Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

A Few Case Studies on the Correlation of Particle Network and Its Stability on the Ionic Conductivity of Solid-Liquid Composite Electrolytes

We discuss here the crucial role of the particle network and its stability on the long-range ion transport in solid liquid composite electrolytes. The solid liquid composite electrolytes chosen for the study here comprise nanometer sized silica (SiO2) particles having various surface chemical functionalities dispersed in nonaqueous lithium salt solutions, viz, lithium perchlorate (LiClO4) in two different polyethylene glycol based solvents. These systems constitute representative examples of an independent class of soft matter electrolytes known as ``soggy sand'' electrolytes, which have tremendous potential in diverse electrochemical devices. The oxide additive acts as a heterogeneous dopant creating free charge carriers and enhancing the local ion transport. For long-range transport, however, a stable spanning particle network is needed. Systematic experimental investigations here reveal that the spatial and time dependent characteristics of the particle network in the liquid solution are nontrivial. The network characteristics are predominantly determined by the chemical makeup of the electrolyte components and the chemical interactions between them. It is noteworthy that in this study the steady state macroscopic ionic conductivity and viscosity of the solid liquid composite electrolyte are observed to be greatly determined by the additive oxide surface chemical functionality, solvent chemical composition, and solvent dielectric constant.

Eye-hand coordination during a double-step task: evidence for a common stochastic accumulator

Many studies of reaching and pointing have shown significant spatial and temporal correlations between eye and hand movements. Nevertheless, it remains unclear whether these correlations are incidental, arising from common inputs (independent model); whether these correlations represent an interaction between otherwise independent eye and hand systems (interactive model); or whether these correlations arise from a single dedicated eye-hand system (common command model). Subjects were instructed to redirect gaze and pointing movements in a double-step task in an attempt to decouple eye-hand movements and causally distinguish between the three architectures. We used a drift-diffusion framework in the context of a race model, which has been previously used to explain redirect behavior for eye and hand movements separately, to predict the pattern of eye-hand decoupling. We found that the common command architecture could best explain the observed frequency of different eye and hand response patterns to the target step. A common stochastic accumulator for eye-hand coordination also predicts comparable variances, despite significant difference in the means of the eye and hand reaction time (RT) distributions, which we tested. Consistent with this prediction, we observed that the variances of the eye and hand RTs were similar, despite much larger hand RTs (similar to 90 ms). Moreover, changes in mean eye RTs, which also increased eye RT variance, produced a similar increase in mean and variance of the associated hand RT. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning.

Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory

This paper presents the stability analysis of functionally graded plate integrated with piezoelectric actuator and sensor at the top and bottom face, subjected to electrical and mechanical loading. The finite element formulation is based on first order and higher order shear deformation theory, degenerated shell element, von-Karman hypothesis and piezoelectric effect. The equation for static analysis is derived by using the minimum energy principle and solutions for critical buckling load is obtained by solving eigenvalue problem. The material properties of the functionally graded plate are assumed to be graded along the thickness direction according to simple power law function. Two types of boundary conditions are used, such as SSSS (simply supported) and CSCS (simply supported along two opposite side perpendicular to the direction of compression and clamped along the other two sides). Sensor voltage is calculated using present analysis for various power law indices and FG (functionally graded) material gradations. The stability analysis of piezoelectric FG plate is carried out to present the effects of power law index, material variations, applied mechanical pressure and piezo effect on buckling and stability characteristics of FG plate.

1D Tight-Binding Models Render Quantum First Passage Time ``Speakable''

The calculation of First Passage Time (moreover, even its probability density in time) has so far been generally viewed as an ill-posed problem in the domain of quantum mechanics. The reasons can be summarily seen in the fact that the quantum probabilities in general do not satisfy the Kolmogorov sum rule: the probabilities for entering and non-entering of Feynman paths into a given region of space-time do not in general add up to unity, much owing to the interference of alternative paths. In the present work, it is pointed out that a special case exists (within quantum framework), in which, by design, there exists one and only one available path (i.e., door-way) to mediate the (first) passage -no alternative path to interfere with. Further, it is identified that a popular family of quantum systems - namely the 1d tight binding Hamiltonian systems - falls under this special category. For these model quantum systems, the first passage time distributions are obtained analytically by suitably applying a method originally devised for classical (stochastic) mechanics (by Schroedinger in 1915). This result is interesting especially given the fact that the tight binding models are extensively used in describing everyday phenomena in condense matter physics.

