Session U19: Computational Methods: Dynamics, Transport, and Plasma

Charged particle and neutron energy deposition in an inertial confinement fusion plasma leading to internal tritium breeding

Plasma heating by charged particles and neutrons, energy exchange between ions and electrons and radiative losses are the primary mechanisms determining the ignition conditions in a thermonuclear plasma. In this work the energy leakage probability has been obtained numerically by including the effect of nuclear scattering, small and large angle Coulomb scattering and collective plasma effects. A simple multigroup approach has been developed for energy deposition by neutrons due to nuclear interaction with the ions. Using this accurate model for energy deposition, the concept of internal tritium breeding in DT fusion pellet has been re-evaluated by numerically solving the rate equations for various participating species and energy balance equations for ions, electrons and radiation within the three temperature model. Internal tritium breeding is found to occur even when all the radiation loss mechanisms such as bremsstrahlung and inverse compton scattering are fully accounted for.   

Breakeven Fusion in Staged Z Pinch

We are studying the prospect for breakeven thermonuclear fusion considering a Mega joule (MJ) class, 100 ns, impulse generator using a modified version of MACH2, a 2-1/2 D, radiation-code. The load is a cylindrical, xenon plasma shell that implodes radially onto a co-axial, deuterium-tritium plasma target. Optimized plasma density and pinch radius lead to a fusion-energy output that is many times the stored capacitor bank energy. In this ``Staged Z-pinch'' shock fronts form that preheat the DT plasma to several hundred eV, before adiabatic compression. During compression, the Xe liner becomes Rayleigh-Taylor (RT) unstable while the DT target remains stable. Proper selection of the initial pinch radius and plasma density is crucial for optimum implosion efficiency.   

Intensity correlations in wave transport through complex media

The intensity-intensity correlations that appear when a wave propagates coherently through a random medium will be discussed within the framework of the random matrix theory (RMT) of transport. We will consider the case of transmitted-transmitted, reflected-reflected and transmitted-reflected correlations. In the case of transmission the spatial correlations can be expressed as the sums of three terms with distinctive spatial dependences. This result coincides with the one obtained in the diffusive regime from perturbative calculations, but here its validity is extended from the quasi ballistic to the localized regime. In the RMT framework, approximate solutions of the DMPK equations allow us to study the dependence of the correlations with the length of the system.   

Modified Transition Matrix Methods

Recently we adapted the transition matrix Monte-Carlo method to general communication systems problems [D. Yevick and M. Reimer, Photon.Technol. Lett. 1529 (2007), IEEE Trans. Commun., submitted, (2007)]. In this presentation, we compare the accuracy and parameter dependence of different multicanonical and transition-matrix methods. We find that the standard multicanonical method can be reformulated more simply and accurately for a single system observable (output variable) within a transition matrix formulation by constructing the intermediate probability density function (density of states) after a small number of Markov transitions from the ratios of the elements of the transition matrix between adjacent histogram bins. Further, we consider an alternative procedure in which transitions only occur either from a given state to itself or to states that have previously been less frequently sampled. Here we show that the numerical error is small unless the self-transition probability is considerable. In this case, despite the violation of detailed balance, numerical precision can be effectively restored by ensuring that the random walker thermalizes within each histogram bin before effecting a transition to a different bin.   

Critical phenomena of Site-Percolation Models with Two Different Sizes of Particles on a Square Lattice

The concept of percolation plays an important role in explaining various important physical phenomena, including transport, mechanical, and electromagnetic properties of disordered systems. To date, many percolation models have been developed. Contrary to the ordinary site percolation models with homogeneous particles, systems have a certain particle-size distribution. Such a distribution may affect the properties of the system in certain ways. In the present study, site-percolation models with two different sizes of particles are systematically introduced on a square lattice to understand the effect of nonhomogeneity of the particles in the system. To estimate the critical phenomena with high accuracy, a finite-size scaling analysis is performed with a Monte Carlo simulation. The critical coverage at the percolation threshold is examined as a function of the size distribution of elements in the system. Fractal dimension and the critical exponentials are also estimated.   

