text:
Mansour Hobeika (* 20. Dezember 1941 in Hadeth-Baalbek, Gouvernement Bekka, Libanon; † 28. Oktober 2014 in Paris) war Bischof der maronitischen Eparchie von Zahlé.

Leben
Mansour Hobeika studierte nach seinem Schulabschluss in Ghazir von 1962 bis 1968 Philosophie und Theologie an der Université Saint-Joseph in Beirut. Er erwarb Abschlüsse in Literaturwissenschaften, Psychologie und Philosophie sowie Theologie. Am 9. Juni 1968 empfing er die Priesterweihe. Anschließend studierte er Kirchenrecht am Istituto per l'Oriente Carlo Alfonso Nallino in Rom und wurde am Angelicum in Rom in Orientalischen Kanonischen Recht promoviert. Er lehrte an der libanesischen Universität La Sagesse, absolvierte einen Studiengang in Islamwissenschaften und sprach neben Arabisch auch Französisch, Italienisch, Deutsch und Englisch.

Im Alter von 60 Jahren, am 12. September 2002, wurde Mansour Hobeika durch Papst Johannes Paul II. zum Bischof von Zahlé ernannt. Die feierliche Bischofsweihe fand am 26. Oktober 2002 durch Kardinal Nasrallah Pierre Sfeir statt; Mitkonsekratoren waren die  Bischöfe Roland Aboujaoudé und Chucrallah Harb.

Quellen
 Who's who in Lebanon. 2005, S. 161
 Annuario pontificio. 2007, S. 827

Weblinks

Maronitischer Bischof
Kirchenrechtler
Hochschullehrer (Universität La Sagesse)
Libanese
Geboren 1941
Gestorben 2014
Mann


text:
\section{Introduction}
\label{intro}
The development of elastic and plastic strain is inherent to the problem of assembly of heterostructures, size effects in nanoscopic materials or thermal and mechanical solicitations of macroscopic materials. Since the discovery of strain induced self-assembly of nanowires and -dots \cite{shchukin}, enormous efforts, both theoretical and experimental, have been devoted to the progress in ``strain engineering''.

In particular, complex geometries of the substrate on which a crystal is deposited are now commonly used to produce highly ordered nanostructures. For example for the semiconductor technology, substrates that are patterned with Si(100) elongated pillars \cite{bergamaschini} are used to produce three-dimensional Ge epitaxial crystals. The resulting structure then depends crucially on the geometry of the substrate and especially on the distance between pillars, from tenth of nanometers to microns.
In the first part of the article we investigate theoretically the crystallization process in a confined geometry \cite{prl,prb} (for example in the inter-space between such pillars) with a lattice misfit between the crystal and the substrate, focussing on the nucleation regime.
Whereas the growth and coarsening under the influence of elastic and plastic effects has been investigated already for a long time (see \cite{BrenerMarchenko2000,BrenerHMK2001,BrenerMarchenko2007,BrenerBoussinot2009,FleckerHueter2010,SpatschekEidel2013} and references therein), their role on heterogeneous nucleation is still far less explored.
We use qualitative scaling arguments to produce a phase diagram giving the nature of the nucleation regime as a function of the crystallization driving force and the degree of confinement.
We complement our analytical study with amplitude equations simulations.

Nanowires, with their almost one-dimensional structure, are intriguing objects from a fundamental point of view, and are promising candidates for future industrial applications on the nanoscale.
Recently, we have elucidated the interplay between elastic and plastic effects on the equilibrium shape of nanowires \cite{boussinot}.
For any technological application, a long term stability of the nanowire is required and a deterioration through the Rayleigh-Plateau instability \cite{Plateau1873,Rayleigh1878,Karim2006} has been shown to exist as a result of surface energy minimization. On the other hand, already long ago, Eshelby found that a screw dislocation may be stabilized at the center of such a nanowire, leading eventually to a torsion of the whole structure, i.e. the Eshelby twist \cite{Eshelby1953}. Combined with Frank's mechanism for crystal growth from a screw dislocation, striking nanostructures are produced in the form of pine trees \cite{Bierman2008}.
We investigate theoretically the interplay between torsion and surface energy minimization in the second part of the article.

\section{Heterogeneous nucleation with lattice misfit in a confined geometry}

The nucleation of a crystalline phase occurs when its free energy density is lower than the one of the vapor (or liquid) phase. In the bulk of the vapor or liquid phase, homogeneous nucleation occurs. If the energy density (energy per unit volume) difference between the phases is $\mu$ and the surface energy of the crystal (energy per unit area) is $\gamma$, the critical nucleus has, according to the classical nucleation theory, a dimension $r^* \sim \gamma/\mu$ and the energy barrier that has to be overcome for the homogeneous nucleation event is $E^* \sim \gamma^3/\mu^2$.

In the presence of a substrate, heterogeneous nucleation occurs on the substrate when the adhesion energy of the nucleated crystal to the substrate is positive. This adhesion energy defines the truncation of the equilibrium shape of the crystal, obtained through the  Wulff construction, taking into account $\gamma_0$, the energy per unit area  of the crystal/substrate interface from which the energy per unit area of the substrate/vapor surface is subtracted. Due to the positive adhesion energy, the energy barrier for heterogeneous nucleation is lower than the energy barrier for homogeneous nucleation. Turnbull showed that their ratio only depends on the wetting angle of the crystal on the substrate \cite{turnbull}. We consider the case where this ratio of the energy barriers is of order unity, i.e. for a wetting angle of order unity.

Here we first study the scenario where the crystal/substrate interface is coherent. The coherency condition produces an elastic strain in the bulk of the crystal and the bulk of the substrate due to a small misfit $\epsilon$ between their lattice parameters.
We define a characteristic elastic energy density (energy per unit volume) $e_{el} = Y \epsilon^2$ where $Y$ is an elastic constant. From the interplay between surface energy and bulk elastic energy, a characteristic length scale arises, i.e. the elasto-capillary length $d=\gamma/e_{el}$.
It is reasonable to assume that $d_0 = \gamma_0/e_{el} < d$ (in many cases one even has $d_0 \ll d$).

At small sizes the misfit strain is relaxed through a continuous change of the shape of the crystal. However, above a critical size, the strain relaxation takes place through the appearance of misfit dislocations \cite{matthews,ertekin,glas}. The characteristic length scale associated to the misfit dislocation mechanism is $b/\epsilon$ where $b$ is the Burgers vector of the dislocations which is of the order of the atomic distance. The system then has a qualitatively different behaviour in the two cases $d \gg b/\epsilon$ and $d \ll b/\epsilon$.

In addition to the introduction of coherency strain effects and their plastic relaxation through the misfit dislocation mechanism, we are investigating the nucleation in a channel of width $H$ between two parallel substrates. This channel may represent the inter-space between pillars on a patterned substrate. $H$ may, in this respect, range from tenth of nanometer to microns and  we therefore consider a continuous macroscopic theory.
First we study the case where $H$ is infinite.
Then we study the influence of $H$ on the nucleation regime. We are interested finally in producing a diagram that predicts the nucleation mechanism as a function of the two parameters $\mu$ and $H$.

\subsection{The case $d \ll b/\epsilon$: Coherent crystal/substrate interface}
\label{sec:1}

In this section, we investigate the nucleation regime when the misfit dislocation mechanism is inhibited.

{\bf{The case $H \gg d$.}}
 It is known that the bulk elastic energy is efficiently relaxed when the coherent crystal elongates perpendicularly to the substrate \cite{muller}. In the extreme case when the volume of the crystal is much larger than $d^3$, the bulk elastic energy contributes significantly to the energy extremization. The crystal has a cylindrical shape with $r$ being the basal dimension of its interface with the substrate, and $h \gg r$ its height perpendicularly to the substrate.
In this case, the elastic energy density is of order $e_{el}$ in a region of volume $r^3$ in the neighborhood of the crystal/substrate interface, and vanishes in the rest of the system \cite{boussinot}. The energy of the system may thus be written:
 \be
 E = -\mu r^2 h + \gamma rh + e_{el} r^3
 \ee
where we neglect the contribution proportional to $r^2$ in the surface energy. The extremization of $E$ gives $r=r_\infty$ and $h=h_\infty$ such that
\bea\label{r_inf}
r_\infty \sim r^* \sim  \frac{e_{el}}{\mu}\; d \;\;\; ; \;\;\;h_\infty \sim r^* \frac{e_{el}}{\mu} \sim \left(\frac{e_{el}}{\mu}\right)^2 d ,
\eea
leading to an energy barrier
$
E_\infty \sim e_{el} d^3 \left(e_{el}/\mu\right)^3 \sim (e_{el}/\mu)  E^* $.
We see that the assumption $r_\infty/h_\infty \ll 1$ requires $\mu/e_{el} \ll 1$. In this regime, the energy barrier for coherent heterogeneous nucleation on the substrate is much larger than the energy barrier for homogeneous nucleation, i.e. $E_\infty \gg E^*$. Heterogeneous nucleation is thus inhibited in this regime. Instead homogeneous nucleation may happen as long as $H \gg r^*$.
When $d \ll H \ll r^*$, i.e. $1 \ll H/d \ll e_{el}/\mu$, homogeneous nucleation cannot take place and it is likely that the phase transition is inhibited.

In the case $\mu/e_{el} \gg 1$, the bulk elastic energy contributes only slightly to the energetics of the system. Therefore the shape of the critical nucleus is close to the one without elastic effects and the energy barrier for nucleation is only slightly corrected. The reduction of the energy barrier due to the positive adhesion energy is thus sufficient to promote coherent heterogeneous nucleation. A transition between heterogeneous nucleation and homogeneous nucleation therefore occurs when $\mu/e_{el} \sim 1$ in the case $H \gg d$.

