Search NASA⌕ Search

SEARCH · Search NASA

Results for “STOCHASTIC PROCESS”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Weak Convergence of a Mass-Structured Individual-Based Model

We propose a model of chemostat where the bacterial population is individually-based, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growth, division and washout). Bacteria interact via consumption. We set the exact Monte Carlo simulation algorithm of this model and its mathematical representation as a stochastic process. We prove the convergence of this process to the solution of an integro-differential equation when the population size tends to infinity. Finally, we propose several numerical simulations.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1994

Physical Models of Cognition

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.

Zak, Michail↗
DOE OSTI2011

Fractional dynamics in the light scattering intensity fluctuation in dusty plasma

Light scattering intensity fluctuation in dusty plasma system is studied. The scattered electric field of the laser light is treated as a stationary stochastic process. A nonstandard form of fractional Langevin equation is solved using Green's function approach to obtain the so-called fractional Ornstein-Uhlenbeck process. The empirical correlation function of light intensity fluctuation is fitted with four model correlation functions which are representative of different mechanisms for monodisperse particle transport, namely, the kinetic (ballistic) model, the hydrodynamical (diffusive) model, the hybrid kinetic-hydrodynamic model, and the fractional kinetic model for polydisperse particles. The shifted fractional derivative index is found to be related to power-law exponent of polydisperse dust mass distribution. It is shown that the correlation model based on fractional Ornstein-Uhlenbeck process may provide a novel insight into the complex transport behaviors in dusty plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

LOCAL GROUP DWARF SPHEROIDALS: CORRELATED DEVIATIONS FROM THE BARYONIC TULLY-FISHER RELATION

Local Group dwarf spheroidal satellite galaxies are the faintest extragalactic stellar systems known. We examine recent data for these objects in the plane of the Baryonic Tully-Fisher Relation (BTFR). While some dwarf spheroidals adhere to the BTFR, others deviate substantially. We examine the residuals from the BTFR and find that they are not random. The residuals correlate with luminosity, size, metallicity, ellipticity, and susceptibility of the dwarfs to tidal disruption in the sense that fainter, more elliptical, and tidally more susceptible dwarfs deviate farther from the BTFR. These correlations disfavor stochastic processes and suggest a role for tidal effects. We identify a test to distinguish between {Lambda}CDM and MOND based on the orbits of the dwarf satellites of the Milky Way and how stars are lost from them.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

A generalized parallel replica dynamics

Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying stochastic process to a quasi-stationary distribution. Two requirements for applying parallel replica dynamics are knowledge of the time scale on which the process converges to the quasi-stationary distribution and a mechanism for generating samples from this distribution. By combining a Fleming–Viot particle system with convergence diagnostics to simultaneously identify when the process converges while also generating samples, we can address both points. This variation on the algorithm is illustrated with various numerical examples, including those with entropic barriers and the 2D Lennard-Jones cluster of seven atoms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

In-plane current induced domain wall nucleation and its stochasticity in perpendicular magnetic anisotropy Hall cross structures

Hall cross structures in magnetic nanowires are commonly used for electrical detection of magnetization reversal in which a domain wall (DW) is conventionally nucleated by a local Oersted field. In this letter, we demonstrate DW nucleation in Co/Ni perpendicular magnetic anisotropy nanowire at the magnetic Hall cross junction. The DWs are nucleated by applying an in-plane pulsed current through the nanowire without the need of a local Oersted field. The change in Hall resistance, detected using anomalous Hall effect, is governed by the magnetic volume switched at the Hall junction, which can be tuned by varying the magnitude of the applied current density and pulse width. The nucleated DWs are driven simultaneously under the spin transfer torque effect when the applied current density is above a threshold. The possibility of multiple DW generation and variation in magnetic volume switched makes nucleation process stochastic in nature. The in-plane current induced stochastic nature of DW generation may find applications in random number generation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Phase multistability in a dynamical small world network

The effect of phase multistability is explored in a small world network of periodic oscillators with diffusive couplings. The structure of the network represents a ring with additional non-local links, which spontaneously arise and vanish between arbitrary nodes. The dynamics of random couplings is modeled by “birth” and “death” stochastic processes by means of the cellular automate approach. The evolution of the network under gradual increasing of the number of random couplings goes through stages of phases fluctuations and spatial cluster formation. Finally, in the presence of non-local couplings the phase multistability “dies” and only the in-phase regime survives.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced performance is observed already for the effectively classical systems, with no significant qualitative change in the quantum cases, which suggests that the noise-induced-coherence-enhancement mechanism is caused by static interference phenomena.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2011

