Evaluation of solar cell materials for a Solar Power Satellite

Alternative solar cell materials being considered for the solar power satellite are described and price, production, and availability projections through the year 2000 are presented. The chief materials considered are silicon and gallium arsenide

White Dwarf Mergers on Adaptive Meshes I. Methodology and Code Verification

The Type Ia supernova progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf merger scenario, which has the potential to naturally explain many of the observed characteristics of Type Ia supernovae. To date there have been relatively few self-consistent simulations of merging white dwarf systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.Comment: Accepted for publication in the Astrophysical Journa

Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations

Typical flows in stellar interiors are much slower than the speed of sound. To follow the slow evolution of subsonic motions, various sound-proof equations are in wide use, particularly in stellar astrophysical fluid dynamics. These low-Mach number equations include the anelastic equations. Generally, these equations are valid in nearly adiabatically stratified regions like stellar convection zones, but may not be valid in the sub-adiabatic, stably stratified stellar radiative interiors. Understanding the coupling between the convection zone and the radiative interior is a problem of crucial interest and may have strong implications for solar and stellar dynamo theories as the interface between the two, called the tachocline in the Sun, plays a crucial role in many solar dynamo theories. Here we study the properties of gravity waves in stably-stratified atmospheres. In particular, we explore how gravity waves are handled in various sound-proof equations. We find that some anelastic treatments fail to conserve energy in stably-stratified atmospheres, instead conserving pseudo-energies that depend on the stratification, and we demonstrate this numerically. One anelastic equation set does conserve energy in all atmospheres and we provide recommendations for converting low-Mach number anelastic codes to this set of equations.Comment: Accepted for publication in ApJ. 20 pages emulateapj format, 7 figure

MAESTRO, CASTRO, and SEDONA -- Petascale Codes for Astrophysical Applications

Performing high-resolution, high-fidelity, three-dimensional simulations of Type Ia supernovae (SNe Ia) requires not only algorithms that accurately represent the correct physics, but also codes that effectively harness the resources of the most powerful supercomputers. We are developing a suite of codes that provide the capability to perform end-to-end simulations of SNe Ia, from the early convective phase leading up to ignition to the explosion phase in which deflagration/detonation waves explode the star to the computation of the light curves resulting from the explosion. In this paper we discuss these codes with an emphasis on the techniques needed to scale them to petascale architectures. We also demonstrate our ability to map data from a low Mach number formulation to a compressible solver.Comment: submitted to the Proceedings of the SciDAC 2010 meetin

Relativistic phase space: dimensional recurrences

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius $R$ and taking the limit as $R \to \infty$. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension.Comment: 13 pages, Latex, to appear in J Phys

Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

An Optimal Execution Problem with Market Impact

We study an optimal execution problem in a continuous-time market model that considers market impact. We formulate the problem as a stochastic control problem and investigate properties of the corresponding value function. We find that right-continuity at the time origin is associated with the strength of market impact for large sales, otherwise the value function is continuous. Moreover, we show the semi-group property (Bellman principle) and characterise the value function as a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of the optimal strategies change completely, depending on the amount of the trader's security holdings and where optimal strategies in the Black-Scholes type market with nonlinear market impact are not block liquidation but gradual liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal execution problem with market impact" in Finance and Stochastics (2014

Warp-X: a new exascale computing platform for beam-plasma simulations

Turning the current experimental plasma accelerator state-of-the-art from a promising technology into mainstream scientific tools depends critically on high-performance, high-fidelity modeling of complex processes that develop over a wide range of space and time scales. As part of the U.S. Department of Energy's Exascale Computing Project, a team from Lawrence Berkeley National Laboratory, in collaboration with teams from SLAC National Accelerator Laboratory and Lawrence Livermore National Laboratory, is developing a new plasma accelerator simulation tool that will harness the power of future exascale supercomputers for high-performance modeling of plasma accelerators. We present the various components of the codes such as the new Particle-In-Cell Scalable Application Resource (PICSAR) and the redesigned adaptive mesh refinement library AMReX, which are combined with redesigned elements of the Warp code, in the new WarpX software. The code structure, status, early examples of applications and plans are discussed

Multiscale Random-Walk Algorithm for Simulating Interfacial Pattern Formation

We present a novel computational method to simulate accurately a wide range of interfacial patterns whose growth is limited by a large scale diffusion field. To illustrate the computational power of this method, we demonstrate that it can be used to simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.Comment: 4 pages RevTex, 6 eps figures; substantial changes in presentation, but results and conclusions remain the sam

Explicitly symmetrical treatment of three-body phase space

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles. We study geometrical properties of the variables involved in elliptic integrals and demonstrate that it is convenient to use the Jacobian zeta function to express the results in four and six dimensions.Comment: 20 pages, latex, 2 postscript figure