A computer program for determining truncation error coefficients for Runge-Kutta methods

The basic structure of a program to generate the truncation error coefficients for Runge-Kutta (RK) methods is reformulated to reduce storage requirements significantly and to accommodate variable dimensioning. This FORTRAN program, SUBROUTINE RKEQ, determines truncation error coefficients for RK algorithms for orders 1 through 10 and extends the order of coefficients through 12 with the 11th- and 12th-order terms determined following the patterns used to establish the lower order coefficients. Both subroutines (the original and RKEQ) are also written to treat RK m-fold methods which utilize m known derivatives of f to increase the order of the algorithm. Setting m = 0 gives the classical RK algorithm

Wave Profile for Anti-force Waves with Maximum Possible Currents

In the theoretical investigation of the electrical breakdown of a gas, we apply a one-dimensional, steady state, constant velocity, three component fluid model and consider the electrons to be the main element in propagation of the wave. The electron gas temperature, and therefore the electron gas partial pressure, is considered to be large enough to provide the driving force. The wave is considered to have a shock front, followed by a thin dynamical transition region. Our set of electron fluid-dynamical equations consists of the equations of conservation of mass, momentum, and energy, plus the Poisson\u27s equation. The set of equations is referred to as the electron fluid dynamical equations; and a successful solution therefor must meet a set of acceptable physical conditions at the trailing edge of the wave. For breakdown waves with a significant current behind the shock front, modifications must be made to the set of electron fluid dynamical equations, as well as the shock condition on electron temperature. Considering existence of current behind the shock front, we have derived the shock condition on electron temperature, and for a set of experimentally measured wave speeds, we have been able to find maximum current values for which solutions to our set of electron velocity, electron temperature, and electron number density within the dynamical transition region of the wave

Phase boundaries in deterministic dense coding

We consider dense coding with partially entangled states on bipartite systems of dimension $d\times d$, studying the conditions under which a given number of messages, $N$, can be deterministically transmitted. It is known that the largest Schmidt coefficient, $\lambda_0$, must obey the bound $\lambda_0\le d/N$, and considerable empirical evidence points to the conclusion that there exist states satisfying $\lambda_0=d/N$ for every $d$ and $N$ except the special cases $N=d+1$ and $N=d^2-1$. We provide additional conditions under which this bound cannot be reached -- that is, when it must be that $\lambda_0<d/N$ -- yielding insight into the shapes of boundaries separating entangled states that allow $N$ messages from those that allow only $N-1$. We also show that these conclusions hold no matter what operations are used for the encoding, and in so doing, identify circumstances under which unitary encoding is strictly better than non-unitary.Comment: 7 pages, 1 figur

Lower Bounds of Concurrence for Tripartite Quantum Systems

We derive an analytical lower bound for the concurrence of tripartite quantum mixed states. A functional relation is established relating concurrence and the generalized partial transpositions.Comment: 10 page

Laid Off: American Workers and Employers Assess a Volatile Labor Market

This Work Trends survey shows that despite economic growth, worker concern for the economy, their job security, and the threat of terrorism is increasing; workers and employers express fear about outsourcing jobs abroad

Entanglement-Saving Channels

The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel $\psi$ is said to be ES if its powers $\psi^n$ are not entanglement-breaking for all integers $n$. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps which, not only preserve entanglement for all finite $n$, but which also sustain an explicitly not null level of entanglement in the asymptotic limit~$n\rightarrow \infty$. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.Comment: 26 page

Scaled Runge-Kutta algorithms for treating the problem of dense output

A set of scaled Runge-Kutta algorithms for the third- through fifth-orders are developed to determine the solution at any point within the integration step at a relatively small increase in computing time. Each scaled algorithm is designed to be used with an existing Runge-Kutta formula, using the derivative evaluations of the defining algorithm along with an additional derivative evaluation (or two). Third-order, scaled algorithms are embedded within the existing formulas at no additional derivative expense. Such algorithms can easily be adopted to generate interpolating polynomials (or dependent variable stops) efficiently

Local and global statistical distances are equivalent on pure states

The statistical distance between pure quantum states is obtained by finding a measurement that is optimal in a sense defined by Wootters. As such, one may expect that the statistical distance will turn out to be different if the set of possible measurements is restricted in some way. It nonetheless turns out that if the restriction is to local operations and classical communication (LOCC) on any multipartite system, then the statistical distance is the same as it is without restriction, being equal to the angle between the states in Hilbert space.Comment: 5 pages, comments welcom

Scaled Runge-Kutta algorithms for handling dense output

Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem