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At least 325 records · Page 18

Quantal diffusion approach for multinucleon transfer processes in the 58,64 Ni + 208 Pb reactions: Toward the production of unknown neutron-rich nuclei

In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power. Purpose: This article aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni + 208 Pb at E c.m. = 268 MeV and 58 Ni + 208 Pb at E c.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from time evolution of occupied single-particle orbitals in TDHF. Secondary de-excitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus de-excitation model, gemini++. Dynamics of a fast isospin equilibration process followed by a slow drift toward the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond-mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, gemini++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. The SMF approach is designed to describe the quantum many-body problem according to an ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool in the search for optimal reaction conditions to produce yet-unknown neutron-rich heavy nuclei through the multinucleon transfer reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Radial diffusion in the Uranian radiatian belts - Inferences from satellite absorption loss models

Low-energy charged particle (LECP) phase space density profiles available from the Voyager/1986 Uranus encounter are analyzed, using solutions of the time-averaged radial diffusion equation for charged particle transport in a dipolar planetary magnetic field. Profiles for lower-energy protons and electrons are first analyzed to infer radial diffusion rate as a function of L, assuming that satellite absorption is the dominant loss process and local sources for these particles are negligible. Satellite macrosignatures present in the experimentally derived profiles are approximately reproduced in several cases, lending credence to the loss model and indicating that magnetospheric distributed losses are not as rapid as satellite absorption near the minimum satellite L shells for the particles. Diffusion rates and L dependences are found to be similar to those previously inferred in the inner Jovian magnetosphere (Thomsen et al., 1977) and for the inner Saturnian magnetosphere (Hood, 1985). Profiles for higher energy electrons and protons are also analyzed using solutions that allow for the existence of significant particle sources as well as sinks. Possible implications for radial diffusion mechanisms in the Uranian radiation belts are discussed.

Hood, L. L.↗

Hall-Effect Thruster Simulations with 2-D Electron Transport and Hydrodynamic Ions

A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.

plasma↗

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗

Molecular-level insights into structure and dynamics in ionic liquids and polymer gel electrolytes

We report designing new electrolytes requires a better understanding of the correlation between their transport properties and their molecular structure. In this work, we present a detailed study of ionic liquids and polymer gel electrolytes probing their structure and dynamics by nuclear magnetic resonance (NMR) spectroscopy. In particular, ammonium- and phosphonium-based ionic liquids (ILs) are combined with different LiTFSI concentrations, and then with different ratios of poly(methylmethacrylate) polymer. The temperature dependence of self-diffusion coefficients of mobile species, D Li+ , D TFSI- and D P4441+ or D N4441+ , measured by pulsed field gradient (PFG) NMR spectroscopy obeys the Arrhenius equation. Diffusivity of [P4441][TFSI] ILs is found to be greater than those of the [N4441][TFSI] ILs in both liquid and gel electrolytes. Solid state NMR experiments including 13 C and 19 F MAS, 13 C{ 19 F}, 13 C{ 1 H} CPMAS probe the local structure and molecular-level interactions between ions and polymer in gel electrolytes, particularly for samples with higher PMMA content (≥25 wt%). Finally, the fast field cycling relaxometry has been used to unveil the rotational and translational dynamics of P4441 + or N4441 + and TFSI - by measuring 1 H and 19 F R 1 relaxation rate profiles at different temperatures. A comprehensive NMR analysis including relaxation studies at low magnetic field provides decisive new insights regarding the formation of ionic clusters and the interaction of ions with the polymer chain in the case of the gel electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

Variational Multiscale Discontinuous Galerkin (VMD↗

AMPE

AMPE is a phase-field code. It evolves in time the Allen-Cahn equations associated with a phase­field model, coupled with the time-evolution of a composition field (in an alloy) and a temperature field which are described by diffusion equations. It can also solve the elasticity equations assuming mechanical equilibrium at every time-step. Grain orientations are described by normalized quaternions which also evolve in time according to Allen-Cahn type equations.

Wickett, Mike↗

Seismic energy transmission in an intensively scattering environment

In order to account for some special features of lunar seismograms, namely, the gradual build-up of the signal, the extremely prolonged tail, and the lack of apparent coherence among three orthogonal components of ground motion, a statistical approach is proposed for describing transmission of seismic energy through a medium in which strong scattering takes place. A seismic diffusion theory is presented for a medium with randomly distributed scatterers of a given size distribution. A solution of the resulting diffusion equation for an impulsive energy source gives a curve which fairly closely reproduces the envelope of typical lunar impact seismograms. Since the model is based on constant diffusivity, long-range transmission will require a combination of diffusion and wave propagation treatments for accurate description.

