57,099 research outputs found
Gevrey estimates of the resolvent and sub-exponential time-decay of solutions
In this article, we study a class of non-selfadjoint Schr{\"o}dinger
operators H which are perturbation of some model operator H 0 satisfying a
weighted coercive assumption. For the model operator H 0 , we prove that the
derivatives of the resolvent satisfy some Gevrey estimates at threshold zero.
As application, we establish large time expansions of semigroups e --tH and e
--itH for t > 0 with subexponential time-decay estimates on the remainder,
including possible presence of zero eigenvalue and real resonances
Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential
In this work, we use scattering method to study the Kramers-Fokker-Planck
equation with a potential whose gradient tends to zero at the infinity. For
short-range potentials in dimension three, we show that complex eigenvalues do
not accumulate at low-energies and establish the low-energy resolvent
asymptotics. This combined with high energy pseudospectral estimates valid in
more general situations gives the large-time asymptotics of the solution in
weighted spaces
Molecular hydrodynamics of the moving contact line in two-phase immiscible flows
The ``no-slip'' boundary condition, i.e., zero fluid velocity relative to the
solid at the fluid-solid interface, has been very successful in describing many
macroscopic flows. A problem of principle arises when the no-slip boundary
condition is used to model the hydrodynamics of immiscible-fluid displacement
in the vicinity of the moving contact line, where the interface separating two
immiscible fluids intersects the solid wall. Decades ago it was already known
that the moving contact line is incompatible with the no-slip boundary
condition, since the latter would imply infinite dissipation due to a
non-integrable singularity in the stress near the contact line. In this paper
we first present an introductory review of the problem. We then present a
detailed review of our recent results on the contact-line motion in immiscible
two-phase flow, from MD simulations to continuum hydrodynamics calculations.
Through extensive MD studies and detailed analysis, we have uncovered the slip
boundary condition governing the moving contact line, denoted the generalized
Navier boundary condition. We have used this discovery to formulate a continuum
hydrodynamic model whose predictions are in remarkable quantitative agreement
with the MD simulation results at the molecular level. These results serve to
affirm the validity of the generalized Navier boundary condition, as well as to
open up the possibility of continuum hydrodynamic calculations of immiscible
flows that are physically meaningful at the molecular level.Comment: 36 pages with 33 figure
Stability of vortex in a two-component superconductor
Thermodynamic stability of composite vortex in a two-component superconductor
is investigated by the Ginzburg-Landau theory. The predicted nature of these
vortices has recently attracted much attention. Here we consider axially
symmetric quantized vortex and show that the stability of vortex depends on
three independent dimensionless parameters: , ,
, where is the Ginzburg-Landau parameter of
individual component, is the ratio of two
coherence lengths. We also show that there exists thermodynamic stable vortex
in type-1+type-2 or type-2+type-2 materials over a range of these three
parameters.Comment: 7 pages, 2 figure
Lenard scheme for two dimensional periodic Volterra chain
We prove that for compatible weakly nonlocal Hamiltonian and symplectic
operators, hierarchies of infinitely many commuting local symmetries and
conservation laws can be generated under some easily verified conditions no
matter whether the generating Nijenhuis operators are weakly nonlocal or not.
We construct a recursion operator of the two dimensional periodic Volterra
chain from its Lax representation and prove that it is a Nijenhuis operator.
Furthermore we show this system is a (generalised) bi-Hamiltonian system.
Rather surprisingly, the product of its weakly nonlocal Hamiltonian and
symplectic operators gives rise to the square of the recursion operator.Comment: Submit to Journal of Mathematical Physic
On Murty-Simon Conjecture II
A graph is diameter two edge-critical if its diameter is two and the deletion
of any edge increases the diameter. Murty and Simon conjectured that the number
of edges in a diameter two edge-critical graph on vertices is at most
and the extremal graph is the complete
bipartite graph .
In the series papers [7-9], the Murty-Simon Conjecture stated by Haynes et al.
is not the original conjecture, indeed, it is only for the diameter two
edge-critical graphs of even order. In this paper, we completely prove the
Murty-Simon Conjecture for the graphs whose complements have vertex
connectivity , where ; and for the graphs whose
complements have an independent vertex cut of cardinality at least three.Comment: 9 pages, submitted for publication on May 10, 201
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