policing. If a dog is particularly unfriendly or misbehaves frequently, an owner can be told to leash their dog. It's the sort of far sighted compromise that this city needs to do more often.
(Full disclosure: I was dog sitting an energetic Vizsla puppy this weekend)
Filed Under: Op/Ed, Parks, Public Space, Quality of Life
'Progressive' West Siders Again Call for MORE Policing in Central Park — With Support of Birder Chris Cooper
By Gersh Kuntzman	| Jun 16, 2020
An Upper West Side community panel has once again called for more NYPD enforcement in Central Park — and this time, it had the support of a prominent victim of the specter of police violence.
Cyclist Injured on Dangerous Riverside Park Bike Bypass — Need For Fix is Obvious
By Julianne Cuba	| Nov 19, 2019
A cyclist was injured over the weekend — and the blame can be laid almost entirely on the Parks Department's construction of a hilly, dark and dangerous detour through Riverside Park.
Mark Your Calendars: Summer Streets Returns in August
By Stephen Miller	| Jul 23, 2015
Another summer, another edition of Summer Streets. For the eighth year, New York's spin on Ciclovia is coming to nearly seven miles of streets on Manhattan's east side. For three Saturdays in August — the 1st, 8th and 15th — Park Avenue, Lafayette Street, and a portion of 72nd Street between Central Park and the Brooklyn […]
Kitty Justice: The Thai Solution for Police Parking Placard Abuse
By Aaron Naparstek	| Jan 3, 2008
Top brass at the NYPD usually (but not always) cast a blind eye toward police officers who show disregard for the city's parking regulations. It's a sharp contrast to the NYPD's "broken windows" school of policing, which promotes aggressive enforcement against minor scofflaws (like my friend Katie who recently spent a night in the box […]
Central Park Drivers Get Bigger Holiday Gift Than Usual
By Noah Kazis	| Dec 6, 2010
In what's shaping up to be a yearly tradition, car-free hours in Central Park have been cut back for the holiday season. Each weekday this month, on the southeast corner of the park drive, the park's pedestrians, joggers, cyclists, and dog-walkers have three fewer hours of quiet and safety. The stretch of the park drive […]
Central Park Administrator Pushes East-West Bike Routes, Car-Free Park
Central Park Conservancy head Douglas Blonsky wants his park to get a lot more bike-friendly, he revealed at a meeting of Manhattan's Community Board 7's parks committee last night. Not only is he working to create shared use paths that would allow cyclists to cross the park east-west safely and legally, he repeatedly announced his […]


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Esko Native Jaxson Turner Becomes North Dakota Football's D1 Sacks Leader
Turner finished with two sacks in Saturday's win over Illinois State, which gave him 21 in his career with the Fighting Hawks.
Sam Ali,
GRAND FORKS, N.D. – This past weekend, Esko native Jaxson Turner became the all-time sack leader for the North Dakota football team in their Division I era. Turner finished with two sacks in Saturday's win over Illinois State, which gave him 21 in his career with the Fighting Hawks.
"Just kind of been working towards it my whole career. For it to finally happen and have that hard work pay off was an unbelievable feeling. Having my parents there and having it happen on Senior Day was a really special moment," said Turner.
The fifth-year linebacker was a star for the Eskomos from 2012 to 2015 and will always remember what he learned during that time.
"I think playing at Esko and not getting looked at by many schools kind of gave me more determination going into college to prove that I could be a good player. So I think that that community gave me a lot there," Turner said.
Turner also gave a shout-out to his alma mater, who clinched a spot in the state semi-finals.
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Q: Using a For loop with BigIntegers creates memory problems with Java. [Android] Im currently trying to loop through a BigInteger like so...
BigInteger y;
BigInteger yu = BigInteger.valueOf(17);
for(y= new BigInteger("96");y.compareTo(yu.add(y)) < 0;y=y.add(BigInteger.ONE)){
      Toast.makeText(getApplicationContext(),"y="+y,Toast.LENGTH_SHORT).show();

        }

For the purposes of this example I only used 96 but the same thing occurs for higher numbers. When I begin the program the screen goes black and log.cat displays the following messages:
10-26 19:15:49.853 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9202K, 48% free 16294K/30792K, paused 162ms, total 162ms

10-26 19:15:50.923 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9530K, 52% free 14955K/30792K, paused 155ms, total 156ms

10-26 19:15:51.983 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9037K, 55% free 14110K/30792K, paused 146ms, total 147ms

10-26 19:15:53.018 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 8207K, 55% free 14094K/30792K, paused 141ms, total 141ms