Wave propagation in a 2D nonlinear structural acoustic waveguide using asymptotic expansions of wavenumbers

Nonlinear acoustic wave propagation in an infinite rectangular waveguide is investigated. The upper boundary of this waveguide is a nonlinear elastic plate, whereas the lower boundary is rigid. The fluid is assumed to be inviscid with zero mean flow. The focus is restricted to non-planar modes having finite amplitudes. The approximate solution to the acoustic velocity potential of an amplitude modulated pulse is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger equation (NLSE). The first objective here is to study the nonlinear term in the NLSE. The sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. Secondly, at other frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonics. This happens when the phase speeds of the waves match and the objective is to identify the frequencies of such interactions. For both the objectives, asymptotic coupled wavenumber expansions for the linear dispersion relation are required for an intermediate fluid loading. The novelty of this work lies in obtaining the asymptotic expansions and using them for predicting the sign change of the nonlinear term at various frequencies. It is found that when the coupled wavenumbers approach the uncoupled pressure-release wavenumbers, the amplitude modulation is stable. On the other hand, near the rigid-duct wavenumbers, the amplitude modulation is unstable. Also, as a further contribution, these wavenumber expansions are used to identify the frequencies of the higher harmonic interactions. And lastly, the solution for the amplitude modulation derived through the MMS is validated using these asymptotic expansions. (C) 2015 Elsevier Ltd. All rights reserved.

Weakly nonlinear acoustic wave propagation in a nonlinear orthotropic circular cylindrical waveguide

Nonlinear acoustic wave propagation is considered in an infinite orthotropic thin circular cylindrical waveguide. The modes are non-planar having small but finite amplitude. The fluid is assumed to be ideal and inviscid with no mean flow. The cylindrical waveguide is modeled using the Donnell's nonlinear theory for thin cylindrical shells. The approximate solutions for the acoustic velocity potential are found using the method of multiple scales (MMS) in space and time. The calculations are presented up to the third order of the small parameter. It is found that at some frequencies the amplitude modulation is governed by the Nonlinear Schrodinger Equation (NLSE). The first objective is to study the nonlinear term in the NLSE, as the sign of the nonlinear term determines the stability of the amplitude modulation. On the other hand, at other specific frequencies, interactions occur between the primary wave and its higher harmonics. Here, the objective is to identify the frequencies of the higher harmonic interactions. Lastly, the linear terms in the NLSE obtained using the MMS calculations are validated. All three objectives are met using an asymptotic analysis of the dispersion equation. (C) 2015 Acoustical Society of America.

Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time beta relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time alpha-relaxation regime.

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Cold gas in cluster cores: global stability analysis and non-linear simulations of thermal instability

We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g. spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in haloes critically depends on the ratio of the cooling time to the free-fall time (t(cool)/t(ff)). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the previous plane-parallel simulations focused on in situ condensation of multiphase gas but spherical simulations studied condensation anywhere in the box. Unlike previous claims, our non-linear simulations show that there are only minor differences in cold gas condensation, either in situ or anywhere, for different geometries. The amount of cold gas depends on the shape of tcool/tff; gas has more time to condense if gravitational acceleration decreases towards the centre. In our idealized plane-parallel simulations with heating balancing cooling in each layer, there can be significant mass/energy/momentum transfer across layers that can trigger condensation and drive tcool/tff far beyond the critical value close to 10.

Wave-soil-pipe coupling effect on submarine pipeline on-bottom stability

Wave-soil-pipe coupling effect on the untrenched pipeline stability on sands is for the first time investigated experimentally. Tests are conducted in the U-shaped water tunnel, which generates an oscillatory how, simulating the water particle movements with periodically changing direction under the wave action. Characteristic times and phases during the instability process are revealed. Linear relationship between Froude number and non-dimensional pipe weight is obtained. Effects of initial embedment and loading history are observed. Test results between the wavesoil-pipe interaction and pipe-soil interaction under cyclic mechanical loading are compared. The mechanism is briefly discussed. For applying in the practical design, more extensive and systematic investigations are needed.

Stability of ZrTiCuNiBe Bulk Metallic Glass Upon Isothermal Annealing Near the Glass Transition Temperature

The stability of Zr41Ti14Cu12.5Ni10Be22.5 bulk metallic glass (BMG) upon isothermal annealing near the glass transition temperature has been investigated by using x-ray diffraction, differential scanning calorimetry, and the pulse echo overlap method. The density, elastic constants, and thermodynamic parameters as well as their annealing time dependence have been determined. The microstructural and properties changes of the annealed BMG were checked by acoustic measurement. Obvious structural and property changes were observed with prolonged annealing of the BMG near the glass transition temperature.

Morphological Stability of Epitaxial Thin Elastic Films by Van Der Waals Force

The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found that only van der Waals force with negative Hamaker constant (A < 0) tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film. The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.

Iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact

We present in this paper an iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact. To retain the advantage of integration on an element-by-element basis which is at the heart of modern hydrocodes, we suggest that the first step should be to solve for accelerations at an advanced time step by using the lumped mass approach, then iterate using a consistent mass matrix to improve the estimate. Examples are given to show the improved resolution with the new method.

The application of B-P constitutive equations in finite element analysis of high velocity impact

We present in this paper the application of B-P constitutive equations in finite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B-P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact.