779 research outputs found

### Invisibility in non-Hermitian tight-binding lattices

Reflectionless defects in Hermitian tight-binding lattices, synthesized by
the intertwining operator technique of supersymmetric quantum mechanics, are
generally not invisible and time-of-flight measurements could reveal the
existence of the defects. Here it is shown that, in a certain class of
non-Hermitian tight-binding lattices with complex hopping amplitudes, defects
in the lattice can appear fully invisible to an outside observer. The
synthesized non-Hermitian lattices with invisible defects possess a real-valued
energy spectrum, however they lack of parity-time (PT) symmetry, which does not
play any role in the present work.Comment: to appear in Phys. Rev.

### A note on the stability of slip channel flows

We consider the influence of slip boundary conditions on the modal and
non-modal stability of pressure-driven channel flows. In accordance with
previous results by Gersting (1974) (Phys. Fluids, 17) but in contradiction
with the recent investigation of Chu (2004) (C.R. Mecanique, 332), we show that
slip increases significantly the value of the critical Reynolds number for
linear instability. The non-modal stability analysis however reveals that the
slip has a very weak influence on the maximum transient energy growth of
perturbations at subcritical Reynolds numbers. Slip boundary conditions are
therefore not likely to have a significant effect on the transition to
turbulence in channel flows

### Discrete breathers at the interface between a diatomic and monoatomic granular chain

In the present work, we develop a systematic examination of the existence,
stability and dynamical properties of a discrete breather at the interface
between a diatomic and a monoatomic granular chain. We remarkably find that
such an "interface breather" is more robust than its bulk diatomic counterpart
throughout the gap of the linear spectrum. The latter linear spectral gap needs
to exist for the breather state to arise and the relevant spectral conditions
are discussed. We illustrate the minimal excitation conditions under which such
an interface breather can be "nucleated" and analyze its apparently weak
interaction with regular highly nonlinear solitary waveforms.Comment: 11 pages, 10 figure

### Circuit QED and sudden phase switching in a superconducting qubit array

Superconducting qubits connected in an array can form quantum many-body
systems such as the quantum Ising model. By coupling the qubits to a
superconducting resonator, the combined system forms a circuit QED system.
Here, we study the nonlinear behavior in the many-body state of the qubit array
using a semiclassical approach. We show that sudden switchings as well as a
bistable regime between the ferromagnetic phase and the paramagnetic phase can
be observed in the qubit array. A superconducting circuit to implement this
system is presented with realistic parameters .Comment: 4 pages, 3 figures, submitted for publication

### Self-consistent simulations of a von K\'arm\'an type dynamo in a spherical domain with metallic walls

We have performed numerical simulations of boundary-driven dynamos using a
three-dimensional non-linear magnetohydrodynamical model in a spherical shell
geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into
motion by the counter-rotation of the two hemispheric walls. The resulting flow
is of von K\'arm\'an type, consisting of a layer of zonal velocity close to the
outer wall and a secondary meridional circulation. Above a certain forcing
threshold, the mean flow is unstable to non-axisymmetric motions within an
equatorial belt. For fixed forcing above this threshold, we have studied the
dynamo properties of this flow. The presence of a conducting outer wall is
essential to the existence of a dynamo at these parameters. We have therefore
studied the effect of changing the material parameters of the wall (magnetic
permeability, electrical conductivity, and thickness) on the dynamo. In common
with previous studies, we find that dynamos are obtained only when either the
conductivity or the permeability is sufficiently large. However, we find that
the effect of these two parameters on the dynamo process are different and can
even compete to the detriment of the dynamo. Our self-consistent approach allow
us to analyze in detail the dynamo feedback loop. The dynamos we obtain are
typically dominated by an axisymmetric toroidal magnetic field and an axial
dipole component. We show that the ability of the outer shear layer to produce
a strong toroidal field depends critically on the presence of a conducting
outer wall, which shields the fluid from the vacuum outside. The generation of
the axisymmetric poloidal field, on the other hand, occurs in the equatorial
belt and does not depend on the wall properties.Comment: accepted for publication in Physical Review