10-26 19:15:54.068 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 8172K, 55% free 14114K/30792K, paused 143ms, total 143ms

Log.cat continues to log 55% as long as the app is running, does anyone know why this is?
Thanks for reading :)

A: 10-26 19:15:49.853 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9202K, 48% free 16294K/30792K, paused 162ms, total 162ms
10-26 19:15:50.923 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9530K, 52% free 14955K/30792K, paused 155ms, total 156ms
10-26 19:15:51.983 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 9037K, 55% free 14110K/30792K, paused 146ms, total 147ms
10-26 19:15:53.018 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 8207K, 55% free 14094K/30792K, paused 141ms, total 141ms
10-26 19:15:54.068 5043-5043/everything.ofjd.com.everythingform D/dalvikvm: GC_FOR_ALLOC freed 8172K, 55% free 14114K/30792K, paused 143ms, total 143ms

Let's take that piece by piece:

*

*GC_FOR_ALLOC means we had to garbage-collect because there was no room for an allocation you tried to make.

*freed 9202K means that the GC managed to free about 9 MB of RAM, so that's good.

*48% free 16294K/30792K means that now, about half of your heap is in use. There is about 14 MB free heap space.

*paused 162ms means that your thread had to wait for 0.162 seconds for this garbage collection to be run.

Now, why are you seeing all of these?
Because you're allocating and throwing aways lots of objects. Those ~9 MB that the garbage collector keeps freeing? They come from objects that are no longer referenced.
I would recommend that you use the "Allocation Tracker" tool in Android DDMS. It'll show you all your allocations, and where each one was made. It should help you track down the source of all these garbage objects being created.
But yeah, like the comments on the question have already stated: your loop was going forever, and creating lots of BigInteger objects -- since each add() call will allocate a new BigInteger. Since it goes forever, those numbers will become pretty big, increasing the size of each individual BigInteger object as well.
But seriously, try the "Allocation Tracker" tool. It's good to know, and you'll gain a better understanding of what went wrong here.

redpajama_set_name: RedPajamaStackExchange


If you are concerned about the protection of your newly purchased Note 8, then take a look at these suggestions to buy the best Samsung Galaxy Note 8 bumper cases and add safety wall.
When we talk about the best stylish yet protective case for any smartphone, we always consider Bumper at peak. Since Note 8 has 6.3 inches Super AMOLED display and built-in Corning Gorilla Glass 5, there is the need for the best Bumper case for Galaxy Note 8. Well, we have already talked about best clear cases and screen protector for Note 8. Today, we will share you're the list of best Samsung Galaxy Note 8 bumper cases.
Here in this post, we have listed top five Note 8 bumper cases which are well constructed from premium quality material to prevent your device from bumps, scrapes, and high impacts. A couple of bumper cases has a hidden slot to carry your essential card, IDs, and cash safely. Without wasting time, check out this list and pick the right one.
The first bumper case that we are presenting is from Elegant Choise, and it has been made from a top quality material. This case is highly compatible with Samsung Galaxy Note 8, and it is precisely made for your latest smartphone. This case is available in many different colors like Black, Blue, Gold, Turquoise, Rose, and Rose Gold.
This stylish case is precisely made for the Samsung Galaxy Note 8.
It ioffers a slot to carry around two cards like credit cards, identity card, license, or cash.
This case is a combination of Anti-scratch PC shell along with rugged TPU cover that absorbs impact from the drops and fall.
This case offers precise cuts for ports and tactile buttons to protect the phone completely.
The air-cushion technology in all the four corners provides anti-shock protection.
This bumper case from Spots8 for Samsung Galaxy Note 8 is a sturdy looking heavy duty case. The look of the case answers all your worries regarding the protection of your valuable smartphone. Unlike other bumper cases on this list, this case offers the comfort of your hands as well, which makes it stand out the crowd.
This case only fits the Samsung Galaxy Note 8.
Besides that the case packed with a screen protector that maintains the 99.9% transparency of your smartphone screen as well as the touch accuracy.
It is made with two different layers in which the exterior is built with hard PC plastic and the inner layer made from the flexible TPU material that offers an extra layer of protection.
Its provides hidden slot where you can put your essential card like ID card or credit card.
This custom made heavy duty case offers complete body protection and it provides reinforced four corners.
The ergonomic side grip provides excellent grip so that your phone never slip out from your hands.
This is another simple but professional bumper case for the Samsung Galaxy Note 8, and MoKo brand produces it. This brand is a known brand for providing top-quality cases for the smartphones. If you want to purchase a bumper case that sticks with its primary features without adding that much fuss to your phone, then this case is an excellent pick.
This case is specially designed for the Samsung Galaxy Note 8.
It is made from flexible and soft TPU and rigid hard PC material that offers excellent protection.
This snugly fits the smartphone, and it engineered to emphasize the thinness without compromising the security of the phone.
The raised bezel keeps the screen away from the scratches while it is placed face-down.
It protects the phone from the dropping, bumping, and scratches as well.
The cuts are precisely deep so that you can access the ports and buttons easily.
Ouba is a very well-known brand on Amazon and market of smartphone accessories, with this clear bumper case for Samsung Galaxy Note 8 it offers excellent protection for this highly expensive smartphone that is what makes it took place on this exclusive list.
This case is made of lightweight and flexible TPU material which makes this case flexible and easy to install.
This case is clear case that offers a super-slim design that will get you feel like a part of your smartphone.
The four curved corners offer scratch resistant and shock-absorbent that protects the phone from accident drops and scratches.
It is constructed with user-friendly technology that provides non-slip grip feel in hands.
It offers precise cutouts for easy access all the ports, buttons and controls.
Look at this beautiful clear bumper case from Profer made especially for the Samsung Galaxy Note 8 only. Because of its exclusive transparency and design of it, you can easily access all the ports, buttons and controls of this latest flagship Samsung smartphone without having any issue. Let see this product in detail.
This case is made from shock absorbent and shatterproof TPU and PC material.
The case offers a perfect fit, and the excellent grip feels while holding it in hands.
It protects against scrapes, scuffs and even from the bumps.
It provides complete protection, and even it protects the camera with the 0.2mm thickness.
With the super-slim profile, it adds minimal bulk to your expensive smartphone.
You can easily clean this case with water and dry it with the lint-free cloth, or you can air dry it.
So, did you like our exclusive list of the best bumper case for Galaxy Note 8? Do let us know your favorite one and do not forget to share your feedback on that product that you have picked from the above list. You can drop your comments in the comment section and even on Facebook, Twitter, and Google Plus.


