Liapunov criteria for weak stochastic stability.
Sufficient conditions for recurrence and positivity of diffusion process defined by stochastic differential equation, using Liapunov function
DIFFERENTIAL EQUATION↗
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Flux-limited diffusion in hydrodynamics
The radiation transport equation, correct to order v/c, is used to derive a flux limiter valid in high-velocity hydrodynamic flows. In the limit v = 0 the widely used result of Levermore and Pomraning (LP) (1982) is recovered. In the case of homologous flow (v varies as R) the LP result remains valid, but in the presence of shock waves and other nonhomologous flows differences may be large. We calculate the Eddington factors, which are significantly altered, and discuss the importance of having them possess the correct form in the presence of a shock wave, e.g., on the neutrino transport during the formation of a supernova.
Cooperstein, J.↗
Effects of free stream turbulence intensity and integral length scale on heat transfer from a circular cylinder in crossflow
A model has been proposed for the momentum eddy diffusivity induced by free stream turbulence intensity and integral length scale. The eddy diffusivity model is applied to a cylinder situated in a uniform crossflow in the presence of free stream turbulence. Numerical solution of the governing momentum and energy equations with the proposed eddy diffusivity model yielded results for the skin friction coefficient and the Nusselt number. The numerical predictions of the present work are compared with experimental data and the agreement between the two is seen to be very good.
Gorla, R. S. R.↗
Analytical Solutions of Transient Drift-Diffusion in P-N Junction Pixel Sensors
Radiation detection in applications ranging from high energy physics to medical imaging rely on solid state detectors, often hybrid pixel detectors with (1) reverse biased p-n junction pixel sensors and (2) readout ASICs, attached by flip chip-bonding. Transient signals characteristics are important in, e.g., matching ASIC and sensor design, modeling and optimizing detector parameters and describing timing and charge sharing properties. Currently analytical forms of transient signals are available for only a few limited cases (e.g., drift or diffusion) or for the steady state (which is not relevant for high energy radiation detection). Tools are available for (relatively slow) numerical evaluation of the transient charge transport. We present here the first analytical solutions of partial differential equations de scribing drift-diffusion-recombination charge transport in planar p-n junction sensors in a variety of conditions: (1) undepleted, (2) fully depleted, (3) taking into account the gradual velocity saturation, and (4) overdepleted. We deduce the Green’s functions which can be applied to any detection problem through simple convolution with the initial conditions. We compare the analytical solutions with Monte Carlo simulations and industry standard simulations (Synopsys Sentaurus), demonstrating good agreement. Using the analytical equations enables fast modeling of the influence of various detector parameters on tracking, imaging and timing performance, describing performance and enabling optimizations for different applications. Finally, we illustrate this model with applications in 3D+T (x,y,z,time) photon tracking and 4D+T (x,y,θ,φ,time) relativistic charged particle tracking.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
A Numerical Study of Forbush Decreases with a 3D Cosmic-Ray Modulation Model Based on an SDE Approach
Based on the reduced diffusion mechanism for producing Forbush decreases (Fds) in the heliosphere, we constructed a three-dimensional (3D) diffusion barrier, and by incorporating it into a stochastic differential equation (SDE) based time-dependent, cosmic-ray transport model, a 3D numerical model for simulating Fds is built and applied to a period of relatively quiet solar activity. This SDE model generally corroborates previous Fd simulations concerning the effects of the solar magnetic polarity, the tilt angle of the heliospheric current sheet (HCS), and cosmic-ray particle energy. Because the modulation processes in this 3D model are multi-directional, the barrier’s geometrical features affect the intensity profiles of Fds differently. We find that both the latitudinal and longitudinal extent of the barrier have relatively fewer effects on these profiles than its radial extent and the level of decreased diffusion inside the disturbance. We find, with the 3D approach, that the HCS rotational motion causes the relative location from the observation point to the HCS to vary, so that a periodic pattern appears in the cosmic-ray intensity at the observing location. Correspondingly, the magnitude and recovery time of an Fd change, and the recovering intensity profile contains oscillation as well. Investigating the Fd magnitude variation with heliocentric radial distance, we find that the magnitude decreases overall and, additionally, that the Fd magnitude exhibits an oscillating pattern as the radial distance increases, which coincides well with the wavy profile of the HCS under quiet solar modulation conditions.
79 ASTRONOMY AND ASTROPHYSICS↗
Fluctuating hydrodynamics of reactive liquid mixtures
Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Effects of a parallel electric field and the geomagnetic field in the topside ionosphere on auroral and photoelectron energy distributions
The consequences of electric field acceleration and an inhomogeneous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one-dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogeneous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of O(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function is investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogeneous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.
