text:
\section*{Introduction}

\label{sec1}

Memcapacitors \cite{diventra09a} are an emerging type of circuit elements
with memory whose instantaneous response depends on the internal state and
input signal. Such devices are prospective candidates for applications in
information storage and processing~\cite{traversa14a,pershin15a}
technologies as their states can be manipulated by the applied voltages or
charges and can store information for long intervals
of time. Several possible realizations of memcapacitors were suggested by
using micro-electro-mechanical systems~\cite{pershin11c}, ionic transport~%
\cite{Lai09a}, electronic effects~\cite{martinez09a}, superconducting qubits
\cite{Shevchenko16}, etc. \cite{pershin11a}

Generally, voltage-controlled memcapacitive systems (memcapacitors) are
described by~\cite{diventra09a}
\begin{eqnarray}
q(t) &=&C\left( x,V,t\right) V(t),  \label{Ceq1} \\
\dot{x} &=&f\left( x,V,t\right) , \label{Ceq2}
\end{eqnarray}%
where $q(t)$ is the charge on the capacitor at time $t$, $V(t)$ is the
applied voltage, $C$ is the \textit{memcapacitance} (memory capacitance), $x$
is a set of $n$ internal state variables, and $f$ is a continuous $n$%
-dimensional vector function. In some cases, it is more convenient to
consider charge-controlled memcapacitors~\cite{diventra09a} such that the
charge instead of voltage is considered as input.

\begin{figure}[b]
\vspace{0.6cm}
\centering{\includegraphics[width=0.5\columnwidth]{Figure-1}}
\caption{Schematics of the membrane memcapacitor
employing a buckled graphene membrane as its top plate~\protect\cite{pershin11c}.}
\label{fig1}
\end{figure}

Among several possible realizations of memcapacitors, the membrane-based
memcapacitors~\cite{pershin11c} are of significant interest as their
geometry makes them intrinsically suitable for non-volatile storage of
binary information. Indeed, the buckled membrane used as the top capacitor
plate (see Fig. \ref{fig1} for schematics) has two
stable buckled states corresponding to two distinct values of capacitance.
It was suggested~\cite{pershin11c} that the switching between these states
can be performed using the attractive interaction of oppositely charged
capacitor plates. Moreover, it was demonstrated theoretically that simple
circuits of membrane memcapacitors offer an in-memory computing
functionality~\cite{pershin15a}.

In this work, we consider a possible realization of membrane-based
memcapacitor~\cite{pershin11c} employing a single- or multi-layer graphene
membrane~\cite{Lindahl12, Weber14, Lambin14, Benameur15, Davidovikj16} as
its bistable plate (see Fig. \ref{fig1}). Our aim is to understand the basic
physical processes and parameters underlying the snap-through transition of
such membrane including details of the membrane dynamics, threshold forces, etc.
For this purpose, we
perform a combined study using MD, DFT and elasticity theory focusing on a
single-layer graphene membrane with clamped boundary conditions. This choice
of boundary conditions is justified by the typically strong adhesion of
graphene to substrates. Our results extend our prior DFT investigation~%
\cite{Sedelnikova2016} of the up-to-down snap-through transition of
graphene membrane with hinged boundary conditions.

The combination of computational/theoretical methods adds breadth and depth
to our analysis. Using MD simulations, we were able to understand main
features of the membrane dynamics in the presence of an external force and
after the force removal. This understanding has helped us to develop
analytical models that resulted in compact algebraic expressions for the
threshold switching forces. DFT calculations were used to validate MD
results for the up-to-down transition.

This paper is organized as follows. In Sec. "\nameref{sec2}" we investigate the
snap-through transition of graphene membranes using molecular dynamics
simulations. In particular, MD simulations of the up-to-down and down-to-up
transitions are reported in Subsec. "\nameref{sec2b}" and "\nameref{sec2c}", respectively,
while MD simulation details can be found in Supplementary Information (SI) Sec. "MD Simulation details".
The standard elasticity theory is applied to the membrane switching in Subsec.~"\nameref{Sec:Elasticity}".
A phenomenological analytical model of the
snap-through transition is presented in Subsec.~"\nameref{sec3}" and in SI Sec. "Phenomenological Elasticity Theory".
Our DFT calculations are summarized in Sec.~"\nameref{Sec:DFTmain}".
The results obtained within different approaches as well as their implications are
discussed in Sec.~"\nameref{Sec:Discussion}".

\vspace{0.2cm}

In this paper, the following notations are used:

\vspace{0.2cm}

$q$ - the charge on capacitor (see Eq. (\ref{Ceq1}))

$V$ - the applied voltage (see Eqs. (\ref{Ceq1}), (\ref{Ceq2}))

$C$ - the (memory) capacitance (see Eq. (\ref{Ceq1}))

$d$ - the distance between fixed sides of membrane (see Fig. \ref{fig1})

$h$ - the distance between the bottom plate and the level of fixed sides (see Fig. \ref{fig1})

$L$ - the membrane length

$w$ - the membrane width

$D= 1.6$ eV - the bending rigidity of graphene

$E_{2D}=340$ N/m - the 2D Young's module

$\zeta$ - the deflection of membrane (see Eq. (\ref{U}))

$\zeta _{\mathrm{c}}$ - the maximum deflection of membrane (see Eq. (\ref%
{U_buckled}))

$\theta _{i}(s)$ - the angle that the membrane makes with the horizontal (see
Eqs. (\ref{eq:theta_s}) and (\ref{eq:theta_ns})),

$s$ - the internal coordinate that changes between $-1/2$ and $1/2$ (see
Eqs. (\ref{eq:theta_s}) and (\ref{eq:theta_ns}))

$A_{i}$ and $c_{i}$ - coefficients (see Eqs. (\ref{eq:theta_s}) and (\ref%
{eq:theta_ns}))

$z_{cm}$ - the center of mass position (see Eq. (\ref{eq22}))

$U_{b}$, $U_{str}$, $U_{ext}$ - the bending, stretching and external potential
contributions to the potential energy of membrane (see Eq.~(\ref{eq:pot_energ}))

$F^\downarrow$ - the up-to-down threshold switching force (see Eqs. (\ref{F_star}), (\ref{eq20}), (\ref{eq888}), and (\ref%
{eq:fsw_nonsym}))

$F^\uparrow$ - the down-to-up threshold switching force (see Eqs. (\ref{Fup}) and (\ref{FZCM}%
))

$\varepsilon_0 $ - the vacuum permittivity

\section{Molecular Dynamics Simulations}\label{sec2}

MD simulations are a well
established modeling tool frequently employed in studies of nanoscale
carbon-based materials~\cite{Yakobson1996, Berber2000, Yao2001, Legoas2003,
Maruyama2003, Lee2006, Shiomi2006, Wang2009, Hu2009, Jiang2009, martins2010,
Neek-Amal2010, Ni2010, Lebedeva2011, Bagri2011, Min2011, Ng2012,
Rajabpour2012, Kalosakas2013, Berdiyorov2014, Kang2015, Yamaletdinov17a}.
We used classical MD simulations to investigate the dynamics of snap-through
transition of buckled graphene membranes. Zigzag graphene nanoribbons (membranes) of two
lengths were considered: the nanoribbon \textbf{\textit{A}}, $L=54$ \AA\ (22
rings), and nanoribbon \textbf{\textit{B}}, $L=103$ \AA\ (42 rings). Both
nanoribbons were of the same width ($w=41$ \AA). In order to implement the
clamped boundary conditions, the first two lines of carbon atoms at shorter
sides were kept fixed. The buckling was realized by changing the distance
between the fixed sides from $L$ to $d<L$. The same external force was
applied to each atom in the downward direction to simulate the attractive
interaction between the plates.

See SI Sec. "MD Simulation details" for the details of MD simulations.

\subsection{Up-to-down transition}

\label{sec2b}

\begin{figure}[tb]
\centering{(a)\includegraphics[width=0.42\columnwidth]{Figure-2a} (b)
\includegraphics[width=0.42\columnwidth]{Figure-2b}}
\caption{Up-to-down transition: the final position (at a time $t_f$) of a
central atom of membrane as a function of the applied force magnitude for
(a) shorter membrane \textbf{\textit{A}} (22 rings length), and (b) longer
membrane \textbf{\textit{B}} (42 rings length). The calculation details are
given in the text. }
\label{fig4}
\end{figure}

In order to simulate the up-to-down transition, the double-clamped graphene
nanoribbon buckled upwards was subjected to the force in the downward
direction. The final state of membrane was found using MD simulations as
described in SI Sec. "MD Simulation details". Figure~\ref{fig4} shows the
final position of a central atom of membrane versus the applied force for
several values of $d/L$ and two membrane sizes. According to Fig.~\ref{fig4},
at fixed $L$, the up-to-down threshold switching force (the minimal force
required for the up-to-down transition) is larger for smaller values of $d/L$.
Moreover, at fixed $d/L$, the threshold switching force is smaller for
longer membranes. Additionally, some curves in Fig. \ref{fig4} exhibit a
noisy threshold (such as $d/L=0.8$ and $d/L=0.98$ in (a)), which can be
related to thermal fluctuations of membranes. All these observations are
intuitively reasonable.

\begin{figure}[tbh]
\centering{(a)\includegraphics[width=0.42\columnwidth]{Figure-3a} \qquad (b) %
\includegraphics[width=0.42\columnwidth]{Figure-3b}}
\caption{Geometries of membrane \textbf{\textit{B}} in the process of
the up-to-down switching at smaller ($F=0.5$ pN/atom) (a) and larger ($F=1.49$ pN/atom) (b) forces.
These geometries were obtained using overdamped MD simulations for $d/L=0.95$ (the simulation parameters are provided in the Supplementary Information). The switching occurs through the non-symmetric path at
smaller forces (exceeding the threshold) (a), and
symmetric path at larger forces (b).}
\label{fig3}
\end{figure}

Depending on the force magnitude, the membrane switching occurs either
through the symmetric or non-symmetric membrane profile (see Fig. \ref{fig3}).
Figure \ref{fig3} was obtained using overdamped simulations of membrane dynamics
(additional results of these simulations can be found in SI Sec. "MD Simulation details").
The non-symmetric profile is associated with a smaller
energy barrier~\cite{Sedelnikova2016} and involved in switching by smaller
forces. Larger applied forces result in the switching through the symmetric
profile. According to our observations and previous work~\cite%
{Sedelnikova2016}, in all cases, the membrane profile is symmetric at short
times. If the force magnitude is sufficient to overcome the energy barrier
for the symmetric profile, then, typically, the switching takes place through the
symmetric path. Otherwise, a symmetry breaking occurs leading to the
switching through the lower energy barrier associated with the non-symmetric
membrane profile. Thermal fluctuations help the symmetry breaking.

\subsection{Down-to-up transition}\label{sec2c}

It was suggested in Ref. \citenum{pershin11c} that the memcapacitor
membrane can be set into the buckled upwards state 0 (see Fig. \ref%
{fig1}) by also using the electrostatic attraction between the capacitor plates. When
the pulled-down membrane is suddenly released, there are conditions such
that the membrane overcomes the potential barrier and ends up in the buckled
upwards state. As the kinetic energy plays an important role in the down-to-up transition, this
process can not be analyzed using the overdamped dynamics.

