text:
\section{Introduction}

Since the early days of nonlinear science and the explosion of interest in integrable models,
it was realized that the nonlinear Schr{\"o}dinger (NLS) equation~\cite{sulem,ablowitz,siambook}
is a universal model describing envelope solitons in dispersive nonlinear media; as such,
it plays a central role in a variety of contexts, ranging from water waves
and plasmas~\cite{infeld} to nonlinear optics~\cite{kivshar} and atomic Bose-Einstein
condensates (BECs)~\cite{emergent}.
Furthermore, already from the 70s, it was found that
the interaction of waves of different frequencies
gives rise to vector (multi-component) NLS models~\cite{manakov,intman1}.
It is thus not surprising that since then a considerable volume
of work was dedicated into multi-component NLS equation settings.
Arguably, the workhorse of many
relevant studies was the Manakov system~\cite{manakov} (which is integrable~\cite{intman2}), characterized by equal nonlinear
interactions within and between components.

Vector solitons of this model have attracted much attention, especially in
the setting of defocusing intra- and inter-component interactions. In such a
case, of particular interest are dark-bright (DB) solitons. In these structures,
the bright soliton, which would not exist in the defocusing setting,
only emerges because of an effective potential well created by the dark soliton
through the inter-component interaction; as such, DB solitons can be thought of
as ``symbiotic'' structures. DB solitons have
attracted much attention~\cite{christo,vdbysk1,vddyuri,ralak,dbysk2,shepkiv,parkshin},
especially due to potential applications in optics, where dark solitons
could be used as adjustable waveguides for weak signals
(see, e.g., Ref.~\cite{kivshar} and references therein).
Importantly, these early theoretical developments, focusing on
the integrable theory, its exact solutions and perturbations
thereof, were also accompanied by pioneering experiments
in photorefractive
media, where DB solitons
were observed and studied~\cite{seg1,seg2}.

Here, we target this specific multi-component setting,
featuring defocusing inter- and intra-component nonlinearities,
and the corresponding solitary waves
(below, we use the term ``soliton'' in a loose sense,
without implying complete integrability);
for focusing multi-component systems and
bright solitons see, e.g., Refs.~\cite{placeholder,emergent}
and references therein.
We will also consider atomic BECs~\cite{stringari,roman}, which
have provided a new spark for this theme~\cite{siambook,emergent}.
Indeed, seminal experiments have realized
multi-component BECs,
as mixtures of, e.g.,
different spin states of the same atom species
({\it pseudo-spinor} condensates)~\cite{Hall1998a,chap01:stamp}, or
different Zeeman sub-levels of the same hyperfine level
({\it spinor} condensates)~\cite{Stenger1998a,kawueda,stampueda}.
In BECs, the soliton
in one species can be the same or different
to that in the other species.
Of particular interest here
will be vector solitons where one component is a dark soliton.

Our presentation is structured as follows. In Sec.~2, we present the model and
discuss its experimental motivation. In Sec.~3, we analyze statics and dynamics
of single and multiple vector solitons. In Sec.~4, we discuss various settings
and parameter regimes for vector solitons. Finally, in Sec.~5, we briefly summarize
our conclusions and discuss future challenges.

\section{Background and experimental motivation}

\subsection{The multi-component NLS model}

A mixture of $\mathcal N$ bosonic components can be described, at the
mean-field level~\cite{stringari}, by
a system of $\mathcal N$ coupled NLS equations
[alias Gross-Pitaevskii equations (GPEs) in this context].
When the different components pertain
to the same atom species, this system reads
(see, e.g., Refs.~\cite{emergent,siambook}):
\begin{equation}
i \frac{\partial \psi_n}{\partial t}=-\frac{1}{2} \nabla^2 \psi_n
+ V_n({\bf r}) \psi_n + \sum_{k=1}^{\mathcal N}\left[ g_{nk}|\psi_k|^2 \psi_n
-\kappa_{nk} \psi_k + (\Delta \mu_{nk}) \psi_n  \right].
\label{2C}
\end{equation}
Here, $\psi_n$ denotes the wavefunction of the $n$-th component
($n=1,\dots,{\mathcal N}$),
$V_n({\bf r})$
is the trapping potential confining the $n$-th component
which is typically parabolic,
$(\Delta \mu_{nk})$ is the
chemical potential (eigenvalue parameter) difference
between components $n$ and $k$,
the nonlinearity coefficients $g_{nk}=g_{kn}$ characterize inter-atomic collisions, while
the linear coupling coefficients $\kappa_{nk}=\kappa_{kn}$ are responsible for
spin state inter-conversion, induced typically by a
spin-flipping resonant electromagnetic wave~\cite{NZ}.
This system conserves the energy $E$ and the total number of atoms,
$N\equiv \sum_{k=1}^{\mathcal N} N_{k}=\sum_{k=1}^{\mathcal N}\int |\psi_k|^2 d\mathbf{r}$;
furthermore, in the absence of linear inter-conversions (i.e., $\kappa_{nk}=0$),
the number of atoms of each component $N_{k}$ is conserved.

The principal paradigm on which our exposition will be based
is that of two bosonic species (${\mathcal N}=2$), where we will
assume that the system is homogeneous ($V_n=0$) or trapped ($V_n \neq 0$).
In the homogeneous case with $\kappa_{nk}=0$ and $(\Delta\mu_{nk})=0$,
the binary mixture is {\it immiscible}
provided that the following {\it immiscibility condition} holds~\cite{miscibility}:
\begin{equation}
\Delta \equiv (g_{12}^2-g_{11}g_{22})/g_{11}^{2} > 0,
\label{Delta}
\end{equation}
where $\Delta$ is the so-called miscibility parameter.
In the experiments,
this parameter
assumes values of the order
of $10^{-3}$ or even less; for example, $\Delta \approx 9 \times 10^{-4}$ or $\Delta \approx 0.036$
for a mixture of two spin states of $^{87}$Rb~\cite{Hall1998a}
or $^{23}$Na~\cite{chap01:stamp} BEC, respectively.
Condition~(\ref{Delta})
corresponds to the
case where
the mutual repulsion between species is stronger than the repulsion
between atoms of the same species.
Then, the two species do not mix and instead
tend to separate by filling two different spatial regions, thus forming,
e.g., a ``ball and shell'' configuration (cf.~experiment of Ref.~\cite{Hall1998a}),
or two
domain-wall structures of a similar type, one in
each component~\cite{Marek}.

In what follows, we will chiefly operate in the
vicinity of this threshold which favors the emergence of
DB solitons, and use $\kappa_{nk}=0$. This setting is relevant both to experiments and
to the mathematically tractable Manakov limit of $g_{nk}=1$~\cite{manakov}.
Experimental results have demonstrated that the
prototypical vector
solitons that may be supported in such quasi one-dimensional (1D) systems
involve
a dark soliton in one component, while the second one may be either
a bright soliton, so that the vector soliton is a dark-bright (DB) soliton~\cite{hamburg,pe1,pe2,pe3,azu},
or a dark soliton,
so that the vector soliton is a dark-dark (DD) soliton~\cite{pe4,pe5}.
It should also be noted that, in theory, dark-antidark solitons (the latter being
humps, instead of dips,
on top of the
background state),
have also been predicted~\cite{EPJD,hadi,jap}.

\subsection{Optics experiments}

\begin{figure}
	\begin{center}
\includegraphics[height=3.1cm]{chen_kivshar1aN.eps}
~
\includegraphics[height=3.1cm]{ol_ostrovskaya3N.jpg.ps}
\caption{(Color Online)
Formation of DB solitons in photorefractive crystals:
the left four panels (adapted from Ref.~\cite{seg1}) showcase
the evolution of an initial condition [panel (a)],
upon propagation under linear evolution, leading to
dispersion [panel (b)], nonlinear evolution of uncoupled components, again
leading to breakup/dispersion [panel (d)], and under coupled nonlinear
evolution [panel (c)].
A similar case example, but for two bright beams,
is shown in the right four panels (adapted from Ref.~\cite{seg2}).
The dark (bright) component is shown in the top (bottom) panel.
}
		\label{revip_fig1}
	\end{center}
\end{figure}

As discussed above, DB soliton states were first observed in pioneering experiments
in optics~\cite{seg1,seg2};
their key findings, summarized also in Fig.~\ref{revip_fig1},
were as follows. Experiments were performed in a photorefractive
(strontium barium niobate) medium, with an input corresponding to a dark soliton (created through
an optical mask) in one component, coupled to a bright soliton
in the second component
[panel (a) in the left of the figure].
For low intensity, i.e., for a linear evolution, both components
underwent dispersion-induced broadening [panel (b)]. On the other hand,
uncoupled nonlinear evolution
[panel (d)] again resulted in
dispersion of the bright component,
since the corresponding structure
was not effectively confined by the presence of the dark one.
Only when the evolution is nonlinear {\it and} the two components are
coupled
[panel (c)], is it possible for the DB soliton state to persist.
Similarly, for initial conditions conducive to a breakup
into two DB waves (right four panels in Fig.~\ref{revip_fig1}),
linear propagation, and
uncoupled nonlinear propagation
[panels (b) and (d)] do not lead to coherent states. Only the
coupled nonlinear evolution [panel (c)] leads to a robust
pair of DB solitons, i.e., a so-called ``solitonic gluon''~\cite{seg2}, or ``soliton molecule''.

\subsection{BEC experiments}

\begin{figure}
	\begin{center}
\includegraphics[height=6cm]{Fig5.eps}
~
\includegraphics[height=6cm]{ExperimentalFig1N.eps}
\caption{(Color Online) The left four panels
(adapted from Ref.~\cite{pe2}),
show: the oscillation of a DB soliton in
a trapped BEC (a); the soliton position
for different ``masses'' of the bright soliton (b); the oscillation
frequency as a function of the bright soliton mass (c) and the
collision of two DB solitons (d). The right panel
(adapted from Ref.~\cite{pe3}) shows
(transient) states bearing 2 (a), 3 (b), 4 (c), 5 (d) and even 6 (e) DB
solitons.
}
		\label{revip_fig2}
	\end{center}
\end{figure}

In the context of BECs, DB solitons
were first predicted and studied in binary BECs in Ref.~\cite{buschanglin}.
While this theoretical work triggered a number of follow-up studies
ramifying the original idea~\cite{siambook},
arguably, it was the Hamburg experiment~\cite{hamburg}, and subsequently those
at Pullman~\cite{pe1,pe4,pe2,pe3,pe5,azu} that put the topic in a fundamentally new
perspective by revealing the experimental possibilities thereof.
In particular, in Ref.~\cite{hamburg} it was demonstrated that DB solitons
can be created by a phase-imprinting technique
in the two-component setting, and
also showcased
their robust oscillations in a quasi-1D parabolic trap. In turn,
a different breed of experiments was introduced later, where both DB~\cite{pe1,pe2,pe3}
and DD~\cite{pe4,pe5} solitons
were generated spontaneously via instability mechanisms
in
counterflow experiments: specifically,
the condensates (composed of two distinct hyperfine states) were
spatially separated and subsequently ``slammed'' against
each other, leading to the spontaneous
emergence of the coherent structures of interest.