To underline the above predictions for nucleation on a rigid substrate we use the amplitude equations model \cite{spatschek_karma} to simulate the heterogeneous nucleation process with a misfit strain $\epsilon$ for bcc structures.
\begin{figure}
\begin{center}
\includegraphics[width=320pt]{figure1}
\caption{Reconstructed atomic density from the amplitude equations for the critical nucleus having different lattice misfit $\epsilon$ with the rigid substrate. The crystal is constrained to have a tensile strain $\epsilon$ at the lower boundary of the simulation box. For each $\epsilon$, only a small part of the simulation box is displayed.}
\label{shapes}
\end{center}
\end{figure}
In Fig. \ref{shapes} we show the atomic density, reconstructed from the complex amplitudes. We choose a dimensionless undercooling of $(T_M-T)/T_M = 0.0008$, where $T$ is the temperature of the system and $T_M$ is the equilibrium temperature (we refer to Ref. \cite{spatschek_karma} for details of the model). At the crystal/substrate interface (the lower boundary of the simulation box), the crystal is in tension due to a lattice misfit $\epsilon=0, 0.04, 0.08, 0.12, 0.16$ with the rigid substrate.
Using several initial configurations, the critical nucleus is found, being the one that neither grows nor decays for an extended simulation time. For small $\epsilon$, the critical nucleus assumes a morphology that is close to the one obtained without elastic effects ($\epsilon=0$). When $\epsilon$ increases, the critical nucleus tends to elongate perpendicularly to the substrate, according to the qualitative picture given by Eq. (\ref{r_inf}).
The strain becomes more and more inhomogeneous in the crystal, and for $\epsilon=0.16$ one can clearly see in Fig.~\ref{shapes} the relaxation of the strain with increasing distance from the substrate.
One should note that for $\epsilon > 0.16$, no critical nucleus is found lying on the substrate, illustrating the transition from heterogeneous nucleation to homogeneous nucleation discussed qualitatively above.

{\bf{The case $H \ll d$.}}
 We investigate now a possible confined nucleation where the nucleus is coherently attached to both substrates and has a dimension $r \gg H$. We present in Fig. \ref{schema} a two dimensional cut of this confined nucleus.
\begin{figure}
\begin{center}
\includegraphics[width=240pt]{figure2}
\caption{\label{schema} Two dimensional cut of the confined nucleus with dimension $r \gg H$.}
\label{fig:1}
\end{center}
\end{figure}
In this confined geometry, the elastic energy density is mainly homogeneous in the crystal and vanishing in the substrate. There exists an intermediate elastic state in a region of volume $rH^2$ in the neighborhood of the crystal/vapor surface (in Fig. \ref{schema} it corresponds to a region of area $H^2$ in the neighborhood of the crystal/vapor surface). We however neglect this contribution.
This assumption is justified in the limit $r/H \to \infty$.

The energy of the system can thus be written as
\be\label{energy_conf}
E = -\mu r^2 H + \gamma rH + \gamma_0 r^2 + e_{el} r^2 H .
\ee
The extremization gives $r=r_c$ such that $r_c \sim d/x$
where $x=\mu/e_{el} - \left( 1 + d_0/H\right)$. The condition $x>0$ provides a threshold for $\mu$, i.e. $\mu > e_{el} + \gamma_0/H$. Here the shift of the transition point is therefore due to elastic effects \cite{brener_JETP} and to the geometrical confinement.
The dimension of the critical nucleus $r_c$ and the corresponding energy barrier $E_c \sim e_{el} d^2 H/x$ diverge when $x \ll 1$.
Here, the assumption $r_c \gg H$ requires $x \ll d/H$.
Using the assumption $d_0 < d$, we may then connect this confined solution to the heterogeneous nucleation solution when $x \sim \mu/e_{el} \sim d/H \gg 1$, i.e. $r_c \sim r^* \sim H$ and $E_c \sim E^* \sim e_{el} dH^2$.

{\bf{The case $H \sim d$.}}
In this case the heterogeneous nucleation process occurs when $\mu/e_{el} \gg 1$ since $r^* \ll d\sim H$. When $\mu/e_{el} \ll 1$, we have $r^* \gg H$ and the phase transition is inhibited (it may be seen as a continuation of the regime $1 \ll H/d \ll e_{el}/\mu$).
In the situation $H/d \sim \mu/e_{el} \sim 1$ homogeneous, heterogeneous and confined nucleation are competing.
The critical dimensions in these three regimes are of the order $H \sim d$.

As a summary we have the different cases listed below, which are represented schematically in Fig. \ref{diagram}:
\bea
1 \ll \frac{e_{el}}{\mu} \ll \frac{H}{d}   &\rightarrow& \mbox{ homogeneous nucleation} \nonumber \\
1  \ll \frac{H}{d} \ll \frac{e_{el}}{\mu}  &\rightarrow& \mbox{ no phase transition} \nonumber \\
\frac{e_{el}}{\mu}  \ll \frac{H}{d} \ll  1 &\rightarrow& \mbox{ heterogeneous nucleation} \nonumber \\
\frac{e_{el}}{\mu} \ll  1  \ll \frac{H}{d} &\rightarrow& \mbox{ heterogeneous nucleation}  \nonumber\\
\frac{H}{d} \ll \frac{e_{el}}{\mu} \ll  1 \;\;\mbox{ and } \;\;\frac{\mu}{e_{el}} > 1+\frac{d_0}{H}  \gg 1&\rightarrow& \mbox{ confined nucleation} \nonumber \\
\frac{H}{d} \ll \frac{e_{el}}{\mu} \ll  1 \;\;\mbox{ and } \;\; \frac{\mu}{e_{el}} < 1+\frac{d_0}{H}  &\rightarrow& \mbox{ no phase transition} \nonumber
\eea

\begin{figure
\begin{center}
\includegraphics[width=250pt]{figure3}
\caption{\label{diagram} Diagram giving the nature of the nucleation process with respect to the two variables $H/d$ and $\mu/e_{el}$ when no misfit dislocation mechanism is present ($d \ll b/\epsilon$). The details of this diagram in the neighborhood of $H/d \sim \mu/e_{el} \sim 1$ are system specific.
}
\end{center}
\end{figure}

\subsection{The case $b/\epsilon \ll d$: Misfit dislocation mechanism}

Another efficient path for a relaxation of the elastic strain is the misfit dislocation mechanism for which dislocations accumulate at the crystal/substrate interface. The length scale associated with this mechanism is $b/\epsilon$ where $b$ is the Burgers vector of the dislocations. When the smallest dimension of the crystal is larger than $b/\epsilon$, a regular array of misfit dislocations builds up and no elastic energy density exists at distances larger than $b/\epsilon$ from the crystal/substrate interface. On the other hand, the energy per unit area of the crystal/substrate interface effectively increases by an amount of order $Yb\epsilon \sim e_{el} b/\epsilon$.

When $b/\epsilon \gg d$, i.e. $Yb\epsilon \gg \gamma$, the analysis presented in the previous section is relevant because the radius of the critical nucleus $r^*$ is of order $b/\epsilon$ when $\mu/e_{el} \sim d/(b/\epsilon) \ll 1$. Since homogeneous nucleation is promoted in this regime, the dislocation mechanism does not play any role.
In the limit $\epsilon \ll 1$, we have the opposite case $d \gg b/\epsilon$. The diagram giving the nucleation regime as a function of $\mu$ and $H$ is then qualitatively changed.
However, no changes exist if $H \ll b/\epsilon$ or $r^* \ll b/\epsilon$, i.e $\mu/e_{el} \gg d/(b/\epsilon)$ because the smallest dimension of the crystal is then smaller than $b/\epsilon$.

{\bf Incoherent heterogeneous nucleation.}
When $H \gg r^* \gg b/\epsilon$, i.e. $d/H \ll \mu/e_{el} \ll d/(b/\epsilon)$, incoherent heterogeneous nucleation occurs. Since, in this case, the energetic cost of the dislocation array is much smaller than the surface energy of the crystal, the dimension of the critical nucleus and the energy barrier change only slightly in comparison to the coherent heterogeneous case. Therefore, when $\mu/e_{el}$ increases, there is a transition from the incoherent heterogeneous nucleation to the coherent heterogeneous nucleation for $\mu/e_{el} \sim d/(b/\epsilon)$, i.e. $r^* \sim b/\epsilon$.

{\bf Incoherent confined nucleation.}
When $r^* \gg H \gg  b/\epsilon$, incoherent heterogeneous nucleation is not possible. Instead, incoherent confined nucleation occurs.
The incoherent confined nucleus is described energetically by Eq. (\ref{energy_conf}) where $e_{el}$ is set to 0 and $\gamma_0$ is replaced by $\gamma_0 + Yb\epsilon$ where $Yb\epsilon$ is the energetic cost per unit area of the misfit dislocation array. The threshold for $\mu$ then reads  $x_{ic}=\mu/e_{el} - (d_0+b/\epsilon)/H >0$. The critical radius reads $r_{ic} \sim d/x_{ic}$
and the energy barrier becomes $E_{ic} \sim e_{el} d^2 H/x_{ic}$, i.e. $r_{ic} \sim \gamma/[\mu-(\gamma_0+Yb\epsilon)/H]$ and $E_{ic}\sim \gamma^2 H/[\mu-(\gamma_0+Yb\epsilon)/H]$.

By decreasing $H$, a transition from the incoherent confined nucleation to the coherent confined nucleation occurs when $H \sim b/\epsilon$. This transition takes place in the range $1+d_0/(b/\epsilon) < \mu/e_{el} < d/(b/\epsilon)$.