In order to simulate the down-to-up transition, every atom of a double-clamped
buckled membrane was subjected to a constant force in -$z$ direction. After
an equilibration period, the forces were removed, and the system was
simulated for a time interval sufficient to reach the steady
state. The final position of a central atom of membrane is presented in Fig. %
\ref{fig6} as a function of the applied force for several values of $d/L$.

\begin{figure}[t]
\centering{(a)\includegraphics[width=0.42\columnwidth]{Figure-4a} (b)%
\includegraphics[width=0.42\columnwidth]{Figure-4b}}
\caption{Down-to-up transition: the final position of a central atom of
membrane as a function of the applied force magnitude for (a) shorter
membrane \textbf{\textit{A}} (22 rings length), and (b) longer membrane
\textbf{\textit{B}} (42 rings length).}
\label{fig6}
\end{figure}

Figure~\ref{fig6} shows that the threshold forces for the down-to-up
transition are larger than those for the up-to-down transition (see Fig. \ref%
{fig4}). Moreover, the threshold forces for the down-to-up transition are
larger for the shorter membrane \textbf{\textit{A}} compared to the longer
membrane \textbf{\textit{B}}. It is interesting that the final state of
membrane oscillates as a function of the applied force (see $d/L=0.98$
curves in Fig. \ref{fig6}). Qualitatively, having a high kinetic energy, the
membrane moves up and down while its energy dissipates. Finally, it gets
trapped in one of two stable buckled states.

Overall, our MD results indicate the possibility of writing one bit of
information into the state of membrane memcapacitor. In this
interpretation, logic 1 corresponds to the membrane buckled downwards, and
logic 0 - to the membrane buckled upwards.
In addition to $0\rightarrow 1$ and $1\rightarrow 0$ transitions presented in Figs. \ref{fig4} and \ref{fig6},
we have verified the occurrence
of $1\rightarrow 1$ and $0\rightarrow 0$ transitions at the same values of
forces required for $0\rightarrow 1$ and $1\rightarrow 0$ transitions,
respectively. Therefore, logic 0 or 1 can be written into the memcapacitor
just by selecting a suitable value of the applied force.

In our work, we considered relatively small nanoribbons, which are mechanically rigid. This is an important requirement for the memcapacitor application as the mechanical nonvolatile information storage is not possible with flexible graphene. From some previous studies~\cite{Schoelz15} it is known that local structural corrugations (ripples)~\cite{Fasolino07a} disappear in the transition from flexible to rigid graphene. In agreement with this previous work~\cite{Schoelz15}, our molecular dynamics simulations have shown the absence of ripples (spontaneous height fluctuations) in nanoribbons of reported sizes and their existence in larger nanoribbons. The latter, however, are not suitable for the memcapacitor application because of their flexibility. To summarize, while our simulation tools provide a means for ripples detection, we did not observe these in the reported structures that are mechanically rigid.

\section{Theory of Elasticity}

Even though the graphene has a thickness of one atom, the graphene membranes
are quantitatively good described by the theory of elasticity \cite{Eriksson13, Tomi15, Abdi16, Bonilla16}. This allows us, on one hand, to
obtain analytical expressions for the buckled membranes~\cite{Qiu04,
Cazottes09, Bitafaran15} and, on the other hand, perform a comparison with
 MD simulations.

There is a number of publications dealing with buckled beams and membranes
under the transverse load (see, for example, Refs.~[\citenum{Medina2014,Chen2015,Krylov2008,Medina2012}]).
Such systems are frequently described in the framework of Euler-Bernoulli
theory, which, however, leads to complex analytically unsolvable equations.
Bubnov-Galerkin decomposition is a one of the best approaches to find the
approximate analytical solution of these equations, although it still
requires a complex phase-diagram analysis. In particular, using such
analysis, the authors of Refs.~[\citenum{Medina2014,Chen2015,Krylov2008,Medina2012}] investigated an
electrostatically loaded double-clamped membrane above a rigid flat
electrode and derived cumbersome conditions for the symmetric snap-through
transition, symmetry breaking, existence of bifurcation and pull-in
instability.

In this Section, we derive compact but sufficiently precise expressions for
the snap-through switching forces based on the theory of elasticity.

\subsection{Buckling and snapping-through within~the~theory~of~elasticity}\label{Sec:Elasticity}

\subsubsection{Description of buckled membranes within the theory of elasticity}

Consider a 2D membrane within the theory of elasticity \cite{Abdi16, Tomi15,
LL}. The total potential energy of membrane is defined by the deflection
$\zeta $ (along the normal direction $z$) as
\begin{equation}
U=\frac{D}{2}\iint \textnormal{d}S\left( \Delta \zeta \right) ^{2}+T\delta S+\iint
\textnormal{d}SF\zeta .  \label{U}
\end{equation}%
Here, $\Delta $ stands for the 2D Laplacian, $T=T_{0}+\delta T$ is the total
tensile force, $T_{0}$ is the force applied by the support and $\delta T$ is
the bending tension resulted from the extension,%
\begin{equation}
\delta T=E_{2\mathrm{D}}\frac{\delta S}{S_{0}},\qquad \delta S=\iint
\textnormal{d}S\left( \nabla \zeta \right) ^{2},  \label{DT}
\end{equation}%
$S_{0}=wL$, and $F$ is the external force density. The compression of membrane
corresponds to $T_{0}<0$.

Given the potential energy, one may also be interested in the dynamics of
membrane, which is defined by the equation
\begin{equation}
\mu \frac{\partial ^{2}\zeta }{\partial t^{2}}+\mu \gamma \frac{\partial
\zeta }{\partial t}-F=-D\Delta \Delta \zeta +T\Delta \zeta ,  \label{eq}
\end{equation}%
where $\mu $\ is the 2D mass density

\subsubsection{Eigenmodes and buckling}

The spatial harmonics (eigenmodes) of clamped membranes can be written
as
\begin{eqnarray}
\zeta _{n}(x) &=&\cosh \left( b_{n}\frac{x}{d}\right) -\cos \left( b_{n}\frac{x}{d}\right) -  \label{zeta_n}\frac{\cosh b_{n}-\cos b_{n}}{\sinh b_{n}-\sin b_{n}}\left( \sinh \left(
b_{n}\frac{x}{d}\right) -\sin \left( b_{n}\frac{x}{d}\right) \right) ,
\end{eqnarray}%
where the numbers $b_{n}$ are the solutions of the equation $\cosh b_{n}\cos
b_{n}=1$. One can find that $b_{n}\approx 3\pi /2+n\pi $ (in particular, $%
b_{0}=4.73$ is close to $3\pi /2=4.65$). The functions $\zeta _{n}(x)$ are
orthonormal.

Consider a buckled membrane shown in Fig. \ref{fig1}.
Its potential energy (Eq. (\ref{U})) calculated for the fundamental $n=0$ mode (taking $\zeta (x)=\zeta _{0}(x)$
with $\zeta (d/2)\equiv \zeta _{\mathrm{c}}$) is
\begin{equation}
U=-\alpha \zeta _{\mathrm{c}}^{2}+\beta \zeta _{\mathrm{c}}^{4}+f\zeta _{%
\mathrm{c}},  \label{U_buckled}
\end{equation}%
where $\alpha = \pi ^{2}w \left( \left\vert
T_{0}\right\vert -T_{\mathrm{c}}\right) /\left(4d\right)$, $\beta =3\pi ^{4}
Dw/(4\varepsilon ^{2}d^{3})$, and $f=\pi Fdw/6$. Here, $T_{\mathrm{c}}=4\pi ^{2}D/d^{2}$
is the critical tension. At $\alpha >0$, that is at $%
\left\vert T_{0}\right\vert >T_{\mathrm{c}}$, the potential is the
double-well potential with minima at symmetric deflections, $\zeta _{c}=\pm
\sqrt{\alpha /2\beta }$, and the potential barrier $\delta U=\alpha
^{2}/4\beta $. (We note that a less realistic case of hinged boundary
conditions would lead to simpler expressions for eigenmodes, $\sim \sin \left( \pi nx/d\right)$,
compared to Eq.~(\ref{zeta_n}), making the hinged boundary conditions preferable for some calculations.
However, this case results in quantitatively different values. For example,
the critical tension differs four times.)

We note that the nanoribbon length is given by
\begin{equation}
L=\int_{0}^{d}\mathnormal{d}x\sqrt{1+\zeta ^{\prime 2}}.
\end{equation}%
Expanding this expression to the second order, one obtains the interrelation
between $L$, $d$, and the maximal deflection $\zeta _{\mathrm{c}}$:%
\begin{equation}
\zeta _{\mathrm{c}}\approx 0.64\sqrt[8]{\frac{d}{L}}\sqrt{L(L-d)}.
\label{z0}
\end{equation}%
On the other hand, the maximal deflection of buckled membrane can be
inferred from the minima of the potential energy, Eq.~(\ref{U_buckled}):
\begin{equation}
\zeta _{\mathrm{c}}^{2}=\frac{\alpha }{2\beta }=\frac{2}{\pi ^{2}}\frac{L^{2}%
}{E_{2\mathrm{D}}}\left( \left\vert T_{0}\right\vert -T_{\mathrm{c}}\right) .
\label{zc}
\end{equation}%
Equations~(\ref{z0}) and (\ref{zc}) link the tensile force $T_{0}$ to the
parameter $d/L$, which  can be considered as a measure of deformation of buckled membrane.
These equations can be used to express the tensile force $T_{0}$ through $d/L$.