Examples illustrating the above mentioned experimental
possibilities and findings are
shown in Figs.~\ref{revip_fig2} and~\ref{revip_fig3}.
In particular, Fig.~\ref{revip_fig2}
depicts robust oscillations of a DB soliton
in a quasi-1D trap [left panel (a)].
The time-series of the wave center position [left panel (b)]
allows to infer the oscillation frequency,
as well as its dependence on the ``mass'' (number of atoms) of the bright component
[left panel (c)]; this suggests that
heavier solitons
become slower, bearing an increasing period.
In addition, collisions between two
separately oscillating DB solitons
are shown [left panel (d)]. The right set of panels
depicts that states with two up to six DB
solitons can (at least transiently)
form during the complex evolution of the counterflow experiments.
This again points to the idea of soliton molecules and progressively
more elaborate states bearing multiple DB solitons.

\begin{figure}
	\begin{center}
\includegraphics[height=4.4cm]{Experiment.eps}
\includegraphics[height=4.4cm]{Fig1.eps}
\caption{(Color Online) The left panels (adapted from Ref.~\cite{pe5})
depict different experimental snapshots of
counterflow experiments of two different BEC components;
the density profiles shown in
the fourth panel correspond to
a spatial region depicted in the third panel. The eight panels on the right
(adapted from Ref.~\cite{azu}) show progressively in time
the interaction of a DB soliton
with a Gaussian barrier: for a sufficiently high energy the wave is transmitted [panels (a-d)],
while for a lower energy it is reflected [panels (e-h)].
}
		\label{revip_fig3}
	\end{center}
\end{figure}

Finally, Fig.~\ref{revip_fig3} motivates some variants on the theme of DB
solitons in BECs, by virtue of additional experiments~\cite{pe3,azu}.
The left panel shows that in the counterflow experiments not only DB
solitons but also DD ones are generated.
The middle and right panels depict the
interaction of a DB soliton
with a potential barrier,
induced by a Gaussian laser beam.
When the barrier is shallow (or equivalently
the wave bears sufficient energy to overcome the barrier), transmission
through the barrier is observed (middle panel), while
in the reverse scenario of a deep barrier (or insufficiently energetic DB solitons),
near perfect reflection is realized (right panel).

\section{Dark-Bright and Dark-Dark Solitons in 1D
}

\subsection{The homogeneous setting}

Motivated by these experimental results, we now turn to a theoretical study
of the DB and DD solitons
in the 1D
setting. There, in the case of two components and
in the absence of linear coupling, Eq.~(\ref{2C})
becomes:
\begin{equation}
\begin{array}{rcl}
i \partial_t \psi_1  &=& -\frac{1}{2}\, \partial_{x}^2 \psi_1 + V(x)\psi_1
+(|\psi_1|^2 + |\psi_2|^2 -\mu_1) \psi_1,
\\[1.5ex]
i\partial_t \psi_2  &=& -\frac{1}{2}\, \partial_{x}^2 \psi_2 +V(x)\psi_2
+ (|\psi_1|^2 + |\psi_2|^2- \mu_2) \psi_2,
\end{array}
\label{deq12}
\end{equation}
where we have considered the Manakov limit with
$g_{ij}=1$~\cite{manakov}.
This is motivated, e.g., by the physically relevant case of the
$^{87}$Rb BEC, where hyperfine states are characterized by
almost equal coupling strengths~\cite{hamburg,pe1}.
For $\mu_1=\mu_2=\mu$, and neglecting ---to a first approximation---
the confining potential, Eqs.~(\ref{deq12}) possess the following
DB soliton solution:
\begin{eqnarray}
\psi_1(x,t) &=& \sqrt{\mu} (\cos\phi\,\tanh \xi+i \sin\phi),
\label{dark_part}
\\
\psi_2(x,t) &=& \eta\, \mathop{\rm sech}\nolimits \xi\, \exp[ikx+i\theta(t)],
\label{bright_part}
\end{eqnarray}
where $\xi=D(x-x_0(t))$, $\phi$ is the phase angle of the dark soliton,
$\cos\phi$ and $\eta$ are the amplitudes of the dark and bright
solitons, while $D$ and $x_0(t)$ describe the inverse width
and the center position of the DB soliton. For this solution to be valid,
$D^2=\mu \cos^2 \phi - \eta^2$, the soliton velocity
is given by $\dot{x}_0=k=D\tan\phi$,
and phase $\theta(t)=(1/2) (D^2-k^2) t + \theta_0$ (with $\theta_0={\rm const.}$).

A
remarkable feature of the above Manakov system
is its invariance under SU$(2)$ rotations, i.e., under the action of
matrices of the form:
\[ U=\left( \begin{array}{ccc}
\alpha & -\beta^{*} \\
\beta & \alpha^{*} \end{array} \right), \]
with $|\alpha|^2 + |\beta|^2=1$, for complex $\alpha, \beta$ (stars denote complex conjugation).
For concreteness, limiting our considerations to the SO$(2)$ case~\cite{pe5},
we choose $\alpha=\cos(\delta)$ and $\beta=\sin(\delta)$. Then, the
respective (time-dependent) densities $n_i= |\psi_i|^2$
of the two components, upon rotation of a DB solution become:
\begin{eqnarray}
n_1
&=& \mu \cos^2(\delta) -(\mu \cos^2(\delta) \cos^2 \phi
- \eta^2 \sin^2(\delta)){\mathop{\rm sech}\nolimits}^2 \xi -\sqrt{\mu} \eta \sin(2\delta)\quad
\nonumber \\[0.25ex]
&\times& \left\{\sin\phi \sin[kx+\theta(t)] + \cos\phi \cos[kx+\theta(t)]\tanh \xi \right\}
{\mathop{\rm sech}\nolimits}\xi,
\label{den1}
\\[2.0ex]
n_2
&=& \mu \sin^2(\delta) -(\mu \sin^2(\delta) \cos^2 \phi
- \eta^2 \cos^2(\delta)){\mathop{\rm sech}\nolimits}^2 \xi +\sqrt{\mu} \eta \sin(2\delta)\quad
\nonumber \\[0.25ex]
&\times& \left\{\sin\phi \sin[kx+\theta(t)] + \cos\phi \cos[kx+\theta(t)]\tanh \xi \right\}
{\mathop{\rm sech}\nolimits}\xi.
\label{den2}
\end{eqnarray}
There are three key features to discern within these
complicated expressions.
This DD soliton family contains the ``standard''
co-located DD solitons in the
$\eta=0$ limit (i.e., in the absence of the bright component).
Second, the DD solitons are generally {\it asymmetric},
unless $\delta=\pi/4$.
Third, the time-dependence
of phase
$\theta(t)$ results in
{\it time-dependent density profiles}, unless $\eta=0$; thus, DD solitons
may feature
time-{\it dependent} densities.
For $\eta \neq 0$, the time-dependence is harmonic,
with
an oscillation frequency $\omega_0$ such that:
\begin{eqnarray}
\frac{1}{2}k^2 < \omega_0 = \frac{1}{2}(k^2+D^2)
= \frac{1}{2}(\mu-\eta^2\sec^2 \phi) < \frac{1}{2} \mu,
\label{om}
\end{eqnarray}
These important
features highlighted above
are illustrated in Fig.~\ref{revip_fig4}.

\begin{figure}
	\begin{center}
		\begin{tabular}{cc}
			\includegraphics[scale=0.2]{SO2N}
			\includegraphics[scale=0.2]{DDN}
\\
\includegraphics[scale=0.21]{DD2N}
			\includegraphics[scale=0.21]{DD1N}
		\end{tabular}
\caption{(Color Online)
Profiles of non-co-located
(for $\eta=0.5$; top panels), and
co-located ($\eta=0$; bottom panels) DD solitons.
For the left (right) panels,
$\delta =\pi/8$ ($\delta=\pi/4$), so density profiles
are asymmetric (symmetric).
Thick solid (dashed) line represents the first (second) component
and the thin solid line is
the total density (adapted from Ref.~\cite{siambook}).
}
		\label{revip_fig4}
	\end{center}
\end{figure}

\subsection{Dark-bright and dark-dark solitons in the trap.}

We now turn to the case where a parabolic trapping potential is present.
In this setting,
the experimental findings depicted in
Fig.~\ref{revip_fig2}
(see also Ref.~\cite{buschanglin}) illustrate that a DB soliton
oscillates in the trap, following the dynamics of a classical
harmonic oscillator.
Such a ``particle-like'' oscillation of the DB soliton can be treated
perturbatively~\cite{vaspra,f3} in the
Thomas-Fermi (TF) limit~\cite{stringari}, where the wave
can be considered as a
Newtonian particle
inside an effective potential.

To elaborate on this, we
first recall that in the TF limit the ground state density of the first component
(assumed to carry the dark soliton) is $|\psi_{1{\rm TF}}|^2 = \max\{\mu-V(x),0\}$~\cite{stringari}. Then, denoting by $u_d$ and $u_b$ the wavefunctions of
the dark and bright soliton, we use $\psi_1 \rightarrow \psi_{1{\rm TF}} u_d$
and $|\psi_2|^2 \rightarrow \mu^{-1} |u_b|^2$, as well as
$t \rightarrow \mu t$ and $x \rightarrow {\sqrt{\mu}}x$, and
derive from Eq.~(\ref{deq12}) the system~\cite{vaspra}:
\begin{equation}
\begin{array}{rcl}
i\partial_tu_d+\frac{1}{2}\partial^2_xu_d-\left(|u_d|^2+|u_b|^2-1\right)u_d &=& R_d,
\\[1.5ex]
i\partial_tu_b+\frac{1}{2}\partial^2_xu_b-\left(|u_b|^2+|u_d|^2-\tilde{\mu}\right)u_b &=& R_b,
\end{array}
\label{u_d_u_b}
\end{equation}
where we have assumed chemical potentials
for the dark and bright solitons $\mu_1=\mu_d=\mu$ and $\mu_2=\mu_b=\mu+\Delta$
(with the difference being $\Delta<0$), so that $\tilde{\mu}=1+\Delta/\mu$.
Finally,
the perturbations $R_d$ and $R_b$
are given by:
\begin{eqnarray}
R_d &\equiv& (2\mu^2)^{-1}[2(1-|u_d|^2)V(x)u_d+V'(x)\partial_xu_d],
\label{R_d}
\\[0.5ex]
R_b &\equiv& \mu^{-2}[(1-|u_d|^2)V(x)u_b].
\label{R_b}
\end{eqnarray}
We now assume adiabatic evolution of the DB soliton in the presence of the
perturbations $R_{d,b}$, so that the soliton preserves its shape but its parameters
become unknown functions of time, namely:
\begin{eqnarray}
D^2(t)=\cos^2\phi(t)-\frac{1}{2} \chi D(t) \quad {\rm and}\quad
\dot{x}_0(t)=D(t)\tan\phi(t).
\label{s2}
\end{eqnarray}
Then, calculating the rate of change of the total energy of the system:
\begin{eqnarray}
E = \frac{1}{2}\int_{-\infty}^{+\infty}
|\partial_{x} u_d|^2+|\partial_{x} u_b|^2+(|u_d|^2+|u_b|^2-1)^2
- 2(\tilde{\mu}-1)|u_b|^2\, dx,
\label{1D:energy}
\end{eqnarray}
we obtain:
\begin{eqnarray}
4\dot{D}D^2+
\chi D\sec^2\phi(\dot{D}+D\dot{\phi}\tan\phi) =
\frac{\cos\phi}{\mu^2}
\left(\sin2\phi-
\chi D\sin\phi\right) V'(x_0).
\label{perturbed}
\end{eqnarray}
We thus derive the dynamical system of Eqs.~(\ref{s2}) and (\ref{perturbed}), which possesses
the fixed point: $x_{0,{\rm eq}}=0$,  $\phi_{\rm eq}=0$,
$D_{\rm eq} = \sqrt{1+\left(\frac{\chi}{4}\right)^2}-\frac{\chi}{4}$.
Linearizing around it, and assuming a parabolic trap of
strength $\Omega$, i.e., $V(x)=(1/2)\Omega^2x^2$, we find the equation of motion
for the DB soliton center:
\begin{equation}
\ddot{x}_0 = - \omega_{\rm osc}^2 x_0
\quad {\rm where} \quad
\omega_{\rm osc}^2 = \Omega^2 \left(\frac{1}{2}- \frac{\chi}{8\sqrt{1+(\chi/4)^2}} \right).
\label{eqmot}
\end{equation}

