A New Godunov Scheme for MHD, with Application to the MRI in disks

We describe a new numerical scheme for MHD which combines a higher order Godunov method (PPM) with Constrained Transport. The results from a selection of multidimensional test problems are presented. The complete test suite used to validate the method, as well as implementations of the algorithm in both F90 and C, are available from the web. A fully three-dimensional version of the algorithm has been developed, and is being applied to a variety of astrophysical problems including the decay of supersonic MHD turbulence, the nonlinear evolution of the MHD Rayleigh-Taylor instability, and the saturation of the magnetorotational instability in the shearing box. Our new simulations of the MRI represent the first time that a higher-order Godunov scheme has been applied to this problem, providing a quantitative check on the accuracy of previous results computed with ZEUS; the latter are found to be reliable.Comment: 11 pages, style files included, Conference Proceedings: "Magnetic Fields in the Universe: from Laboratory and Stars to Primordial Structures", More information on Athena can be found at http://www.astro.princeton.edu/~jstone/athena.htm

Energetics in MRI driven Turbulence

In these proceedings we present recent efforts to understand the energetics of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational instability (MRI). These studies are carried out in the local (shearing box) approximation using the Athena simulation code. Athena is a higher order Godunov algorithm based on the piecewise parabolic method (PPM), the corner transport upwind (CTU) integration algorithm, and the constrained transport (CT) algorithm for evolving the magnetic field. This algorithm is particularly suited for these studies owing to the conservation properties of a Godunov scheme and the particular implementation of the shearing box source terms used here. We present a variety of calculations which may be compared directly to previously published results and discuss them in some detail. The only significant discrepancy found between the results presented here and in the published literature involves the turbulent heating rate. We observe the presence of recurrent channel solutions in calculations involving a mean vertical magnetic field and the associated time lag between the energy injection and thermalization rate. We also present the results of a shearing box calculation which includes an optically thin radiative term with a cooling rate selected to match the turbulent heating rate. Some properties which we find uniformly present in all of the calculations presented here are compressible fluctuations, spiral waves and weak shocks. It is found that these compressible modes dominate the temporal fluctuations in the probability distribution functions for most of the thermodynamic variables; only the specific entropy is relatively immune to their effects.Comment: 14 pages, Conference Proceedings: "Magnetic Fields in the Universe: from Laboratory and Stars to Primordial Structures

Fourier's Law for Quasi One--Dimensional Chaotic Quantum Systems

We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system

Target search on a dynamic DNA molecule

We study a protein-DNA target search model with explicit DNA dynamics applicable to in vitro experiments. We show that the DNA dynamics plays a crucial role for the effectiveness of protein "jumps" between sites distant along the DNA contour but close in 3D space. A strongly binding protein that searches by 1D sliding and jumping alone, explores the search space less redundantly when the DNA dynamics is fast on the timescale of protein jumps than in the opposite "frozen DNA" limit. We characterize the crossover between these limits using simulations and scaling theory. We also rationalize the slow exploration in the frozen limit as a subtle interplay between long jumps and long trapping times of the protein in "islands" within random DNA configurations in solution.Comment: manuscript and supplementary material combined into a single documen

Effect of the Coriolis Force on the Hydrodynamics of Colliding Wind Binaries

Using fully three-dimensional hydrodynamic simulations, we investigate the effect of the Coriolis force on the hydrodynamic and observable properties of colliding wind binary systems. To make the calculations tractable, we assume adiabatic, constant velocity winds. The neglect of radiative driving, gravitational deceleration, and cooling limit the application of our models to real systems. However, these assumptions allow us to isolate the effect of the Coriolis force, and by simplifying the calculations, allow us to use a higher resolution (up to 640^3) and to conduct a larger survey of parameter space. We study the dynamics of collidng winds with equal mass loss rates and velocities emanating from equal mass stars on circular orbits, with a range of values for the ratio of the wind to orbital velocity. We also study the dynamics of winds from stars on elliptical orbits and with unequal strength winds. Orbital motion of the stars sweeps the shocked wind gas into an Archimedean spiral, with asymmetric shock strengths and therefore unequal postshock temperatures and densities in the leading and trailing edges of the spiral. We observe the Kelvin-Helmholtz instability at the contact surface between the shocked winds in systems with orbital motion even when the winds are identical. The change in shock strengths caused by orbital motion increases the volume of X-ray emitting post-shock gas with T > 0.59 keV by 63% for a typical system as the ratio of wind velocity to orbital velocity decreases to V_w/V_o = 2.5. This causes increased free-free emission from systems with shorter orbital periods and an altered time-dependence of the wind attenuation. We comment on the importance of the effects of orbital motion on the observable properties of colliding wind binaries.Comment: 12 pages, 17 figures, accepted for publication in Ap

An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions

We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by Gardiner & Stone (2005) to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ``MHD source terms'' and naturally respect the balance implicit in these terms by the ${\bf\nabla\cdot B}=0$ condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.Comment: Extended version of the paper accepted for publication in JC

Measurement-based approach to entanglement generation in coupled quantum dots

Measurements provide a novel mechanism for generating the entanglement resource necessary for performing scalable quantum computation. Recently, we proposed a method for performing parity measurements in a coupled quantum dot system. In this paper we generalise this scheme and perform a comprehensive analytic and numerical study of environmental factors. We calculate the effects of possible error sources including non-ideal photon detectors, ineffective spin-selective excitation and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifying the success of the parity measurement