\subsubsection{Snap-through transition}

Here we present a convenient method to describe the dynamics of membrane subjected to an external force and find the
minimal force causing its snap-through transition. The main idea is to expand $\zeta (x,t)$ in
harmonics $\zeta _{n}(x)$\ (given by Eq. (\ref{zeta_n})) with amplitudes $q_{n}(t)$ as
\begin{equation}
\zeta (x,t)=\sum_{n}q_{n}(t)\zeta _{n}(x),  \label{expansion}
\end{equation}%
and limit the sum to few first terms. We found that in order
to describe the symmetric and non-symmetric transitions, it is sufficient to
consider $n=0,2$ and $n=0,1$ terms in Eq. (\ref{expansion}), respectively. The calculation consists
in the following. First, we substitute the expansion (\ref{expansion}) in Eq.~(\ref%
{eq}). Second, the resulting equation is multiplied by $\zeta _{m}(x)$ and integrated
taking into account the orthogonality of harmonics. Here we emphasize that for
the harmonics (\ref{zeta_n}), the integrals are readily calculated,
and instead of the integro-differential equation one obtains a system of
differential equations for the functions $q_{n}(t)$. Inserting the obtained
functions $q_{n}(t)$ back into Eq.~(\ref{expansion}) gives us the description
of membrane dynamics. In the following, the results of these
calculations (performed using the time normalized by the
membrane characteristic frequency $\omega _{%
\mathrm{c}}=(1/L^{2})\sqrt{D/ \mu }$ and $t_{\mathrm{c}%
}=1/\omega _{\mathrm{c}}$)~\cite{Gomez17} are analyzed for membrane \textbf{\textit{B}}.

\begin{figure}[t]
\centering{\includegraphics[width=0.7\columnwidth]{Figure-5a} }\includegraphics[width=0.7	%
\columnwidth]{Figure-5b} \includegraphics[width=0.7\columnwidth]{Figure-5c}
\caption{Up-to-down transition within the theory of elasticity.
(a)~Fully symmetric switching. (b) Non-symmetric
switching caused by a small asymmetry in the applied force. (c) More
realistic switching scenario based on a symmetric force, where the initial
symmetric distortion becomes non-symmetric at longer times. For all panels $%
d/L=0.95$.}
\label{Fig:i}
\end{figure}

Consider the results presented in  Fig.~\ref{Fig:i}.
Fig.~\ref{Fig:i}(a) demonstrates the case of fully symmetric switching, when the dynamics can be described by
$n=0$ and $2$ harmonics. Next, we introduce a small asymmetry into the
problem via a small non-symmetric modification of the force (of the order of $0.1\%$). This results in the non-symmetric dynamics of
Fig.~\ref{Fig:i}(b), which can be described in terms of $ n=0$ and $1$ harmonics.
 We note that the force needed for the non-symmetric
snap-through transition is smaller than that for the symmetric one,
which will also be analyzed below in more detail. Finally, in Fig.~\ref{Fig:i}(c) we illustrate
a combination of the above regimes found using a symmetric force, when
a tiny fluctuation in the numerical solution changes the symmetric dynamics to the
non-symmetric one. Note that this case is close to the one discussed in Ref.~\citenum{Sedelnikova2016}.

Figure~\ref{Fig:ii}(a) depicts the dependence of the final position of
membrane center, $\zeta _{\mathrm{c}}(t_{f})$, on the
applied force $F$. At a certain value of force, $F=F^{\downarrow }$, the
membrane switches from the buckled upwards state to the buckled downwards state. Our
calculations show that the threshold force is proportional to the initial
central-point deflection $\zeta _{\mathrm{c}}$ and is different for the symmetric (s) and non-symmetric (ns) dynamics. Namely, this force, being multiplied by the membrane area $wL$, reads
\begin{eqnarray}
\frac{F_{\mathrm{s,ns}}^{\downarrow }}{F_{0}} &=&C_{\mathrm{s,ns}}\sqrt{2.44}%
\frac{\zeta _{\mathrm{c}}}{d}=C_{\mathrm{s,ns}}\left( \frac{L}{d}\right)
^{3/8}\sqrt{\frac{L}{d}-1},  \label{F_star} \\
F_{0} &=&\frac{Dw}{L^{2}},\qquad C_{\mathrm{ns}}=253.4,\qquad C_{\mathrm{s}%
}=359.1.  \label{Asa}
\end{eqnarray}%
Since the non-symmetric transition is energetically favorable, we expect that this value of force is the one to be
used in the device design/experiment analysis. We note that estimations based on Eq. (\ref{F_star}) are in a
good agreement with results found by other methods as we discuss
later and illustrate in Fig.~\ref{fig9}. Figure~\ref{Fig:ii}(b) presents the time-dependence of harmonics' amplitudes $q_{n}(t)$
in the up-to-down transition. Importantly,
the dynamics is well described by  $n=0$, $1$, and $2$ harmonics, while $%
n=3$ and $4$ harmonics amplitudes are negligibly small.

\begin{figure}[t]
\centering{\includegraphics[width=0.49\columnwidth]{Figure-6a}
\includegraphics[width=0.49\columnwidth]{Figure-6b}}
\caption{Numerical simulation of up-to-down transition. (a) The final
central-point deflection $\protect\zeta _{\mathrm{c}}$ versus the applied
transverse force $F$ for several values of $d/L$. (b) Time-dependence of the
first few harmonics' amplitudes $q_{n}(t)$.}
\label{Fig:ii}
\end{figure}

Our calculations (similar to the consideration of the up-to-down force above) demonstrate that the minimal force needed for the down-to-up
transition is proportional to $\zeta _{\mathrm{c}}^{2}$ as
\begin{eqnarray}
\frac{F^{\uparrow }}{F_{0}} &=&C^{\uparrow }2.44\left( \frac{\zeta _{\mathrm{%
c}}}{d}\right) ^{2}=C^{\uparrow }\left( \frac{L}{d}\right) ^{3/4}\left(
\frac{L}{d}-1\right) ,  \label{Fup} \\
C^{\uparrow } &=&8.48\cdot 10^{4}.
\end{eqnarray}%
See also SI Sec. "Down-to-up transition", where the down-to-up transition is
illustrated graphically.

\subsection{Phenomenological elasticity theory}

\label{sec3}

In this Section, in order to avoid all complications associated with the
Bubnov-Galerkin decomposition, we elaborate a different approach describing
the up-to-down and down-to-up transitions in a compact analytical form.

\subsubsection{Ansatz}

\label{sec3a}

Following our observation of the existence of the symmetric and
non-symmetric membrane profiles in the snap-through transition (see Fig.~\ref%
{fig3}), we introduce two simplest polynomial functions to describe such
symmetric (s) and non-symmetric (ns) shapes of membrane:
\begin{eqnarray}
\theta _{\text{s}}(s) &=&A_{\text{s}}\left( s^{2}-\frac{1}{4}\right) s\left(
s^{2}-c_{0}^{2}\right) ,  \label{eq:theta_s} \\
\theta _{\text{ns}}(s) &=&A_{\text{ns}}\left( s^{2}-\frac{1}{4}\right) \left(
s-c_{1}\right) \left( s-c_{2}\right) .  \label{eq:theta_ns}
\end{eqnarray}%
Here $\theta _{i}(s)$ is the angle that the membrane makes with the horizontal, $%
s$ is the internal coordinate that changes between $-1/2$ and $1/2$, $A_{i}$
and $c_{i}$ are coefficients, and $i=\{\text{s},\text{ns}\}$. Clearly, Eqs. (\ref%
{eq:theta_s}) and (\ref{eq:theta_ns}) describe the double-clamped membrane
as $\theta _{i}(\pm 1/2)=0$.

\subsubsection{Up-to-down transition}

\label{sec3b}

Our goal here is to estimate the minimal force required for the snap-through
transition. In this subsection, we assume that the snap-through transition
is induced by a slowly increasing force such that the system always stays in
the potential energy minimum. At zero applied force, there are two minima of
the potential energy corresponding to the two stable states of membrane. The
applied force modifies the potential energy landscape such that, starting at
a certain force, the potential energy has a single minimum. Here, this value
of force is found and considered as an estimation for the threshold
switching force.

In the presence of a constant force $F$ in the downward direction, the
membrane potential energy is given by
\begin{equation}
U=U_{b}+U_{str}+U_{ext}=\frac{Dw}{2L}\int\limits_{-1/2}^{1/2}\left[ \frac{%
\partial \theta} {\partial s} \right]^2\textnormal{d}s+U_{str}+U_{ext},
\label{eq:pot_energ}
\end{equation}
where $U_b$ is the bending energy, $U_{str}$ is the stretching energy, $%
U_{ext}$  is the potential energy due to the applied force. Then, using $U_{ext}=F z_{cm}$, where $z_{cm}$ is $z$
coordinate of the center of mass, and neglecting $U_{str}$ term not
important for the up-to-down transition (see, e.g., Fig.~S1 that
indicates the insignificance of $U_{str}$ in buckled membrane), we get the
following equation for the potential energy extrema:

\begin{equation}
F=-\frac{\text{d} U_b}{\text{d} z_{cm}}=-\frac{\text{d} U_{b}}{\text{d}c_i}%
\left(\frac{\text{d}z_{cm}}{\text{d}c_i}\right)^{-1},  \label{eq22}
\end{equation}
where $i=\{0,1\}$ corresponds to  $\{\text{s},\text{ns}\}$,  respectively. Equation (\ref{eq22}) allows
finding $c_0$ and $c_1$ for a given strength of the applied
force.

The minimal force needed for the snap-through transition corresponds to the
maximum of $F(z_{cm})$ and, for the transition through the symmetric shape,
is given by
\begin{equation}
F^\downarrow_\text{s}=440\frac{Dw}{L^2}\sqrt{\frac{L-d}{L}} \label{eq20}
\end{equation}
taking place at $c_0=0.3589$ (the corresponding membrane profile is
presented in Fig.~S4). At this value of $c_0$, the bending energy is
$U_{b,\text{s}}=108Dw(L-d)/L^2$.

Performing the same calculations for the non-symmetric shape, one can find
that the force needed to support the equilibrium non-symmetric shape
decreases with the progress of switching. A zero force is reached at $%
c_{1}=-c_{2}=1/(2\sqrt{5})$ that corresponds to the maximum of $%
U_{b,\text{ns}}=90Dw(L-d)/L^{2}$. A possible (rough) estimation for the threshold
switching force can be obtained taking the limit $c_{1}\rightarrow \infty $
leading to
\begin{equation}
F_{\text{ns}}^{\downarrow}=281\frac{Dw}{L^{2}}\sqrt{\frac{L-d}{L}}  \label{eq888}
\end{equation}%
and $U_{b,\text{ns}}=42Dw(L-d)/L^{2}$.

In fact, a realistic scenario of the switching through the non-symmetric
shape can be imaged as follows. We start with a symmetric membrane at $F=0$
and slowly increase the force. The symmetry breaking occurs at a certain
value of force, say, $F^{\downarrow}$. The dynamics of switching is a complex
process significantly relying on thermal fluctuations. As the switching
dynamics can not be reached within the framework of our model, for
estimation purposes, we assume that $F^{\downarrow}$ corresponds to the point where
the bending energies and applied forces for the symmetric and non-symmetric
shapes are the same. One can find that both conditions are satisfied at $%
c_0=0.4683$ and $c_1=0.6948$, so that $U_b=47.8Dw(L-d)/L^2$ and
\begin{equation}  \label{eq:fsw_nonsym}
F^\downarrow=263.53\frac{Dw}{L^2}\sqrt{\frac{L-d}{L}}.
\end{equation}
Consequently, at $F<F^{\downarrow}$, the membrane keeps the symmetric shape and
switches to the non-symmetric one as soon as $F$ reaches $F^{\downarrow}$. As there
is no barrier involved in the non-symmetric switching, no further increase
in the applied force is required to complete the snap-through transition
through the non-symmetric shape.