Note that the oscillation frequency can also be derived via a
Bogolyubov-de Gennes (BdG) analysis~\cite{stringari,siambook}
as follows.
Denoting by $u_{d,b}^{(0)}$ the dark and bright components of a stationary DB soliton
in the trap (cf.~left panel of Fig.~\ref{revip_fig5} for an example),
we use the ansatz
\begin{eqnarray}
u_d(x,t) &=& e^{-i \mu_d t} \left[ u_d^{(0)}(x) + \epsilon
\left(a(x) e^{\lambda t} + b^{\star}(x) e^{\lambda^{\star} t} \right)\right],
\label{darkp}
\\
u_b(x,t) &=& e^{-i \mu_b t} \left[ u_b^{(0)}(x) + \epsilon
\left(c(x) e^{\lambda t} + d^{\star}(x) e^{\lambda^{\star} t} \right)\right],
\label{brightp}
\end{eqnarray}
where $(a,b,c,d)^T$ is the eigenvector of the perturbation
and $\lambda$ is its corresponding eigenvalue.
Substituting Eqs.~(\ref{darkp})-(\ref{brightp})
in the equations of motion, and linearizing in the small parameter $\epsilon$,
we derive an eigenvalue problem for $[\lambda,(a,b,c,d)^T]$.
The essence of the BdG analysis is that,
once this problem is solved and $\lambda$ are found,
if ${\rm Re}\{\lambda\}>0$
then the solution is unstable; else
it is spectrally stable.
The BdG analysis in our case reveals that the eigenvalues are
imaginary, attesting to the DB soliton stability.

The middle and right panels of Fig.~\ref{revip_fig5} show the dependence of the
imaginary part of the lowest nonzero eigenvalue
on the chemical potential of the dark and bright component, respectively.
It is observed that the
lowest nonzero eigenfrequency,
associated with an internal mode (so-called {\it anomalous mode}~\cite{stringari,siambook})
of the wave describing its oscillation in the trap,
is in very good agreement with
the theoretical prediction of Eq.~(\ref{perturbed}).

\begin{figure}
	\begin{center}
\includegraphics[scale=0.25]{one_db_stationaryNN}
\includegraphics[scale=0.25]{one_db_frequency_vs_mu_dNN.eps}
\includegraphics[scale=0.25]{one_db_frequency_vs_mu_bNN.eps}
		\caption{(Color Online) Left panel: a stationary
		DB soliton in a parabolic trap;
solid blue (dashed green) line depicts the dark (bright) component.
Middle and right panels: dependence of the
eigenvalues (normalized to the trap strength)
on the chemical potential of the dark and bright component, respectively, as
obtained numerically via the BdG analysis.
The lowest nonzero eigenfrequency
is in very good agreement with
the theoretical prediction (red dashed line) of Eq.~(\ref{perturbed})
(adapted from Ref.~\cite{pe3}). }
		\label{revip_fig5}
	\end{center}
\end{figure}

The analytical approach
presented above is rather general in its nature:
this energy balance methodology can be used to study the
dynamics of coherent structures of different nature, and even different dimensionality,
in Hamiltonian models in the presence of
perturbations.
On the other hand,
it is relevant to remark that the SU$(2)$ and SO$(2)$ transformations
are {\it unaffected} by the presence of the trap, and hence apply to the
case of DD solitons
with time-dependent density (so-called ``beating DD solitons''~\cite{pe5})
as they do for the DB ones.
Hence, the beating DD solitons
have the same oscillation frequency [cf.~Eq.~(\ref{eqmot})] as the DB ones~\cite{pe5}.
Lastly, we note
that the above BdG results for the
1D setting,
indicate that the DB soliton
is generally robust/spectrally stable;
however, in the full 3D setting
DB solitons turn out to be more prone to instabilities~\cite{pe2}.

\subsection{Multiple vector solitons and solitonic gluons
}

The next experimental aspect that we address
is that of the emergence
of bound states of multiple DB solitons.
Such {\it solitonic gluons} (or ``soliton molecules'') were observed first
in optics~\cite{seg2} and also,
more recently, in BEC experiments~\cite{pe3}. To provide an understanding for such states, we
employ the variational approach of Ref.~\cite{pe3}, and use the following ansatz for
two equal-amplitude DB solitons
traveling in opposite directions:
\begin{eqnarray}
\!\!\!\!\!\!
u_d(x,t)
&\!\!=\!\!&\left(\cos\phi\tanh X_{-}+i\sin\phi \right)
\left(\cos\phi\tanh X_{+}-i\sin\phi\right),
\label{eq15}
\\[1.0ex]
\!\!\!\!\!\!
u_b(x,t)
&\!\!=\!\!& \eta\, {\mathop{\rm sech}\nolimits} X_{-}\, e^{i\left[kx+\theta)+(\tilde{\mu}-1)t\right]}
+\eta\, {\mathop{\rm sech}\nolimits} X_{+}\, e^{i\left[-kx+\theta)+(\tilde{\mu}-1)t\right]}\,
e^{i\Delta\theta}, \quad
\label{eq16}
\end{eqnarray}
where $X_{\pm} = D\left(x \pm x_0(t)\right)$, $2x_0$ is the relative distance between
the two waves, and $\Delta\theta$ is the relative phase between
the two bright components. Substituting the above ansatz into the energy
of the system [cf.~Eq.~(\ref{1D:energy})], and considering low-velocity and well-separated
($x_0\gg 1$) solitons, it is found that
the energy of the system assumes the form:
\begin{eqnarray}
E = 2E_1+ E_{\rm DD}+ E_{\rm BB} + 2E_{\rm DB},
\label{energyf}
\end{eqnarray}
i.e., the energy consists of twice the energy $E_1$ of one
DB soliton,
the interaction energies $E_{DD}$ and $E_{BB}$ between the two dark and the two bright solitons,
and twice the cross interaction energy $E_{DB}$ of the dark component of one soliton
with the bright of the other (cf.~Ref.~\cite{pe3} for
expressions of these energies).
We can then find the evolution of the soliton parameters from the energy conservation, $dE/dt=0$,
as in the previous case of the single DB soliton in the trap. This way,
for low-velocity, almost black solitons,
energy conservation leads to the following equation for the soliton center:
\begin{eqnarray}
\ddot{x}_0 = F_{\rm int} \equiv F_{\rm DD}+F_{\rm BB}+2F_{\rm DB},
\label{Fint}
\end{eqnarray}
where we have used the same notation for the respective interaction forces.
To the leading order of approximation, it can be found that~\cite{pe3}:
\begin{equation}
F_{\rm BB} \propto {\rm e}^{-2 D_{\rm eq} x_0}\cos(\Delta\theta),
~~
F_{\rm DD}\propto {\rm e}^{-4 D_{\rm eq} x_0},
~~
F_{\rm DB} \propto {\rm e}^{-2 D_{\rm eq} x_0}\cos(\Delta\theta).
\end{equation}
The key feature
here is that while the
DD interaction is always repulsive, the BB and DB ones
depend on the relative
phase $\Delta\theta$ between the bright components. In particular, if $\Delta\theta=0$
then the BB interaction is also repulsive,
rendering impossible
a stationary ``molecular'' state. However, if $\Delta \theta=\pi$
(as
found in Ref.~\cite{seg2}),
then the repulsive nature of the DD interaction dominates at short
distances, while the attractive nature of the BB interaction at long
ones, yielding the potential for a ``bound state'', the solitonic
gluon.

The above analysis allows for the identification of this state
numerically (even in the absence of a trap),
and also provides the dependence of
the center of the solitonic gluon on,  e.g.,
the bright component chemical potential.
Equally importantly, linearization around
the equilibrium position $x_{\rm eq}$ (i.e., the distance between the constituent DB
solitons forming the stationary solitonic gluon)
suggests the existence of an internal mode of the two DB solitons,
involving their out-of-phase oscillation with a frequency
$\omega_0^2= - \frac{\partial F_{\rm int}}{\partial x_0} \big|_{x_0 = x_{\rm eq}}$.
These predictions are illustrated in Fig.~\ref{revip_fig6}.

\begin{figure}
	\begin{center}
\includegraphics[height=2.6cm]{DB_fig1_newNN.eps}
\includegraphics[height=2.6cm]{two_db_homogeneous_equilibrium_compareNN.eps}
\includegraphics[height=2.6cm]{two_db_homogeneous_frequency_compareNN.eps}
		\caption{(Color Online)
The dark (solid blue line) and bright (dashed green line) components of
a solitonic gluon in the homogeneous case (left panel).
The equilibrium distance between
two DB solitons (middle panel)
and the out-of-phase oscillation frequency (right panel) as functions
of the bright component chemical potential;
red stars denote the theoretical prediction and blue
circles the numerical result (adapted from Ref.~\cite{pe3}). }
		\label{revip_fig6}
	\end{center}
\end{figure}

These molecular states can be generalized in the presence of a trap:
in this case, the equation of motion for the center $x_0$ of the solitonic gluon
involves not only the pairwise interaction force $F_{\rm int}$, but also
the restoring force of the trap $F_{\rm tr}$, inducing an in-trap oscillation with
a frequency $\omega_{\rm osc}$  [cf.~Eq.~(\ref{eqmot})].
Hence, the equation of motion for $x_0$ reads:
\begin{equation}
\ddot{x}_0 = F_{\rm tr} + F_{\rm int}.
\label{eqmot2}
\end{equation}
Thus, in this setting,
a molecular state exists even when the two DB solitons
are in-phase, because
their DD and BB (and DB) repulsion is counterbalanced by $F_{\rm tr}$.
An additional consequence is that, inside the trap, a pair of DB solitons
will bear two, rather than one, internal modes.
The lowest one,
pertains to their in-phase oscillation,
characterized by the frequency $\omega_{\rm osc}$;
the other internal mode
corresponds to their out-of-phase motion,
characterized by the frequency
$\omega_1^2 = \omega_0^2 + \omega_{\rm osc}^2$.

Motivated by the
observation of
multi-DB-solitons
(cf.~right panel of Fig.~\ref{revip_fig2}), we may also consider
``lattices'' of such states.
In particular, lattices of DB solitons, with
out-
or in-phase bright neighbors respectively read~\cite{f3}:
\begin{eqnarray}
u_d &=& A_1 ~{\rm sn}(b x, k),  \quad
u_b = A_2 ~{\rm cn}(b x, k),
\label{latti1}
\\
u_d &=& A_1 ~{\rm sn}(b x, k),  \quad
u_b = A_2 ~{\rm dn}(b x, k),
\label{latti2}
\end{eqnarray}
where suitable (explicit) conditions connect
amplitudes,
$A_1,~A_2$, and width as well as
inter-soliton separation parameters $b$ and $k$.
Such solutions exist
for general nonlinearity coefficients $g_{ij}$, and can be
numerically found
even well beyond
the regime of validity of
the analytical
solutions~\cite{f3}.

Furthermore, in Ref.~\cite{wen}, it was found that the lattice states
can still be described via the above particle model
characterizing the pairwise interactions between the nearest-neighbor DB solitons.
Moreover, a notion of ``kinetic temperature'' was introduced,
depending on the solitons' initial kinetic energy.
In that light, a (gradual) transition of the dynamics of a large
number of solitons
could be identified as follows. When
the kinetic energy (and hence the kinetic temperature) of the system
was low, the array of the DB
solitons behaved as a crystal. As the
kinetic temperature was increased, the DBs progressively demonstrated a more
gaseous behavior with a large number of collision events.
Intriguingly, these also included an exchange of mass between
the bright components, rendering the particle description less
accurate in this limit. This is a topic worthwhile of further exploration.

