7,732 research outputs found
On the Dynamical Stability and Instability of Parker Problem
We investigate a perturbation problem for the three-dimensional compressible
isentropic viscous magnetohydrodynamic system with zero resistivity in the
presence of a modified gravitational force in a vertical strip domain in which
the velocity of the fluid is non-slip on the boundary, and focus on the
stabilizing effect of the (equilibrium) magnetic field through the non-slip
boundary condition. We show that there is a discriminant , depending on
the known physical parameters, for the stability/instability of the
perturbation problem. More precisely, if , then the perturbation problem
is unstable, i.e., the Parker instability occurs, while if and the
initial perturbation satisfies some relations, then there exists a global
(perturbation) solution which decays algebraically to zero in time, i.e., the
Parker instability does not happen. The stability results in this paper reveal
the stabilizing effect of the magnetic field through the non-slip boundary
condition and the importance of boundary conditions upon the Parker
instability, and demonstrate that a sufficiently strong magnetic field can
prevent the Parker instability from occurring. In addition, based on the
instability results, we further rigorously verify the Parker instability under
Schwarzschild's or Tserkovnikov's instability conditions in the sense of
Hadamard for a horizontally periodic domain.Comment: 51 page
On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics
We investigate the stabilizing effects of the magnetic fields in the
linearized magnetic Rayleigh-Taylor (RT) problem of a nonhomogeneous
incompressible viscous magnetohydrodynamic fluid of zero resistivity in the
presence of a uniform gravitational field in a three-dimensional bounded
domain, in which the velocity of the fluid is non-slip on the boundary. By
adapting a modified variational method and careful deriving \emph{a priori}
estimates, we establish a criterion for the instability/stability of the
linearized problem around a magnetic RT equilibrium state. In the criterion, we
find a new phenomenon that a sufficiently strong horizontal magnetic field has
the same stabilizing effect as that of the vertical magnetic field on growth of
the magnetic RT instability. In addition, we further study the corresponding
compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which
the strength of a horizontal magnetic field decreases with height, and also
show the stabilizing effect of a sufficiently large magnetic field.Comment: 33 page
On the Inhibition of Thermal Convection by a Magnetic Field under Zero Resistivity
We investigate the stability and instability of the magnetic
Rayleigh--B\'enard problem with zero resistivity. An stability criterion is
established, under which the magnetic B\'enard problem is stable. The proof
mainly is based on a three-layers energy method and an idea of magnetic
inhibition mechanism. The stable result first mathematically verifies
Chandrasekhar's assertion in 1955 that the thermal instability can be inhibited
by strong magnetic field in magnetohydrodynamic (MHD) fluid with zero
resistivity (based on a linearized steady magnetic B\'enard equations). In
addition, we also provide an instability criterion, under which the magnetic
Rayleigh--B\'enard problem is unstable. The proof mainly is based on the
bootstrap instability method by further developing new analysis technique. Our
instability result presents that the thermal instability occurs for a small
magnetic field.Comment: 4
Ground State Properties of Cold Bosonic Atoms At Large Scattering Lengths
In this letter, we study bosonic atoms at large scattering lengths using a
variational method where the condensation amplitude is a variational parameter.
We further examine momentum distribution functions, chemical potentials and
speed of sound, and spatial density profiles of cold bosonic atoms in a trap in
this limit. The later two properties turn out to bear similarities of those of
Fermi gases. Estimates obtained here are applicable near Feshbach resonances,
particularly when the fraction of atoms forming three-body structures is small
and can be tested in future cold atom experiments.Comment: 4 pages, 3 figures, published versio
Probabilistic Topic and Syntax Modeling with Part-of-Speech LDA
This article presents a probabilistic generative model for text based on
semantic topics and syntactic classes called Part-of-Speech LDA (POSLDA).