We summarize the different nucleation regimes as listed below in the case where $b/\epsilon \ll d$. Two cases should be considered:
\begin{enumerate}
\item
$H \ll b/\epsilon$
\bea
\mu/e_{el} \gg d/H &\to& \mbox{ coherent heterogeneous nucleation} \nonumber \\
1+ d_0/H < \mu/e_{el} \ll d/H &\to& \mbox{ coherent confined nucleation}  \nonumber \\
\mu/e_{el} < 1+ d_0/H  &\to& \mbox{ no phase transition}  \nonumber
\eea
\item
$H \gg b/\epsilon$
\bea
\mu/e_{el} \gg d/(b/\epsilon) &\to& \mbox{ coherent heterogeneous nucleation} \nonumber \\
d/H \ll \mu/e_{el} \ll d/(b/\epsilon) &\to& \mbox{ incoherent heterogeneous nucleation} \nonumber \\
(d_0+b/\epsilon)/H <  \mu/e_{el} \ll d/H &\to& \mbox{ incoherent confined nucleation} \nonumber \\
\mu/e_{el} < (d_0+b/\epsilon)/H  &\to&  \mbox{ no phase transition}  \nonumber
\eea
\end{enumerate}
These different regimes are represented schematically in Fig. \ref{diagram_inc_1}.

\begin{figure
\begin{center}
\includegraphics[width=250pt]{figure4}
\caption{\label{diagram_inc_1} Diagram giving the nature of the nucleation process with respect to the two variables $H/d$ and $\mu/e_{el}$ when $b/\epsilon \ll d$.}
\end{center}
\end{figure}

\subsection{Conclusion}
We have studied theoretically the influence of lattice misfit $\epsilon$ and of the confinement in a channel of width $H$ on the heterogeneous nucleation process. We have used scaling arguments to draw a phase diagram giving the nucleation regime as a function of $\mu/e_{el}$, the ratio of driving force $\mu$ and elastic energy density $e_{el}$, and $H$. Two regimes, with their corresponding phase diagram, have to be considered whether the misfit dislocation mechanism takes place or not.

In addition to the analytical qualitative investigations we have studied the critical nucleus when the height $H$ is infinite, using amplitude equations. The morphology of the critical nucleus agrees well with the qualitative analytical statements obtained using scaling laws, i.e. the critical nucleus elongates perpendicularly to the substrate when $\epsilon$ increases. Moreover, we found the transition from heterogeneous to homogeneous nucleation around $\epsilon=0.16$.
Beyond this point we are in the regime where the surface energy $\gamma$ is small enough to prohibit the dislocation entrance.

\section{Eshelby twist and Rayleigh-Plateau instability in nanowires}

Nanowires are structures with a typical diameter of less than 100 nm and a large aspect ratio from length to diameter of more than about 100.
These nanostructures can develop based on heterogeneous nucleation processes at a substrate, usually accelerated by catalytic processes.
Usually, they are produced via vapor-liquid-solid (VLS) growth, where a liquid catalyst is placed on a substrate, on which the nanowire grows from a supersaturated gas phase.
The gas atoms are absorbed by the interface layer between solid and melt, from which the growth proceeds.
The diameter of the nanowires is determined by the droplet size of the liquid catalyst.
Nanowires have many fascinating electronic and mechanical properties due to their almost one-dimensional structure.
Nanowires belong to the best controlled structures on the nanoscale.
As combination of p- and n-doped types they are promising candidates for various semiconductor applications like field effect transistors, diodes, LEDs, complex logical gates, lasers, sensors or solar cells \cite{Lieber2007,Bierman2009}.

For any technological application the long term stability of nanostructures is essential to guarantee functionality and to prevent the generation of ``nano-hazard''.
Here in particular the large surface-to-volume ratio can play an important role.
The reduction of surface energy can lead to morphological instabilities of the wire, which finally leads to the decomposition into droplets for long wave-perturbations, known as Rayleigh-Plateau instability \cite{Plateau1873,Rayleigh1878}.
This has been demonstrated experimentally for gold nanowires, which show the decomposition at rather low temperatures below 500$^\circ$C within a few hours \cite{Karim2006}.
On the other hand, this a priori detrimental development of an instability may be used on purpose e.g.~for thermoelectric purposes.
Here it has been noticed that the thermal conductivity can be reduced by a factor of about 100 for nanowires with a rough instead of a flat surface, which increases the thermoelectric efficiency substantially \cite{Martin2010}.

In this respect, pine tree nanowires may appear as an interesting nanostructure.
They have the special feature that they grow around an axial screw dislocation \cite{Bierman2008}.
By the adjustment of the gas partial pressures during the VLS growth pine tree nanowires can be grown in a very controlled way.
The presence of the screw dislocation induces a torsion of the wire, known as Eshelby twist, which stabilizes the defect in the center of the wire \cite{Eshelby1953}.
Since the dislocation additionally induces elastic stresses, a morphological instability can be substantially influenced by elastic effects \cite{Gugenberger2008,SpatschekFleck2007,SpatschekHartmann2006,BrenerSpatschek2003,SpatschekBrener2001}.
The combination of the Eshelby twist and surface stability is the subject of the following theoretical investigations.

\subsection{Eshelby twist}

In the following we assume isotropic linear elasticity, which means that stress and strain are related by Hooke's law, $\sigma_{ij} = 2\mu \epsilon_{ij} + \lambda \delta_{ij} \epsilon_{kk}$.
The strain $\epsilon_{ij}$ is obtained from the displacement field $u_i$ via $\epsilon_{ij}=(\partial_i u_j + \partial_j u_i)/2$.

Let us assume that the nanowire is aligned along the $z$ axis and has constant diameter $R_0$.
A screw dislocation with Burgers vector $b$ is pointing in $z$ direction, at a distance $x_0$ from the centre of the wire, see Fig.~\ref{wire::fig1a}.
\begin{figure}
\begin{center}
\includegraphics[trim=1cm 9cm 0cm 0cm, clip=true, width=10cm]{figure5.pdf}
\caption{Sketch of the geometry of a nanowire.
A straight screw dislocation is located at $x=x_0$, which is not visible in the left panel.
It shows a FEM discretized nanowire, which contains also a surface corrugation.
Parameters there are $L/R_0=10$, $\delta R/R_0=0.1$ and $kR_0=2\pi$.
We use here 60 nodes in a cross-section and 121 nodes in longitudinal direction.
The right panel is a cross section of the nanowire.
 }
\label{wire::fig1a}
\end{center}
\end{figure}

The displacement field reads
\begin{eqnarray}
u_x &=& -\tau y z, \qquad u_y = \tau x z,  \label{wire::eq1} \\
u_z &=& \frac{b}{2\pi} \left( \arctan \frac{y}{x-x_0} - \arctan \frac{y}{x-R_0^2/x_0} \right). \label{wire::eq3}
\end{eqnarray}
Here, $\tau$ is the torsion angle per length.
The $z$ component of the displacement field contains as first term the field of a screw dislocation located at $x=x_0, y=0$ in infinite space.
Since boundary conditions demand the absence of tractions on the wire boundary $r=R_0$ (in polar coordinates $r, \theta$), additionally the field of a ``mirror charge'' appears as second term in the expression.
This mirror term is not present in the singular limit $x_0=0$.

The elastic energy $E$ per unit length of the wire follows from integration of the elastic energy density $e=\sigma_{ij}\epsilon_{ij}/2$ as
\begin{equation}
E(x_0, \tau)/L = \frac{1}{4} \mu \tau^2 \pi R_0^4 + \frac{\mu b}{2} (R_0^2 - x_0^2)\tau + \frac{\mu b^2}{4\pi} \ln \frac{R_0^2-x_0^2}{R_0 r_0}.
\end{equation}
Here we have introduced a cutoff radius $r_0$ for the singular core of the screw dislocation.
This energy expression consists of three contributions:
The first term is the energy of the torsion, the last the energy of the screw dislocation, and the second term reflects a coupling between the defect and the torsion.
In particular, without twist, $\tau=0$, the energy is highest for $x_0=0$ and reduced if the dislocation moves closer to the perimeter.

So far, we have assumed the torsion angle to be given.
For a long wire with free ends it will adjust such that the energy is minimized, $dE/d\tau=0$.
From this follows the Eshelby twist
\begin{equation} \label{wire::eq5}
\tau(x_0) = - \frac{b}{\pi R_0^4}(R_0^2-x_0^2)
\end{equation}
and for the minimized energy
\begin{equation}
E(x_0)/L = \frac{\mu b^2}{4\pi} \left( \ln\frac{R_0^2-x_0^2}{R_0 r_0} - \frac{(R_0^2-x_0^2)^2}{R_0^4} \right).
\end{equation}
The energy as function of the dislocation position is sketched in Fig.~\ref{wire::fig1b}.
It is reduced in comparison to the case without a spontaneous twist.
\begin{figure}
\begin{center}
\includegraphics[width=8cm]{figure6.pdf}
\caption{Elastic energy per length for a cylindrical nanowire with screw dislocation as function of the position of the dislocation. The centre position $x_0=0$ is metastable.
The graph shows both the analytical theory and the results from finite element simulations, where we use an aspect ratio of $L/R=10$ and a dislocation core radius $r_0/R=0.05$. The wire is discretized by 100 nodes in the circular cross section and 11 nodes in longitudinal direction.}
\label{wire::fig1b}
\end{center}
\end{figure}
Eshelby has derived the same result using a torque balance instead of energy minimisation \cite{Eshelby1953}.
The result is surprising:
The energetic most favourable situation is a case without screw dislocation, as then the elastic energy is zero.
Nevertheless, the centre position $x_0=0$ is metastable, and therefore the dislocation can stay there without being pushed out of the wire by the interaction with the mirror dislocation.

\subsection{Torsion of nanowires with non-constant diameter}

In this section we investigate the interplay of torsion of the wire with the initial state of a Rayleigh-Plateau instability.
This instability is driven by a decay of interfacial energy.
Here, however, we will omit the discussion of interfacial contributions and focus on elastic effects, to highlight their role;
the usual interfacial terms can be added to the elastic terms in a straightforward way.
The nanowire is studied here in absence of a screw dislocation, which means that the torsion is imposed by torques acting at the opposite ends of the wire.
We use here an approximative treatment in the framework of the theory of torsion \cite{Landau1986}.
Due to the variation of the wire radius, $R=R(z)$, the absolute torsion angle $\phi$ becomes $z$ dependent.
This angle is related to the torsion per length by $\tau=\phi'(z)$, and intuitively the torsion $\tau$ is larger in the thinner regions of the wire.