\subsubsection{Down-to-up transition}

\label{sec3d}

As the stretching energy $U_{str}$ (see Eq. (\ref{eq:pot_energ})) plays an important role in the down-to-up transition, it needs to be taken into account. For our purposes, it is sufficient to approximate $U_{str}$ as
\begin{equation}
U_{str} = \frac{E_{2D} w}{2 L} \Delta L^2 ,  \label{eq437}
\end{equation}
where $\Delta L$ is the change in the membrane length. In the approximation of small elongation, $\Delta L\ll L$, one can assume that both $U_b$ and the shape of the stretched membrane are not significantly modified compared to $F=0$ case. In this situation,
at the threshold of transition, the stretching energy (Eq. (\ref{eq437})) is equal to the difference between the maximal and minimal bending energies (the energy conservation condition).
Using the energies given below Eq. (S8) we find
\begin{equation}  \label{eq:dtu_energ}
\frac{E_{2D} w}{2 L} \Delta L^2=U_b^{max}-U_b^{min} = 161 D w \frac{L-d}{L^2}.
\end{equation}

Moreover, at equilibrium
\begin{equation}
F(z_{cm})=\frac{E_{2D}w}{2L}\cdot \frac{\text{d}(\Delta L^{2})}{\text{d}
z_{cm}}.  \label{eq:dtu_force}
\end{equation}%
Under the condition of small $\Delta L\ll L$, the center of mass position of
membrane (buckled downwards) can be expressed as
\begin{equation}
{z_{cm}}^{\ast }=-0.3187\sqrt{L(L-d)}+\frac{\text{d}z_{cm}}{\text{d}(\Delta
L)}\Delta L,  \label{eq:z_cm1} \\
\end{equation}%
with
\begin{equation}
\frac{\text{d}z_{cm}}{\text{d}(\Delta L)}=0.3187\frac{2L-d}{2\sqrt{L(L-d)}}.
\label{eq:z_cm2}
\end{equation}%
Using Eqs. (\ref{eq:dtu_energ}) and (\ref{eq:z_cm2}), Eq. (\ref{eq:dtu_force}%
) can be rewritten as
\begin{equation}
F^\uparrow=79.62\sqrt{2DE_{2D}}\frac{w}{L}\frac{L-d}{2L-d}.  \label{FZCM}
\end{equation}%
We have verified that the threshold switching force for the down-to-up
transition given by Eq. (\ref{FZCM}) is in agreement with our typical MD
simulations results. A very good agreement was obtained with MD simulations
performed with very small energy dissipations.

\section{Density Functional Theory}\label{Sec:DFTmain}

A DFT investigation of the up-to-down transition was
performed following the previously reported study of the
up-to-down switching of buckled graphene membrane~\cite{Sedelnikova2016}.
In the present calculations, we focused on the effects of boundary conditions and
buckling strength on the up-to-down threshold switching force.
DFT computational details can be found in SI Sec. "DFT Calculations".

\begin{figure}[t]
	\centering{\includegraphics[width=0.40\columnwidth]{Figure-15}}
	\caption{Geometries of membranes C1 (hinged boundary conditions, (a)) and D1 (clamped boundary, (b) and (c))
		in the process of the up-to-down switching. The switching occurs through non-symmetric paths (a) and (b), and initially symmetric path (c). These geometries were found using DFT optimization of geometries obtained utilizing a progressive displacement of central atoms.}
	\label{Fig:DFT1}
\end{figure}

We investigated a buckled zigzag graphene nanoribbon specified in SI.
Two types of boundary conditions
were examined: 1) hinged boundary conditions (configurations C1 with $d/L=0.96$, Fig.~\ref{Fig:DFT1}(a),
C2 with $d/L=0.78$, and C3 with $d/L=0.63$), and 2) clamped boundary
conditions (configuration D1 with $d/L=0.96$, Fig.~\ref{Fig:DFT1}(b) and (c)).
The initial geometries of nanoribbons corresponded to the buckled upwards state. In order to simulate the
up-to-down transition, we used the approach developed in  Ref.~[\citenum{Sedelnikova2016}].
Specifically, we performed a series of DFT calculations with the central chain of membrane atoms
(marked red in Fig.~\ref{Fig:DFT1}) gradually displaced in $-z$ direction from its position in the buckled upwards state.
The membrane geometry found at the preceding deformation step was used to build its
subsequent modification. In contrast to Ref.~[\citenum{Sedelnikova2016}], in the present calculations only $z$ coordinates of the central chain of atoms were constrained.

The deformation energies of buckled graphene are reported in SI. Our force estimation shows that the threshold switching force for the up-to-down
transition is about $3.8$ pN/atom for C1, $11.1$ pN/atom for C2, and $16.4$ pN/atom for C3.
Moreover, the non-symmetric switching force for D1 is $3.7$ pN/atom and the symmetric one is about $11.5$ pN/atom.
As the non-symmetric switching forces for D1 and C1 are close to each other, we  use the results for C1-C3 for the order-of-magnitude comparison with MD and elasticity theory results.

\section{Discussion}

\label{Sec:Discussion}

\subsection{Four methods to describe the snap-through transitions}
As the key finding, Figure~\ref{fig9} presents the dependence of the
up-to-down threshold switching force (calculated with different approaches) on the
membrane deformation parameter $d/L$. In particular, this figure demonstrates
that the threshold forces obtained by a number of different methods are in
good agreement with each other.

We emphasize that:

(i) MD is widely used approach to describe the dynamics of nanoscale
systems. In our work, MD clearly shows the possibility of $0\rightarrow 1$
and $1\rightarrow 0$ transitions of graphene membrane. We have also verified
the occurrence of $1\rightarrow 1$ and $0\rightarrow 0$ transitions at the
same values of forces required for $0\rightarrow 1$ and $1\rightarrow 0$
transitions, respectively.

(ii) In the framework of elasticity theory, the membrane is described
by means of an integro-differential equation for the deflection $\zeta (x,t)$. Expanding the function $\zeta (x,t)$ into  membrane's harmonics allows reducing
the integro-differential equation to a system of differential equations.
This approach was utilized in Sec.~\nameref{Sec:Elasticity}. There it was shown that the
up-to-down threshold switching force depends linearly on the initial central-point deflection, $%
F^{\downarrow }\propto \zeta _{\mathrm{c}}$,\ while the down-to-up
snap-through force at low dissipation depends quadratically on the initial
deflection, $F^{\uparrow }\propto \zeta _{\mathrm{c}}^{2}$. Besides,
we have demonstrated that with a high accuracy, the relevant membrane's dynamics
can be described (and visualized) just by two harmonics.

(iii) The phenomenological approach based on the theory of elasticity has allowed
us to obtain analytical expressions for the up-to-down and down-to-up
switching forces for buckled graphene membrane. The forces for $0\rightarrow
1$ and $1\rightarrow 0$ transitions are in a good agreement with MD
simulations results.

(iv) DFT is a non-standard method for studying mechanical properties of
membranes. Similarly to other methods, DFT  has shown that the non-symmetric
switching pathway is the preferable one. This method also provides a consistent estimation
for the up-to-down threshold switching force.

\begin{figure}[tb]
\centering{\includegraphics[width=0.50\columnwidth]{Figure-7}}
\caption{Comparison between the up-to-down threshold forces, calculated by
four different approaches. Green, red, and blue lines \ were calculated in
the non-symmetric, adiabatic and dynamic symmetric switching regimes,
respectively. The results of our MD simulations are shown with squares for
nanoribbon \textbf{\textit{A}} and circles for \textbf{\textit{B}}. The
forces calculated by means of the elasticity theory, Eq.~(\protect\ref%
{F_star}), are shown with the magenta solid line for the non-symmetric
snap-through and with the orange dashed line for the symmetric transition.
The DFT results are presented by triangles.}
\label{fig9}
\end{figure}

\subsection{Implications for memcapacitor design}

\label{sec4}

From the application point of view, the membrane memcapacitor should have a
strong 'memory content', namely, the device characteristics in its two logic
states should be sufficiently different so as to provide a significant
influence on other elements of electronic circuits~\cite{diventra13a}. For
this purpose, it is desirable that both the distance between the fixed edge of membrane and
second electrode ($h$ in Fig.~\ref{fig1}) and the maximal deflection of
membrane ($z_{s}(0)$) are chosen (much) smaller than the membrane length.
Moreover, the gap between electrodes should be larger than the maximal
membrane deflection, $h>z_{s}(0)$ (see Eq. (S2) for the definition
of $z_{i}(s)$). For given capacitances $C_{0}$ and $C_{1}$ of the states 0
and 1 (logic 1 corresponds to the membrane buckled downwards, and logic 0 -
to the membrane buckled upwards) such that $C_{1}/C_{0}<3.01$, one can find
that
\begin{equation}  \label{eq27}
h=0.3210\sqrt{L(L-d)}\frac{C_{1}+C_{0}}{C_{1}-C_{0}}.
\end{equation}

Next, we need an expression for the force applied to the membrane expressed
through the input variable of memcapacitor such as the applied voltage $V$
(see Eqs. (\ref{Ceq1}) and (\ref{Ceq2})). Since the energy of the plate can
be written as
\begin{equation}  \label{eq28}
U_{ext}(z_{cm})=-\frac {\varepsilon_0 V^2 A}{2(h+z_{cm})},
\end{equation}
where $\varepsilon_0 $ is the vacuum permittivity and $A=d\cdot w$ is the
plate area, the force is given by
\begin{equation}
F(z_{cm})=-\frac {\varepsilon_0 V^2 A}{2(h+z_{cm})^2}.  \label{eqFFads}
\end{equation}

The overall scheme of memcapacitor switching is schematically presented in
Fig.~\ref{fig11}. Let us consider first the up-to-down transition (path
(a-c,f) in Fig.~\ref{fig11}). As mentioned in  SI Sec.~"Phenomenological Elasticity Theory"
, the smallest threshold force for this transition is associated with the
switching through the non-symmetric state and corresponds to $c_{1}^{\ast
}=0.6948$. In this way, the buckled upwards membrane (structure (a) in Fig.~%
\ref{fig11}) evolves into the buckled downwards state according to (b) and
(c) in Fig.~\ref{fig11}. After the voltage removal, the membrane remains in
the buckled downwards state ((e) in Fig.~\ref{fig11}). In order to estimate
the minimal (threshold) voltage required for this transition, Eq. (\ref%
{eq:fsw_nonsym}) is rewritten accounting for Eq. (\ref{eqFFads}):
\begin{equation}
\frac{\varepsilon _{0}V^{2}dw}{2(h+z_{cm}(c_{1}^{\ast }))^{2}}=263.53\frac{Dw%
}{L^{2}}\sqrt{\frac{L-d}{L}}.  \label{eq:sw_cond_utd_1}
\end{equation}%
Consequently,
\begin{equation}
V_{0\rightarrow 1}=22.96\frac{h+z_{cm}(c_{1}^{\ast })}{L}\sqrt{\frac{D}{
\varepsilon _{0}\cdot d}\sqrt{\frac{L-d}{L}}},  \label{eq:sw_cond_utd}
\end{equation}%
where $z_{cm}(c_{1}^{\ast })=0.3203\sqrt{L(L-d)}$. Eq. (\ref{eq:sw_cond_utd}%
) provides an easy way to find the threshold voltage necessary for the
up-to-down transition of membrane.

\begin{figure}[tb]
\centering{\includegraphics[width=0.50\columnwidth]{Figure-8}}
\caption{ Schematic representation of transition pathways in the switching
of membrane memcapacitor (red arrows represent the applied electrostatic
force, bold blue arrows represent the movement of membrane). The buckled
upwards membrane (structure (a)) evolves into the buckled downwards state (c)
through a non-symmetric transition state (b). Note that in the presence of force, (c) is
also a transition state. After a slow voltage
removal (dashed green arrow), the membrane remains in the buckled
downwards state (e) (the up-to-down transition). In case of fast force
removal, the membrane does not have enough time to relax its tension (d) and start
moving into the upward state (a) through a symmetric transition state (f) (the
down-to-up transition).}
\label{fig11}
\end{figure}

In the down-to-up transition, the initial buckled downwards membrane ((e) in
Fig.~\ref{fig11}) is first stretched by the applied force ((c) in Fig.~\ref%
{fig11}). When the force is removed, the membrane state becomes (d). If the
potential energy of (d) is sufficient to overcome the potential barrier
height symmetrically (f), then the membrane may end up in the buckled upwards
state (a). These general processes are partially described by Eqs. (\ref%
{eq:dtu_energ}), (\ref{eq:dtu_force}). Because of the membrane elongation in
(c,d), a refined value of $z_{cm}$ should be used in relevant calculations.