U.S. Geological Survey, Reston, Virginia, U.S.A.
North Dakota Geological Survey, Bismarck, North Dakota, U.S.A.
The Fort Union Formation in the Williston Basin of North Dakota, South Dakota, and Montana comprises chronostratigraphic and depositional sequences of Paleocene age. Individual chronostratigraphic sequences are defined by palynostratigraphic (pollen and spore) biozones and radiometric (40Ar/39Ar) ages obtained from tonsteins or volcanic ash layers. Analyses of depositional sequences are based on lithofacies constrained by the radiometric ages and biozones.
The lower Paleocene (biozones P1-P3) contains three marine parasequences (landward stepping) in southwestern North Dakota that sequentially onlapped westward between 65 and 61 Ma (lower Ludlow and Cannonball Members). Maximum flooding (transgressive systems tract) occurred during an approximate 1-m.y. interval from 65 to 64 Ma, which regionally is correlated biostratigraphically to a tidally influenced, distributary-shoreface, and fluvial-channel complex in the Cave Hills, northwestern South Dakota, and to channel-dominated fluvial (low-stand incised paleovalley systems) and tidally influenced, flood-plain-deltaic transition facies in the Ekalaka area of southeastern Montana.
The progradational parasequences in the Cannonball Member consist of shore-face sandstone beds (with ravinement lag deposits) deposited by strand-plain barrier systems. Landward of the barrier systems, tidal-estuarine and mire deposits included thick but laterally discontinuous peat accumulations (e.g., Beta and Yule coal beds in the Ludlow Member, southwestern North Dakota). However, landward of the coastal deposits, the laterally equivalent T-Cross-Big Dirty coal zone (dated 64.78 Ma) in southeastern Montana formed as thick, laterally extensive peat accumulations in mires in a fluvial setting. In the flood-plain-deltaic, tidal transition zone near Ekalaka, Montana, the Ludlow Member consists of flood-plain facies, discontinuous coal beds, and rooted and burrowed horizons that contain the marine or brackish trace fossil Skolithos. The flood-plain-deltaic tidal transition zone facies are incised by a massive, agglomerated channel sandstone complex (paleovalley fill) that is exposed along the modern Snow Creek drainage south of Mill Iron, Montana. The flood-plain-tidal transition zone was reworked during the maximum sea level highstand during the early Paleocene. This event was followed by a fall of sea level and deposition of the paleovalley fill.
Sea level fall during the mid-Paleocene (biozones P3 and P4) produced a regressive shallow-marine and lower deltaic tidal system (seaward stepping) that deposited strata that thin toward the east. These strata are overlain by a widespread paleosol (Rhame bed) and, in turn, a lignite-bearing fluvial facies (Tongue River Member) containing the laterally persistent Harmon-Hanson coal zone (61.23 Ma). Upper Paleocene biozone P5 is represented by fluvial, coal-bearing strata that contain several economically minable coal beds (HT Butte, Hagel, and Beulah-Zap zones, Sentinel Butte Member).
The Fort Union Formation of the Williston Basin contains significant coal resources. These coal deposits are now being explored for their potential coal-bed gas resources. A better understanding of the depositional setting for these deposits can lead to improved exploration and exploitation practices and a better understanding of regional paleogeography and paleoclimate during the Paleocene.