The elastic energy of the torsion is given by \cite{Landau1986}
\begin{equation}
E = \frac{1}{2} \int_0^L C(z) [\phi'(z)]^2 dz + E_{ext}
\end{equation}
with the length of the wire $L$ and the external work $E_{ext}$ due to the torques, which are assumed to act only at the faces at $z=0$ and $z=L$.
Here the torsion resistance $C(z)$ is given by
\begin{equation}
C(z) = 4\mu \int (\nabla\chi)^2 df
\end{equation}
which consists of an integral in the plane $z=const$.
The function $\chi$ has to fulfill a Laplace equation, $\nabla^2\chi=0$, inside the wire plane and vanishes on the stress free surfaces, $\chi=0$.
For a cylinder with radius $R(z)$ the solution is
\begin{equation}
C(z) = \frac{\mu\pi R^4(z)}{2}.
\end{equation}
Mechanical equilibrium demands the minimization of energy with respect to the torsion $\phi(z)$.
The variation of energy gives
\begin{equation}
\delta E = - \int_0^L \frac{d}{dz} \left( C(z)\frac{d\phi}{dz} \right) \delta\phi\,dz + \delta E_{ext} = 0,
\end{equation}
where the variation $\delta\phi$ is assumed to vanish at the ends, $\delta\phi(0)=\delta\phi(L)=0$.
Since the external forces act only at the ends, they do not contribute to the bulk variation, and we obtain the generalised torsion condition
\begin{equation}
\frac{d}{dz} \left( C(z)\frac{d\phi}{dz} \right) = 0.
\end{equation}
We therefore get
\begin{equation}
\phi'(z) = C_0 R^{-4}(z),
\end{equation}
in agreement with the expectation that the torsion is larger in the regions with lower diameter.
The integration constant $C_0$ follows from the given total rotation $\phi(0)=0$ and $\phi(L)=\alpha$,
\begin{equation}
C_0 = \alpha \left( \int_0^L R^{-4}(z) dz \right)^{-1}.
\end{equation}
For a sinusoidal perturbation
\begin{equation} \label{wire::eq14}
R(z) = R_0 + \delta R \cos(kz)
\end{equation}
we obtain for the energy
\begin{equation}
E = \frac{\mu\pi \alpha^2}{2}  \frac{\big(R_0^2 - (\delta R)^2\big)^{7/2} }{\big(3 (\delta R)^2 + 2 R_0^2\big) R_0 L}.
\end{equation}
Apparently, the energy vanishes for complete necking, $\delta R=R_0$.
Noticeable, the torsion energy does not depend on the wavelength of the perturbation.
For a small perturbation, $\delta R\ll R_0$, we get in the framework of the torsion theory
\begin{equation} \label{wire::eq16}
E = \frac{1}{4}\mu\pi\alpha^2\left(\frac{R_0^4}{L}-\frac{5 R_0^2}{L}(\delta R)^2\right) + O[(\delta R)^4].
\end{equation}
Apparently, the first term corresponds to the energy of torsion without perturbation.
The second term lowers the energy as a precursor of necking.
Notice that so far interfacial effects are not taken into account in the above expression;
the torsion itself therefore supports the decay into droplets via the curvature driven Rayleigh-Plateau instability.

Finally, up to first order in $\delta R$ the torsion is
\begin{equation} \label{wire::eq17}
\tau(z) = \frac{\alpha}{L} \left( 1 - 4\frac{\delta R}{R_0} \cos kz \right).
\end{equation}

\subsection{Pine-tree nanowires with non-constant diameter}

Here we additionally consider the presence of the screw dislocation in the wire, in combination with a perturbation of the radius, to analyze the interplay between the Eshelby twist and the Rayleigh-Plateau instability.
This problem is treated here in perturbation theory, in a similar spirit as for core-shell nanowires \cite{Wang2008,Schmidt2008}.
The elastic problem is solved via Papkovich-Neuber potentials, and we restrict the analysis to the special case $x_0=0$, i.e. the screw dislocation is sitting in the centre of the nanowire.
More general cases will be discussed below using numerical computations.
Since the calculations are lengthy, we only give essential steps and the final result.

The displacement field is written as
\begin{eqnarray}
\vec{u} &=& 4(1-\nu)\vec{\Psi}-\nabla(\vec{r}\cdot\vec{\Psi} + \Phi), \\
\nabla^2\vec{\Psi} &=& 0, \qquad \nabla^2 \Phi = 0
\end{eqnarray}
with the Poisson ratio $\nu$.

To zeroth order, the fields are given as those of a cylindrical nanowire (constant radius) with a screw dislocation in its centre.
From the above expressions (\ref{wire::eq1}), (\ref{wire::eq3}) follows the stress field in cylindrical coordinates to zeroth order (denoted by the superscript) as
\begin{equation}
\sigma_{rr}^0 =
\sigma_{\theta\theta}^0 =
\sigma_{zz}^0 =
\sigma_{\theta r}^0 =
\sigma_{rz}^0 = 0,\qquad
\sigma_{\theta z}^0 = \frac{1}{2}\frac{\mu b}{\pi r} - \frac{\mu b r}{\pi R_0^2},
\end{equation}
where we used the equilibrium twist according to Eq.~(\ref{wire::eq5}) for $x_0=0$.

Since the main goal is to calculate the elastic energy, which contains the first nontrivial contribution at order $(\delta R)^2$, we determine also the elastic fields up to second order.
For that, the Papkovich-Neuber potentials are written as
\begin{eqnarray}
\Phi(r,z) &=& c_1 I_0(kr)\cos(kz), \\
\Psi_r(r,z) &=& c_2 I_1(kr) \cos(kz), \qquad \Psi_z(r,z) = 0, \\
\Psi_{\theta}(r,z) &=& c_3 I_1(kr) \sin(kz) +
c_4 I_1(2kr) \sin(2kz) + c_5 I_1(2kr) \cos(2kz),
\end{eqnarray}
with the modified Bessel functions of first kind $I_n$.
The terms involving $2k$ correspond to the second order contributions.
In the end, it turns out that only the first order terms contribute to the elastic energy up to second order.

The coefficients $c_i$ are determined by the stress free boundary conditions at the perimeter of the wire, $\sigma_{ij}n_j=0$.
We obtain for the first order expansion coefficients
\begin{equation}
c_1 = 0,\qquad c_2 =0,\qquad c_3= \frac{b\delta R}{8\pi R_0 (\nu - 1)}\frac{1}{I_2(kR_0)}.
\end{equation}
Based on this, also the second order coefficients $c_4$ and $c_5$ can be obtained from the boundary conditions, resulting in lengthy expressions.
Finally, the elastic energy can be calculated from these fields, and it is compared for particular cases in the next section with finite element simulation data.

We can also compare the results from this rigorous perturbation theory with the torsion method from the previous section.
For that, we consider the special case $b=0$, i.e.~the absence of the screw dislocation, and instead a twist which is imposed by an external torque.
First, using the Papkovich-Neuber potentials we obtain for the twist the expression (\ref{wire::eq17}), using the representation $u_\theta=r\phi(z)$.
Next, the stress fields in the framework of the torsion approximation are
\begin{eqnarray}
\sigma_{rr} &=& \sigma_{\theta\theta} = \sigma_{zz} = \sigma_{r\theta} = \sigma_{rz} = 0,\\
\sigma_{z\theta} &=& \mu\tau(z) r = \mu r \frac{\alpha}{L}\left(1-4\frac{\delta R}{R_0}\cos(kz)\right).
\end{eqnarray}
with only one non-vanishing component.
From the rigorous perturbation theory we get
\begin{eqnarray}
\sigma_{rr} &=& \sigma_{\theta\theta} = \sigma_{zz} = \sigma_{rz} = 0, \\
\sigma_{r\theta} &=& -\mu kR_0\tau \frac{I_2(kr)}{I_2(kR_0)}\sin(kz)\delta R, \\
\sigma_{z\theta} &=& \mu\tau r -\mu kR_0\tau\frac{I_1(kr)}{I_2(kR_0)}\cos(kz)\delta R \approx \mu r \frac{\alpha}{L}\left(1-4\frac{\delta R}{R_0}\cos(kz)\right),
\end{eqnarray}
where in the last step we used the long wave limit $k R_0\ll 1$, thus $I_1(x)\simeq x/2$ and $I_2(x)\simeq x^2/8$.
Hence in this limit the stress field agrees with the torsion approximation in all components apart from $\sigma_{r\theta}$.
Since this shear component also enters into the expression for the elastic energy, we get from the perturbation theory an expression, which slightly differs from Eq.~(\ref{wire::eq16}),
\begin{equation}
E = \frac{1}{4}\mu\pi\alpha^2\left(\frac{R_0^4}{L}-\frac{5 R_0^2}{9L}(\delta R)^2\right) + O[(\delta R)^4].
\end{equation}
We can therefore conclude that the torsion approximation gives qualitatively a correct description, but does not accurately describe the energy of the perturbation.
It is nevertheless useful in particular since it is easy to obtain and works also beyond the limit of small perturbations of the wire diameter, even predicting the necking transition correctly.

\subsection{Finite element modelling of pine-tree nanowires}

A complete analytical treatment of a nanowire with screw dislocation and surface corrugation is not possible if the dislocation line is not in the centre, $x_0\neq 0$.
We therefore use a finite element implementation based on FreeFEM++ to solve the problem numerically \cite{freefem}.