### Marginally unstable Holmboe modes

Marginally unstable Holmboe modes for smooth density and velocity profiles
are studied. For a large family of flows and stratification that exhibit
Holmboe instability, we show that the modes with phase velocity equal to the
maximum or the minimum velocity of the shear are marginally unstable. This
allows us to determine the critical value of the control parameter R
(expressing the ratio of the velocity variation length scale to the density
variation length scale) that Holmboe instability appears R=2. We then examine
systems for which the parameter R is very close to this critical value. For
this case we derive an analytical expression for the dispersion relation of the
complex phase speed c(k) in the unstable region. The growth rate and the width
of the region of unstable wave numbers has a very strong (exponential)
dependence on the deviation of R from the critical value. Two specific examples
are examined and the implications of the results are discussed.Comment: Submitted to Physics of Fluid

### The period of a classical oscillator

We develop a simple method to obtain approximate analytical expressions for
the period of a particle moving in a given potential. The method is inspired to
the Linear Delta Expansion (LDE) and it is applied to a large class of
potentials. Precise formulas for the period are obtained.Comment: 5 pages, 4 figure

### A pulsed atomic soliton laser

It is shown that simultaneously changing the scattering length of an
elongated, harmonically trapped Bose-Einstein condensate from positive to
negative and inverting the axial portion of the trap, so that it becomes
expulsive, results in a train of self-coherent solitonic pulses. Each pulse is
itself a non-dispersive attractive Bose-Einstein condensate that rapidly
self-cools. The axial trap functions as a waveguide. The solitons can be made
robustly stable with the right choice of trap geometry, number of atoms, and
interaction strength. Theoretical and numerical evidence suggests that such a
pulsed atomic soliton laser can be made in present experiments.Comment: 11 pages, 4 figure

### Evolution of a barotropic shear layer into elliptical vortices

When a barotropic shear layer becomes unstable, it produces the well known
Kelvin-Helmholtz instability (KH). The non-linear manifestation of KH is
usually in the form of spiral billows. However, a piecewise linear shear layer
produces a different type of KH characterized by elliptical vortices of
constant vorticity connected via thin braids. Using direct numerical simulation
and contour dynamics, we show that the interaction between two
counter-propagating vorticity waves is solely responsible for this KH
formation. We investigate the oscillation of the vorticity wave amplitude, the
rotation and nutation of the elliptical vortex, and straining of the braids.
Our analysis also provides possible explanation behind the formation and
evolution of elliptical vortices appearing in geophysical and astrophysical
flows, e.g. meddies, Stratospheric polar vortices, Jovian vortices, Neptune's
Great Dark Spot and coherent vortices in the wind belts of Uranus.Comment: 7 pages, 4 figures, Accepted in Physical Review

### Dynamics and stability of vortex-antivortex fronts in type II superconductors

The dynamics of vortices in type II superconductors exhibit a variety of
patterns whose origin is poorly understood. This is partly due to the
nonlinearity of the vortex mobility which gives rise to singular behavior in
the vortex densities. Such singular behavior complicates the application of
standard linear stability analysis. In this paper, as a first step towards
dealing with these dynamical phenomena, we analyze the dynamical stability of a
front between vortices and antivortices. In particular we focus on the question
of whether an instability of the vortex front can occur in the absence of a
coupling to the temperature. Borrowing ideas developed for singular bacterial
growth fronts, we perform an explicit linear stability analysis which shows
that, for sufficiently large front velocities and in the absence of coupling to
the temperature, such vortex fronts are stable even in the presence of in-plane
anisotropy. This result differs from previous conclusions drawn on the basis of
approximate calculations for stationary fronts. As our method extends to more
complicated models, which could include coupling to the temperature or to other
fields, it provides the basis for a more systematic stability analysis of
nonlinear vortex front dynamics.Comment: 13 pages, 8 figure

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