\section{Variations on the theme}

We now turn to a number of case examples in which variants of the standard
homogeneous or trapped DB
solitons are of relevance/interest.

\subsection{The case of unequal masses}

\begin{figure}
	\begin{center}
		\begin{tabular}{ccc}
			\includegraphics[scale=0.21]{1st_antisymm_init_prof2.eps}
			\includegraphics[scale=0.21]{1st_symm_init_prof2.eps}
\includegraphics[scale=0.21]{2nd_antisymm_init_prof2.eps}
		\end{tabular}
		\caption{(Color Online)
Excited states of bright solitons trapped by the dark soliton for $D<1$.
Left, middle and right panels show, respectively, the first,
the second (for $D<1/3$), and the third (for $D<1/6$) excited state.
The dark and bright component
profiles are
depicted by black and blue lines, respectively (adapted from Ref.~\cite{s2}).
 }
		\label{revip_fig7}
	\end{center}
\end{figure}

Motivated by studies of spin-orbit coupled BECs~\cite{spinorbit1,spinorbit2},
it was recently shown~\cite{vaszb} that pertinent GPEs can be reduced to an
effective Manakov-type system but with
``unequal masses'' (i.e., unequal dispersion coefficients)
among the two components of Eq.~(\ref{deq12}).
Assuming that $D$ is the mass ratio of dark and bright components,
and seeking stationary solutions of
the GPEs~(\ref{deq12}) of the form $\psi_{1,2}=\upsilon_{d,b}(x)\exp(-i\mu_{d,b}t)$,
we obtain the system:
\begin{equation}
\begin{array}{rcl}
\mu _{d}\, \upsilon _{d} &=&-\frac{1}{2}\left( \upsilon _{d}\right) ^{\prime \prime
}+\left( \upsilon _{d}^{2}+ \upsilon _{b}^{2}\right) \upsilon _{d}+V(x)\, \upsilon_{d},
\\[1.0ex]
\mu _{b}\, \upsilon_{b} &=&-\frac{D}{2}\left( \upsilon_{b}\right) ^{\prime \prime
}+\left( \upsilon_{d}^{2}+ \upsilon_{b}^{2}\right) \upsilon_{b}+V(x)\, \upsilon_{b}.
\end{array}
\label{-+}
\end{equation}
The existence of DB solitons
can be explored upon realizing
that the dark soliton $u _{d}(x)=\sqrt{\mu _{d}}\tanh \left( \sqrt{\mu _{d}}x\right)$
[for $V(x)=0$] acts as an effective potential for the bright component~\cite{s2}.
This way, linearization of Eq.~(\ref{-+}) for a small bright component
gives rise to the eigenvalue problem:
\begin{equation}
\begin{array}{c}
\mathcal{L}\,\upsilon_{b}=
\lambda \,\upsilon_{b}
\quad {\rm with} \quad
 {\mathcal{L}=\frac{D}{2}}\frac{d^{2}}{dx^{2}}{+\mu _{d}\,
\mathrm{sech}^{2}\left( \sqrt{\mu _{d}}x\right) },
\end{array}
\label{quantum}
\end{equation}
where $\lambda=\mu_d-\mu_b$, while the Schr{\"o}dinger operator $\mathcal{L}$
corresponds to
the
P{\"o}schl-Teller potential, known from quantum mechanics~\cite{LL}.
Equation~(\ref{quantum}) supports
bound states for
integers $n$ satisfying
$D<D_{\mathrm{crit}}^{(n)}=\frac{2}{n\left( 1+n\right)}$.
Hence,
a fundamental (bound) state
of the bright component, pertaining to the DB soliton,
always exists.
Furthermore, for $D<1$ (for $n=1$), it
is also possible for the dark component
to trap a first excited state in the bright one
(i.e., a two-bright-soliton anti-phase pair). For $D<1/3$, it
will be possible to trap a second excited state, and so on.
Examples of such states, which were identified in Ref.~\cite{s2}, are shown in Fig.~\ref{revip_fig7}.

\subsection{Dissipative dynamics under the action of thermal effects}

Dissipative effects, induced by the interaction of the BEC with the thermal cloud,
can be studied in the framework of the so-called {\it dissipative GPE} model~\cite{pitas}.
In the two-component setting, this model arises from Eq.~(\ref{deq12})
upon the substitution
$i \partial_t \psi_{1,2} \rightarrow (i- \gamma_{1,2})\partial_t \psi_{1,2}$~\cite{vasnjp}, where parameters $\gamma_{1,2}$ depend on
temperature~\cite{proukakis}.
The dissipative GPE system describes phenomenologically,
via the presence of losses, the transfer of atoms from the condensate
to the thermal cloud.
The dissipative dynamics of
DB solitons in this setting can be studied
upon generalizing the methodology of Sec.~3.2. This way,
it is possible to derive an equation for motion for the DB soliton center, of the form:
$\ddot{x}_0-a\,\dot{x}_0+\omega_{\rm osc}^2\,x_0 = 0$~\cite{vasnjp}, where
\begin{eqnarray}
a = \frac{2}{3}\mu\left(\gamma_1-
\frac{1}{8}\chi^2 \gamma_2\right) +\frac{1}{6}\mu
\left(\gamma_2-\gamma_1+
\frac{1}{8}\chi^2 \gamma_2\right)\frac{\chi}{\sqrt{1+(\chi/4)^2}}.
\label{aa}
\end{eqnarray}
The generic positivity of parameter $a$
suggests that the newly introduced term, $-a\dot{x}_0$, represents an effective {\it anti-damping}.
This term characterizes the interaction of the DB soliton
with the thermal cloud. It results in the acceleration of the soliton
toward the velocity of sound, i.e., the dark component becomes continuously grayer and,
eventually, the wave transforms to the ground state of the BEC.
A similar situation,
in addition to their
internal mode motion, is encountered in the case of multiple DB solitons.
The accuracy of this effective particle picture in capturing
the anti-damped
dynamics is shown
in Fig.~\ref{revip_fig8}.

It is important to note that, although this dynamics is similar to that of
dark solitons in single BECs~\cite{proukakis},
the analysis of Ref.~\cite{vasnjp} reveals that
the effect of the bright (``filling'') component is to partially
stabilize dark solitons against temperature-induced dissipation,
thus providing longer lifetimes.

\begin{figure}
	\begin{center}
\includegraphics[height=4cm]{dynamics_one_db_gamma_002N.eps}
\includegraphics[height=4cm]{dynamics_two_db_oop_gamma_001NN.eps}
		\caption{(Color Online)
Examples of the anti-damped dynamics of one (left panels) and two (right panels) DB
solitons; top (bottom) panels depict the dark (bright) component. Dashed (blue)
lines depict the analytical predictions (adapted from Ref.~\cite{vasnjp}).
 }
		\label{revip_fig8}
	\end{center}
\end{figure}

\subsection{Dark-bright solitons in spinor condensates}

We now proceed with a case involving more than two components,
and study, more specifically, spinor BECs. The latter, have been realized
by employing optical trapping techniques, which allow for the confinement of
atoms regardless of their spin hyperfine state; thus, spinor BECs
formed by atoms with spin $F$, are described by a macroscopic wave function
with $2F+1$ components~\cite{stringari}. It is relevant
to highlight that spinor BECs
give rise to various phenomena that are not present
in single-component BECs, including formation of spin domains, spin textures,
topological states, and others~\cite{kawueda,stampueda}.

Here, we
only consider a case example, namely a quasi-1D spinor $F=1$ BEC, described
by the following dimensionless mean-field model~\cite{ofymispin,bdspinor}:
\begin{eqnarray}
i\partial_{t}\psi_{\pm 1} &=&H_{0}\psi_{\pm 1}+\delta
\left[(|\psi_{\pm 1}|^{2}+|\psi_{0}|^{2}-|\psi_{\mp 1}|^{2})\psi_{\pm 1}
+\psi_{0}^{2}\psi_{\mp 1}^{\ast}\right] ,
\label{dvgp1} \\[1ex]
i\partial_{t}\psi_{0} &=&H_{0}\psi_{0}+\delta \left[(|\psi_{-1}|^{2}+|\psi_{+1}|^{2})\psi_{0}
+2 \psi_{-1}\psi_{0}^{\ast}\psi_{+1}\right].
\label{dvgp2}
\end{eqnarray}
Here, the components $\psi_{0,\pm1}$ correspond
to the three values of the vertical spin component $m_F=0,\pm1$, while
$H_{0}\equiv -(1/2)\partial_{x}^{2}+V(x)+|\psi_{-1}|^2+|\psi_{0}|^2+|\psi_{+1}|^2$,
and $\delta$ is the ratio of the strengths of the spin-dependent and
spin-independent interatomic interactions.
Note that $\delta$ is positive (negative) for {\it polar} ({\it ferromagnetic})
spinor BECs as, e.g., in the case of $^{23}$Na ($^{87}$Rb) atoms, where this
parameter takes the value $\delta =+3.14\times 10^{-2}$ ($\delta =-4.66\times 10^{-3}$).

As shown in Ref.~\cite{ofymispin}, for $\delta>0$
the background state (on which a dark soliton may be supported)
is modulationally stable; this suggests that DB soliton solutions
of Eqs.~(\ref{dvgp1})-(\ref{dvgp2}) may be possible. Indeed, in Ref.~\cite{bdspinor},
exploiting the smallness of $\delta$, a multiscale expansion method was used
[for $V(x)=0$] to show
that such states do exist, and assume the following form:
\begin{equation}
\begin{array}{rcl}
\psi_{\pm1}&=&\sqrt{\left( \mu /2\right) +\delta \rho(X,T)}
\exp\left[-i\mu t + (2i\delta/\mu) \int \rho(X) dX \right],
\\[1.0ex]
\psi_{0}&=& \delta^{3/4} q(X,T)\exp(-i\mu t),
\end{array}
\label{ps12}
\end{equation}
where $\mu$ is the chemical potential, $X=\sqrt{\delta}(x-\sqrt{\mu}t)$ and $T=\delta t$
are stretched variables,
while functions the $\rho(X,T)$ and $q(X,T)$ obey the following system:
\begin{equation}
\begin{array}{c}
\partial _{T}\rho =-\frac{1}{2}\sqrt{\mu}\partial_{X}\left( |q|^{2}\right), \quad
i\partial _{T}q+\frac{1}{2}\partial _{X}^{2}q-2\rho q=0.
\end{array}
\end{equation}
The above is the Yajima-Oikawa (YO) system, which was originally derived to
describe the interaction of Langmuir and sound waves in plasmas~\cite{yajima}.
This system is completely integrable, and possesses
soliton solutions of the form
$\rho \propto -{\rm sech}^2(k_s X-\omega_s T)$ and $q \propto {\rm sech}(k_s X-\omega_s T)$,
where $k_s,~\omega_s$ are constants. These expressions, when
substituted into Eq.~(\ref{ps12}), give rise to approximate
dark-dark-bright (for the $m_{F}=+1,-1,0$ spin components) solitons,
while a similar analysis can also lead to bright-bright-dark ones.
As shown in Ref.~\cite{bdspinor}, these small-amplitude structures
persist for large amplitudes and, in the presence of a parabolic trap,
they perform harmonic oscillations, in a way
reminiscent of the two-component case.