To avoid the appearance of the displacement discontinuity of the dislocation in the weak formulation of the elastic problem we separate this part and treat it analytically.
Hence we write $u_i=u_i^0 + \delta u_i$, where the field $u_i^0$ contains the part described by Eqs.~(\ref{wire::eq1}) and (\ref{wire::eq3}).
From this, the fields $\epsilon_{ij}^0$ are derived from the definition of the strain and $\sigma_{ij}^0$ from Hooke's law.
The weak form of the static elastic equation $\partial\sigma_{ij}/\partial x_j=0$ becomes then after multiplication with a test function $v_i$ and integration over the volume $V$ of the wire
\begin{equation}
\int\limits_V \delta\sigma_{ij} w_{ij} dV + \int\limits_{\partial V_\mathrm{jacket}} \sigma_{in}^0 v_i dS - \int\limits_{\partial V_\mathrm{down}} \delta\sigma_{in}v_i dS + \int\limits_{\partial V_\mathrm{up}} \sigma_{in}^0 v_i dS = 0,
\end{equation}
where we used Gauss' theorem and defined $w_{ij}=(\partial_j v_i+\partial_i v_j)/2$.
We fix here the displacement on the lower surface but let the upper one stress free, such that the Eshelby twist can develop.
The surface $\partial V$ splits into the jacket, $r=R(z)$, upper surface $z=L$ and lower surface $z=0$.
In the bulk, the dislocation core region $(x-x_0)^2+y^2<r_0^2$ is omitted from the volume integral.

Fig.~\ref{wire::fig1b} shows the result of FEM simulations for a nanowire with constant diameter and a straight screw dislocation inside.
With free ends, the wire forms the Eshelby twist as predicted theoretically, and the plot shows the relaxed elastic energy in comparison with the theoretical prediction, demonstrating a good agreement between both of them.

For an additional surface corrugation, $R=R(z)$, the nanowire is discretised appropriately as shown in Fig.~\ref{wire::fig1a}.
The elastic energy as function of the perturbation amplitude $\delta R/R_0$ is shown in the left panel of Fig.~\ref{wire::fig3} using the analytical expression obtained from the perturbation theory for $x_0=0$.
\begin{figure}
\begin{center}
\includegraphics[width=6cm]{figure7a.pdf}
\includegraphics[width=6cm]{figure7b.pdf}
\caption{Left: Comparison of the elastic energy for a nanowire with perturbed surface, using perturbation theory for $x_0=0$ and two different offset positions using FEM simulations. We use $r_0/R_0=0.05$, $L/R_0=10$, $kR_0=2\pi$ and a discretisation of $60\times 121$ nodes.
Right: Elastic energy as function of the dislocation core position with ($\delta R/R_0=0.1$) and without perturbation ($\delta R/R_0=0$), for the same parameters as above and a $150\times 101$ mesh.
}
\label{wire::fig3}
\end{center}
\end{figure}
It is compared to numerical results for two different positions $x_0$ of the screw dislocation.
At low amplitudes $\delta R/R_0\ll 1$ we find very good agreement between theory and the FEM results.
At larger amplitudes, the decay of the elastic energy is weaker than predicted by perturbation theory.
The dependence of the energy on the position of the screw dislocation is rather weak, in agreement with the knowledge that the centre position $x_0=0$ is a metastable minimum, and therefore changes are only quadratic in $x_0$.
The right panel of Fig.~\ref{wire::fig3} compares the elastic energy of the pine tree nanowire as function of the dislocation position $x_0$ for a situation with and without perturbation.
Here we see that the general structure of the energy landscape does not change by the perturbation, i.e.~the centre position $x_0=0$ remains metastable, but the energy is lowered by the perturbation, which promotes the capillary-driven Rayleigh-Plateau instability.

\subsection{Amplitude equations modelling of pine tree nanowires}

In the descriptions above we focused exclusively on static situations and used the energy to distinguish between stable, metastable and unstable configurations.
In this section we show how the concept of amplitude equations can be used to get insights also into the dynamics of pine tree nanowires.
Here we are interested in particular in the dynamics of the dislocation and the formation of the twist in the nanowire.

Since this -- also in conjunction with the Rayleigh-Plateau instability -- is an interfacial pattern formation problem, the use of phase field methods is suggested.
However, a conventional phase field model may be able to capture elastic effects and defects like cracks \cite{SpatschekHartmann2006,Spatschek11,FleckPilipenk2011,SpatschekBrener2008,Nestler2007}, but a proper representation of dislocations calls for a description using atomic resolution.
Here, during the past years the amplitude equations methods, which can be derived from phase field crystal or classical density functional theory descriptions, have turned out to be useful, and shall therefore be used also for the modelling of pine tree nanowires.
For a thorough introduction into this modelling technique we refer to \cite{spatschek_karma,kar13,Adland:2013ys}.

For the simulations we embed the wire
into a liquid or vapour phase.
Since at the bulk coexistence point the wire would ``melt'' due to curvature effects, we either have to lower the temperature to stabilise it (we use a Lagrange multiplier to conserve the amount of the solid phase), or we embed the wire into an inhomogeneous temperature field, which is below the melting point inside the wire and above outside.
We use both methods, which both have the advantage that the wire can elastically deform, as the surrounding liquid phase does not support stresses, and therefore the surfaces of the wire are traction free.
As a result, the Eshelby twist builds up in order to minimise the elastic energy, and this is shown in Fig. \ref{wire::fig4}.
\begin{figure}
\begin{center}
\includegraphics[trim=10cm 0cm 10cm 0cm, clip=true, width=5cm]{figure8.png}
\caption{Amplitude equations model of a pine tree nanowire. The atomic positions are reconstructed from the amplitudes.
Different colour coding is used for two atomic layers, which are separated by a few lattice units. The upper layer (blue) is rotated clockwise against the lower layer (red) due to the Eshelby twist.}
\label{wire::fig4}
\end{center}
\end{figure}

We can consider also a case where the wire is clamped at its end, and then the Eshelby twist cannot develop.
In this case, the centre position for the dislocation $x_0=0$ is no longer metastable but a maximum of the energy, and therefore a dislocation always drifts out of the wire.
In the amplitude equations model the dislocations are mobile, and this is illustrated in Fig.~\ref{wire::fig5}, which shows how the dislocation is ejected from the nanowire to minimize the elastic energy.
\begin{figure}
\begin{center}
\includegraphics[trim=14cm 6cm 14cm 6cm, clip=true, width=4cm]{figure9a.png}
\includegraphics[trim=14cm 7cm 14cm 5cm, clip=true, width=4cm]{figure9b.png}
\includegraphics[trim=14cm 6cm 14cm 6cm, clip=true, width=4cm]{figure9c.png}
\caption{Amplitude equations modelling of a pine tree nanowire with fixed ends at $x=0$ and $x=L$, hence the Eshelby twist cannot develop. Then the dislocation does not have a metastable position at $x_0=0$ and therefore drifts out of the wire. The figures show cross sections of snapshots of the temporal evolution. Initially, the screw dislocation is located in the centre and then diffuses out of the wire.}
\label{wire::fig5}
\end{center}
\end{figure}

\section{Conclusion}

We have studied theoretically elastic and plastic effects on heterogeneous nucleation and nanowire formation. In the first part of the article, we have investigated the nucleation of a crystalline phase in a confined geometry between two parallel substrates having a lattice misfit with the crystal. We use scaling laws for the elastic energy of the system that are allowing to describe analytically the different nucleation regimes as a function of the thermodynamic driving force for nucleation and the degree of confinement.
From that, we have predicted the corresponding phase diagrams. In the case of no confinement, we have complemented this analytical study with amplitude equations simulations that are supporting the qualitative statements derived from scaling laws, and especially the elongation of the critical nucleus perpendicularly to the substrate with increasing lattice misfit.

In the second part of the article, we have studied the interplay between Eshelby twist and the Rayleigh-Plateau instability in nanowires. We show  analytically that the torsion, inherited from the presence of the screw dislocation in Eshelby's investigation, promotes the undulation of the surface of the nanowire.
In particular, our analytics predict the necking transition of the nanowire, i.e. the decay of the nanowire into separate droplets driven by elastic effects alone, also with an externally applied torque. We show moreover that the finite-element method and amplitude equations of the phase-field crystal model are efficient numerical tools to tackle this problem.

The authors acknowledge support by the DFG priority program SPP 1296.

