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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Stochastic simulation for the propagation of high-frequency acoustic waves through a random velocity field

In-service inspection of Sodium-Cooled Fast Reactors (SFR) requires the development of non-destructive techniques adapted to the harsh environment conditions and the examination complexity. From past experiences, ultrasonic techniques are considered as suitable candidates. The ultrasonic telemetry is a technique used to constantly insure the safe functioning of reactor inner components by determining their exact position: it consists in measuring the time of flight of the ultrasonic response obtained after propagation of a pulse emitted by a transducer and its interaction with the targets. While in-service the sodium flow creates turbulences that lead to temperature inhomogeneities, which translates into ultrasonic velocity inhomogeneities. These velocity variations could directly impact the accuracy of the target locating by introducing time of flight variations. A stochastic simulation model has been developed to calculate the propagation of ultrasonic waves in such an inhomogeneous medium. Using this approach, the travel time is randomly generated by a stochastic process whose inputs are the statistical moments of travel times known analytically. The stochastic model predicts beam deviations due to velocity inhomogeneities, which are similar to those provided by a determinist method, such as the ray method.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2012

Stochastic fluctuations of dust particle charge in RF discharges

In addition to RF oscillations, intrinsic stochastic fluctuations due to the discreteness of electrons and ions could be important to the charging of a dust particle in RF discharges. These fluctuations are studied in the present work for three cases [M. Bacharis et al., Plasma Sources Sci. Technol. 19, 025002 (2010)] relevant to RF discharges employing a recently proposed model [B. Shotorban, Phys. Rev. E 83, 066403 (2011)] valid for stochastic charging at nonstationary states. The cases are concerned with a time varying electron number density relevant to sheaths, a time varying electric field relevant to the bulk plasma, and a time-dependent bi-Maxwellian distribution of electrons in a low pressure discharge. Two dust particles with different sizes are individually studied in each case. The radius of one is ten times larger than the radius of the other. In all of the cases, for the larger dust particle, the root-mean-squre of charge stochastic fluctuations is about an order of magnitude smaller than the amplitude of RF charge oscillations, while for the smaller dust particle, they are comparable in magnitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Proper orthogonal decomposition-based spectral higher-order stochastic estimation

A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Stochastic growth logistic model with aftereffect for batch fermentation process

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Disease mapping based on stochastic SIR-SI model for Dengue and Chikungunya in Malaysia

This paper describes and demonstrates a method for relative risk estimation which is based on the stochastic SIR-SI vector-borne infectious disease transmission model specifically for Dengue and Chikungunya diseases in Malaysia. Firstly, the common compartmental model for vector-borne infectious disease transmission called the SIR-SI model (susceptible-infective-recovered for human populations; susceptible-infective for vector populations) is presented. This is followed by the explanations on the stochastic SIR-SI model which involve the Bayesian description. This stochastic model then is used in the relative risk formulation in order to obtain the posterior relative risk estimation. Then, this relative estimation model is demonstrated using Dengue and Chikungunya data of Malaysia. The viruses of these diseases are transmitted by the same type of female vector mosquito named Aedes Aegypti and Aedes Albopictus. Finally, the findings of the analysis of relative risk estimation for both Dengue and Chikungunya diseases are presented, compared and displayed in graphs and maps. The distribution from risk maps show the high and low risk area of Dengue and Chikungunya diseases occurrence. This map can be used as a tool for the prevention and control strategies for both diseases.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Gompertzian stochastic model with delay effect to cervical cancer growth

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

A multilevel stochastic collocation method for SPDEs

We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Computational stochastic model of ions implantation

Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On Volterra quadratic stochastic operators with continual state space

Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

On a theory of stability for nonlinear stochastic chemical reaction networks

We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Comparison of different moment-closure approximations for stochastic chemical kinetics

In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Stabilization of the stochastically forced equilibria for nonlinear discrete-time systems with incomplete information

A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Dynamics of the stochastic Lorenz chaotic system with long memory effects

Little seems to be known about the ergodic dynamics of stochastic systems with fractional noise. This paper is devoted to discern such long time dynamics through the stochastic Lorenz chaotic system (SLCS) with long memory effects. By a truncation technique, the SLCS is proved to generate a continuous stochastic dynamical system Λ. Based on the Krylov-Bogoliubov criterion, the required Lyapunov function is further established to ensure the existence of the invariant measure of Λ. Meanwhile, the uniqueness of the invariant measure of Λ is proved by examining the strong Feller property, together with an irreducibility argument. Therefore, the SLCS has exactly one adapted stationary solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Confinement and diffusion modulate bistability and stochastic switching in a reaction network with positive feedback

Positive feedback is a common feature in signal transduction networks and can lead to phenomena such as bistability and signal propagation by domain growth. Physical features of the cellular environment, such as spatial confinement and the mobility of proteins, play important but inadequately understood roles in shaping the behavior of signaling networks. Here, we use stochastic, spatially resolved kinetic Monte Carlo simulations to explore a positive feedback network as a function of system size, system shape, and mobility of molecules. We show that these physical properties can markedly alter characteristics of bistability and stochastic switching when compared with well-mixed simulations. Notably, systems of equal volume but different shapes can exhibit qualitatively different behaviors under otherwise identical conditions. We show that stochastic switching to a state maintained by positive feedback occurs by cluster formation and growth. Additionally, the frequency at which switching occurs depends nontrivially on the diffusion coefficient, which can promote or suppress switching relative to the well-mixed limit. Taken together, the results provide a framework for understanding how confinement and protein mobility influence emergent features of the positive feedback network by modulating molecular concentrations, diffusion-influenced rate parameters, and spatiotemporal correlations between molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Effective computation of stochastic protein kinetic equation by reducing stiffness via variable transformation

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Symmetries of stochastic differential equations: A geometric approach

A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an algebra of strong symmetries for a modified SDE is proved under suitable regularity assumptions. This general approach is applied to a stochastic version of a two dimensional symmetric ordinary differential equation and to the case of two dimensional Brownian motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