We note in passing that similar asymptotic reductions of other multi-component GPEs,
have been used to construct vector soliton solutions
described by integrable systems, such as the Yajima-Oikawa (already mentioned above)
and the Davey-Stewartson (DS) ones~\cite{aguero}, the Mel'nikov system~\cite{aguero,f1},
and a coupled Korteweg-de Vries (KdV) equations system~\cite{vectordark}.

\subsection{Vector solitons in higher-dimensions}

\begin{figure}[tbp]
	\begin{center}

\includegraphics[height=3.5cm]{vortex.jpg.ps}
\includegraphics[height=3.5cm]{dipole2.jpg.ps}
		\caption{(Color Online)
The left panel quartet shows a single vortex-bright solitary wave, while
the middle and right quartets show, respectively, dipoles thereof,
with in-phase or out-of-phase bright components (adapted from Ref.~\cite{pola}).
Top (bottom) panels depict the vortex (bright) component, while
left (right) panels depict densities (phases).
 }
		\label{revip_fig9}
	\end{center}
\end{figure}

The
concept that one component
acts as a potential to trap the other,
is one that transcends dimensionality. Indeed, considering
the 2D variant of Eq.~(\ref{deq12}),
a vortex (which is a prototypical coherent structure
in 2D repulsive BECs~\cite{siambook}) in
component $\psi_1$ can play the role of a potential
trapping a bright soliton in component $\psi_2$.
A case example of a vortex-bright soliton
is shown in Fig.~\ref{revip_fig9}. Note that these
structures bear different names in different communities, such as
vortex-bright solitons~\cite{kodyprl,pola},
half-quantum vortices~\cite{tsubota} or baby Skyrmions~\cite{cooper}.
Various studies have been devoted to the stability~\cite{skryabin,kodyprl}
and dynamics~\cite{kodyprl,tsubota} of these structures.
Moreover, it was found that they feature
intriguing interactions that decay as $1/r^3$~\cite{tsubota}.
They also allow much of the phenomenology discussed previously,
including their potential to form
molecular states with out-of-phase and
in-phase bright solitons in the presence of the trap
(cf.~middle and right panels of Fig.~\ref{revip_fig9}, as well as the work of
Ref.~\cite{pola}).

Another quasi-2D
state,
is the ring DB soliton explored in Ref.~\cite{ringrds}. The matter-wave ring dark
soliton (RDS), introduced in Ref.~\cite{usrds},
is a 2D radial generalization of the dark soliton
which, however,
is generically unstable due to breakup into vortex-antivortex polygonal structures
(squares, hexagons, etc.). Nevertheless, in the two-component setting, the RDS in one component
can form an effective potential that supports a bright ring soliton structure
in the
other component. As found in Ref.~\cite{ringrds}, although the presence of
the bright component
weakens the instability of the RDS, it is not possible to eliminate it completely.
Nevertheless, the instability
gives rise to states of interest in their
own right, such as vortex-bright polygons and DB soliton stripes.

\subsection{The double-well potential perspective}

Lastly, as regards the variants considered herein,
when two dark solitons
(or two vortices) trap
two bright ones, one can also view the relevant molecule
under a different prism, namely that of
topological states in the first component forming an effective {\it double-well}
potential for the second one. This perspective was used
in the cases of DB solitons in 1D~\cite{vag},
and vortex-bright solitons in 2D~\cite{pola}. Importantly,
given their genuine topological nature,
vortices form, in a sense,
a more ``robust'' double-well. Namely,
while this approach neglects
the back-action of the bright components on the dark ones
(i.e., this is a ``soft'' potential, rather than a hard,
externally imposed, one),
this feedback mechanism is present and
is more significant in 1D than in 2D. Nevertheless,
in both settings, this approach enabled the observation of
features associated with double-well potentials, such as
symmetry-breaking bifurcations, Josephson
oscillations, and so-called $\pi$-states emerging from
the bifurcations
(see Ref.~\cite{malomedbook} and references therein).

\section{Conclusions \& Outlook}

In this review, we examined
coherent structures arising
in coupled defocusing nonlinear Schr{\"o}dinger equations, especially so in
the vicinity of the so-called Manakov limit of equal self- and
cross-interactions.
There (but also away from that
limit), a fundamental concept
emerges, namely
that a ``dark structure'' in one component (be it a dark soliton
in 1D or a vortex in 2D)
acts as
a potential well for the second component.
This enables the confinement therein of a bright soliton
and the formation of ``dark-bright states''. These states also
persist in the presence of external (e.g., parabolic) potentials,
wherein they
oscillate as Newtonian particles. Molecular states involving multiple
dark-bright waves
may exist for
appropriate phase difference between the bright components in the homogeneous setting
(solitonic gluons), and in the presence of external traps.
Moreover, rotated versions of
such dark-bright solitons also emerge in experiments, in the
form of the so-called beating dark-dark solitons.

Additionally,
variations on these themes were recognized and explored.
The dark structure potential well was, for instance, recognized
as possibly trapping higher-excited states. Another possibility
concerned the
prototypical characterization of the thermal-induced dissipation, that leads
to anti-damping and eventual expulsion of
dark-bright solitons
from trapped atomic condensates.
The relevance of higher-component settings
bearing spinor analogues of the
considered states was also discussed.
Here, dark-dark-bright, or
bright-bright-dark states were found via a
multiscale asymptotic analysis. Another equally important and experimentally tractable
generalization arose in higher-dimensional settings, where
vortex-bright solitons,
as well as dark-bright ring solitons
were presented.
Finally,
molecular states bearing two (or more) dark entities were
also perceived as double (or, respectively, multi-) well potentials, thus
enabling
related phenomena.

We hope that it is clear
that the above ideas and paradigms are powerful and broad beyond any one
of the particular examples used, and could lead to a wealth
of future possibilities and explorations, both in
theory and experiments.
As a small sample of
the questions that merit future consideration, we pose the
following. Is it possible to identify dark-bright solitonic
states (and their variants) in the context of the intensely studied
recently spin-orbit coupled
BECs~?
Can a quantitative
understanding of the scattering of vector solitons
off of Gaussian barriers (or wells)
be achieved~?
Can we trap higher-excited states in higher-dimensional settings
(radial and/or azimuthally dependent ones)~? Can an analogue
of dark-dark states be observed in higher-dimensions~? What
are the implications of these ideas in three-dimensional
settings~?
All these are important open questions,
a number of which are under active current consideration and, we
expect, will lead to numerous discoveries ahead...

\section*{Acknowledgments}

The invaluable contribution of all of our collaborators, co-authors and friends,
including our past and present students and postdocs,
is gratefully acknowledged. We are especially indebted to Ricardo Carretero-Gonz{\'a}lez
for his extremely valuable input and help. The support of
NSF-DMS-1312856 (PGK) is gratefully acknowledged.

\section*{References}

\bibliographystyle{elsarticle-num}

redpajama_set_name: RedPajamaArXiv


The Beast from the East has blown its way across the British countryside, leaving thigh high snowdrifts barring paths and roads, and my workshop with iced buckets holding their few flowers in a cement-like grip.
I'm normally crouched in my blocks, ready for the starter's gun to fire on the first day of March – sprinting off (metaphorically at least) for my seed packets and taking over the house with a compost invasion. But with the mercury hovering below zero throughout the past week, I've only so far sowed a bit of Larkspur and Molucella – leaving them to freeze their proverbial bits off in my unheated greenhouse, figuring that any seed which likes a period of cold would relish the unseasonal conditions (and if I can do this in the greenhouse it saves my family a nasty shock when they open the fridge). In a week's time, I'll be nice to these frozen seed trays and bring them into the warm to see if they will reward me with an instant burst into life. It's a nice theory anyway – seeds bursting into life feels like a distant glimmer as snow still drips all around me. Sowing seeds right now is nigh on impossible as all I have to hand are a few giant compost ice cubes, and the workshop temperature feels even lower than the outdoors so I can't even put the bags in there to thaw.
I'm doing a trial of Fertile Fibre seed and potting compost this year, so am itching to find out how that goes – it certainly feels like a beautifully soft and light material to handle, and I'm eager to see how it compares with standard multi-purpose.
The week before the Beast arrived the garden felt quite optimistic, with hellebores nodding in the morning mists, and tulips starting to get a wriggle on, lifting their leaves above the damp crust of soil. I did cover up my hellebores with dry, straw-like debris, upturned plant pots, hedge pruning and anything else I could lay my hands on before the Beast arrived, in an attempt to cosset them through the worst of the weather as I'd dearly love them to make themselves available for my spring weddings later in the season. With temperatures forecast to be in positive single figures again next week, I'll disentangle everything to see if the strategy worked.
I'm also holding my breath to see if the ranunculus have made it through the big freeze as they are not known for their resilience to prolonged sub-zero conditions. Tales of them parting from frozen root systems without so much as a sigh abound on Flowers from the Farm chat forums, and I can only hope that mine exhibit a bit more spine, but I fear it may be a vain expectation.
Such is the joy of being a flower grower – you never know what the weather is going to throw at you and just because one year you have things in flower at the start of March, there's no guarantee that this will be repeated in future seasons. Last year's late spring heatwave brought me peonies in May (a month early), but on the bright side, this year's 'proper' winter should encourage the tulips to elongate their stems from the grumpy stumpy incarnations which they've evolved into in the last three years mild conditions.
I'm waiting for the snow to clear to make an assessment of casualties. I suspect my established Rosemary plants my well choose to disestablish themselves in the face of un-Mediterranean conditions, and my gloriusly perfumed Daphne, which already looked petulant before the onslaught, may have finally picked up its ball and taken it home for good.


text:
Hammarby Sjöstad (« la ville du lac Hammarby ») est un écoquartier situé dans la périphérie sud-est de Stockholm, capitale de la Suède. Le quartier a une superficie d'environ 200 hectares de terrain et sa proximité directe avec le centre-ville de Stockholm et de la réserve naturelle de Nacka en font un espace de grande influence dans la capitale. Il est considéré comme une référence mondiale dans le domaine des solutions écologiques appliquées à la cité.

Historique du site : un projet de réurbanisation

Situé au sud-est du centre-ville, le quartier de Hammarby Sjöstad est une ancienne zone industrielle et portuaire sur les rives du , juste séparé par une écluse de la mer Baltique. Les autorités ont lancé un plan de reconversion dans le cadre de la candidature pour l'organisation des Jeux Olympiques d'été de 2004. Il s'agissait d'aménager un village olympique à la pointe de l'innovation environnementale. , les autorités rationalisèrent sur le long terme ce qui n'était encore qu'une « potentielle exigence temporaire » d'accueillir les Jeux. Et si ces mêmes Jeux n'eurent finalement pas lieu à Stockholm, le projet écologique quant à lui aboutit.

Jusqu'aux années 1990, le paysage du quartier était fait de baraquements et d'infrastructures industrielles.

Les premières phases de réurbanisation ont commencé au milieu des années 1990 au nord du quartier. On y prévoyait  construits pour un total de . L'aménagement est fini depuis 2010 et compte finalement une capacité d'accueillir .

Désormais, l'ensemble des bâtiments répondent aux normes HQE et ont été construits par plus d'une vingtaine d'entrepreneurs différents pour éviter une trop grande homogénéité de style. Tous les matériaux, les consommables, ainsi que le système d'assainissement répondent aux normes environnementales les plus strictes.

Le modèle des « Éco-Cycles »

Un modèle écologique cohérent a aussi permis de relier les sources d'énergie aux besoins de proximité de manière optimale, ce, pour une économie d'énergie, pour une récupération, et une valorisation en fin de cycle : la zone urbaine, telle une entité organique, est ainsi totalement intégrée à son environnement. Le modèle « Éco-cycles » vise à doubler les performances énergétiques par rapport à Stockholm. Pour cela le projet essaie de lier l'offre d'électricité, le chauffage, la climatisation et l'eau à la gestion des déchets et des eaux usées.