redpajama_set_name: RedPajamaArXiv


text:
J.K. Rowling Outed as Secret Writer of Crime Novel
"The Cuckoo's Calling" shot up to no. 1 on Amazon after the "Harry Potter" author's role was revealed.
More Stories by Associated Press
Club Q Shooting Suspect Charged With Hate Crimes
Nick Bollettieri, Tennis Coach Who Worked With Andre Agassi and Other Stars, Dies at 91
Walmart Store Shooting Leaves Six People Dead
J.K. Rowling's (Neil Blair, Kleinberg Lopez) first post-"Harry Potter" novel, "The Casual Vacancy," will be adapted by the BBC as a series.
LONDON (AP) — An ex-military man tries his hand at writing, publishes a debut detective novel, and wins critical acclaim. But here's the twist in the tale: The true identity of the author is none other than Harry Potter creator J.K. Rowling.
After Rowling confirmed that she was the author of the The Cuckoo's Calling, the book skyrocketed to no. 1 on Amazon's sales chart. It had been just no. 166,836 before the news broke.
It's impressive literary wizardry by Rowling, who said she relished the freedom of writing the novel under the pseudonym Robert Galbraith.
"I hoped to keep this secret a little longer because being Robert Galbraith has been such a liberating experience," she said in a statement released by her publicist on Sunday. "It has been wonderful to publish without hype or expectation, and pure pleasure to get feedback from publishers and readers under a different name."
STORY: BBC to Turn J.K. Rowling's 'The Casual Vacancy' Into TV Series
The Cuckoo's Calling, a story about a war veteran turned private investigator who is called in to probe the mysterious death of a model, was published to rave reviews in April by Sphere, part of publisher Little, Brown & Co.
The Sunday Times claimed it was investigating "how a first-time author with a background in the army and the civilian security industry could write such an assured debut novel" when it connected the dots. The paper said clues included the fact that Rowling and Galbraith shared the same agent and editor, and that Little, Brown published Rowling's novel for adults, The Casual Vacancy. It also said the book's style and subject matter resembled Rowling's work.
In her statement, Rowling thanked her editor David Shelley, the publishing staff who worked on the book without knowing her identity, and the reviewers who praised it without knowing about her authorship.
She added that "Galbraith" planned to keep writing the series, and her publisher said that the second book is expected to be published next summer. Now that her identity is revealed, Little, Brown said The Cuckoo's Calling will be reprinted with a revised author biography.
On its website, the publisher marketed the book as a classic crime novel in the tradition of P.D. James and Ruth Rendell. It said the novel, whose central character is named Cormoran Strike, was the first of a series of crime novels to come.
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The publisher lists many favorable reviews to the book, including critics who called it "a scintillating debut novel" and who praised Galbraith for his "superb flair as a mystery writer."
Rowling recently turned to writing for grown-ups after becoming the world's most successful living writer with the Harry Potter books, which sold more than 450 million copies worldwide.
Reviews for her highly-anticipated novel The Casual Vacancy, published last year, were mixed. Some praised the book, a bleak tale about class warfare and the darker sides to a community in small-town England, for tackling difficult subjects, but others thought it lacked the magic touch that made Rowling's books of wizardry so popular.
Hollywood Not Wild for New J.K. Rowling Book 'The Casual Vacancy'
Up All Night Mya Rudolph Rachel Dratch - P 2012
Stars at Wimbledon: J.K. Rowling, Matthew Morrison, Pippa Middleton Among Fans at the Tournament
J.K. Rowling Renews Call for U.K. Press Regulation
Penske Media Corporation
Penske Media Eldridge Acquires Dick Clark Productions
Marilyn Manson Settles Sexual Assault Suit Brought by Esmé Bianco
Penske Media Taps Hannah Woodard as Senior Director of Communications
Elon Musk's Twitter Bows to India Request to Censor Links to BBC's Narendra Modi Doc
10 Killed in Monterey Park Mass Shooting Near Lunar New Year Fest; Suspect Dies of Self-Inflicted Gunshot Wound
Lisa Marie Presley Remembered During Graceland Memorial Service

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text:
Streetside Classics - Nashville
Sedan Car for sale by Streetside Classics - Nashville in LaVergne, Tennessee 37086
6000 Reliance Dr
LaVergne, TN 37086
Hi, I am interested in your 1995 BMW 525i (stock #1376-NSH) listed on Autotrader for $8,995. I'd like to get more information about this vehicle and confirm its availability.
A Roundup of the Best New Cars Revealed at Pebble Beach
After an 18-year hiatus, BMW has revived the 8 Series name with the BMW Concept 8 Series. The automaker's new flagship model could help the manufacturer compete against Mercedes-Benz, which overtook BMW last year as the world's largest luxury automaker.
The third-generation BMW 5-Series is that perfect grand touring sedan that combines modern driving appeal with a growing collector car status. So, this nicely maintained and quite affordable 1995 BMW 525i is sure to be on the short list of European car fans everywhere. Upgraded with one of the most reliable powertrains ever made by the volks behind the Ultimate Driving Machine, this Bimmer is a very special sport sedan. As you look at the details up close youll see a few flaws, after all this fivers been enjoyed, but take it all in and it becomes clear that this is a premium sedan for those who like to both collect and drive. The black rubber rub strips are still dark and pliable, and they provide a nice separation line for the lower red paint. An M-sport badge on the hood suggests that theres a monster that lies within, and other than the BMW roundel on the decklid, the slick red sedan is bereft of any badging or decals. And we love the streamlined look. Plus, the AC Schnitzer 17-inch alloys give the car distinction without looking out of place. This executive-level sedan still wears its BMW heritage with pride, which is exactly why it still commands respect on arrival. The 5-Series offers plenty of room for passenger front and rear, which is why these powerful cars have always been so popular. But because BMW makes the Ultimate Driving Machine, that means they focus all the important pieces around you. This restored-to-stock interior boasts some of the eras most comfortable bucket seats, and they are power adjustable to strike the perfect balance for grand touring comfort. The factory wheel engineered to give you a clear view at the full gauge package and the short-shifter with ZHP shift knob is exactly where you always want to rest your right hand. And as a premium vehicle, BMWs engineers expertly worked to make sure that it was luxurious without being distracting. You are always just a short reach away from features like the power windows, power locks, a power sunroof, and cold factory air conditioning. The stereo has been upgraded to an AM/FM/CD stereo unit that send tunes through a subwoofer installed in the very spacious trunk. Under the hood appears to be an exceptionally stock looking engine bay, which is exactly what the pros that dropped in the S52 had in mind. Along with the 5-speed manual transmission, the 3.2L that now fits snugly in the clean engine bay of this 5-series was donated from a 1999 M3. It marries up perfectly with its new host, and many find the S52 to be at the top of the list in the long line of famous inline-six engines at the bedrock of BMWs premium and sporting reputation. But this superior status doesnt just come from the motor. The fully-independent suspension has been engineered to be one of the best of the era and has been almost completely updated/maintained and features a 2-inch spring drop and Bilstein Sport shocks. Plus, grip is always in hand with the four-wheel disc brake package and modern high-performance tires. Add in great long-distance features like the 5-speed manual transmission, power steering, and cruise control, and you have a total package modern classic thats fun to drive near or far. Complete with an extensive write-up of the full build and maintenance over the last several years, we bet you never knew a status symbol like this could be so affordable. But youre not the only one who desires the best from BMW, so dont miss out. Call today!!!
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As this our vacation day, the Dōgo Onsen is a priority. This hot spring is said to be Japan's oldest with 3,000 year history and is the most well known bath houses in all of Japan. Unfortunately it is being renovated and only one small hot bath was available for women. None the less, we felt the magic of being there. How nice to share this bit of history with Christine.
How do you top this off? Sushi for lunch.


text:
Ariunbold Naranbat, né le , est un coureur cycliste mongol. En 2010, il représente la Mongolie lors des championnats du monde de cyclo-cross. Il abandonne au même titre que son compatriote Boldbaatar Bold-Erdene.

Palmarès sur route

Par années
 2005
  du championnat de Mongolie sur route
 2006
  du championnat de Mongolie sur route
 2009
 Khuregchid-Eregtey

Classements mondiaux

Palmarès en VTT
 2005
  du championnat de Mongolie de cross-country

Notes et références

Liens externes

Naissance en mai 1980
Coureur cycliste mongol
Cyclo-crossman mongol

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text:
Q: Mathematical problems reducing to the traveling salesman problem The superpermutation problem is: what is the shortest word that contains every permutation of $k$ letters as a substring. This can phrased as a Travelling Salesman Problem, where the nodes of your graph are permutations, and the weight of edges correspond to the number of letters it takes to go from one permutation to another.
I have done some work on the above problem, and came up with some interesting ideas to get lower bounds. I am eager to try applying my methods on other graphs, and am trying to find significant, or at least not completely unmotivated, candidates.
So, my question is: what other mathematically interesting problems are concerned with finding lower bounds for the shortest weighted path in a (graph/family of graphs)?