Development of a Simple Sintering Law for Fractal Aggregates Composed of Unequal Sized Primary Particles

Sintering of silicon nanoparticle chain aggregates composed of unequal sized primary particles are investigated using molecular dynamics (MD) simulations at 1500 K. We consider straight chain aggregates consisting of up to 40 2.5 and 5.4 nm primary particles. The sintering time increases with increase in the total volume of the chain aggregate or with increase in the exposed initial surface area of the chain. A mathematical model was developed to describe the dynamics of sintering of such chain aggregates. The model is a power law modification of the Frenkel sintering equation with the Koch-Friedlander model to include primary particle size dependence. We found that the particle size effect is a local process, and important only at the initial stage of the sintering. Thus, the effect is not significant when the aggregate becomes large. The model is amenable for use in aerosol models that might include sintering effects.   

Toward a new criteria of soliton/ domain wall creation in condensed matter systems?

We do an extension of prior work where we applied a quasi 1-Dimensional wavefunctional formulation of tunneling Hamiltonians to a physical transport problem characterized by a perturbed washboard potential. To do so beforehand in the quasi one dimensional situation, we considered tunneling between states that were modeled as wavefunctionals of a scalar quantum field. I-E curves that matched Zener curves --- were used to fit data from an experimental stand point with quasi one dimensional wavefunctionals congruent with the false vacuum hypothesis. We generalize this to the case of higher dimensional formulations of the wave functionals, and also present a minimum criteria for the formation of soliton/ instanton structure in higher dimensions.   

Use of Space-Time Basis Sets for Solving Initial-Value Problems

A new algorithm for solving Quantum Mechanical initial-value problems such as the time-dependent Schroedinger equation and the Liouville equation is described. The method avoids the use of the time-translation operator which inevitably results in an essentially sequential algorithm and instead turns the problem into the solution of simultaneous equations, which produces a highly parallelizable algorithm. A basis set in time as well as spatial degrees of freedom is used. The basis may be spectral, finite element, or spectral element and may be continuous or discrete (discrete variable representation--DVR). The time-axis may have an arbitrary size of time element including only one element. The larger the time step, the larger the size of the time basis that is required. The Hamiltonian may be time-independent or time-dependent. In the case of a time-independent Hamiltonian, an extremely efficient algorithm results. For the time-dependent case, the problem of time-ordering does not arise. Several applications involving laser-atom interactions will be given.   

Propagating the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme, analogous to the propagation of linear Schroedinger equations, results from a special operator whose properties ensure the correct propagation. Using this scheme we prove the correctness of higher-order integrators for the Gross-Pitaevskii equation and its multi-component generalizations.   

Reconstructing the dynamics of water sheared between charged plates using inelastic x-ray scattering

Understanding the dynamical behavior of water under confinement or near surfaces is fundamental to tribology and many transport processes in cell biology. To achieve angstrom and femtosecond resolution in water dynamics, we reconstruct the space-time longitudinal (density) response function from high-resolution inelastic x-ray scattering (IXS) studies of water and, together with linear response theory, investigate how water behaves between two moving 2-D charge lattices at different charge densities and inter-plate separations. We find that the density profile varies with plate separation with a periodicity close to the diameter of a water molecule ($\sim$2.6{\AA}), in agreement with surface forces apparatus measurements, and that the hydration patterns of charges on the surfaces are strongly velocity dependent.   

Ergodicity of Isothermal Molecular Dynamics Method

A condition for equations of motion for isothermal dynamics is derived, and the Nos\'e--Hoover method is generalized on the basis of this condition. The ergodicity of the one-variable thermostats are studied, and it is shown that the one-variable thermostat coupled with the one-dimensional harmonic oscillator loses its ergodicity with large enough relaxation time. A stochastic process of the Nos\'e--Hoover method is also discussed based on the Markovian approximation.   

Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation

The statistics of the occupation variables of a stochastic lattice Boltzmann simulation is analyzed in terms of a generalized lattice gas. We show that the most probable state of this model corresponds to the equilibrium distribution of the lattice Boltzmann equation. Stochastic collision rules are described in terms of a Monte Carlo process satisfying detailed balance. This allows a straightforward derivation of the discrete Langevin equation for the fluctuating modes. Detailed balance requires to thermalize all non-conserved modes. A Chapman--Enskog analysis shows that the approach is fully consistent with macroscopic fluctuating hydrodynamics.