"Violet Flame Heart" is a twin flame angel art print in my reiki energy line of chakra wall decor.
This violet flame angel art print would be an uplifting and healing wall decoration in a meditation room, yoga studio, reiki healing room, spa, massage therapy room, bedroom, nursery, living room or office of the person looking for a colorful and original piece of rainbow spiritual wall art infused with positive energy.
"Violet Flame Heart" is intended for those challenging times with our twin flames when we clash and get out of balance and harmony, symbolized by the jaggedy lines. The Violet Flame contained within a heart symbolizes the love based process of throwing our inharmonious thoughts, words, and actions into the violet flame for transmutation into pure light. The twin flame angels are joining hands in an act of unity with each other and the higher good. Twin moons represent multiple realities and ask us to honor and respect our differences.


La Liga is back! The Spanish first division returned this weekend after its three-month break. The Big Three all picked up points, new boys debuted, and of course, there was controversy. Let's round it up!
Last year's runners-up started the season in fine form, I'd say. Lionel Messi scored twice as ten-men Barça ran riot on the Valencian side. La Masia product Munir El Haddadi scored the other goal for Luis Enrique's club, and holy Ivan Rakitić, Batman! The Croatian fired off 112 passes in his competitive debut. No Neymar, no Suárez, no problem.
The reigning Spanish champions endured a disappointing start to their season: a scoreless draw at the Campo de Fútbol de Vallecas. Atlético, Supercopa winners three days ago, played their third game in a week and will be without manager Diego Simeone for seven more weeks after the RFEF suspended him for his actions during Friday's game. Rayo enjoyed 60% possession and Atleti finished with a lowly 68% passing. The champs have adjustments to make.
Karim Benzema scored his first goal for Real since April as the European Cup winners kept the Andalusians at bay. This was Córdoba's first Liga game in 42 years, and they managed to keep a fatigued Real within striking distance until Cristiano Ronaldo's goal in the 90th minute. Not a bad result for the new boys, all told.
Eibar's first-ever La Liga couldn't have gone any better: a Basque derby which ended in a victory. Javi Lara's free-kick just before half gave the Liga Adelante winners a famous win in front of only 5,000 supporters. Lara pretty much did it all in the victory, accruing three total shots, five tackles, four key passes, and two interceptions.
The weekend's opening game featured a highly controversial ending. Luis Alberto, scored 34 minutes in, slotting home a rebound after his penalty was stopped by Gorka Iraizoz. Speaking of Iraizoz, it was late in second-half injury time when the keeper headed home what should have been the equalizer. But #SpanishRefs struck, the goal was disallowed, and Málaga escaped.
Granada 2-1 Deportivo, Sevilla 1-1 Valencia, Almería 1-1 Espanyol, Celta Vigo 3-1 Getafe, Levante 0-2 Villarreal.
This entry was posted in La Liga, Roundups and tagged atletico, barcelona, cristiano ronaldo, Ivan Rakitić, Karim Benzema, La Liga, lionel messi, Luis Enrique, Munir El Haddadi, Rayo Vallecano, real madrid. Bookmark the permalink.


I posted my 6 words this morning and then headed out to grocery shop as the roads are open after being closed for a couple of days.
Yes, I was sitting on the bottom step and lying on my back!
Pingback: Some greenery in a white winter. – David Meredith's photo blog.
Very clever and a beautiful staircase beautifully photographed, Debbie.
The world loves a trier, my Mam used to say, Debs, and these are absolutely stunning!
I really like that last image.
A good app to play with. Happy weekend!