Nakamura, Y.↗

The expected cosmic ray density and stream distributions at the heliolatitudinal asymmetry of solar wind

The results of the spatial distribution of cosmic ray density, gradients, and anisotropy obtained on the basis of the numerical solution of the anisotropic diffusion equation with an account of solar wind velocity change depending on the latitudinal angle theta of the form U=u sub oe sup alpha theta and the diffusion coefficient depending on the spatial coordinates and the particle rigidity are presented. It is shown that the increase of the solar wind velocity and the diffusion coefficient with heliolatitude leads to gradient distributions that are in accord with experimental data observed in space. The results of the energetic spectrum of 11 and 22-year cosmic ray variations obtained with an account of direction of the general magnetic field of the Sun are presented are given.

Alania, M. V.↗

Mason–Weaver theory: Revised and extended for a semi-infinite domain

Mason and Weaver developed equations to describe small particles settling under the influence of gravity and Brownian motion, including the limiting case for an infinitely deep suspension. We encountered this common convection–diffusion equation and no-flux boundary conditions in a model for dynamics of adsorbed polymers in dead end pores of a depolymerization catalyst. Close examination reveals that the Mason–Weaver solution is not correct for the infinite domain with a non-uniform initial condition. In this paper, we obtain the time dependent Green’s function for the no flux boundary condition and also for a more general reactive boundary condition. We demonstrate how the results provide solutions, via superposition, which provide solutions for several boundary conditions and all initial conditions.

Chen, Ziqiu↗

Superresolution Diffuse Optical Imaging by Localization of Fluorescence

The multiple scattering of light presents major challenges in realizing useful in vivo imaging at tissue depths of more than about one millimeter, where many answers to health questions lie. Visible through near-infrared photons can be readily and safely detected through centimeters of tissue; however, limited information is available for image formation. One strategy for obtaining images is to model the photon transport and a simple incoherent model is the diffusion equation approximation to the Boltzmann transport equation. Such an approach provides a prediction of the mean intensity of heavily scattered light and hence provides a forward model for optimization-based computational imaging. While diffuse optical imaging methods have received substantial attention, they remain restricted in terms of resolution because of the loss of high-spatial-frequency information that is associated with the multiple scattering of photons. Consequently, only relatively large inhomogeneities, such as tumors or organs in small animals, can be effectively resolved. We introduce a superresolution imaging approach based on point localization in a diffusion framework that enables over two orders of magnitude improvement in the spatial resolution of diffuse optical imaging. The method is demonstrated experimentally by localizing a fluorescent inhomogeneity in a highly scattering slab and characterizing the localization uncertainty. The approach allows imaging through centimeters of tissue with a resolution of tens of microns, thereby enabling cells or cell clusters to be resolved. More generally, this high-resolution imaging approach could be applied with any physical transport or wave model and hence to a broad class of physical problems. Finally, paired with a suitable optical contrast mechanism, as can be realized with targeted fluorescent molecules or genetically modified animals, superresolution diffuse imaging should open alternative dimensions for in vivo applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime

Characteristics-based methods for the advection-diffusion equation are presented and directly applied to study thermal convection with extremely large Rayleigh number (Ra). It is shown that the operator-splitting method for advection-diffusion problems is very accurate for determining the advected field at extremely high Peclet number (Pe). The technique presented is considered to have great potential for solving advection-dominated problems, while the Langrangian method is more accurate for lower Pe. It is noted that the accuracy of these characteristics-based methods strongly depends on the quality of interpolation. The computational time for the operator-splitting method grows with the number of time steps employed. The Langrangian method was used for simulations of convection at very high Ra, up to 3 x 10 to the 9th, and time-dependent, thermal convection solutions were obtained for infinite Prandtl number.

Malevsky, A. V.↗

Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods

A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.

Atkins, Harold L.↗

Diffusion in random networks

The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt $-$1/4 rather than xt $-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.

97 MATHEMATICS AND COMPUTING↗

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗

New approach to cosmic-ray diffusion theory.

We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our method incorporates essential effects of the magnetic fluctuations in the lowest order particle orbits. Significant corrections to the usual quasilinear diffusion coefficient for cosmic rays with pitch angles near 90 deg are a consequence. Monte Carlo results bear out the validity of our theory.

Jones, F. C.↗

Numerical study of solar flare particle propagation in the heliosphere

Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation. For low-rigidity particles the radial mean free path so obtained is significantly larger than the mean free path calculated from the scattering coefficient due to the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between the scattering mean free path and the theoretical predictions may be resolved by these calculations.

Gombosi, T. I.↗