The threshold voltage can be estimated based on the energy conservation (Eq.
(\ref{eq:dtu_energ})) and force equilibrium (Eq. (\ref{eq:dtu_force}))
conditions accounting for $z_{cm}^*$ from Eqs. (\ref{eq:z_cm1}) and (\ref%
{eq:z_cm2}). One can find that
\begin{equation}
\frac {\varepsilon_0 V^2 d\cdot w}{2(h+ z_{cm}^*)^2} = 79.62 \sqrt{2DE_{2D}}
\frac{w}{L} \frac{(L-d)}{(2L-d)}
\end{equation}
and
\begin{equation}
V_{1\rightarrow 0} = 12.62(h+z_{cm}^*)\sqrt{\frac{\sqrt{2 D E_{2D}}}{%
\varepsilon_0\cdot d\cdot L }\frac{(L-d)}{(2L-d)}} .  \label{eq1122}
\end{equation}

An additional aspect of membrane dynamics --
an estimation of thermally-induced switching time -- is considered
in SI Sec. "Stability of buckled membrane".

\section{Concluding Remarks}

\label{sec6}

We have investigated the snap-through transition of a buckled graphene membrane
using a variety of computational and theoretical tools. The main results of
this paper are the expressions for the threshold switching forces (Eq. (\ref%
{F_star}, \ref{eq:fsw_nonsym}) for the up-to-down transition and Eq. (\ref%
{Fup}, \ref{FZCM}) for the down-to-up one) and corresponding voltages (Eqs. (%
\ref{eq:sw_cond_utd}) and (\ref{eq1122})). Our analytical results are
supported by the results of numerical simulations, MD and DFT calculations.
We expect that our findings will find applications in the design,
fabrication and analysis of membrane-based memory devices.

\section*{Acknowledgments}
This work has been supported by the Russian Science Foundation grant No.
15-13-20021. OVI and SNS acknowledge a partial support by the State Fund for
Fundamental Research of Ukraine (grant No. F66/95-2016).

\section{Author contributions statement}

R.D.Y. and Y.V.P. did the MD calculations and developed the \nameref{sec3}.
O.V.I. and S.N.S. developed the \nameref{Sec:Elasticity}. O.V.S. did the DFT calculations.
All authors discussed the results and co-wrote the manuscript.

\section{Additional information}

\textbf{Competing financial interests: }The authors declare no competing
financial interests.

redpajama_set_name: RedPajamaArXiv


A winery with great history. Their grandfathers, who came from Sparta, sold oil on the island of Syros. At some time western winds washed them ashore to Santorini, where they realised that the wine here had great potential. So, they settled here permanently and got intent exclusively on wine. Within 20 years they constructed their own ships and started exporting to Russia, from 1870 to 1917. What makes the winery special is the impressive museum at the undercover canavas, where is presented the whole history of the Santorini wine and Santorini vine-grower from 1660 until today.