Collecte souterraine des déchets

En 1999 la particularité de Hammarby Sjöstad pour la collecte des déchets sur la voie publique tient au fait que tous les points de récupération sont connectés à un réseau souterrain. Il n'y a ainsi pas de personnels ni de véhicules affectés à la collecte. Les poubelles à triple compartiment se connectent à un système de canalisation sous vide, où les déchets sont aspirés par de puissants courants d'air.

Un opérateur est informé en temps réel par des capteurs du niveau de remplissage des trois compartiments respectifs sur l'ensemble du réseau. Il peut donc procéder à un enlèvement sélectif. À côté de chaque point de collecte, une prise d'air est ouverte, et seul un des compartiments est ouvert pour éviter que les différents types de déchets ne se mélangent. Les canalisations sous vide se pressurisent de nouveau entraînant les déchets par des flux éoliens jusqu'à . Ceux-ci convergent au point d'enlèvement, vers des conteneurs centralisés.

Notes et références
Voir aussi

 Écoquartier
 Haute qualité environnementale
 Développement durable
 Urbanisme
 Ville durable

Liens externes

  Hammarby Sjöstad

Communauté urbaine de l'agglomération de Stockholm
Écoquartier

redpajama_set_name: RedPajamaWikipedia


Who is Coyote? Trickster, Helper, Teacher, or Fool? Over fifty writers from across America tell Coyote's story in poetry and prose, shamanics and myth. Read and learn -- and watch your chickens! 1982 Bookbuilders West Award for best quality trade paperback.
ils:.b43595133|Book|Books|1st ed.|English|Wingbow,|1982.|156 pages : illustrations ; 22 cm.


I've sent you a private message requesting your account details so we can process your request. You can access your private messages by clicking on your avatar on the upper righthand corner and then selecting the envelope icon.
Still nothing is updated and no one has responded to my email.
Can someone please provide an update?
Glad to hear that you have returned that form to our Customer Service team, whose email address is in the email. As mentioned on the form itself, it can take up to 5 business days upon receipt of the forum for those changes to be processed. When our team have processed those changes from the form then you will receive a confirmation of this by email.
I know you said five days but that turn around time is abit ordinary. Could you atleast confirm custmer support received my request?
I've checked with our team and they can confirm that they did receive the form. They have also advised me that they did send a response as there was some additional information that they required to process the form.
Can they resend the email request, I didnt receive anything.
I have passed your request onto the appropriate team to resend that email. As our team do send out numerous emails, our team are currently doing their best to locate that specific email to resend it to you.
Still no response...really disappointed with the service and how clunky owner and adminstrator change over system works.
Sorry for the delay. I tried giving you a call this afternoon. Your account details have been updated and you should have received a confirmation email about the changes that were made.
If you have any further queries or get stuck please reply to the email or this post.


The Blue Angels are seen practicing over Annapolis in 2015 in preparation for their show during Commissioning Week.
Commissioning Week offers everything from grease to angels.
When it comes to logically questionable annual rituals we nonetheless eagerly anticipate, the Herndon Monument climb is right up there with the Naval Academy-St. John's croquet game and, perhaps, sessions of the General Assembly.
For the academy's plebes, it marks the end of their freshman year — and their moment in the sun in a Commissioning Week that, for obvious reasons, spotlights the graduating class. So after all the rigors of learning the ropes at the academy, starting with Plebe Summer, it all comes down to getting a plebe's hat — a "Dixie cup" — off the top of a 21-foot granite monument, after upperclassmen have thoughtfully slathered the obelisk with 50 pounds of vegetable shortening.
So, our congratulations to the Class of 2018 for performing the cap switch in one hour, 38 minutes and 36 seconds, a respectable time.
We'd have difficulty explaining exactly why plebes have been scaling the obelisk since 1940, but it is clearly an object lesson in persistence and teamwork. You can do marvelous things with those two virtues, as the Blue Angels, the Navy's aerobatic team, will be illustrating over the Severn River starting at about 2 p.m. today, in an even more eagerly anticipated Commissioning Week ritual.
The week, of course, brings lots of extra activity to area businesses. But we'd like Commissioning Week even if it didn't sell one additional T-shirt or crabcake. It's a celebration of an institution that is interwoven with the history of Annapolis, and of the great work that institution has done for 170 years in guaranteeing the security of this country. And it heralds the coming of summer. What could be better than that?
A unanimously passed County Council resolution expressing support for a study isn't much of an attention-grabber. Still, Monday's vote in favor of a resolution by Chairman Jerry Walker and Councilman Andrew Pruski was worth noticing. It shows the council wants a serious look at the implications of use of police body cameras, with the expectation these may play a role in local law enforcement before too long.
The governor signed the law setting up the state study commission last week, and the president wants to create a three-year, $263 million federal program to make the cameras more affordable to states and local jurisdictions.
The county resolution urges the cooperation of Anne Arundel's police and sheriff's departments in the study. Pruski said it's important to figure out the legal and financial aspects before deciding if there's a need locally. "We need to be ahead of the game," he said. "It's going to come down the pike at some point."
He's right about both things.
A plane from the Blue Angels flight team is obscured by a tree at it flies low over Annapolis.
Two planes from the Blue Angels flight team make a close pass, rehearsing for their show for the Naval Academy Commencement.


text:
module KeypayIntegration
  module Data
    module Member
      class EmergencyContactMapper
        extend Base

        class << self
          def fields_mapper
            {
              'emergencyContact1_Name' => 'name',
              'emergencyContact1_ContactNumber' => 'daytime',
              'emergencyContact1_AlternateContactNumber' => 'after_hours_no',
              'emergencyContact1_Relationship' => 'relationship',
            }
          end
        end
      end
    end
  end
end

redpajama_set_name: RedPajamaGithub


text:
Q: SSH reverse tunneling: Address family not supported by protocol I am trying to create a reverse SSH tunnel to stream a RTSP stream.
When I connect to my server with this command: ssh -Nf -R serverIP:serverPort:localhost:554 user@serverIP it seems to be working but if I connect to my stream using VLC the console prints socket: Address family not supported by protocol.
I have already searched everywhere but I haven't found anything.
My server configurations:
#       $OpenBSD: sshd_config,v 1.100 2016/08/15 12:32:04 naddy Exp $

# This is the sshd server system-wide configuration file.  See
# sshd_config(5) for more information.

# This sshd was compiled with PATH=/usr/local/bin:/usr/bin

# The strategy used for options in the default sshd_config shipped with
# OpenSSH is to specify options with their default value where
# possible, but leave them commented.  Uncommented options override the
# default value.

# If you want to change the port on a SELinux system, you have to tell
# SELinux about this change.
# semanage port -a -t ssh_port_t -p tcp #PORTNUMBER
#
#Port 22
AddressFamily inet
#ListenAddress 0.0.0.0
#ListenAddress ::

HostKey /etc/ssh/ssh_host_rsa_key
#HostKey /etc/ssh/ssh_host_dsa_key
HostKey /etc/ssh/ssh_host_ecdsa_key
HostKey /etc/ssh/ssh_host_ed25519_key

# Ciphers and keying
#RekeyLimit default none

# Logging
#SyslogFacility AUTH
SyslogFacility AUTHPRIV
#LogLevel INFO

# Authentication:

#LoginGraceTime 2m
#PermitRootLogin yes
#StrictModes yes
#MaxAuthTries 6
#MaxSessions 10

#PubkeyAuthentication yes

# The default is to check both .ssh/authorized_keys and .ssh/authorized_keys2
# but this is overridden so installations will only check .ssh/authorized_keys
AuthorizedKeysFile      .ssh/authorized_keys

#AuthorizedPrincipalsFile none

#AuthorizedKeysCommand none
#AuthorizedKeysCommandUser nobody

# For this to work you will also need host keys in /etc/ssh/ssh_known_hosts
#HostbasedAuthentication no
# Change to yes if you don't trust ~/.ssh/known_hosts for
# HostbasedAuthentication
#IgnoreUserKnownHosts no
# Don't read the user's ~/.rhosts and ~/.shosts files
#IgnoreRhosts yes

# To disable tunneled clear text passwords, change to no here!
#PasswordAuthentication yes
#PermitEmptyPasswords no
PasswordAuthentication yes

# Change to no to disable s/key passwords
#ChallengeResponseAuthentication yes
ChallengeResponseAuthentication no

# Kerberos options
#KerberosAuthentication no
#KerberosOrLocalPasswd yes
#KerberosTicketCleanup yes
#KerberosGetAFSToken no
#KerberosUseKuserok yes

# GSSAPI options
GSSAPIAuthentication yes
GSSAPICleanupCredentials no
#GSSAPIStrictAcceptorCheck yes
#GSSAPIKeyExchange no
#GSSAPIEnablek5users no

# Set this to 'yes' to enable PAM authentication, account processing,
# and session processing. If this is enabled, PAM authentication will
# be allowed through the ChallengeResponseAuthentication and
# PasswordAuthentication.  Depending on your PAM configuration,
# PAM authentication via ChallengeResponseAuthentication may bypass
# the setting of "PermitRootLogin without-password".
# If you just want the PAM account and session checks to run without
# PAM authentication, then enable this but set PasswordAuthentication
# and ChallengeResponseAuthentication to 'no'.
# WARNING: 'UsePAM no' is not supported in Red Hat Enterprise Linux and may cause several
# problems.
UsePAM yes

AllowAgentForwarding yes
AllowTcpForwarding yes
#GatewayPorts no
X11Forwarding yes
#X11DisplayOffset 10
#X11UseLocalhost yes
#PermitTTY yes
#PrintMotd yes
#PrintLastLog yes
TCPKeepAlive yes
#UseLogin no
#UsePrivilegeSeparation sandbox
#PermitUserEnvironment no
#Compression delayed
#ClientAliveInterval 0
#ClientAliveCountMax 3
#ShowPatchLevel no
#UseDNS yes
#PidFile /var/run/sshd.pid
#MaxStartups 10:30:100
PermitTunnel yes
#ChrootDirectory none
#VersionAddendum none

# no default banner path
#Banner none

# Accept locale-related environment variables
AcceptEnv LANG LC_CTYPE LC_NUMERIC LC_TIME LC_COLLATE LC_MONETARY LC_MESSAGES
AcceptEnv LC_PAPER LC_NAME LC_ADDRESS LC_TELEPHONE LC_MEASUREMENT
AcceptEnv LC_IDENTIFICATION LC_ALL LANGUAGE
AcceptEnv XMODIFIERS

# override default of no subsystems
Subsystem       sftp    /usr/libexec/openssh/sftp-server

# Example of overriding settings on a per-user basis
#Match User anoncvs
#       X11Forwarding no
#       AllowTcpForwarding no
#       PermitTTY no
#       ForceCommand cvs server

GatewayPorts yes
ClientAliveInterval 60

A: I solved editing the client's (RPi's) configurations. I disabled IPv6 in /etc/hosts.

redpajama_set_name: RedPajamaStackExchange


text:
package com.codeabovelab.dm.cluman.job;

import com.fasterxml.jackson.core.Version;
import com.fasterxml.jackson.databind.Module;
import com.fasterxml.jackson.databind.module.SimpleDeserializers;
import com.fasterxml.jackson.databind.module.SimpleSerializers;
import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.boot.autoconfigure.condition.ConditionalOnBean;
import org.springframework.stereotype.Component;

/**
 */
@Component
@ConditionalOnBean(JobParameterDescriptionSerializer.class)
public class JobJacksonModule extends Module {

    private JobParameterDescriptionSerializer jobParameterDescriptionSerializer;