It’s all in the crystals…

Protein surface engineering is increasingly used as a routine tool to enhance the crystallization propensity of proteins. Future possibilities include the use of multi-site protein variants, rational modulation of solubility and the development of strategies to tackle membrane proteins. Macromolecular crystallography relies on the availability and quality of single crystals; these are typically obtained through extensive screening, which has a very low intrinsic success rate. Crystallization is not a completely stochastic process and many proteins do not succumb to crystallization because of specific microscopic features of their molecular surfaces. It follows that rational surface engineering through site-directed mutagenesis should allow a systematic and significant improvement in crystallization success rates. Here, one such established strategy, surface-entropy reduction (SER), is discussed, including its successes, limitations and possible future developments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

A GLOBAL VIEW OF VELOCITY FLUCTUATIONS IN THE CORONA BELOW 1.3 R {sub ⊙} WITH CoMP

The Coronal Multi-channel Polarimeter (CoMP) has previously demonstrated the presence of Doppler velocity fluctuations in the solar corona. The observed fluctuations are thought to be transverse waves, i.e., highly incompressible motions whose restoring force is dominated by the magnetic tension, some of which demonstrate clear periodicity. We aim to exploit CoMP’s ability to provide high cadence observations of the off-limb corona to investigate the properties of velocity fluctuations in a range of coronal features, providing insight into how (whether) the properties of the waves are influenced by the varying magnetic topology in active regions, quiet Sun and open field regions. An analysis of Doppler velocity time-series of the solar corona from the 10747 Å Iron xiii line is performed, determining the velocity power spectrum and using it as a tool to probe wave behavior. Further, the average phase speed and density for each region are estimated and used to compute the spectra for energy density and energy flux. In addition, we assess the noise levels associated with the CoMP data, deriving analytic formulae for the uncertainty on Doppler velocity measurements and providing a comparison by estimating the noise from the data. It is found that the entire corona is replete with transverse wave behavior. The corresponding power spectra indicate that the observed velocity fluctuations are predominately generated by stochastic processes, with the spectral slope of the power varying between the different magnetic regions. Most strikingly, all power spectra reveal the presence of enhanced power occurring at ∼3 mHz, potentially implying that the excitation of coronal transverse waves by p -modes is a global phenomenon.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Higher order matrix differential equations with singular coefficient matrices

In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Summability of Connected Correlation Functions of Coupled Lattice Fields

We consider two nonindependent random fields ψ and ϕ defined on a countable set Z. For instance, Z=ℤ{sup d} or Z=ℤ{sup d}×I, where I denotes a finite set of possible “internal degrees of freedom” such as spin. We prove that, if the cumulants of ψ and ϕ enjoy a certain decay property, then all joint cumulants between ψ and ϕ are ℓ{sub 2}-summable in the precise sense described in the text. The decay assumption for the cumulants of ψ and ϕ is a restricted ℓ{sub 1} summability condition called ℓ{sub 1}-clustering property. One immediate application of the results is given by a stochastic process ψ{sub t}(x) whose state is ℓ{sub 1}-clustering at any time t: then the above estimates can be applied with ψ=ψ{sub t} and ϕ=ψ{sub 0} and we obtain uniform in t estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any ℓ{sub 1}-clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green–Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

On Weibull's Spectrum of Nonrelativistic Energetic Particles at IP Shocks: Observations and Theoretical Interpretation

Some interplanetary shocks are associated with short-term and sharp particle flux enhancements near the shock front. Such intensity enhancements, known as shock-spike events (SSEs), represent a class of relatively energetic phenomena as they may extend to energies of some tens of MeV or even beyond. Here we present an SSE case study in order to shed light on the nature of the particle acceleration involved in this kind of event. Our observations refer to an SSE registered on 2011 October 3 at 22:23 UT, by STEREO B instrumentation when, at a heliocentric distance of 1.08 au, the spacecraft was swept by a perpendicular shock moving away from the Sun. The main finding from the data analysis is that a Weibull distribution represents a good fitting function to the measured particle spectrum over the energy range from 0.1 to 30 MeV. To interpret such an observational result, we provide a theoretical derivation of the Weibull spectrum in the framework of the acceleration by “killed” stochastic processes exhibiting power-law growth in time of the velocity expectation, such as the classical Fermi process. We find an overall coherence between the experimental values of the Weibull spectrum parameters and their physical meaning within the above scenario. Hence, our approach based on the Weibull distribution proves to be useful for understanding SSEs. With regard to the present event, we also provide an alternative explanation of the Weibull spectrum in terms of shock-surfing acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Cauchy's formulas for random walks in bounded domains

