Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

Neutron star matter in the quark-meson coupling model in strong magnetic fields

The effects of strong magnetic fields on neutron star matter are investigated in the quark-meson coupling (QMC) model. The QMC model describes a nuclear many-body system as nonoverlapping MIT bags in which quarks interact through self-consistent exchange of scalar and vector mesons in the mean-field approximation. The results of the QMC model are compared with those obtained in a relativistic mean-field (RMF) model. It is found that quantitative differences exist between the QMC and RMF models, while qualitative trends of the magnetic field effects on the equation of state and composition of neutron star matter are very similar.Comment: 16 pages, 4 figure

A Natural Formalism for Microlensing

If the standard microlensing geometry is inverted so that the Einstein ring is projected onto the observer plane rather than the source plane, then the relations between the observables (\theta_E,\tilde r_E) and the underlying physical quantities (M,\pi_rel) become immediately obvious. Here \theta_E and \tilde r_E are the angular and projected Einstein radii, M is the mass of the lens, and \pi_rel is the lens-source relative parallax. I recast the basic formalism of microlensing in light of this more natural geometry and in terms of observables. I then find that the relations between observable and physical quantities assume an exceptionally simple form. In an appendix, I propose a set of notational conventions for microlensing.Comment: 8 pages, 1 figure tells all. Interested parties are requested to vote on a proposed standard for microlensing notation given in the appendix. Submitted to Ap

Solvable senescence model with positive mutations

We build upon our previous analytical results for the Penna model of senescence to include positive mutations. We investigate whether a small but non-zero positive mutation rate gives qualitatively different results to the traditional Penna model in which no positive mutations are considered. We find that the high-lifespan tail of the distribution is radically changed in structure, but that there is not much effect on the bulk of the population. Th e mortality plateau that we found previously for a stochastic generalization of the Penna model is stable to a small positive mutation rate.Comment: 3 figure

Crystal lattice properties fully determine short-range interaction parameters for alkali and halide ions

Accurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements of aqueous solution properties such as hydration free energies and ion-water distribution functions. This dependency limits transferability of the resulting parameters because of the variety and known limitations of water models. We present a solvent-independent approach to calibrating ion parameters based exclusively on crystal lattice properties. Our procedure relies on minimization of lattice sums to calculate lattice energies and interionic distances instead of equilibrium ensemble simulations of dense fluids. The gain in computational efficiency enables simultaneous optimization of all parameters for Li+, Na+, K+, Rb+, Cs+, F-, Cl-, Br-, and I- subject to constraints that enforce consistency with periodic table trends. We demonstrate the method by presenting lattice-derived parameters for the primitive model and the Lennard-Jones model with Lorentz-Berthelot mixing rules. The resulting parameters successfully reproduce the lattice properties used to derive them and are free from the influence of any water model. To assess the transferability of the Lennard-Jones parameters to aqueous systems, we used them to estimate hydration free energies and found that the results were in quantitative agreement with experimentally measured values. These lattice-derived parameters are applicable in simulations where coupling of ion parameters to a particular solvent model is undesirable. The simplicity and low computational demands of the calibration procedure make it suitable for parametrization of crystallizable ions in a variety of force fields.Comment: 9 pages, 5 table

Sound velocity and absorption measurements under high pressure using picosecond ultrasonics in diamond anvil cell. Application to the stability study of AlPdMn

We report an innovative high pressure method combining the diamond anvil cell device with the technique of picosecond ultrasonics. Such an approach allows to accurately measure sound velocity and attenuation of solids and liquids under pressure of tens of GPa, overcoming all the drawbacks of traditional techniques. The power of this new experimental technique is demonstrated in studies of lattice dynamics, stability domain and relaxation process in a metallic sample, a perfect single-grain AlPdMn quasicrystal, and rare gas, neon and argon. Application to the study of defect-induced lattice stability in AlPdMn up to 30 GPa is proposed. The present work has potential for application in areas ranging from fundamental problems in physics of solid and liquid state, which in turn could be beneficial for various other scientific fields as Earth and planetary science or material research

Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations

A discrete stochastic Razumikhin-type theorem is established to investigate whether the Euler--Maruyama (EM) scheme can reproduce the moment exponential stability of exact solutions of stochastic functional differential equations (SFDEs). In addition, the Chebyshev inequality and the Borel-Cantelli lemma are applied to show the almost sure stability of the EM approximate solutions of SFDEs. To show our idea clearly, these results are used to discuss stability of numerical solutions of two classes of special SFDEs, including stochastic delay differential equations (SDDEs) with variable delay and stochastically perturbed equations

Frontiers of the physics of dense plasmas and planetary interiors: experiments, theory, applications

Recent developments of dynamic x-ray characterization experiments of dense matter are reviewed, with particular emphasis on conditions relevant to interiors of terrestrial and gas giant planets. These studies include characterization of compressed states of matter in light elements by x-ray scattering and imaging of shocked iron by radiography. Several applications of this work are examined. These include the structure of massive "Super Earth" terrestrial planets around other stars, the 40 known extrasolar gas giants with measured masses and radii, and Jupiter itself, which serves as the benchmark for giant planets.Comment: Accepted to Physics of Plasmas special issue. Review from HEDP/HEDLA-08, April 12-15, 200

Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance