Relativistic stochastic processes
Random processes in Brownian motion for solving relativistic Fokker-Planck equation
Wayland, J. R., Jr.↗
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Chemical reaction in a turbulent flow field with uniform velocity gradient
Statistical transport, energy and chemical reaction rate in turbulent flow field with uniform velocity gradient, using Brownian motion theory
Chung, P. M.↗
A turbulence description of couette flow
Statistical mechanics for wall shear turbulence in couette flow based on Brownian motion and comparison with stochastic theory based on Navier-Stokes equation
Chung, P. M.↗
Astronautics and aeronautics, 1969 Chronology on science, technology, and policy
Statistical mechanics for wall shear turbulence in Couette flow based on Brownian motion and comparison with stochastic theory based on Navier-Stokes equation
Source record↗
Linear minimum variance filters applied to carrier tracking
A new approach is taken to the problem of tracking a fixed amplitude signal with a Brownian-motion phase process. Classically, a first-order phase-lock loop (PLL) is used; here, the problem is treated via estimation of the quadrature signal components. In this space, the state dynamics are linear with white multiplicative noise. Therefore, linear minimum-variance filters, which have a particularly simple mechanization, are suggested. The resulting error dynamics are linear at any signal/noise ratio, unlike the classical PLL. During synchronization, and above threshold, this filter with constant gains degrades by 3 per cent in output rms phase error with respect to the classical loop. However, up to 80 per cent of the maximum possible noise improvement is obtained below threshold, where the classical loop is nonoptimum, as demonstrated by a Monte Carlo analysis. Filter mechanizations are presented for both carrier and baseband operation.
Gustafson, D. E.↗
A diffusion model for use with directional samplers
The paper presents a mathematical model for describing dispersion processes of airborne particles in the atmosphere. The process is described as a superposition of independent Brownian motion processes with drifts and a boundary at zero. It is assumed that the terrain is flat and of a homogeneous roughness. All sources are assumed to be point sources. The time dependencies of emission rates, wind speed, wind direction, and atmospheric conditions are taken into account.
Anbar, D.↗
Stochastic partial differential equations in turbulence related problems
The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.
Chow, P.-L.↗
Relatively low-temperature pyrolysis of silane in free space
The continuous flow pyrolyzer is a free space reactor that is used to study the effects of concentration, flow rate and temperature in making solar-grade silicon by pyrolysis of silane gas. Work with the continuous flow pyrolyzer is within the DOE-sponsored Low-Cost Solar Array Project. The work has led to a new theoretical treatment of silane pyrolysis in free space at relatively low temperatures (550 C to 750 C). It involves a sequential, three-step mechanism of particle growth: first, silicon atom generation by homogeneous reaction; second, coagulation to a 0.1 micron particle due to Brownian motion and van der Waals forces; and finally, chemical vapor deposition by heterogeneous reaction to final particle size.
Levin, H.↗
Random element method for numerical modeling of diffusional processes
The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.
Ghoniem, A. F.↗
Transition density of one-dimensional diffusion with discontinuous drift
The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.
Zhang, Weijian↗
Notes on initial disturbance fields for the transition problem
Initial disturbance fields are categorized and discussed with respect to modes of disturbance and the variants which occur for each test technique. Attention is focused on four fluctuation modes included under the category of stream turbulence: vorticity fluctuations, entropy disturbances or temperature spottiness, noise, and concentration fluctuations. The mechanisms by which particulate matter can affect transition are discussed, along with electrostatic discharges with frequencies in the range from 200 KHz to 30 MHz which is within the critical disturbance-frequency range for many high-speed flows. Acoustic radiation from own vehicle, roughness, and Brownian motion are also covered.
Bushnell, Dennis↗
Theoretical study of the design of a catalyst for para to ortho hydrogen conversion
The theory of Petzinger and Scalapino (1973) was thoroughly reviewed, and all of the basic equations for paramagnetic para to ortho hydrogen catalysis re-derived. There are only a few minor phase errors and errors of omission in the description of the theory. Three models (described by Petzinger and Scalapino) for the rate of para to ortho H2 catalysis were worked out, and uniform agreement obtained to within a constant factor of 2 pi. The analytical methods developed in the course of this study were then extended to two new models, which more adequately describe the process of surface catalysis including transfer of hydrogen molecules onto and off of the surface. All five equations for the para to ortho catalytic rate of conversion are described. The two new equations describe the catalytic rate for these models: H2 on the surface is a 2-D gas with lifetime tau; and H2 on the surface is a 2-D liquid undergoing Brownian motion (diffusion) with surface lifetime tau.
Coffman, Robert E.↗
Microgravity combustion of dust suspensions
Unlike the combustion of homogeneous gas mixtures, there are practically no reliable fundamental data (i.e., laminar burning velocity, flammability limits, quenching distance, minimum ignition energy) for the combustion of heterogeneous dust suspensions. Even the equilibrium thermodynamic data such as the constant pressure volume combustion pressure and the constant pressure adiabatic flame temperature are not accurately known for dust mixtures. This is mainly due to the problem of gravity sedimentation. In normal gravity, turbulence, convective flow, electric and acoustic fields are required to maintain a dust in suspension. These external influences have a dominating effect on the combustion processes. Microgravity offers a unique environment where a quiescent dust cloud can in principle be maintained for a sufficiently long duration for almost all combustion experiments (dust suspensions are inherently unstable due to Brownian motion and particle aggregation). Thus, the microgravity duration provided by drop towers, parabolic flights, and the space shuttle, can all be exploited for different kinds of dust combustion experiments. The present paper describes some recent studies on microgravity combustion of dust suspension carried out on the KC-135 and the Caravelle aircraft. The results reported are obtained from three parabolic flight campaigns.
Lee, John H. S.↗
Quantum harmonic oscillator in a thermal bath
The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.
Zhang, Yuhong↗
Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)
The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.
Yeh, Leehwa↗
Evolution of wave function in a dissipative system
For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.
Yu, Li-Hua↗
Dynamics of Granular Materials
Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, l/f noise, and fractional Brownian motion provide examples. Work beginning at Duke will focus on gravity driven convection, mixing and gravitational collapse. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. In the absence of a steady energy input, granular materials undergo a rapid collapse which is strongly influenced by the presence of gravity. Fluctuations on laboratory scales in such quantities as the stress can be very large-as much as an order of magnitude greater than the mean.
Behringer, Robert P.↗
Chain Dynamics in a Dilute Magnetorheological Fluid
The structure, formation, and dynamics of dilute, mono-dispersive ferrofluid emulsions in an external magnetic field have been investigated using dynamic light scattering techniques. In the absence of the magnetic field, the emulsion particles are randomly distributed and behave like hard spheres in Brownian motion. An applied magnetic field induces a magnetic dipole moment in each particle. Dipolar interactions between particles align them into chains where correlation functions show two decay processes. The short-time decay shows the motion of straight chains as a whole where the apparent chain length increases with the applied magnetic field and the particle volume fraction. Good scaling results are obtained showing that the apparent chain length grows with time following a power law with exponent of 0.6 and depends on the applied field, particle volume fraction, and diffusion constant of the particles. The long-time decay in the correlation function shows oscillation when the chains reach a certain length with time and stiffness with threshold field This result shows that chains not only fluctuate, but move in a periodic motion with a frequency of 364 Hz at lambda = 15. It may suggest the existence of phonons. This work is the first step in the understanding of the structure formation, especially chain coarsening mechanism, of magnetorheological (MR) fluids at higher volume fractions.
Liu, Jing↗