text:
Full-Time RVing
27 AprEl Morro NM: What It Means To Leave Your Mark – PWPR 3
Written by Sarah V-K
Categorised Podcast
A park well known for historical graffiti – El Morro National Monument is a hidden gem of the National Park System. We speak with Ranger Wendy Gordge about the park's unique history, what it means to leave your mark, and the camel corp.
Show Notes found at: https://www.virtualkamper.com/pwpr3/
Help keep the show on the road: https://www.patreon.com/virtualkamper/
Podcast Resources:
Plan you visit to El Morro.
History, Preservation, and Power at El Morro National Monument
El Morro National Monument – Nomad
About Ranger Wendy Gordge
The Difference Between a National Monument and a National Park?
About El Morro National Monument
Ancestral Puebloans
The Spaniards
The Camel Corp
Why leave their mark?
Modern Camel Corp Reenactment
Wendy Gordge's Love for El Morro NM
Volunteer Efforts at El Morro
Let's Connect More!
Wendy Gordge is the lead interpretive ranger at El Morro National Monument. She worked at ten different National Parks, but for the past 10 years, she's called El Morro home.
She grew up visiting National Parks as a kid and wanted to work outdoors with the public. So, the National Park Service is a great fit.
The biggest difference between the two is how they are added to the National Park System. Presidential Proclamation designates National Monuments. National Parks are created via congressional vote.
The name, El Morro, means the headland in Spanish. The National Monument is the second place to receive such a designation in 1906, by President Teddy Roosevelt.
Located in the Northwest corner of New Mexico in a high desert plain, the bluff stands out as very intricate, unusual and beautiful. Made of beautiful Zuni sandstone, and its base is a small pond. The mesa top is composed of slick rock with tall trees growing on the surface.
It's famous for historic inscriptions — over 2000 inscriptions and several hundred Native American petroglyphs are on the sandstone bluff.
The Ancestral Puebloans built a village on the top of the mesa. The location is ideal because at the base of the mesa, there's a pool of water — the only water source for many miles. People climb down the cliff to retrieve water via hand-and-toe holds carved into the cliff face. Additionally, small depressions in the rock, called tinajas, catch water to drink.
Archaeologists believe about 600 people called the mesa home. Today, the modern Puebloan people call the place Atsinna, place of writing on the rock.
The Ancestral Puebloans drew Petroglyphs on the sandstone. But, their meaning is unknown. Depicted are carvings of bighorn sheep and paw prints of a grizzly bear.
A western viewpoint might see the village site and believe it's abandoned. However, the descendants of the Ancestral Puebloans don't see it that way. The spirit of their ancestors still dwells here. The modern Puebloan people consider this place sacred and return to visit their ancestors.
The people who maintain the village site are primarily from the local Zuni who descended from the Ancestral Puebloans. The Laguna and the Acoma Pueblos have strong ties as well.
Why venture north into America? The Conquistadors followed rumors of the 7 cities of gold. Quests to missionize native people, colonize, and gain wealth through land and settlement are also common.
Juan de Oñate is the first Spaniard to inscribe his name in the rock in 1605, 15 years before the Pilgrims landed in the US.
A favorite story of Wendy's: Early Spanish explorer and conquistador Gaspar Pérez de Villagrá, part of the Oñate's expedition, fell behind and rushed to catch up with the group. He became separated from his horse and wandered through the desert for days.
He walked backward to thwart being tracked by hostile parties. Then, he walked with his shoes on backward. At last, he found the pool at the base of El Morro which ensured his survival. His never carved his name on the bluff. However, he later wrote poetry about how El Morro helped him survive.
In 1848, via the Treaty of Guadalupe Hidalgo, the area becomes US soil. Shortly after in 1849, gold is discovered in California, and people journeyed westward.
Richard H Kern, an artist and part of an army topographical expedition, was one of the first Americans to inscribe his name on the rock. He sketched all the inscriptions he found, and there were no English ones at the time.
Pioneer families began to head west to settle in California, and both men and women inscribed their names into El Morro. Sallie Fox, a 12-year-old girl, maybe the youngest who wrote her name in the rock. Her inscription has weathered and begun to fade.
The army attempted to create better routes to California and sent an expedition of the US camel corp to test the usefulness of the animals on a long journey across the desert. The camels were successful and often outperformed horses and mules.
But, we don't see camels today in our history books. The civil war caught people's attention, and after the war, the railroad began to run to California. Additionally, Jefferson Davis, president of the Confederacy, had originally come up with the idea, and no one wanted to pursue any of his ideas after the civil war ended.
El Morro was a difficult place to get to, and it was a point of pride to say that they made it there.
The Rose-Baley wagon train, of which Sallie Fox was a member, indicated they were the first pioneer train to make it to El Morro. As they continued on, it became insufferably hot and water became scarcer.
They reached the boundary between Arizona and California and attempted to cross the Colorado River. Then, Mojave Indians attacked as they crossed the river. The livestock scattered, and several of people in the party died, many became injured.
They traveled 600 miles back to Albuquerque rather than continue the last 300 miles into California due to fear of the unknown. They returned by way of El Morro, but none of them inscribed their names on the way back.
Water drew people here and water will dismantle the marks people left due to how easily sandstone erodes.
First attempts by the NPS at preservation were well-meaning:
Gasoline and hot paraffin were used in an attempt to waterproof the monument. (The Gasoline was meant to pull the paraffin deeper into the rock.)
Inscriptions were outlined with Number 2 pencil.
Efforts to seal in an inscription can cause water to travel laterally through cracks. The diversion of water only causes problems with other inscriptions.
Today, we preserve the inscriptions with:
High definition photography
3D scans of the inscriptions
Cataloging them and their content in a database
If an inscription is chipping or flaking, conservators can use special epoxies work to put it back together. The inscriptions at El Morro National Monument won't last forever. In time, nature will take its toll.
In 2014, 2016 and 2018, Wendy Gordge arranged for camels from Texas to visit the National Monument as a commemoration of the camel corp which passed through in 1857.
A historical reenactor, Doug Baum, sets up an encampment with 4 camels. Several days of special programs and school programs bring kids to the monument. The reenactment will occur later this year in 2018.
Wendy loves El Morro National Monument and is a favorite place of employment.
The history, stories and natural beauty of the place fascinate her. It's rather unusual to find a National Monument in a small concise space with so much history in crossroads of different cultures.
Some people are well known, and others are everyday folk with amazing stories to tell.
The National Park Service resonates with Wendy because it preserves and protects the best the country has to offer. The amazing beauty and our history of who we are and who we hope to become.
El Morro National Monument is always looking for volunteers. Volunteers staff the desk, walk the trails and give interpretive talks. Additionally, if you have a specialized skill set and have a project you'd like to help the park with, feel free to give them a call.
At El Morro, volunteers help with database management, artistic renderings of events, and junior ranger programming. Whether your background is in art, technology or education, the park service can put it to use.
Contact the park at 505-783-4226 to inquire about opportunities.
Thanks to Our Listeners – Let's Connect More!
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text:
SYTYCD 9.14-Asian Fusion and Gold Bowties
It's Wednesday, it's 8 o'clock pm Eastern Standard Time, Jesse Tyler-Ferguson is BACK(!) and there are people in spandex with giant fans on stage, it must be So You Think You Can Dance time!!
Let's talk about that opening number first, before we jump too deeply into the requisite "enhanced dancer background" pre-rehearsal chit chat, which will inevitably include home videos. First of all, I have to say, for some reason this intro dance caught me a little off-guard, not terribly off-guard, just a little "huh...oh". Is it wrong that if I was titling this dance it would be "Asian Fusion"? It's all red and black, mandarin collars and exotic prop fans. Both Cole and Chehon get nice stand-out leaps but Will and Cyrus get the short end of the stick, reduced to lots of reaching, dramatic plies. Eliana gets the closest to standing our for the ladies, who are pretty much forced to unison moves the whole time. With the soaring strings and pounding percussion, it all feels very dramatic, but not necessarily emotional.
Intro Group Dance Song: "Run Boy Run" by Woodkid
As for the individual introductions, I like that Cole didn't bother to change out of ninja mode, he realizes it fits his style the best. Also Cat looks fantastic, that dress is classic, it just had to be said. Oh it looks like we're going to be getting individual solos along with the couple numbers, so that's how they're going to fill the time with the dwindling contestant numbers
Tiffany's solo song: "I Was Here" by the cast of 'Glee'
Couple #1: Whitney & Twitch
Choreographer: Luther Brown
Style: Hip Hop
Artist: Lil' Wayne f/Big Sean
Song: My Homie's Still
I think Whitney totally holds her own here. It was definitely hardcore hip hop, with lots of hits and lots of beats TO hit and although the choreography during the choruses feels like it was made up as they went along, the rest was lots of attitude and precision. Nigel pumps himself up by telling Whitney that he's glad that they've saved her, Mary rambles off a ton of adjectives that signal she's trying just a little too hard to keep with the hip hop theme, while Jesse, as almost always, has the best comments, even if they're not about dancing. He and his rockin' gold bowtie (bowties ARE cool) tell Whitney that she looked beautiful and how she danced in those "diaper pants" he'll never know and that his favorite part was when they were doing the "waiting for the bus move". Someone needs to make a GIF of him interpreting this move stat.
Will's solo song: "Better Man" by James Morrison
Couple #2: Cole & Allison
Style: creepy contemporary (you know what Sonya does best)
Artist: Bjork
Song: Possibly Maybe
There is too much to love about this routine to list. Also, there has been a severe lack of Ms. Tayeh's choreography this season. Allison is an absolutely amazing dancer and she brings everything here. The air she gets on the assisted one-armed lift that Cole partners her for is unbelievable. If any criticism, I would just say that I feel like Cole doesn't get a lot of chances to show off his own skills, but when he does it's impressive. Jesse says that it was like an "American Horror Story promo" and he's totally right. He loves the performances of both dancers. Mary says "the name of that song was possibly, maybe. Possibly you'll be in the finale, maybe you'll be in the finale; if you keep dancing like that, PROBABLY you'll be in the finale". Nigel says it was "powerful, it was dramatic...slightly quirky and scary" and that Cole brings a "uniqueness" to all of his performances.
Lindsay's solo song: "Senorita" by BOND
Couple #3: Eliana & Ryan
Theme: Desperate Housewife
Artist: Caro Emerald
Song: That Man
Oh, Ryan, I didn't realized I'd miss him until now.
Take a moment to watch my favorite Ryan performance:
There's a bit of Broadway camp in this routine and I'm curious what Mary will have to say about the technique. From where I sit, I thought Eliana's frame in the traveling sequences is fantastic and the lifts are really impressive (including the flip into another ridiculously gymnastic move. Mary says she was "spectacular". Jesse quotes Ms. Murphy and then says that Eliana's "range of emotion is extraordinary" and that she's very "accessible". Nigel thought her technique was the best that he's seen a non-ballroom dancer do.
Chehon's solo song: "On the Nature of Daylight" by Max Richter- I can't lie, with the family stuff and the letting the guard down, Chehon could begin to grow on me. Why didn't you do this all season?!?! I knew this song sounded familiar. It's because I'm used to it being paired with "This Bitter Earth"
Couple #4: Lindsay & Alex
Choreographer: Sonya Tayeh (it's a two-fer night guys!!)
Theme: Chemistry, tension, all that intense stuff
Artist: Gotye
Song: Somebody that I Used to Know
It's finally happened people, someone has finally used Gotye's song on So You Think You Can Dance. I'm unnaturally excited. Yes, now I know for sure, there simply hasn't been enough Sonya Tayeh for me this season. This is another awesome routine. I hope somewhere someone's made a "Alex Wong can do no wrong" shirt because this guy is another simply amazing dancer. I think I actually like this dance better than the Cole routine, but it could be just because I love that song. Cole and Allison's was a more emotional piece though. Nigel says he didn't feel Alex and Lindsay's chemistry, but that their technicality was great. Mary also jumps on the lacking chemistry bandwagon. Jesse, aside from agreeing with Mary and Nigel, also calls Lindsay "a-ding-dong-dorable".
Couple #5: Will & Lauren
Theme: Dance the pain away
Artist: Wye Oak
Song: Dance My Pain Away (I swear I didn't know the song choice, it's almost too easy)
I feel like there's so much prop work that they should get credit just for the difficulty. I thought the majority of their work in unison was really impressive and that, although there were some parts where Will didn't hit as hard as he could have, the choreography was also lyrical enough to allow him to get away with a lot. I like Lauren's work here a lot more than in her last routine. Mary loves the routine and thinks it was "articulate and precise". Jesse really liked that Will pulled back the adorable a bit and clearly thinks Will is great. Nigel says that it was "really important" to pull back the personality and then brings on the perve factor before simply saying it was a "really good job".
Whitney's solo song: "Where Have You Been" by Rihanna
Cole's solo song: "Arise" by E.S. Posthumus (either this song is in a million movie trailers or it should be) I seriously just think he's amazing
Couple #6: Cyrus & MELANIE!!!
Theme: This is how the cool kids roll
Artist: Freddy Fresh f/ Fatboy Slim
Song: Badder Badder Schwing
I feel like this is the first week that I've seen legitimate growth in technicality from Cyrus. His musicality has always been great and there's no doubt that he can pick up the moves easily, but this was much more engaging. This is definitely one of his best routines. Also, Melanie's up to her old trick of being awesome, so it's a great pairing. Jesse says Cyrus' "charisma and your spirit and those pants kept my eyes on you" and says that Cyrus' uniqueness will keep him synonymous with the show. Nigel says "America must love you" and that Cyrus is a people-magnet. Mary is in awe of Cyrus animator moves and says that even though it wasn't perfect that Cyrus blows her mind.
Eliana's solo song: "Infra 8" by Max Richter
Couple #7: Chehon & Anya
Choreographer: Miriam and Leonardo
Style: Tango
Theme: This is what a Tango is
Artist: Jesse Cook
Song: "Breathing Below Surface"
I have to say, this doesn't remind me much of the "Scent of a Woman" tango, but what do I know? The beginning makes use of Chehon's amazing balletic prowess, but Cat, along with the judge's standing ovation, assure us that this was a special routine, so what do I know?! Mary calls it her favorite number tonight and applauds Chehon's performance. I will say he's danced better tonight than any of his previous performances. Jesse states, and I agree, that tonight is full of really amazing performances. Where was this the rest of the season?! He also comments on Chehon's nachos aka "ganchos"(the quick footwork) and puts him on his Jalapeno Bus. Nigel loves the connection.
Cyrus' solo song: "Existence (VIP)" by Excision & Downlink- he clearly gets the loudest response of the solos of the evening.
Couple #8: Tiffany & Ade
Theme: Epic song=epic dance?
Song: "The Power of Love"
Ade is just such a strong partner. That was an impressive dance as well. The lifts were amazing because, as I've said before Tiffany looks like she's about equal with a feather on the scale. Jesse says "the partner work was insane". Mary says Tiffany is "extraordinary" and that this was "her best performance of the season". Nigel says he thought it was "going to be fantastic and it was" and then he quotes One Direction right after Cat makes the reference, keep up Nigel.
And it's immediately into the bummer part of it all, the results:
Chehon
Oh no, I don't feel good about this at all. With all of the solos being part of the show, there's no need for the judges to see them again, so they're just going to get straight to the point.
I do appreciate that they don't pad the results portion with drama and drawn out commercial breaks, I can't help feeling it's cruel in a way to just put up the chopping block after everyone is probably feeling really great from awesome performances. Well, there's no complaining now, we're only two episodes away from the finale. Don't forget we're crowning a Favorite King AND Queen this year, so the season is even shorter. Well until next week, same time, same place, I'll be busy working on how to incorporate fans and jumping on furniture into my daily life.
So You Think You Can Dance SYTYCD 9