    @Autowired(required = false)
    public void setJobParameterDescriptionSerializer(JobParameterDescriptionSerializer jobParameterDescriptionSerializer) {
        this.jobParameterDescriptionSerializer = jobParameterDescriptionSerializer;
    }

    @Override
    public String getModuleName() {
        return getClass().getName();
    }

    @Override
    public Version version() {
        return new Version(1, 0, 0, null, null, null);
    }

    @Override
    public void setupModule(SetupContext setupContext) {
        SimpleSerializers serializers = new SimpleSerializers();
        addSerializers(serializers);
        setupContext.addSerializers(serializers);

        SimpleDeserializers deserializers = new SimpleDeserializers();
        addDeserializers(deserializers);
        setupContext.addDeserializers(deserializers);
    }

    @SuppressWarnings("unchecked")
    private void addDeserializers(SimpleDeserializers deserializers) {
    }

    private void addSerializers(SimpleSerializers serializers) {
        if(jobParameterDescriptionSerializer != null) {
            serializers.addSerializer(JobParameterDescription.class, jobParameterDescriptionSerializer);
        }
    }

}


text:
£240k in grants helps to create 176 jobs in region
Burslem company Sydney Heath & Son is the latest recipient of the grant funding
Laura JamesBusiness Editor
Martin Coats, managing director at EGS.
Small and medium sized manufacturers in Staffordshire have created more than 170 new jobs – as part of a programme designed to help businesses boost performance and increase sales.
The Manufacturing Growth Programme (MGP) – funded by the European Regional Development Fund (ERDF) and Economic Growth Solutions (EGS) – has contributed a total of more than £240,000 to firms in Stoke-on-Trent and Staffordshire since the beginning of last year.
And its latest grant – of around £2,000 – has been handed over to family-run manufacturer Sydney Heath & Son, based in Burslem.
University plan boosted by £1m of EXTRA funding
Sydney Heath is a manufacturer and supplier of bespoke foam, sponge and rubber products for industry, with a long and proud history of supplying Stoke-on-Trent's pottery companies for more than 100 years.
The company supplies the ceramic sector's major players – including Wedgwood, Churchill and Steelite International – and exports around 50 per cent of its products worldwide.
Finance and commercial director Jonathan Barnes said: "The business has experienced a good deal of change as a result of succession planning.
"The current chief executive, Godfry Heath, is preparing to take a step back and his daughter Gemma, who is my wife, and myself are laying the foundations to take the business forward."
Sydney Heath – which employs around 30 staff – used the recent cash boost to enrol a handful of its key members of staff on a four-day course to learn about new business processes and company culture.
Sydney Heath is a manufacturer and supplier of bespoke foam, sponge and rubber products for industry.
Jonathan said: "Our staff are very capable and bright, but we wanted them to learn about good business practice.
"The new processes we are introducing are in their very early stages, but we need to get them to the most efficient levels they can be before we can start growing the business more proactively.
"The focus is on modernising and improving efficiencies across the manufacturing side of the business and so far it is having a very positive effect, especially on the more long-standing members of staff."
Sunny climbs beckon as travel agency marks 15th birthday
He added: "Over the last four or five years revenues have grown around 10 per cent year-on-year – this year has been our biggest year.
"Our focus to date has been on baking in that organic growth, servicing our existing long-standing customer base.
"The fruit of this funding is providing more bandwidth to explore targeted business development opportunities."
The MGP was set up to fill the void left by the Manufacturing Advice Service (MAS) by providing access to specialist assistance to help manufacturers grow and improve.
Martin Coats, managing director at EGS, said: "We are continually proving that the right support, delivered at the right time and by the right people, can make a significant difference to manufacturers.
New engineering academy is an 'ACE' idea
"More than £240,000 has been awarded in the form of grants so far and this has been used by firms across Stoke-on-Trent and Staffordshire to improve the way they manufacture, launch new products or access additional or new markets.
"This has already equated to 176 new jobs, with 49 more expected to be created once projects are completed."
He added: "The difference with MGP is that it is delivered by manufacturing experts who understand the challenges companies are facing.
"They understand the language managing directors are talking and can guide them on making the right decisions, before bringing in specialists on specific issues they are facing or opportunities they're looking to explore."

redpajama_set_name: RedPajamaCommonCrawl


Asiad Steels is one of the well-known distributors of ASTM A194 GR.8M Stainless Steel Hex Nuts, which has a number of outstanding attributes to provide like Lightweight, Various sizes, Best materials used, Highly durable, Reliable, Corrosion resistance and more. These ASME SA 194 GR.8M SS Hex Nuts are provided in extensive collection of sizes, grades and thickness to match the demands of our customers at reasonable prices. These ASME SA 194 GR.8M SS Hex Nuts are fabricated with large quantities of finest material that raises the level of resistance to corrosion and heat-induced softening or weakness. Accurately developed and designed, these ASTM A194 GR.8M Stainless Steel Coupler Nuts are very much required for their reliable performance and tough construction. These ASTM A194 GR.8M Stainless Steel Nylon Insert Nuts are generally used in Food processing machinery, mainly in beer brewing, wine making and milk processing. They are also used in Kitchen benches, troughs, sinks machinery and appliances. ASTM A194 GR.8M Stainless Steel Nylon Nuts are perfectly used for dissimilar project establishing in eminent industries.
In the In the ASTM A194 GR.8M Stainless Steel Self-Locking Nuts is mass-produced by using the best quality of raw material and present technology in compliance by means of the set industry norms at our well-furnished production unit. We are the finest supplier of ASTM A194 GR.8M Stainless Steel Lock Nutsthat is accordingly considered for superior performance and quality. We are known as one of the prominent names in the industry involved in offering a widespread array of ASTM A194 GR.8M Stainless Steel Heavy Hex Nuts to the customers. Buy Stainless Steel Nutsat reasonable prices from us.
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We are Suppliers of ASTM A194 Grade 8M Hex Nuts in India Such as Mumbai, Aberdeen, Haryana, Al Jubail, Noida, Hong Kong, Rio de Janeiro, Al Khobar, Secunderabad, Los Angeles, Brisbane, Pimpri-Chinchwad, Hanoi, Muscat, Milan, Toronto, Surat, Ankara, Ahvaz, Indore, Geoje-si, Pune, Caracas, Gimhae-si, Dallas, Karachi, Algiers, Abu Dhabi, Kanpur, Ludhiana, Chandigarh, Singapore, Bangkok, Vung Tau, Ahmedabad, Moscow, Baroda, Melbourne, Gurgaon, La Victoria, Bhopal, Colombo, Atyrau, Nashik, Vadodara, Riyadh, Sydney, Thane, Coimbatore, Calgary, Rajkot, Istanbul, Ho Chi Minh City, Kuwait City, Bengaluru, Visakhapatnam, Busan, Lahore, Mexico City, Nagpur, Montreal, Bogota, Jeddah, Thiruvananthapuram, Port-of-Spain, Jaipur, Doha, Jamshedpur, Hyderabad, Navi Mumbai, Jakarta, Faridabad, Ulsan, Edmonton, Chiyoda, Houston, Kolkata, London, Courbevoie, Lagos, Mumbai, Dubai, Petaling Jaya, Kuala Lumpur, New Delhi, Ranchi, Dammam, Perth, Madrid, Howrah, Ernakulam, Sharjah, Cairo, Manama, Tehran, Santiago, Chennai, Granada, Seoul, New York.