Cauchy's formula was originally established for random straight paths crossing a body B⊂R{sup n} and basically relates the average chord length through B to the ratio between the volume and the surface of the body itself. The original statement was later extended in the context of transport theory so as to cover the stochastic paths of Pearson random walks with exponentially distributed flight lengths traversing a bounded domain. Some heuristic arguments suggest that Cauchy's formula may also hold true for Pearson random walks with arbitrarily distributed flight lengths. For such a broad class of stochastic processes, we rigorously derive a generalized Cauchy's formula for the average length traveled by the walkers in the body, and show that this quantity depends indeed only on the ratio between the volume and the surface, provided that some constraints are imposed on the entrance step of the walker in B. Similar results are also obtained for the average number of collisions performed by the walker in B.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Hanbury Brown-Twiss interferometry and second-order correlations of inflaton quanta

The quantum theory of optical coherence is applied to the scrutiny of the statistical properties of the relic inflaton quanta. After adapting the description of the quantized scalar and tensor modes of the geometry to the analysis of intensity correlations, the normalized degrees of first-order and second-order coherence are computed in the concordance paradigm and are shown to encode faithfully the statistical properties of the initial quantum state. The strongly bunched curvature phonons are not only super-Poissonian but also superchaotic. Testable inequalities are derived in the limit of large-angular scales and can be physically interpreted in the light of the tenets of Hanbury Brown-Twiss interferometry. The quantum mechanical results are compared and contrasted with different situations including the one where intensity correlations are the result of a classical stochastic process. The survival of second-order correlations (not necessarily related to the purity of the initial quantum state) is addressed by defining a generalized ensemble where super-Poissonian statistics is an intrinsic property of the density matrix and turns out to be associated with finite volume effects which are expected to vanish in the thermodynamic limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Multiwavelength Variability Study of the Classical BL Lac Object PKS 0735+178 on Timescales Ranging from Decades to Minutes

We present the results of our power spectral analysis for the BL Lac object PKS 0735+178, utilizing the Fermi -LAT survey at high-energy γ -rays, several ground-based optical telescopes, and single-dish radio telescopes operating at GHz frequencies. The novelty of our approach is that, by combining long-term and densely sampled intra-night light curves in the optical regime, we were able to construct for the first time the optical power spectrum of the blazar for a time domain extending from 23 years down to minutes. Our analysis reveals that: (1) the optical variability is consistent with a pure red noise, for which the power spectral density can be well approximated by a single power law throughout the entire time domain probed; (2) the slope of power spectral density at high-energy γ -rays (∼1) is significantly flatter than that found at radio and optical frequencies (∼2) within the corresponding time variability range; (3) for the derived power spectra, we did not detect any low-frequency flattening, nor do we see any evidence for cutoffs at the highest frequencies down to the noise floor levels due to measurement uncertainties. We interpret our findings in terms of a model where the blazar variability is generated by the underlying single stochastic process (at radio and optical frequencies), or a linear superposition of such processes (in the γ -ray regime). Along with the detailed PSD analysis, we also present the results of our extended (1998–2015) intra-night optical monitoring program and newly acquired optical photo-polarimetric data for the source.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stochastic quasi-steady state approximations for asymptotic solutions of the chemical master equation

In this paper, we propose two methods to carry out the quasi-steady state approximation in stochastic models of enzyme catalytic regulation, based on WKB asymptotics of the chemical master equation or of the corresponding partial differential equation for the generating function. The first of the methods we propose involves the development of multiscale generalisation of a WKB approximation of the solution of the master equation, where the separation of time scales is made explicit which allows us to apply the quasi-steady state approximation in a straightforward manner. To the lowest order, the multi-scale WKB method provides a quasi-steady state, Gaussian approximation of the probability distribution. The second method is based on the Hamilton-Jacobi representation of the stochastic process where, as predicted by large deviation theory, the solution of the partial differential equation for the corresponding characteristic function is given in terms of an effective action functional. The optimal transition paths between two states are then given by those paths that maximise the effective action. Such paths are the solutions of the Hamilton equations for the Hamiltonian associated to the effective action functional. The quasi-steady state approximation is applied to the Hamilton equations thus providing an approximation to the optimal transition paths and the transition time between two states. Using this approximation we predict that, unlike the mean-field quasi-steady approximation result, the rate of enzyme catalysis depends explicitly on the initial number of enzyme molecules. The accuracy and validity of our approximated results as well as that of our predictions regarding the behaviour of the stochastic enzyme catalytic models are verified by direct simulation of the stochastic model using Gillespie stochastic simulation algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