Min, Q.-L.↗
Effects of a Parallel Electric Field and the Geomagnetic Field in the Topside Ionosphere on Auroral and Photoelectron Energy Distributions
The consequences of electric field acceleration and an inhomogencous magnetic field on auroral electron energy distributions in the topside ionosphere are investigated. The one- dimensional, steady state electron transport equation includes elastic and inelastic collisions, an inhomogencous magnetic field, and a field-aligned electric field. The case of a self-consistent polarization electric field is considered first. The self-consistent field is derived by solving the continuity equation for all ions of importance, including diffusion of 0(+) and H(+), and the electron and ion energy equations to derive the electron and ion temperatures. The system of coupled electron transport, continuity, and energy equations is solved numerically. Recognizing observations of parallel electric fields of larger magnitude than the baseline case of the polarization field, the effect of two model fields on the electron distribution function in investigated. In one case the field is increased from the polarization field magnitude at 300 km to a maximum at the upper boundary of 800 km, and in another case a uniform field is added to the polarization field. Substantial perturbations of the low energy portion of the electron flux are produced: an upward directed electric field accelerates the downward directed flux of low-energy secondary electrons and decelerates the upward directed component. Above about 400 km the inhomogencous magnetic field produces anisotropies in the angular distribution of the electron flux. The effects of the perturbed energy distributions on auroral spectral emission features are noted.
Min, Q.-L.↗
The dynamics of oceanic fronts. Part 1: The Gulf Stream
The establishment and maintenance of the mean hydrographic properties of large scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density. The full time dependent diffusion and Navier-Stokes equations for a constant Coriolis parameter are used in this study. Scaling analysis reveals three independent length scales of the problem, namely a radius of deformation or inertial length scale, Lo, a buoyance length scale, ho, and a diffusive length scale, hv. Two basic dimensionless parameters are then formed from these length scales, the thermal (or more precisely, the densimetric) Rossby number, Ro = Lo/ho and the Ekman number, E = hv/ho. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on E alone for problems of oceanic interest. Under this scaling, the solutions are similar for all Ro. It is also shown that 1/Ro is a measure of the frontal slope. The governing equations are solved numerically and the scaling analysis is confirmed. The solution indicates that an equilibrium state is established. The front can then be rendered stationary by a barotropic current from a larger scale along-front pressure gradient. In that quasisteady state, and for small values of E, the main thermocline and the inclined isopycnics forming the front have evolved, together with the along-front jet. Conservation of potential vorticity is also obtained in the light water pool. The surface jet exhibits anticyclonic shear in the light water pool and cyclonic shear across the front.
Kao, T. W.↗
Transport equation for plasmas in a stationary-homogeneous turbulence
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean parallel electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of the fluctuations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
High-order solution methods for grey discrete ordinates thermal radiative transfer
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Spectrum of spin waves in cold polarized gases
The spin dynamics of cold polarized gases are investigated using the Boltzmann equation. The dispersion relation for spin waves (transverse component of the magnetic moment) and the spin diffusion coefficient of the longitudinal component of the magnetic moment are calculated without using fitting parameters. The spin wave frequency and the diffusion coefficient for rubidium atoms are estimated numerically.
74 ATOMIC AND MOLECULAR PHYSICS↗
Synthesis, Characterization and Experimental Studies of Nano Zn–Al–Fe{sub 3}O{sub 4} Blended Alginate/Ca Beads for the Adsorption of Rhodamin B
In the present study, adsorptive removal of rhodamin-B (RMN-B) from aqueous solution was investigated by using nano Zn–Al–Fe{sub 3}O{sub 4} incorporated sodium alginate (SA) beads. SA is a natural polysaccharide, non toxic and biodegradable material. The incorporation of Zn–Al–Fe{sub 3}O{sub 4} into SA was done by ionic polymerization method using CaCl{sub 2}. A batch mode study was used for the adsorption of RMN-B onto Zn–Al–Fe{sub 3}O{sub 4}/ alginate beads. The adsorption efficiency of RMN-B was investigated by the following modeling equations like Freundlich, Langmuir, Pseudo-first order, Pseudo-second order, Intraparticle diffusion, Gibbs free energy, Enthalpy and Entropy. The predicted experimental results of various modeling equations were implied that the process follow Langmuir and pseudo-second order equations. The intraparticle diffusion parameters indicate that the diffusion between RMN-B and nano beads were predominant in throughout of process. The surface morphology of nano beads of before and after adsorption were show that RMN-B is strongly adhered on whole surface of the nano material. The FTIR spectrum indicates that the RMN-B strongly adsorbed on the surface and TGA study reveals that the alginate/Zn–Al–Fe{sub 3}O{sub 4}/Ca material has an excellent temperature withstand capacity.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Galactic civilizations - Population dynamics and interstellar diffusion
A model is developed of the interstellar diffusion of galactic civilizations which takes into account the population dynamics of such civilizations. The problem is formulated in terms of potential theory, with a family of nonlinear partial differential and difference equations specifying population growth and diffusion for an organism with advantageous genes that undergoes random dispersal while increasing in population locally, and a population at zero population growth. In the case of nonlinear diffusion with growth and saturation, it is found that the colonization wavefront from the nearest independently arisen galactic civilization can have reached the earth only if its lifetime exceeds 2.6 million years, or 20 million years if discretization can be neglected. For zero population growth, the corresponding lifetime is 13 billion years. It is concluded that the earth is uncolonized not because interstellar spacefaring civilizations are rare, but because there are too many worlds to be colonized in the plausible colonization lifetime of nearby civilizations, and that there exist no very old galactic civilizations with a consistent policy of the conquest of inhabited worlds.