text:
Florence's Duomo Cathedral Inspired Every Inch of This Destination Wedding in Italy
By Sara Dickinson
The couple invited 98 guests from the United States, Turkey, and Iran to watch them tie the knot abroad, in a destination surrounded by history.
Then-law students Saghar Esfandiaarifard and Ben Herold first crossed paths in August 2012. Three years later, they found themselves in Italy; the pair took a trip to Florence together, and although they weren't yet engaged, they talked about how incredible it would be to host a wedding there. "We couldn't have pictured a more picturesque location!" Saghar says. Six-and-a-half years into their relationship, Ben popped the question on Valentine's Day at the pair's favorite restaurant in Williamsburg, Brooklyn: Walter Foods.
Planning a faraway celebration gave the couple an excuse to travel to Florence twice; once as a couple and once with their families. Back home, the pair entrusted Daniela Tripodi from The Tuscan Wedding to help them breach the language barrier—and make the long-distance planning process a bit easier. "Many of our vendors we met for the first time on the day of our welcome dinner or at the wedding," the bride shares, noting that she, Ben, and Daniela worked together to curate a big-day team.
There were, of course, multiple parts of the planning process that Saghar and Ben took on firsthand—this included sourcing a venue. When the couple saw Villa Cora Hotel for the first time, they knew the locale would allow them to host a timeless celebration with great food and drinks; the destination also provided the romantic Italian ambience they had been searching for. "It was elegant, but not stuffy, and charming. Plus, the staff and management really understood and cared about delivering top-level hospitality," explains the bride. The venue was the ultimate place to host the couple's 98 guests, who traveled from all over the United States, Turkey, and Iran for their June 8, 2019, nuptials.
A Weekend in Italy
The couple's stationery suite paid homage to the city of Florence and the several venues incorporated into their wedding weekend, complete with maps and a custom crest with their initials. The set's color palette was inspired by the Cattedrale di Santa Maria del Fiore, located in the Piazza del Duomo, featuring blush, muted greens, and off-white shades.
Destination Wedding Invitations That Celebrate Your Faraway Locale
Saghar and Ben hosted an outdoor dinner at Villa Medicea Di Liliano to welcome guests to Florence. One long table was topped with a white runner, a garland of greenery, and table settings that featured a bold blue glass at each seat for a pop of color.
At the welcome dinner, guests found their seating assignments on hand-painted leaves that were pinned to bright yellow lemons.
Have Some Gelato
For dessert, the couple served gelato from a turquoise Fiat 500.
When Life Gives You Lemons
They sent guests on their way with bottles of limoncello, presented in a vintage wicker cart.
Expert-Approved Ideas for Your Wedding Welcome Party
A Dream Gown
Saghar had always envisioned herself in a lace wedding dress with long sleeves, and thoroughly enjoyed sourcing the gown that played into that vision during the shopping process. "It felt great to love the skin I was in," she recalls of the positive experience. She wore a custom lace Oscar de la Renta number with long sleeves, an open back, and a plunging neckline.
She completed her look with a veil, also from Oscar de la Renta, simple pearl stud earrings, and Bella Belle flats with pearl embellishments.
Saghar's bouquet included peonies, English roses, and greenery tied with a blush ribbon. The arrangement actually went missing moments before the ceremony, causing a slight delay. "It was literally the only thing that went 'wrong' that day!" the bride shares.
Ultra-Romantic Peony Wedding Bouquets
The Groom's Look
Ben donned a custom tuxedo by Johnathan Behr with a white shawl-collared jacket. His bride gifted him custom cuff links featuring a picture of the couple's dog, Otter. "Otter has been in my life for 10 years. He's been a lovable third-wheel for us since we met," the groom says.
Bridesmaids in Black
With a black-tie dress code, Saghar thought it would be appropriate for her bridesmaids to wear classic ensembles. They stepped into black satin dresses in varying styles from Bella Bridesmaids in Beverly Hills. "I selected four options, and each of the four girls liked one of the options the most, so it was perfect!" Saghar says. The bride's maid of honor, her sister, had a black dress custom-made by their mom's friend, who also made their mother's dress for the big day.
Mismatched Groomsmen
The groomsmen received a few attire directions from Ben: They needed to wear black peaked lapel tuxedos with French-cuffed shirts and black patent leather shoes. "My groomsmen are the best people I know, but are not particularly adept at following directions," Ben says. "So, while they all wore tuxedos, some wore sneakers, some wore different jackets, and none of us matched. In the end, though, I loved it!"
This couple didn't want to miss a minute of their cocktail hour, so they planned a first look below the terrace at Villa Cora. "Once we saw each other, we forgot all about the hours leading up to that moment and got lost for a few seconds," Saghar recalls.
The Ceremony Setup
The outdoor ceremony space was decorated with gold and glass lanterns, ceramic urns holding flower arrangements, a eucalyptus garland (which along the final row of gold chairs), and white flower petals down the aisle.
A Cultural Spread
The ceremony incorporated traditional elements of Persian Sofreh design, some of which were brought to Italy from Los Angeles by the bride's mother and aunt. The spread, which included grapes, candles, and a prayer book, was laid out on a table with two stools for the bride and groom to sit.
Ways to Personalize a Religious Wedding Ceremony
A Personalized Service
Saghar is Iranian American, so it was important to the couple to have the ceremony in both English and Farsi. The bride made her way down the aisle accompanied by her parents while "Crazy Love" by Van Morrison played. The couple exchanged vows they wrote for each other and opted to skip traditional readings.
Italian Cocktails
The newlyweds served signature drinks during the cocktail hour; the bride chose an Aperol spritz, while the groom opted for a negroni. The bar also offered Prosecco, beer, and wine.
Missing Their Dog
Although the couple's pup, Otter, couldn't attend the wedding, the pair included him by emblazoning their napkins and cocktail stirrers with his hand-drawn portrait, along with the phrase "I'll Have an-Otter!"
Ways to Ensure Your Dog Is the Guest of Honor at Your Wedding
The Serenade
While guests enjoyed the signature cocktails and passed appetizers, an Italian folk trio played the accordion, guitar, and violin.
Versailles, But in Florence
The reception took place in the hotel's Mirror Room, where original mural paintings from the 19th-century created an instant feeling of grandeur.
Scroll Details
Guest's names were calligraphed on small scrolls and placed inside Champagne flutes. "They were perfect for the first toasts and getting the energy going," the bride reflects.
Trending Now: Scroll Wedding Details
On the Tables
Round tables were topped with creamy linens and paired with gold Chiavari chairs. All-white centerpieces were placed on each table, along with candles in varying heights.
Attendees enjoyed a four-course plated meal that began with millefeuille eggplants with mozzarella, tomato, and parmesan, followed by cacio e pepe, filet mignon with potatoes, and chocolate gelato with hazelnut crumble—in lieu of a traditional wedding cake.
Some Advice
To couples unsure of whether or not a destination celebration is right for them, Saghar says, "Go with your gut and lean in all the way. While a destination wedding can have its challenges, it was perfect for us and our guests, who, to this day, describe it as a memorable day and trip for them!"
Photography, Anya Kernes Photography
Welcome Party Venue, Villa Medicea Di Liliano
Welcome Party Catering, Galateo Ricevimenti
Welcome Party Lighting, Alma Project
Wedding Venue and Catering, Villa Cora Hotel
Event Planning and Design, The Tuscan Wedding
Videography, Waterfall Visuals
Flowers, Flowers Living
Invitations, Laura Sherma of Jolly Edition
Paper Products, The Wedding Letters
Ring Bearer Signage, La Precisina
Bride's Robe, Homebodii
Bride's Gown, Oscar de la Renta
Bride's Shoes, Bella Belle Shoes
Hair and Makeup, Natalia Issa
Bridesmaids' Robes, Le Rose
Bridesmaids' Dresses, Bella Bridesmaids
Groom's Attire, Johnathan Behr Bespoke Clothiers
Ring Box, Mrs. Box
Vow Books, Ciarra Claire
Music, The Sax Man; DJ Sam Young; Deji Carr
Lighting, Wedding Music and Lights
Photo Booth, Funny Booth
Styling Ceramics, Simple Things Ceramics
Custom Napkins and Cocktail Stirrers, The Emerald Hound
2 of 25 A Weekend in Italy
3 of 25 A Warm Welcome
4 of 25 Find Your Seat
5 of 25 Have Some Gelato
6 of 25 When Life Gives You Lemons
7 of 25 A Dream Gown
8 of 25 The Finishing Touches
9 of 25 The Bouquet
10 of 25 The Groom's Look
11 of 25 Bridesmaids in Black
12 of 25 Mismatched Groomsmen
13 of 25 The First Look
14 of 25 The Ceremony Setup
15 of 25 A Cultural Spread
16 of 25 A Personalized Service
17 of 25 Italian Cocktails
18 of 25 Missing Their Dog
19 of 25 The Serenade
20 of 25 Versailles, But in Florence
21 of 25 Scroll Details
22 of 25 On the Tables
23 of 25 Dinner Is Served
24 of 25 Some Advice
25 of 25 Sources


1. What is High Intensity Interval Training? Give some examples.
3. Through this particular training, how does this impact the nervous and endocrine systems? What parts of the brain are affected? What are the primary hormones involved?
4. What are their physiological roles, and how they impact the body?
5. What has research concluded about High Intensity Interval Training? What are its effects on health and performance?
6. Attach two annotated bibliography to support this argument.
7. Explain why you believe High Intensity Interval Training cannot provide health and performance benefits. Support your conclusions based on your research findings, and relate them to your understanding of neuroendocrinology.
High intensity interval training (HIIT) is characterized by relatively short, intermittent loads at sub maximal or maximal intensity. On a scale of one to 10 perceived exertion, high intensity would be anything over an effort of seven. If one were to use max heart rate as a guide, high intensity would be exercising above 80 percent of max heart rate. Depending on the activity and individual, the load can vary from several seconds to several minutes, followed by several minutes of rest or an exercise phase at low intensity. The entire training session can take 20 to 40 minutes. High intensity training can be performed outside (running, biking) or on treadmills, swimming, stair climbers or bikes.
A typical high intensity interval training session would call for a five to 10 minute warm up where perceived exertion increases gradually from a three to a five. After this, work intervals begin. The appropriate work to recovery ration for HIIT is one minute of work to ever two to three minutes of active recovery (ACE, 2009). Staying active during the recovery phase helps to remove metabolic waste and produce more energy.
One might run at the fastest pace possible on a track for 200 meters, followed by jogging for 400 meters. This could be repeated up to 10 or 12 cycles. Another example would be cycling for two minutes at a perceived exertion of seven or eight, followed by four-minute intervals working at a RPE of four or five.
High intensity interval training is alluring to a great number of people: for the inactive it represents a promise of short workouts, for the active, promises are made of improved performance.
The benefit of HIIT is the ability to use appropriate work to recovery intervals in order to train the body to be more efficient at producing and using energy from the anaerobic energy system. This type of workout can train the body to effectively remove metabolic waste between intervals. It can also serve to increase VO2 max without extensive time spent running, cycling or swimming. However, because the level of intensity is so great it is wise to do no more than two days of HIIT per week, with at least one full day of recovery between sessions. Furthermore, HIIT is not a wise exercise choice for new exercisers. IDEA states "HIIT may increase the chance for injury and muscle soreness" (Zuhl & Kravitz, 2012). Many are exploring this type of training, since it represents one of the top fitness fads recently. However, it is not a safe type of exercise for a large amount of the population. One must have a base before beginning HITT training. For the totally inactive, HIIT is likely to be too uncomfortable, going from a sedentary lifestyle to a RPE of 7 or 8 seems unreasonable and a recipe for disaster. Those with a history of cardiovascular disease would be cautioned to stay away from this type of training. HIIT is designed for trained athletes and before starting a HIIT program, an individual "should be able to exercise for at least 20 to 30 minutes at 85% to 90% of (their) estimated maximum heart, without exhausting themselves or having problems" (Heart and Stroke, 2010). Individuals with recurrent angina or bone or muscle problems are discouraged from HIIT. Dr. Franklin, who is the director of the cardiac-rehabilitation program and exercise laboratories at the William Beaumont Hospital states, ""I'm still not convinced ... that taking people with coronary disease and exercising them at 95% of their [maximum] heart rate is a safe procedure" (Hobson, 2011).
This detailed solution defines High Intensity training, gives its pros and cons, the effect it has on endocrine and nervous system, information about research on HIIT, and includes an annotated bibliography plus APA formatted references.


Joshimath town, at 1890 m above mean sea level, is one of the most interesting places in the inner Himalayan range of Garhwal. Joshimath, apart from being a Tehsil and Block headquarters of administrative entities of the same names, is also the headquarters of an army brigade and home to the Garhwal Scouts paramilitary force. But, while the town of Joshimath have its own importance and significance in the realm of administration and defence, this website will be primarily focusing on the potential of Joshimath as a base camp and hub for experiencing the outstanding natural scenery and trekking potential of the adjoining areas.
In winters, Auli is the most hot tourist destination. People visit Auli for its panoramic view and snow sports like snow trekking, skiing etc. For more on Auli and the package cost please click here.
There are several hotels …………. read more.
For those on a Char-Dham tour, Joshimath is a suitable place for overnight stay before departure next day to Sri Badrinath, a further 40 km away. Joshimath has its historical significance in its contribution to this legendary saga of Char dhams. The magnificent scenery, climate and well socked market needed for a tourist is also one of the reasons for its developing as a major halting station for all types of tourists visiting this area.
The town of Joshimath derives its name from the Jyotirmath. Adiguru Shankracharya was on a mission to revive Hinduism which had been eclipsed by Buddhism. At fist a Math was established by him at Joshimath and Dham at Sri Badrinath. The math established in Joshimath in the 8th century C.E., today known by the name Jyotirmath, has a huge mulberry tree in its precincts. This huge mulberry tree is said to be around 2400 years old and located atop a cave where Adiguru had meditated. Today hundreds of pilgrims visit Adiguru's seat at jyotirmath to listen to the holy discourse called parvachan every evening.
There are also numerous temples in Joshimath. The most famous are Narsingh temple and Durga temple. It is written in Rajatarangani that the temple of Narsingh was established in eighth century AD by King Lalitaditya Yukta Pida during his digvijayayatra. The statue of Lord Narsinghis finely carved of Shaligram and interestingly, one of the arms is thin as a needle. It is believed that the day this fine arm of the statue breaks in kalyug, the mountains of Jaya and Vijaya at Vishnuprayag will collapse and close the way to Sri Badrinath. This will bring catastrophe and disaster in world. A new era will then emerge and Lord Badrinathwill appear at a new place called Bhawishya Badri. This place is 17 km from Joshimath towards the Tapovan valley. Joshimath is also the winter seat of Lord Badrinath and during that period the main temple in Badrinath is closed in winter, the Lord Badrinath is worshipped here.
Joshimath town itself is located on a gentle, beautiful north-facing slope. Several peaks including Nilkanth (6596 m), Dronagiri (7066 m), Nanda Devi (7816 m), Hahi Parvat (6727 m) etc. are visible from various corners of Joshimath……. read more.
In addition to the religious significance, Joshimath is a natural and convenient base or hub for many famous places and treks.
The climate in Joshimath falls under mountainous climate of Himalaya. The altitude of Joshimath is around 1890 m. From March to the beginning of October, the temperature in the town remains pleasant. The summer time (April to June) is extremely pleasant. During rainy season, the continuous rainfall dips the temperature. The autumn season is also pleasant, but needs precaution against cold morning and night.… read more.
Note: Night journey is not allowed in Garhwal region starting from Rishikesh (25 km from Haridwar).


There is nothing cooler than seeing a bit of someone's personality peek out from beneath their dress slacks. Imagine if your boss wore these Walkout socks featuring Roman Reigns? Suddenly you'd have a little more respect for "The Big Dog" - pun intended.