18,970 research outputs found
Almost sure exponential stability of numerical solutions for stochastic delay differential equations
Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the Borel–Cantelli lemma
Approximate solutions of stochastic differential delay equations with Markovian switching
Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local Lipschitz condition. As an application, our results are used to discuss a stochastic delay population system with Markovian switching
Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
Model lattices consisting of balls connected by central-force springs provide
much of our understanding of mechanical response and phonon structure of real
materials. Their stability depends critically on their coordination number .
-dimensional lattices with are at the threshold of mechanical
stability and are isostatic. Lattices with exhibit zero-frequency
"floppy" modes that provide avenues for lattice collapse. The physics of
systems as diverse as architectural structures, network glasses, randomly
packed spheres, and biopolymer networks is strongly influenced by a nearby
isostatic lattice. We explore elasticity and phonons of a special class of
two-dimensional isostatic lattices constructed by distorting the kagome
lattice. We show that the phonon structure of these lattices, characterized by
vanishing bulk moduli and thus negative Poisson ratios and auxetic elasticity,
depends sensitively on boundary conditions and on the nature of the kagome
distortions. We construct lattices that under free boundary conditions exhibit
surface floppy modes only or a combination of both surface and bulk floppy
modes; and we show that bulk floppy modes present under free boundary
conditions are also present under periodic boundary conditions but that surface
modes are not. In the the long-wavelength limit, the elastic theory of all
these lattices is a conformally invariant field theory with holographic
properties, and the surface waves are Rayleigh waves. We discuss our results in
relation to recent work on jammed systems. Our results highlight the importance
of network architecture in determining floppy-mode structure.Comment: 12 pages, 7 figure
Performance of Photosensors in the PandaX-I Experiment
We report the long term performance of the photosensors, 143 one-inch
R8520-406 and 37 three-inch R11410-MOD photomultipliers from Hamamatsu, in the
first phase of the PandaX dual-phase xenon dark matter experiment. This is the
first time that a significant number of R11410 photomultiplier tubes were
operated in liquid xenon for an extended period, providing important guidance
to the future large xenon-based dark matter experiments.Comment: v3 as accepted by JINST with modifications based on reviewers'
comment
On an elliptic Kirchhoff-type problem depending on two parameters
In this paper, we consider the Dirichlet problem associated to an elliptic
Kirchhoff-type equation depending on two parameters. Under rather general and
natural assumptions, we prove that, for certain values of the parameters, the
problem has at least three solutions
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
This paper develops necessary and sufficient conditions for the preservation
of asymptotic convergence rates of deterministically and stochastically
perturbed ordinary differential equations with regularly varying nonlinearity
close to their equilibrium. Sharp conditions are also established which
preserve the asymptotic behaviour of the derivative of the underlying
unperturbed equation. Finally, necessary and sufficient conditions are
established which enable finite difference approximations to the derivative in
the stochastic equation to preserve the asymptotic behaviour of the derivative
of the unperturbed equation, even though the solution of the stochastic
equation is nowhere differentiable, almost surely
Elasticity of highly cross-linked random networks
Starting from a microscopic model of randomly cross-linked particles with
quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary
cross-link densities. Considering pure shear deformations, S takes the form of
the elastic energy of an isotropic amorphous solid state, from which the shear
modulus can be identified. It is found to be an universal quantity, not
depending on any microscopic length-scales of the model.Comment: 6 pages, 5 figure
- …