Newman, W. I.↗
Stagnation point heat transfer augmentation due to free stream turbulence
A model has been proposed for the momentum eddy diffusivity induced by free stream turbulence intensity and integral length scale. The eddy diffusivity model is applied to the stagnation point of a cylinder situated in a uniform crossflow in the presence of free stream turbulence. A numerical solution of the governing momentum and energy equations with the proposed eddy diffusivity model yielded results for the skin friction coefficient and the Nusselt number. The numerical predictions of the present work are compared with experimental data and the agreement between the two is seen to be very good.
Gorla, R. S. R.↗
Thermoelectric transport coefficients in mono-layer MoS{sub 2} and WSe{sub 2}: Role of substrate, interface phonons, plasmon, and dynamic screening
The thermoelectric transport coefficients of electrons in two recently emerged transition metal di-chalcogenides (TMD), MoS{sub 2} and WSe{sub 2}, are calculated by solving Boltzmann transport equation using Rode's iterative technique in the diffusive transport regime and the coupled current (electrical and heat) equations. Scattering from remote phonons along with the hybridization of TMD plasmon with remote phonon modes and dynamic screening under linear polarization response are investigated in TMDs sitting on a dielectric environment. The transport coefficients are obtained for a varying range of temperature and doping density for three different types of substrates—SiO{sub 2}, Al{sub 2}O{sub 3}, and HfO{sub 2}. The Seebeck co-efficient for MoS{sub 2} and WSe{sub 2} is found to be higher than 3D semiconductors even with diffusive transport. The electronic thermal conductivity is found to be low, however, the thermoelectric figure of merit is limited by the high phonon thermal conductivity. It is found that judicious selection of a dielectric environment based on temperature of operation and carrier density is crucial to optimize the thermoelectric performance of TMD materials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The effects of diffusion on population gratings and the stability of ring lasers
The effects of diffusion on the coupling between counterpropagating modes in a two-level medium are studied in the rate equation limit. It is shown that diffusion can greatly decrease saturation gratings in low-pressure gases. Among many other effects which rely on spatial hole burning, this can alter the stability of bidirectional solutions of the third-order Lamb equation model of a ring laser.
Lawandy, N. M.↗
Simulation of 2-dimensional viscous flow through cascades using a semi-elliptic analysis and hybrid C-H grids
A semi-elliptic formulation, termed the interacting parabolized Navier-Stokes (IPNS) formulation, is developed for the analysis of a class of subsonic viscous flows for which streamwise diffusion is neglible but which are significantly influenced by upstream interactions. The IPNS equations are obtained from the Navier-Stokes equations by dropping the streamwise viscous-diffusion terms but retaining upstream influence via the streamwise pressure-gradient. A two-step alternating-direction-explicit numerical scheme is developed to solve these equations. The quasi-linearization and discretization of the equations are carefully examined so that no artificial viscosity is added externally to the scheme. Also, solutions to compressible as well as nearly compressible flows are obtained without any modification either in the analysis or in the solution process. The procedure is applied to constricted channels and cascade passages formed by airfoils of various shapes. These geometries are represented using numerically generated curilinear boundary-oriented coordinates forming an H-grid. A hybrid C-H grid, more appropriate for cascade of airfoils with rounded leading edges, was also developed. Satisfactory results are obtained for flows through cascades of Joukowski airfoils.
Ramamurti, R.↗