text:
The Tsonga
Tsonga Origins
© Dr Peter Magubane
A Tsonga family in front of their traditional homestead.
Developing Tribe
The first Tsonga-speakers to enter the former Transvaal probably did so during the 18th century. They were essentially traders who followed rivers inland, where they bartered cloth and beads for ivory, copper and salt. In the early 1820s, they were joined by co-linguists pushed from the coast by Nguni raiders. At this time the Tsonga living on the coastal plain constituted a loose cluster of linguistically related peoples who shared a few distinguishing customs but had no single governing identity. Their small groups could offer only limited resistance to the invading Nguni.
The last Nguni group to come to the area was a remnant of the Ndwandwe army, under Shoshangane, which had suffered a mauling at the hands of Shaka and his Zulu impis on the Mhlatuze River banks, near present-day Ulundi. The refugees settled along the Tembe River, south-east of what is today Swaziland, but before long they turned on the Tsonga, moving north in a gentle sweep to the Limpopo Valley. An uneasy peace developed as the Ndwandwe, or Shangaan, began to incorporate Tsonga-speakers into their ranks.
Shoshangane
A Nguni state on Zululand's northern border was an irritation to the Zulu, serving as a home for political dissidents and threatening the important trade route to Lourenço Marques, now Maputo. A new Zulu expedition was sent north in 1833 to attack Shoshangane and punish his allies. They seized Lourenço Marques and impaled the governor of the town on the beach. In the face of this Zulu resurgence, Shoshangane and his followers fled from their settlement in the lower Limpopo Valley. They advanced to the Zambezi River before going south to settle in Mosapa, Zimbabwe.
From here Shoshangane began to subdue and incorporate the Shona-speaking Ndau. Using his expanded forces, he strengthened his power over the area between the Zambezi River and Delagoa Bay. Steadily the Gaza kingdom, named in honour of Shoshangane's grandfather who had lived in the Mkuze district of Zululand, began to emerge along the eastern edge of the escarpment and in the steamy bush of the coastal plain. A period of relative peace ensued, during which the Ndwandwe from the south and the Tsonga, who had been in the region for centuries, steadily influenced each other. This was intensified after 1838 when many of Shoshangane's soldiers died in a smallpox epidemic, and he moved back to the Limpopo Valley.
His troops devastated the area, as he punished his enemies, enslaved women and children, and demanded heavy payments of tribute. This turmoil dislodged two streams of refugees from the coastal plain. The Nkuna and other small groups moved west along the Olifants River to place themselves under the Sotho-speaking tribes, Kaha and Lovedu, on the western Lowveld.
Second Wave of Refugees
The second wave of refugees - Maluleke, Baloyi, Tshauke and Sono - followed the Limpopo to settle along the Levubu 'Pafuri' River or in the lowlands to the east of the Soutpansberg and the Drakensberg. Small bands of refugees retained their chiefs by settling in inhospitable, high malaria risk areas but, if they wished to live around the healthier highlands they had to seek the protection of leaders like the Sotho-speaking Modjadji, Podile and Maake in the south or the Venda-speaking Pafuri in the north. In the 1850s Tsonga immigrants made their home in the Spelonken foothills of the Soutpansberg where a Portuguese adventurer, Joäo Albasini, was building a personal kingdom out of profits made from the sale of slaves and ivory.
While the Tsonga refugees in the interior started to form small communities, their kinsmen on the coast had to withstand continuing political upheavals. In 1858 Shoshangane died and the kingdom began to disintegrate as his sons, Muzila and Mawewe, locked horns over the throne. Shoshangane had named Muzila as successor, which Mawewe contested; this led to almost 10 years of continuous fighting. Aided by Albasini and traders at Lourenço Marques, Muzila gained the upper hand.
Mawewe fled to Swaziland, where he sought the help of King Mswati l, finally settling in northern Swaziland on the border with Gazaland. Muzila had shifted the centre of the Gaza state back to the safety of Mosapa, leaving the Delagoa Bay hinterland unprotected. Each winter the Swazi launched devastating raids into the area. In 1884 Muzila died and his son, Gungunyana, succeeded him. The new king rapidly tried to re-establish control over southern Gazaland. In 1889 he moved his capital to the lower Limpopo, colonizing the southern reaches of his empire. The ensuing disruption initiated a new wave of immigration into the Transvaal and brought Gungunyana into conflict with the Portuguese.
New Wave of Emigration
©Dr Peter Magubane
Geometrical patterns decorate the walls of this enclosure.
As the natural port for the Witwatersrand, Lourenço Marques had grown with the newly discovered gold fields. This gave the Portuguese the desire and means to establish control over southern Mozambique; in 1895 an expedition from Lisbon defeated Gungunyana and exiled him to the Azores. His son, Thulilamahanxi, then a minor, and the regent, Mpisane, fled to the Transvaal Republic and settled north of the Sabi River along the foothills of the Drakensberg mountain range, in the present district of Mhala.
The crushing of the Gaza was completed two years later when an uprising led by one of Gungunyana's generals was mercilessly subdued. This initiated a new wave of emigration as the remnants of the Gaza empire crossed the border and entered the Transvaal. In 1910 Mpisane renounced his regency in favour of Thulilamahanxi, who was recognized by the family council as heir in the absence of the still exiled Buyisonto, the legitimate successor to Gungunyana. In 1922 Buyisonto came out of exile and moved to Mhala to become the leader of the descendants of the old Gaza kingdom.
By this time Tsonga-speakers constituted about four percent of the total South African population. In the Transvaal they lived in distinct areas. In the north, quite large chiefdoms, such as those of Xikundu, Mhinga, Xigalo and Makuleke, occupied reserves adjoining or near the Kruger National Park. Further south, scattered communities eked out a living in the Lowveld. Near the headwaters of the Levubu and Small Letaba rivers, Christian converts stayed on Swiss Mission farms at Valdezia, Elim and Kurulen, their children attending the celebrated Lemana College.
Further south, the Nkuna and several small groups lived on the edge of the Escarpment. The descendants of the Nguni-speaking Shangaans, with their Tsonga-speaking wives and followers, occupied the land between Acornhoek-Bushbuckridge and the southern end of the Kruger Park. Probably the largest single group of Tsonga-speakers was in the Ingwavuma—Ubombo districts of northern Zululand. These were the descendants of the Maputo 'Mabudhu' in Zulu, whose kingdom was cut in two by the border between South Africa and Mozambique. Unlike the Tsonga in the Transvaal, they had close ties with the Zulu.


text:
Exploring the Life in Reading
About Book Corner
Meet the Reviewers
Authors and Publishers
Contact Book Corner
Emma Lou the Yorkie Poo
SKU 978-1-61599-456-4
Meet Emma Lou, the Yorkie Poo - a little dog with big worries. She loves playing with her best friend, Pearl, but Pearl doesn't always pay attention to Emma Lou's worries. With the help of some new friends, Caleb the Calico cat, Patrick the pig and Gigi the ginormous giraffe, Emma Lou and Pearl begin to learn a new technique to calm their minds and bodies. Parents, educators, counselors - and especially children - can benefit from Emma Lou and her friends' curious adventure to a mindful experience.
Readers will:
Learn how to help a child that worries
Teach children a simple technique to practice mindfulness
Support your child's emotional growth through experiencing a delightful adventure
"Emma Lou the Yorkie Poo: Breathing in the Calm is a playful approach to real concerns that kids have on a daily basis. Kim uses relatable animal characters to bring to light concerns that impact children everywhere - along with a great strategy to help!"
-- Marie Robinson, M.Ed., principal, pre-K to 12
"For over 20 years, I have noted our children experiencing increasing levels of joy-blocking anxiety. In this whimsical and engaging story, Kim has created a very useful therapeutic tool. She captured the essence of a hopeful way out that children can readily identify with and rapidly incorporate, just like Emma Lou did!"
-- John Pasquarelli, LCSW, LADC
"Kim is a warm, kind and compassionate social worker dedicated to improving the lives of others. Her book is an easy read for children to learn about managing anxiety and contains techniques that can be applied right away."
-- Gwen M. Ackley, LCSW
"With excessive exposure to flashing changing screens, children are having a hard time settling their brains. Their thinking is fragmented and their focus is fractured. In Emma Lou the Yorkie Poo: Breathing In The Calm, Kim Larkins cleverly and creatively invites children into an animal-friendly storyline of learning how to calm themselves. Although Larkins addresses worry, Emma Lou is a valuable tool for releasing stress throughout the nervous system, induced from screen stimulation."
-- Holli Kenley, author of Power Down & Parent Up
From Loving Healing Press www.LHPress.com
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Dropping the Eyelids: Nonfiction for the Soul
Book giveaway for you
A Piece of Peace
by Sweta Srivastava Vikram
Giveaway ends September 21, 2021.
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Separately, credit ratings agency Fitch Ratings said a failure by United States officials to raise the federal debt ceiling in a timely manner would prompt it to review the United States sovereign rating, "with potentially negative implications".
Trump Threatens Government Shutdown Over Border Bucks, but Could It Backfire?
North Korea has conducted a series of ballistic missile tests this year. - Three North Korea short-range ballistic missiles failed on Saturday, a temporary blow to Pyongyang's rapid nuclear and missile expansion, USA military officials said.
The spokesperson said that both ships are a safe distance from the stop and will make a brief stop in New Orleans on Saturday. The ships will instead stop in New Orleans, Louisiana, Saturday to replenish fuel, water and food supplies, she said.


Famous Recipes by Famous People: G-Man Turtle Soup by J. Edgar Hoover, Famous Recipes by Famous People: Here's a recipe from the famous (infamous?) Director of the F.B.I., J. Edgar Hoover, as it appeared in Famous Recipes by Famous People, 1936, 1940.
Famous Recipes Famous People: Famous Recipes by Famous People, compiled by Herbert Cerwin and published in 1940 by Sunset, the Magazine of Western Living, Lane Publishing Co., San Francisco, in cooperation with the Hotel Del Monte. Hard cover with dust jacket, 62 pages. And, the people ARE famous. Walt Disney (Silly Symphony Souffle,) Robert Ripley (Believe It or Not Spinach,) John Steinbeck (Of Beef and Men,) Gertrude Stein (Chowder Alice B. Toklas,) J. Edgar Hoover (G-Man Turtle Soup,) Rube Goldberg (Veal Cutlets a la Baseball,) Mrs. Franklin D. Roosevelt (My Supper,) plus many famous chefs!
Apparently, everyone who was anyone in 1936 gathered at the Hotel Del Monte to exchange recipes. These recipes, then, were gathered and annotated by Herbert Cerwin and illustrated by Paul Whitman. The resulting booklet was published by the Hotel Del Monte, Del Monte, California, in 1936. That paperback cookbook was the 1936 first edition, first printing. This cookbook, with a different cover from the more colorful cover, is the 1940 first edition, first printing of the Lane Publishing edition. This cover has lots of shelf wear, but it is now safely encased in Mylar. The pages of the book are uniformly tanned, especially at the edges. Other than the tanning, the book is in mint, never-read condition.


text:
Mendes Pimentel is een gemeente in de Braziliaanse deelstaat Minas Gerais. De gemeente telt 6.684 inwoners (schatting 2009).

Aangrenzende gemeenten
De gemeente grenst aan Central de Minas, Divino das Laranjeiras, Itabirinha en São Félix de Minas.