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text:
Roger Federer on His New Gig: Swiss Tourism Spokesman
Tell us about some of the Swiss tennis clubs where visitors can have a great meal and play some tennis.
When you come back to Switzerland from abroad, what are the Swiss dishes or treats you crave? And if that includes chocolate, are you more of a milk chocolate guy or a dark chocolate guy?
Play the role of travel agent for us. Where should we go if we have a week or two in your country?
I love to walk through small villages where life is still normal. Small places where people are driving tractors and there is one baker, one church. The people in these places aren't multitasking. They go about their days in a normal way. Someone shows up and they want to know, "Hey, what brought you here?" It's very friendly, so you can always have a chat with people.
Tennis club life in Switzerland is important. This is how I grew up. There are many scenic places where you can play tennis in Switzerland. Tennis Club Geneva, where the Geneva Open tournament is played is very beautiful. Tennis Club de Genève Eaux-Vives is also really nice. The clubs in Basel where I played growing up in the Interclub competition are quite nice.
There was a boom building tennis clubs when I was growing up, so every second village has its own club. We have to protect this tennis culture we have. The restaurants at the tennis clubs are very important. A lot of the clubs where I've played, they have really good chefs, really good service and very high quality. People spent a lot of their time at the clubs, so the food has to be good and it's usually at a good price, too.
I mean, chocolate, hello, you have to love chocolate if you're Swiss. I used to be white, then I was milk, and now I even like going dark. I like it all. Then I like the Bündner Nusstorte, which is like a nut tart from the region of Graubünden. That's beautiful. And then, of course, there's rösti, a potato fritter dish. We have a dish called Zürcher Geschnetzeltes that's like minced meat with a mushroom sauce, and I love to eat cordon bleu — that's beautiful, too.
Fly into Zurich or Geneva and go from there. In the summer, I think you would want to visit Lucerne and Interlaken and maybe visit the Jungfrau, Basel, Zurich, Bern, the capital — its inner city is also really beautiful. We also have some incredible museums in Switzerland. The Fondation Beyeler art museum is great. I grew up visiting the Tinguely Museum, which is very interesting.
In Lucerne, there is the Swiss Museum of Transport, which is still my favorite place to take my children. It's a wonderful place where you can see old trams, trains, planes, cars, bikes, you name it.
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Luxury Tag Heuer Replica Watches – Best Swiss Fake Watches UK ®
Category: Watch
The Most Popular Replica Panerai L'Astronomo Luminor 1950 in 2018
Posted OnSeptember 3, 2018 , By
Generally speaking, the latest big releases from Panerai happened to come in the paradoxical form of the brand's smallest fake watch ever, a simple automatic Luminor that measures 38mm across, and an update at its entry level Luminor Base Logo. However, if you know something about Panerai, you know the brand always makes a point of presenting a talking piece or two at SIHH. What we have here is a 50mm tourbillon with displays for the equation of time, a second time zone, and, for the first time ever in a Panerai, the phases of the moon.
Actually, this is not the first time that the replica Panerai watches has combined this tourbillon with an equation of time display. That replica watch was manufactured on the occasion of the 400th anniversary Galileo's celestial observations made as a result of the invention of the telescope. The real defining factors of this year's L'Astronomo are the fact that the movement is now skeletonized and that an interesting moonphase display has been included on the rear side of the movement. The earlier version came with a closed dial and a sky map on its back.
As you can see, it's a totally modern interpretation of a skeletonized movement, which comes in handy visually because it allows an open look onto the many, and I mean many, displays to be found on this watch's front and back. The movement alone comprises some 451 components.
The dial of this replica watch – actually "dials" of this replica watch – effectively are the movement, front and back. Beginning from the central axis, we see the hours and the minutes, as well as a GMT hand. Just below the axis is a linear scale that shows the difference between solar time and mean solar time, according to the equation of time.
At the same time, the back of the dial is fitted with a twist on the traditional moon phase display. The upper disk is a day/night indicator that performs one rotation every 24 hours and clearly shows the day as a radiant sun and the night as a starry sky.
I've never had a wristwatch that's 50mm in diameter, and to be honest, it's difficult to imagine someone wearing a cheap replica watch this large on a regular basis. The case material can be customized when ordering this watch, so a lightweight titanium version seems like it would make the most sense, from a purely ergonomic standpoint. But steel and precious-metal options are available for those who might want them. The color of the hands and the choice of strap are also subject to customization.
Luxury Replica Rolex Double Red Sea-dweller
Posted OnFebruary 25, 2018 , By
Rolex had already gained a great reputation for manufacturing wristwatches that could meet the demanding conditions of the ocean. Well, owing to new experiments with saturation diving – a method in which helium is used to replace nitrogen in the air mixture, enabling commercial divers to work at deeper depths and stay down longer – a new type of dive watch was needed, one that could survive the unique rigors of this kind of deep sea diving.
The manufacture of this fake rolex Sea-Dweller lasted into the early 1980s, during which time it underwent a number of minor changes. For the first ten years of its production, Rolex made the Sea-Dweller with both the Submariner and Sea-Dweller names printed in red ink on its dial. These "Double Red Sea-Dweller" watches frequently had their dials replaced by Rolex Service Centers with later-era versions that had all white text and lacked the Submariner name entirely. As a result of this practice, original "Double Red" dials have become quite rare and valuable among collectors today.
The extended periods of time spent in pressurized chambers would force helium molecules into the cases of the divers' watches. Upon decompression, the trapped helium would expand, often generating enough force to cause the crystals to pop off their replica watches. The Rolex's solution to this problem was the Sea-Dweller, which incorporated a gas release valve into the side of the case, allowing trapped helium to safely exit the watch during decompression. Although a number of early prototype Sea-Dweller watches were manufactured, the Rolex Sea-Dweller made its official debut..
Even though it is not necessary to track down a Double Red Sea-Dweller, it has become much harder to find one with its original dial still in pristine, unaltered condition. This special Double Red Sea-Dweller has succeeded to survive all these years without its dial sustaining any inadvertent damage from bent hands, moisture intrusion, or careless watchmakers. Besides, the tritium hour markers have developed a rich, patina, which only adds to this watch's well-preserved, unmistakably vintage aesthetic.
The Double Red Sea-Dweller was the first commercially available iteration of Rolex's most capable line of professional sports watches, and marked a lot of firsts – both for the Rolex brand and the dive watch industry as a whole. It has made the replica Rolex Double Red Sea-Dweller a true classic and a common target for serious collectors looking to own an iconic piece with its rich history, timeless design, and unmistakably vintage aesthetic.
Top Quality Omega Seamaster Aqua Terra Replica Watch
Omega launched a large number of new Seamaster Aqua Terra 150M models last year, which offered easy to miss, albeit important changes to the brand's premier sports lifestyle dress watch. Sport-style dress fake watches are important in many markets such as the USA, where elegance as well as masculinity are main factors of interest for many consumers. Let's take a close look at just one of the some versions of the updated Aqua Terra timepieces here.
While some of us think of hardcore dive replica watches when they consider the replica Omega Seamaster collection, the more casually-themed Aqua Terra better represents the first Omega Seamaster watches. At the time the Seamaster wasn't a serious sport watch, but was rather a sportier dress watch that a "well to do father could wear while playing with his children and not worry about getting wear or experiencing some shock." Therefore, from the beginning the Seamaster was a luxury lifestyle item, and not the serious diving instrument that versions of the Seamaster later evolved into.
As a sportier timepiece, the Seamaster Aqua Terra will easily handle the most part of what a wearer could throw at it. 150m of water resistance easily allows for even recreational diving, and the chunky metal case is robust enough to put up with its share of abuse and wear. The dial also happens to be highly legible, with enough lume for a clear view in darker environments. Generally speaking, the Seamaster Aqua Terra is a very capable sport watch though its intent is to be a status-symbol dress watch at what are almost entry-level prices from the brand.
However, lots of people admire Omega for Speedmaster chronographs and Planet Ocean divers, models such as the Aqua Terra and other models are those which Omega intends for the wrists of professionals needing a handsome timepiece for urban or business professional needs. It's supposed to be just sporty enough to suggest an active lifestyle (or an appreciation thereof), but with an elegance which lends itself well to more formal attire.
The interesting thing is that the fake tag heuer latest marketing for the Aqua Terra sees its wearers (some of which are the brand's celebrity ambassadors) on boats, traveling, and generally doing things one might not consider work, but rather leisure. This lends itself well to attractive visuals, but the replica Omega's point is more that people who wear Aqua Terra watches regularly reward themselves for working hard – and this makes the Aqua Terra a timepiece for hard working professionals.
The Omega replica has long since wanted the Aqua Terra to rival some of Rolex's similar sporty/dressy timepieces ranging from the Milgauss to the Datejust. Today the Aqua Terra is more directly a competitor of the Milgauss – even though Omega is clearly more prolific with its design choices and even has different size options.
So Many Different Newly Established Replica Watches in the World
Posted OnJanuary 12, 2018 , By
Matching supply with demand is a main priority at Richemont these days. It soared to the top of Richemont's agenda last year when the company took the unusual actions of spending lots of money to buy back excess watches, to stop them from being sold to unauthorized dealers. Two-thirds were Replica tag heuer watches in China and Hong Kong; the rest were from Vacheron Constantin, and other brands in Richemont's Specialist Watchmakers division.
Clearly Richemont itself had been something of a force-feeder of retailer geese. The fake tag heuer inventories started to rise after China initiated its crackdown on corruption, and the practice of "gift-giving" to officials of the regime. With stock at unhealthy levels, Richemont bit the bullet and bought back the merchandise. "We went specifically to the dealers and repurchased inventory that we oversold, that they overbought, admittedly under different conditions when the market was booming," Grund explained. "That inventory was lying there for two to three years and was not turning, and we helped them repair the balance sheet. It was clearly designed to help our trade partners get rid of excess inventory. If you don't do that, it goes into unauthorized distribution channels."
There are newly established fake watches sell at heavy discounts. "That will affect brand equity over the long term," Grund said. To avoid that, he continued, "we buy back, we deconstruct or we destroy, to take that stock permanently off the market."
It also led to a double-digit boost in Richemont's replica watch business in the April through September period. Richemont issues sales data by division, not by individual brand, but it said Rolex sales grew by double-digits "with good performance in jewelry and tag heuer watches."
The experience has made the outspoken Rupert to preach against the evils of overproduction. "For our major Maisons, our sell-in is less than our sell-out. Therefore, the stock is gradually reducing. Is your sell-in smaller than your sell-out? That's really the question to ask the entire industry," he told the financial analysts in May.
And he warned that the glut will hamper a recovery. "How long will it take for the watch industry to recover? I think there still have stock in parts of the world – America, parts of Asia – so it's going to be a gradual process."
Several days ago, Rupert announced the promotion of Cartier's Head of International Sales, Emmanuel Perrin, to Head of Specialist Watchmakers Distribution. "In this newly created position, he will be responsible for the coordination of all Specialist Watchmakers distribution strategies," Rupert said. "A prime area of focus will be matching supply with end-customer demand."