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Home Drones Russia Claims to have Shot Down More than 100 Terrorists' Drones near Hmeymim Air Base over Past two Years
DronesMilitary Aviation
Russia Claims to have Shot Down More than 100 Terrorists' Drones near Hmeymim Air Base over Past two Years
by Dario Leone Oct 10 2019
written by Dario Leone Oct 10 2019
Thanks to S-400, Tor-M2 and Pantsyr-S1 capabilities the Russian military at Hmeymim can strike all types of air targets at a range of 20 km to 250 km.
Defense Ministry Spokesman Major-General Igor Konashenkov recently revealed that Air defense and electronic warfare systems deployed at Russia's Hmeymim air base in Syria have shot down or disabled over 100 drones during terrorists' attempted attacks on the military facility over the past two years.
"Terrorists are trying to break through the Hmeymim base's air defenses. If we speak about figures, 118 unmanned aerial vehicles of terrorist groupings have been destroyed over the past two years, including 58 drones since January 1 this year," the Russian general said.
According to TASS most drones were launched from the Idlib security zone, in particular, from the communities of al-Latamna, Khan Sheikhoun and other areas, he said.
"Moreover, our Pantsyr-S1 and Tor-M2 air defense missile systems also thwart terrorists' attempts to deliver a strike with rockets. Since January 1, 2019, 27 rocket-propelled shells of terrorist groupings launched mostly from the Idlib security area have been destroyed," the general added.
Konashenkov said that these 27 rockets were struck by 31 missiles of the Pantsyr-S1 and Tor-M2 surface-to-air missile systems.
A Russian Tor-M1 and an S-300V SAM
"That is, the striking efficiency is close to 1: one target, one missile," the general stressed.
On Aug. 11, 2019 terrorists attempted a new massive air raid involving five attack unmanned aerial vehicles and one control drone, Konashenkov pointed out.
"That is, these five drones carried striking elements with explosives, bolts and bars to achieve the maximum destruction effect. One drone can carry up to 10 striking elements fasted to the wings," he said.
The terrorists carried out the latest attack on the Hmeymim air base on Sep. 3.
"This raid involved two drones. Moreover, they approached the air base from different directions. Characteristically, one drone came from the area of the Mediterranean Sea. That is, apparently the drone was launched from a vessel," the Defense Ministry spokesman said.
The Russian general did not rule out that the temporary calm could be related to the liberation of Khan Sheikhoun and Al-Latamna in the Idlib de-escalation zone where workshops for assembling drones and sites for their launches were found, which was demonstrated to foreign journalists.
Pantsyr-S1 Weapon System. In the Center the EHF phased-array tracking Radar. Two twin-barrel 2A38M automatic anti-aircraft guns and 12 ready to launch missile-containers each containing one 57E6-E command guided surface to air missile.
The air defense systems deployed at Russia's Hmeymim military base in Syria are aimed to defend the airfield facilities and the Tartus naval facility against strikes by unmanned aerial vehicles and rocket shells, as well as against tactical aviation and cruise missiles, the commander of the anti-aircraft missile regiment based at Hmeymim specified.
"A layered air defense system has been set up here. It comprises S-400 long-range surface-to-air missile systems and Tor-M2 and Pantsyr-S1 short-range complexes," he said.
Thanks to S-400, Tor-M2 and Pantsyr-S1 capabilities the Russian military at Hmeymim can strike all types of air targets at a range of 20 km to 250 km, he explained.
"The Tor-M2 anti-aircraft missile system and the Pantsyr-S1 surface-to-air missile/gun complex effectively cope with the tasks of striking small-size unmanned aerial vehicles with a small radar cross section, and also fast-speed shells of factory-produced and improvised multiple launch rocket systems actively employed by terrorists," the regiment commander said.
The radio-technical battalion's radars, as well as the reconnaissance capabilities of the regiment's command post and the anti-aircraft missile battalions gather all the data on the air situation, the commander said.
"Combat operations are controlled in the fully automated mode, from the time of detecting air objects and locking them on to the time of making a decision to destroy air targets," the regiment commander said.
Don't miss the perfect Aviation Geek Bundle! CLICKE HERE TO GET YOURS.
Photo credit: Russian Defence Ministry, Vitaliy Ragulin and Vitaly V. Kuzmin via Wikipedia
Hmeymim air baseS-400surface-to-air missileSyria
Dario Leone
Dario Leone is an aviation, defense and military writer. He is the Founder and Editor of "The Aviation Geek Club" one of the world's most read military aviation blogs. His writing has appeared in The National Interest and other news media. He has reported from Europe and flown Super Puma and Cougar helicopters with the Swiss Air Force.
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