Gemeente in Minas Gerais

redpajama_set_name: RedPajamaWikipedia


text:
Miasanrot Roundtable: Mailbag October 2018
Another month brings the first "crisis" of the season. It has been a tumultuous four weeks for the reds going winless in four consecutive games prior to the international break capped off by controversial presser by Uli Honess and Karl-Heinz Rummenigge.
Marc October 26, 2018
Joining me to break down your questions this month are ESPN's Mark Lovell and Miasanrot's Maurice, Rick, and Dennis.
(Image: Christof Stache/AFP/Getty Images)
The first question is from @me_unplugged20 on twitter. "How much of the "mini crisis" do you think is down to Kovac? What do you think are the reasons for the crisis and what is required to get out of it?"
Maurice: Kovac took over Bayern at an uneasy time. Most of his key players missed at least part of the preparation and when they came back were unsatisfied because of their rather poor performances at the World Cup. It must have been a tough task for a young, rather unaccomplished coach to win over that locker room. Yet, it is something Kovac managed to do. What he failed to do was adapting to opponents changing their game plan on the fly and fixing some of the tactical problems that lay within that Bayern team, e.g. the distances and positioning in midfield.
Rick: The coach is always the first target in situations like this. Kovac may have coached the Croatian national team and Eintracht Frankfurt, but Bayern was always going to be a major step up. He has to be allowed to find his feet a little. For what it is worth, I believe that many of the "problems" between the players and the new coach are the products of media fiction. Yes, he has made mistakes. But injury problems have not helped.
Mark: Kovac was left in the lurch a little, taking over an ageing group and losing useful squad members like Arturo Vidal, Sebastian Rudy and Juan Bernat. Don't forget Kovac started with 7 straight wins and was chasing Carlo Ancelotti's record before things turned. As Ancelotti knows only too well, players get you the sack and sadly there's no Jupp Heynckes to save the day this season. Furthermore, Bayern are still overly reliant on Robert Lewandowski's goals, this is nothing new.
Dennis: Currently one can get the impression of a common development between Kovac's first weeks in office and the team's performances in the first phases of the games. Both start off pretty well and with good energy only to get out of rhythm for no apparent reason. One major area of improvement for Kovac will lie in a in-game management that can give his team a second positive push. If this impact from the sideline is missing, his days in Munich will continue to be criticised for a lack of development.
Marc: Certainly some of the blame lies at the feet of Kovac. The inconsistent play, lack of cohesion, fundamental mistakes and lack of in game adjustments are issues that Kovac has to figure out. While everything eventually comes down to the players, he has to inspire and demand enough respect from them in order for the team to get better. We are currently in, at least a "mini" version of, the scenario that many questioned how Kovac would handle when he was hired. It is obvious that Bayern is struggling both tactically and to find their form. Kovac's ability to navigate these type of situations by adapting his tactics and improving areas of weakness will ultimately decide how successful the team and his tenure in Munich will be.
(Image: Sebastian Widmann/Bongarts/Getty Images)
Our second question comes from @harishb997 on twitter. "Should Bayern have started the transition from the older generation to the younger sooner? How can the coach find the perfect balance between the two generations, especially when both expect to play?"
Maurice: The transition of generations has been going on, but not at the pace the club might have needed. The task of keeping both parties satisfied will be a tough one for Kovac and can only be accomplished, if he has the support from the guys upstairs. Because only then the Croatian can make unpopular decisions like benching Ribery in big games, which – let's face it – might be way overdue.
Rick: I think they've tried, but circumstances have not helped. At nearly every opportunity, the replacements have broken down or failed to fire. At some point, we were all ready to see Robben and Ribéry eased out by Kingsley Coman and Douglas Costa. One spent most of his time on the treatment table, while the other was not really a great fit for the team. The result was that the old order was restored. I think it is perfectly possible to find the perfect balance, but the old stagers need to be phased out in a constructive manner.
Mark: Kingsley Coman's injury was a major blow so early in the season. That meant an extended run for Bayern's longest-serving player Franck Ribery, close friend of Hoeness and always the first to run to Uli about the coach when things are not going well. It's easy to forget Ribery last CL goal was in March 2015 and his best days are long behind him. Man-of-the match against Athens, Gnabry will only improve but needs to score more goals. While Arjen Robben has a little bit more left in the tank than his veteran teammate Ribery, both stalwarts though are one serious injury away from the end of their careers. Originally, I didn't think Alphonso Davies would be given an immediate shot but judging by the YouTube links (same methods used as Hasan Salihamidzic) the classy Canadian looks like he could help Bayern in the short-term.
Dennis: Just as Maurice mentioned, the overall squad management has already started towards a transition. Injuries and lacking personal development have hindered the official changing of the guards. Nevertheless a stronger willingness to either give the young guns more minutes (at least in insignificant Bundesliga games) or to alter the overall strategy to focus less on the wings hasn't gained enough momentum. Gnabry and Coman will have to step up their game (or regain their level) very quickly, to diminish the reliance on the aging Robbery.
Marc: I don't think Bayern are as old as some people make them out to be. The obvious exception to that is on the wing where we are about two to three years past the time where we should be relying on Robben and Ribery, especially given the inexperience of Gnabry and the injury history of Coman. Bayern will need to either adjust away from a wing based system (as Dennis said) or purchase some reinforcements. I am doubtful that Davies will be able to have an immediate impact at this level which means it will probably be a difficult year out wide.
Central defense is the other area that looks like it will be an issue soon. Sule is both young and improving but Boateng and Hummels have both shown some regression so far this year. The only other alternative in the squad, Javi Martinez, has always been somewhat slow, isn't any younger and is not a natural central defender. I'm hopeful, but not optimistic, the club will start to integrate Lars Lukas Mai and perhaps begin looking for other players around Europe to solidify the defense going forward.
(Image: Stuart Franklin/Bongarts/Getty Images)
Our third question comes from @M_Friedrichs on twitter. "How do you explain Friday's press conference? Do you think it was an attempt to distract from Kovac and the players?"
Maurice: I think the main thought behind the presser was to set an example and prove that the club has the back of the coach and the players. Something that was recognized and pointed out by Kimmich for example. While this certainly was the intention, it turned into something else rather quickly. There are just too many instances were Hoeness and Rummenigge have contradicted themselves in the past and the members of the press were eager to point those instances out to them. It was at that moment that both chairmen failed to apologize for previous statements and show some self-reflection.
Rick: There was hyperbole. Rummenigge invoking the Grundgesetz, for example. There was contradiction, with Uli then laying into Juan Bernat. But the main intention in my view was to call out some elements of the media for promoting their own agenda, which is to whip up gossip and create FC Hollywood where it does not exist. Stories of player spats, disputes over post-match cycling sessions and so on. It may go against many informed opinions, but in spite of cringing a little I am still happy to stand beside Kalle and Uli.
Mark: It was definitely an attempt to take the heat off Kovac and a momentarily-misfiring team, yet it was ill-advised, embarrassing, pathetic, unbefitting a club of Bayern's stature. Anybody wanting to go into comedy, should watch the news conference closely for tips. Instead of being a show of strength, it exposed Bayern's current frailties and nervousness both on and off the pitch. Using "Abteilung Attacke" approach is nothing new but this might have been better timed after mighty Wolfsburg, AEK Athens (x2), Mainz and Rodlinghausen have all been disposed of. After six Bundesliga titles in succession, surely the hierarchy should have a thicker skin? After their struggles in recent seasons and with Hoeness and Rummenigge always ready to put the boot in on BVB; I expect Aki Watzke and co at Borussia Dortmund will have especially enjoyed the epic comic show. On the pitch, BVB have been empowered, taking strength from Bayern's bizarre show of weakness with their two strongest performances of the season against Atleti and VFB following. Bayern's game in Dortmund in two weeks time looms large.
Dennis: There is a German saying "Das Gegenteil von gut ist gut gemeint" (literally translated "The opposite of good is well-intentioned") that summarises it neatly. The initial intention (support coach and team) and the main people attacked (Springer Press) did make sense, but somehow the show got out of hand. The contrast of blaming Bernat and requesting respect for the Bayern players from the media was the most poignant image. The bosses disserviced themselves.
Marc: As the others have said, I think the reasoning was multifold; shift the attention of the media, show support for Kovac and the players and address some issues they've had with certain journalists. The method they chose to achieve this however was truly bizarre. The whole press conference felt like a meme that culminated in Uli's tirade on Bernat. Classically, he preceded this by admitting his choice of words when discussing Bellarabi and Ozil were poor, while in the same breath insulting them again. Regardless of the intentions, they presented themselves as petulant children who are not only crass but incapable of handling the current climate and criticism with the slightest amount of dignity. I expect more composure from the leaders of this club.
Our fourth question comes from @kingston_elenwo on twitter. "Given the relatively thin player count at fullback, do you think Bayern should be in the market for someone to challenge Alaba and Kimmich or merely a backup for them this season?"
Maurice: I don't think Bayern should or will invest in another fullback this season. There has been a poor track record for including players during a season, as they need quite some time to adapt to the new system. For next season, however, Bayern should definitely be on the lookout for an extra fullback.
Rick: I think it might be worthwhile looking at an option at left back, for two reasons. First, David Alaba is not as consistent as he used to be, and could do with a genuine challenger for the spot. Second, the Austrian has been prone to injury over the last couple of seasons. I do think an extra man is the answer, but a genuine challenger who can be used in a sensible squad rotation. We tried the "extra man" approach with Bernat, and that did not end well.
Mark: After the summer sales, the treasure chest is overflowing…reinforcements will definitely be on the way next summer. In their search for the next big thing, Bayern will be looking to be one step ahead of the PL elite, as they often were under Sammer / Reschke. You can expect Salihamidzic to have been ever so busy on Youtube, while head scout Laurent Busser (ex-Leverkusen) has obviously close links to the top French talent. Bayern very rarely buy during the winter break, Luis Gustavo from Hoffenheim was the last big purchase if I recall correctly during the last months of LVG's tenure. Don't forget (oh you have?) Marco Friedl is on loan at Werder Bremen and could return at some stage, while the likes of Chris Richards impressed at the ICC in the States. Who knows, maybe Kovac will switch Alphonso Davies to left-back (insert ironic smiley.)?
Dennis: Bayern is between a rock and a hard place here. When everyone knows your war chest is overflowing and you're in need, every possible transfer discussion will be very unpleasant. This is especially problematic given the left full-back position is one of, if not the position with the smallest pool of talent worldwide (just ask Jogi Löw). Without someone like Michael Reschke and his global net of scouting expertise I think Bayern's chances of finding a better replacement than Bernat are almost zero, which makes his departure even more bizarre.
Marc: There are very few scenarios in which I can imagine Bayern purchasing a full back in the winter. The integration issues, high prices and lack of availability seem insurmountable in the short term. Long term, I am of the opinion that a younger player that is capable of slotting in on both sides is probably the best option. What is really worrisome however, is that Rafinha's contract is also up at the end of the season. What is an undesirably thin position could become even more alarming if they are unable or do not want to bring him back.
In 10 competitive matches since the start of the Bundesliga season, Bayern have allowed 10 goals and have managed just 3 shutouts. Who is primarily to blame for this dismal defensive record? Kovac, the back line or Manuel Neuer?
Maurice: It is tough to single out one particular player and blame him as this was certainly a team "effort". The center backs, especially Boateng and Hummels, seem a step slower this year. Neuer has also been quite error-prone after returning from his injury. Furthermore the defensive stability has been off for quite some time now, especially on the left flank. This last area should be a major concern and therefore a big working point for Kovac.
Rick: I think we can look at Neuer for the Augsburg goal. Apart from that, it has been a mix of the backline and being susceptible to the fast break. Against Berlin, Boateng was at fault for both the penalty and living space open for the second goal. Against Gladbach, we were ripped apart. Even against Wolfsburg, Hummels was too slow and Kimmich was woefully out of position.
Mark: Despite the late gift to Augsburg which derailed Bayern's 100% winning start, any talk of Neuer's demise is very premature. Kimmich is devastatingly brilliant going forward, a fantastic crosser as well but is a very average defender when put under pressure. He could be better used in midfield (see Germany) but obviously due to the naive squad-planning Bayern are massively short of manpower in defence, especially when the inevitable injuries strike. Boateng and Hummels' bodies seem to be increasingly creaky with age, both will need to step up their game to shake off the challenge of the reliable new rock at the back Sule.
Dennis: Bayern continue to look weak in the moment of defensive transition. This has been an issue for a couple of seasons. Either by Guardiola's positional play and his Gegenpressing or by the world class performances of Boateng and Hummels, these issue were mostly under control. Currently the dip in form by the two centre backs in combination with the "open midfield" (created by the high positioning of the eights) is unable to close down the opponents. It's on Kovac to alter Bayern's play accordingly.
Marc: It would be very unfair to put Bayern's defensive woes on any one party. There have been a lot of mistakes in the build up play that have led to simple counter attacks for the opposition. All of the defenders and several of the midfielders have been prone to errors when put under pressure so far this season. This is something that should be correctable by Kovac and his team in practice. The midfield is culpable here as well. They have largely done a poor job of moving off the ball and making themselves available when the defenders are put under pressure.
Personally, I'm of the opinion that the criticisms of Neuer are way overblown. The one goal people legitimately point to is the one allowed against Augsburg, which to me was an aberration where his own player undercut him in his attempt to gather the ball. The bottom line is that Kovac has to work with the players on ball security and improve movement off the ball to create triangles and situations where they won't make so many mistakes. If they can do that while more effectively pressing the opposition, they will improve defensively
gnabry
hoeneß
kovac
rummenigge
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