Best Replica Jaeger-LeCoultre Reverso for Actors
Posted OnNovember 11, 2017 , By
I know when I'd reach for a Reverso to dress a character's wrist, even though I'm no prop master. It would be when they had a scene in a suit. It would be at a point in their character trajectory where they were at highest confidence, when their outward style is tapping into the traditional, the iconic, and the timeless. And also when the brand of badass they're seeking to project is more brains than brawn. You suspect this was exactly the thought process of the art directors and prop masters that did just that with these kings of the screen.
Leo. Damn, Leo! Has the boy add some unique idea into this outfit or what, pairing not only a dress replica watch and band to his formal attire, but also dial color to his tie. His self-satisfied look says it all.
Ah, Pierce. He may have bombed as Bond but the man knows how to work black tie. The key is to have an accessory in the mix that pops on the monochrome backdrop, and few accessories can compete with a gold dress watch with white face and black leather strap. The other fact that it's an unusual shape also catches attention. This is a perfect power play.
Jon Hamm. The most powerful pairing is just in this list by so far. There were many fake tag heuer watches in Mad Men over the years. Everything from the Tudor, Rolex and replica Jaeger LeCoultre is really lesser-knowns such as a Hamilton Electric. But none could step up to the peerless aesthetics of the show quite like Don Draper's Reverso.
Adrien Brody. None of what Adrien's wearing is red-carpet appropriate and he looks almost apologetic, as you would be, but you know what? I actually love this dressed-down, slightly sloppy and bordering on casual look from The Pianist.
Clive Owen. With a look that is at the same time velvety and villainous, Owen demonstrates that the Reverso is not just a quaint dress watch but a serious piece of kit to get an F-You attitude across when required. Love it.
Michael Douglas. Probably the weakest species on this list, Douglas is closer to the stereotype of the Reverso as a multimillionaire's daily dress watch that elsewhere here is being disrupted. He's rich, he's dressed conservatively, and he has some seriously unintentional bro-flow happening with his hair. Don't be like Michael when you're wearing your Reverso is probably the key tip here.
4 Sports Luxury Watches that live up to the Name
Posted OnOctober 13, 2017 , By
It is common sense that the sports luxury is one of those ephemeral subgenres in watchland that hides a multitude of sins. It's easy for a tag heuer watch maker to label any oversized solid-gold diver as sports luxe, but the reality is that most of these watches will never see any actual sports time. Obviously, that's not good enough. So we found a select handful of timepieces that you could wear with ease on the court or in the boardroom.
Montblanc TimeWalker Date
The fake Montblanc's recently gave their hallmark TimeWalker line an automotive makeover, one which leans heavily on chronographs. But I actually think the simpler time and date offering is a perfect sporty-luxe piece at an entry-level price with its bright, appealing dial, simple steel case with neat cutaways and a ceramic bezel. On rubber, this thing is perfectly suited to action, adventure and well, the office.
Hublot Classic Fusion Racing Grey
Hublot Replica is a sporty brand, of course. Big and bold are some of the adjectives that spring to mind. The Classic Fusion line shares this sporty aesthetic and DNA but in a dressier, more refined package. Plus the rubber-backed leather straps mean you don't have to be too concerned about building up a sweat.
Rolex Yacht-Master 40 Oysterflex
It's an obvious choice, but this Everose beauty's inclusion isn't solely because of the action-ready and oh-so-comfy Oysterflex. The slim case profile and Cerachrom bezel are also key attributes in the Yacht-Master's success as a sports-ready status symbol.
I was never really on team Aquanaut, but then I caught up with David and his 'one watch' Patek Philippe replica, and I just got it. Like the replica tag heuer, the Aquanaut has the winning combo of rubber strap and slender case. But beyond that there's a dazzling mix of finishings, an interesting dial and top-notch movement.
If I'm totally honest, this Louis Vuitton is a more luxury than sports, but with it's comfortable newly redesigned steel case, rubber strap and practical GMT functionality, there's surely no reason why you shouldn't wear this beauty for a quick round of casual racquetball before a spot of sunning yourself on the deck of your (super) yacht.
Omega Replica Watch In 'Dunkirk' Film & Omega's Role in WW2
Posted OnSeptember 22, 2017 , By
Dependable timekeeping was a crucial factor of warfare, therefore, watches are dispensable tools for our daily life, even though it is a replica watch. And it is specially and extremely important to pilots, who relied on watches for navigation. And in Dunkirk, we see Hardy's character depending heavily on his watch, which played a necessary part in the film. It's not really a spoiler, but the watch's most pivotal role is when his fuel gauge gets damaged, he asks the other pilot for a fuel reading, and scribbles it along with the time on the plane's dashboard.
The watch chosen for Hardy's character was the fake Omega CK2129. The choice was apt because Omega reportedly supplied about half of all watches used by the British RAF. In addition, the Omega CK2129 was the most commonly worn Omega watch by RAF personnel in the Second World War.
The origins of the Omega CK2129 came about in January 1940, shortly after the start of WW2. It was then that the British RAF decided it needed watches with rotating bezels and asked the Omega replica to make 2,000 such watch es. Wisth rotating bezels, pilots could make calculations and time events more easily and accurately. The Omega CK2129 watch was eventually delivered in March of the same year.
The Omega CK2129 was designed for ease of use and legibility. It had a cream dial, blue hands, large Arabic hour markers, a large rotating bezel, and two oversized crowns. The two large crowns made it easy for pilots to handle and wind the watch when wearing gloves. Besides, the second crown at 4 o'clock was used to lock the rotating bezel so that timings couldn't be misread by accidental knocks inside the tight confines of the plane's cockpit.
It was a fairly large replica watch for its time, around 33mm, and featured easy-to-read blue hands and large Arabic hour markers on a cream dial. Where it differed from the CK2129 was the movement. The Omega CK2292 used the more sophisticated Calibre 30T2, which performed very well at observatory trials. The Calibre 30T2 is also more resistant to magnetic forces thanks to new alloys used in the balanced spring, and this was especially beneficial to pilots of the Hurricanes and Spitfires who sat near powerful engines which generated huge magnetic fields.
Of the three, the CK2444 was distinct. Because it was used by the general armed forces, and not by the air forces exclusively, it dispensed with a central seconds hand and had a subsidiary seconds dial instead. Also, it had a black dial. Nevertheless, it remained highly legible thanks to its thick sword-style hands and large Arabic hour markers in white.
At this point, it goes without saying that the fake Omega's role in the Second World War was significant – other watch manufacturers, of course, also played important roles, but that is a longer story for another article. Besides, for tag heuer replica watches, their involvement in the war also helped them advance their watchmaking knowhow and refined their manufacturing techniques and processes.
But more importantly, Dunkirk is a great film. Of all the films that I have seen this summer, it easily ranks as one of the best. In fact, I would even go as far as to say it is one of the best war films ever. The appearance of the Omega CK2129 certainly is a nice addition, but most of all, Dunkirk is authentic and beautifully shot. Go catch it if you haven't already.
Rubber B Watch Straps for the fake Rolex Sky-Dweller
As the very first company to create integrated rubber straps for replica Rolex sport watches in 2010, Rubber B introduced vulcanized rubber straps that featured blocked case integration and Oyster clasp compatibility for a few select Rolex replica watches, including the Daytona, Submariner, and GMT Master. Initial reception by the fake Rolex community was vehemently mixed, and a gentle path to mainstream acceptance was paved with a long-term focus on promoting quality craftsmanship. Seven years later, Rubber B has become a mainstay, having grown exponentially to include over 175 different strap options that accommodate passionate watch owners of many various luxury brands.
The fake Rolex had only produced a limited number of gem-set Datejust watches in the past that came with their own fashionable rubber strap with inlaid diamonds, but this new foray into rubber straps for sport models certainly has broadened the field of strap options available to Rolex enthusiasts.
The purpose of Rubber B was firstly to offer discerning Rolex watch owners with a viable selection to their original fake Rolex bracelet, while they enjoyed comfort, individuality, and customization. However, in the case of the beautiful Sky-Dweller that comes originally from Rolex on a crocodile band, such owners can now have the added benefit of bathing, swimming, and perspiring without worry, all while wearing their exclusive Rolex watch.
This uniquely integrated Rubber B watchband for the Rolex Sky-Dweller, which recently released, represents the latest and most high-tech evolution in rubber strap manufacturing. Although Rubber B straps are made exclusively in an industry-leading Swiss factory, the Sky-Dweller strap presented quite a challenge during development. This new design is significantly more structured than previous Rubber B models.
It is an overly-used phrase these days, but Rolex owners truly do understand and appreciate the value of Swiss quality engineering. Every aspect of a Rubber B strap must maintain an integral respect to its intended watch. For instance, the bezel-influenced fluted grooves and subtle color patterns of this special strap are intended to compliment the various Sky-Dweller models and dials currently available from Rolex. Beyond such design elements, the customer's best interest must be profoundly considered. For, it is only upon the wearer's long-term endearment of their strap, that the reputation of the strap-maker can be organically built.
For those of you who may have a Sky-Dweller on a stainless steel, gold, or two-tone Oyster bracelet, no need to worry – there is a new Rubber B strap for your model currently in production at the Swiss factory, and scheduled for release in Spring 2018. You can sign up here to be notified upon its arrival.
Excellent Performance Meets Rugged Style in the New Replica Breitling Superocean
Breitling may be best famous for aviation-focused timepieces, but when it pulls a dive watch like the new steel Superocean 44 Special out of its arsenal we sit up and take pay attention to. The newest addition to the brand's Superocean range which was first released in 1957, the 44 Special seems like a lethally capable piece of kit, and its specs don't disappoint, with a depth rating of 1,000 meters or 3,300 feet.
The aeronautical Breitling collection has shifted their focus from the skies to the sea with the new Superocean 44. A ceramic unidirectional rotating bezel announces its tool replica watch cred and it also features a security valve for balancing out pressure differences, marking it as worthy of professional use. Add a ratcheted profile for ease of handling even with gloves and luminescent dial details to enhance underwater legibility and you can see why this might make the Planet Ocean boys at the fake Omega a little nervous.
The Superocean 44, sized at 44mm of course, comes in two versions: black dial and bezel with a classic black or blue rubber replica Breitling "ocean racer" strap; and blue dial and bezel on stainless steel. Both feature a twin-gasket screw-locked crown and house a mechanical self-winding movement chronometer-certified by COSC. A seconds hand with a red tip and a small luminescent triangle allows the wearer to verify that the movement is operating at any given time. The steel case on both pieces is satin-finished on top and polished on the sides and crown. Baton-type hands distinguish hours from minutes while differently shaped hour-markers indicate five-minute intervals, quarters and 12 o'clock. Finally the sapphire crystal is "glareproofed" on both sides to enhance legibility in any conditions.
The brand's signature "ocean racer" strap is always one of our favorite strap designs and we recommend it as an option for any Breitling timepiece whose style fits the bill. It is a hybrid between a classic rubber dive strap and a racing-inspired "rally" strap with a row of holes, it's rugged and unique. The fake Breitling's other rubber strap is also pretty cool, featuring a raised Breitling signature and finished in blue, giving it a bit more of an aeronautical vibe. Only Panerai does it better, though a Luminor is generally a less accessible timepiece than the tag heuer replica. However, the 44 Superocean is in line with Breathing's return to larger timepieces and matches the size of most Luminors. Which would you want strapped to your wrist in the event of an underwater emergency?
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