POSLDA simultaneously uncovers short-range syntactic patterns (syntax) and
long-range semantic patterns (topics) that exist in document collections. This
results in word distributions that are specific to both topics (sports,
education, ...) and parts-of-speech (nouns, verbs, ...). For example,
multinomial distributions over words are uncovered that can be understood as
"nouns about weather" or "verbs about law". We describe the model and an
approximate inference algorithm and then demonstrate the quality of the learned
topics both qualitatively and quantitatively. Then, we discuss an NLP
application where the output of POSLDA can lead to strong improvements in
quality: unsupervised part-of-speech tagging. We describe algorithms for this
task that make use of POSLDA-learned distributions that result in improved
performance beyond the state of the art.Comment: Currently under review for the journal Computational Linguistic
Non-Hermitian skin effect and chiral damping in open quantum systems
One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian
skin effect, namely that the eigenstates are exponentially localized at the
boundary of the system. For open quantum systems, a short-time evolution can
often be well described by the effective non-Hermitian Hamiltonians, while
long-time dynamics calls for the Lindblad master equations, in which the
Liouvillian superoperators generate time evolution. In this Letter, we find
that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and
uncover its unexpected physical consequences. It is shown that the
non-Hermitian skin effect dramatically shapes the long-time dynamics, such that
the damping in a class of open quantum systems is algebraic under periodic
boundary condition but exponential under open boundary condition. Moreover, the
non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a
sharp wavefront. These phenomena are beyond the effective non-Hermitian
Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged
open quantum dynamics.Comment: 9 pages, 4 figures, including supplemental materia
Non-Hermitian Chern bands
The relation between chiral edge modes and bulk Chern numbers of quantum Hall
insulators is a paradigmatic example of bulk-boundary correspondence. We show
that the chiral edge modes are not strictly tied to the Chern numbers defined
by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional
bulk-boundary correspondence stems from the non-Bloch-wave behavior of
eigenstates (non-Hermitian skin effect), which generates pronounced deviations
of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers
that faithfully predict the numbers of chiral edge modes. The theory is backed
up by the open-boundary energy spectra, dynamics, and phase diagram of
representative lattice models. Our results highlight a unique feature of
non-Hermitian bands and suggest a non-Bloch framework to characterize their
topology.Comment: 11 pages, 12 figures, including supplemental materia
Global weak solutions to the two-dimensional Navier-Stokes equations of compressible heat-conducting flows with symmetric data and forces
We prove the global existence of weak solutions to the Navier-Stokes
equations of compressible heat-conducting fluids in two spatial dimensions with
initial data and external forces which are large and spherically symmetric. The
solutions will be obtained as the limit of the approximate solutions in an
annular domain. We first derive a number of regularity results on the
approximate physical quantities in the "fluid region", as well as the new
uniform integrability of the velocity and temperature in the entire space-time
domain by exploiting the theory of the Orlicz spaces. By virtue of these a
priori estimates we then argue in a manner similar to that in [Arch. Rational
Mech. Anal. 173 (2004), 297-343] to pass to the limit and show that the
limiting functions are indeed a weak solution which satisfies the mass and
momentum equations in the entire space-time domain in the sense of
distributions, and the energy equation in any compact subset of the "fluid
region".Comment: 19 page
Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible Viscous Magnetohydrodynamic Flows
We investigate the nonlinear instability of a smooth Rayleigh-Taylor
steady-state solution (including the case of heavier density with increasing
height) to the three-dimensional incompressible nonhomogeneous
magnetohydrodynamic (MHD) equations of zero resistivity in the presence of a
uniform gravitational field. We first analyze the linearized equations around
the steady-state solution. Then we construct solutions of the linearized
problem that grow in time in the Sobolev space , thus leading to the
linear instability. With the help of the constructed unstable solutions of the
linearized problem and a local well-posedness result of smooth solutions to the
original nonlinear problem, we establish the instability of the density, the
horizontal and vertical velocities in the nonlinear problem. Moreover, when the
steady magnetic field is vertical and small, we prove the instability of the
magnetic field. This verifies the physical phenomenon: instability of the
velocity leads to the instability of the magnetic field through the induction
equation.Comment: 46 pages. arXiv admin note: substantial text overlap with
arXiv:1205.227
Majorana corner modes in a high-temperature platform
We introduce two-dimensional topological insulators in proximity to
high-temperature cuprate or iron-based superconductors as high-temperature
platforms of Majorana Kramers pairs of zero modes. The proximity-induced
pairing at the helical edge state of the topological insulator serves as a
Dirac mass, whose sign changes at the sample corner because of the pairing
symmetry of high- superconductors. This sign changing naturally creates at
each corner a pair of Majorana zero modes protected by time-reversal symmetry.
Conceptually, this is a topologically trivial superconductor-based approach for
Majorana zero modes. We provide quantitative criteria and suggest candidate
materials for this proposal.Comment: 15 pages, 9 figures, including supplemental material. Published
versio
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