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Frequency generation by a magnetic vortex-antivortex dipole in spin-polarized current
Get PDFA vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element.
We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane applied magnetic field and a Slonczewski spin-torque term with in-plane polarization.
We establish that the vortex dipole is set in steady state rotational motion.
The frequency of rotation is due to two independent forces:
the interaction between the two vortices and
the external magnetic field.
The nonzero skyrmion number of the dipole is responsible for both forces giving rise
to rotational dynamics.
The spin-torque acts to stabilize the vortex dipole motion at a definite vortex-antivortex separation distance.
We give analytical and numerical results for the angular frequency of rotation
and VA dipole features as functions of the parameters
Finite volume methods for unidirectional dispersive wave model
Get PDFWe extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdV–BBM-type equation. Explicit and implicit–explicit Runge–Kutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants’ conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interaction
Relative entropy methods for hyperbolic and diffusive limits
Get PDFWe review the relative entropy method in the context of hyperbolic and diffusive relaxation limits of
entropy solutions for various hyperbolic models. The main example consists of the convergence from
multidimensional compressible Euler equations with friction to the porous medium equation \cite{LT12}.
With small modifications, the arguments used in that case can be adapted to the study of the
diffusive limit from the Euler-Poisson system with friction to the Keller-Segel system \cite{LT13}.
In addition, the --system with friction and the system of viscoelasticity with memory are then reviewed,
again in the case of diffusive limits \cite{LT12}.
Finally, the method of relative entropy is described for the multidimensional stress relaxation model converging to elastodynamics \cite[Section 3.2]{LT06}, one of the first examples of application of the method to hyperbolic relaxation limits
Filtering deterministic layer effects in imaging
Get PDFSensor array imaging arises in applications such as nondestructive
evaluation of materials with ultrasonic waves, seismic exploration,
and radar. The sensors probe a medium with signals and record the
resulting echoes, which are then processed to determine the location
and reflectivity of remote reflectors. These could be defects in materials
such as voids, fault lines or salt bodies in the earth, and cars,
buildings or aircraft in radar applications. Imaging is relatively
well understood when the medium through which the signals propagate
is smooth, and therefore non-scattering. But in many problems the
medium is heterogeneous, with numerous small inhomogeneities that
scatter the waves. We refer to the collection of inhomogeneities as
clutter. It introduces an uncertainty in imaging because it is unknown
and impossible to estimate in detail. We model the clutter
as a random process. The array data is measured in one realization
of the random medium, and the challenge is to mitigate cumulative
clutter scattering so as to obtain robust images that are statistically
stable with respect to different realizations of the
inhomogeneities.
Scatterers that are not buried too deep in clutter can be imaged
reliably with the coherent interferometric (CINT) approach. But in
heavy clutter the signal to noise ratio (SNR) is low and CINT alone does not work. The
``signal'', the echoes from the scatterers to be imaged are
overwhelmed by the ``noise'', the strong clutter reverberations.
There are two existing approaches for imaging at low SNR: The first
operates under the premise that data are incoherent
so that only intensity of the scattered field can be used. The unknown coherent
scatterers that we want to image are modeled as changes in the coefficients of diffusion or radiative
transport equations satisfied by the intensities, and the problem
becomes one of parameter estimation. Because the estimation is
severely ill posed, the results have poor resolution, unless
very good prior information is available and large arrays are used. The second approach
recognizes that if there is some residual coherence in the data, that is,
some reliable phase information is available, it
is worth trying to extract it and use it with well
posed coherent imaging methods, to obtain images with better
resolution.
This paper takes the latter approach, and presents a first attempt
at enhancing the SNR of the array data by suppressing medium
reverberations. It introduces filters or annihilators of layer
backscatter, that are designed to remove primary echoes from strong,
isolated layers in a medium with additional random layering at
small, sub-wavelength scales. These strong layers are called
deterministic because they can be imaged from the data. However, our
goal is not to image the layers, but to suppress them and thus
enhance the echoes from compact scatterers buried deep in the
medium. Surprisingly, the layer annihilators work better than
intended, in the sense that they suppress not only the echoes
from the deterministic layers but also multiply scattered ones
in the randomly layered structure.
Following the layer annihilators presented here, other filters of
general, non-layered heavy clutter have been developed. We review
these more recent developments and the challenges of imaging in heavy
clutter in the introduction in order to place the research
presented here in context. We then present in detail the layer
annihilators and show with analysis and numerical simulations how
they work
Remarks on the Contributions of Constantine M. Dafermos to the Subject of Conservation Laws
Get PDFThis is an expository article highlighting certain of the contributions of Constantine M. Dafermos on the subject of Conservation Law
Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise
Get PDFWe consider an initial- and Dirichlet boundary- value problem for
a linear Cahn-Hilliard-Cook equation, in one space dimension,
forced by the space derivative of a space-time white noise.
First, we propose an approximate regularized stochastic parabolic
problem discretizing the noise using linear splines. Then
fully-discrete approximations to the solution of the
regularized problem are constructed using, for the discretization
in space, a Galerkin finite element method based on
piecewise polynomials, and, for time-stepping, the Backward
Euler method.
Finally, we derive strong a priori estimates for the modeling error and
for the numerical approximation error to the solution of the regularized problem
Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential
Get PDFThe use of coherent optical dressing of atomic levels allows the
coupling of ultracold atoms to effective non-dynamical gauge fields. These can be
used to generate effective magnetic fields, and have the potential
to generate non-Abelian gauge fields. We consider a model of a gas
of bosonic atoms coupled to a gauge field with symmetry, and
with constant effective magnetic field. We include the effects of
weak contact interactions by applying Gross-Pitaevskii mean-field
theory. We study the effects of a non-Abelian gauge field on the vortex
lattice phase induced by a uniform effective magnetic field,
generated by an Abelian gauge field or, equivalently, by rotation of
the gas. We show that, with increasing non-Abelian gauge field, the
nature of the groundstate changes dramatically, with structural
changes of the vortex lattice. We show that the
effect of the non-Abelian gauge field is equivalent to the introduction of effective
interactions with non-zero range. We also comment on the
consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall
states
Surface optical Bloch oscillations in semi-infinite waveguide arrays
Get PDFWe predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a ‘matched’ termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries
Another construction of BV solutions to rate-independent systems
Get PDFWe study one kind of weak solutions to rate-independent systems, which is constructed by using the local minimality in a small neighborhood of order ε and then taking the limit ε → 0. We show that the resulting solution satisfies both the weak local stability and the new energy-dissipation balance, similarly to the BV solutions constructed by vanishing viscosity introduced recently by Mielke, Rossi and Savare