Calculation of Blocking Probabilities in Multistage Interconnection Networks with Redundant Paths

The blocking probability of a network is a common measure of its performance. There exist means of quickly calculating the blocking probabilities of Banyan networks; however, because Banyan networks have no redundant paths, they are not inherently fault-tolerant, and so their use in large-scale multiprocessors is problematic. Unfortunately, the addition of multiple paths between message sources and sinks in a network complicates the calculation of blocking probabilities. A methodology for exact calculation of blocking probabilities for small networks with redundant paths is presented here, with some discussion of its potential use in approximating blocking probabilities for large networks with redundant paths.

An empirical equation for the calculation of retention time with extrapolation of temperature in gas chromatography

An empirical equation is proposed to accurately correlate isothermal data over a wide range of temperature With the equation ln k = A* + B*/T-lambda the retention times of different solutes tested on OV-101, SE-54 and PEG 20M capillary columns have been achieved even when lambda is assigned a constant value of 1.7 Comparison with ln k = A + B/T and in k = c + d/T+ h/T-2, shows that the proposed equation is of higher accuracy and is applicable to extrapolation calculation, especially from data at high temperature to those at low temperature. Parameters A* and B* as well as A and B are also discussed. The linear correlation of A* and B* is weaker than that of A and B.

Calculation of the multimode Franck-Condon factors based on the coherent state method

The equivalence of two ways for the calculation of overlap integrals, i.e. the Sharp Rosenstock generating function method and the Doktorov coherent state method, has been proved. On the basis of the generating function of the overlap integrals, a new closed form expression for the Franck - Condon integrals for overlap multidimensional harmonic oscillators has been exactly derived. In addition, some useful analytical expressions for the calculations of the multimode Franck - Condon factors have been given.

Space saving calculation of symbolic resultants

Lloyd, Noel G., and Pearson, Jane M., 'Space saving calculation of symbolic resultants', Mathematics in Computer Science, 1 (2007), 267-290.

Fast Approximate Reconciliation of Set Differences

We present new, simple, efficient data structures for approximate reconciliation of set differences, a useful standalone primitive for peer-to-peer networks and a natural subroutine in methods for exact reconciliation. In the approximate reconciliation problem, peers A and B respectively have subsets of elements SA and SB of a large universe U. Peer A wishes to send a short message M to peer B with the goal that B should use M to determine as many elements in the set SB–SA as possible. To avoid the expense of round trip communication times, we focus on the situation where a single message M is sent. We motivate the performance tradeoffs between message size, accuracy and computation time for this problem with a straightforward approach using Bloom filters. We then introduce approximation reconciliation trees, a more computationally efficient solution that combines techniques from Patricia tries, Merkle trees, and Bloom filters. We present an analysis of approximation reconciliation trees and provide experimental results comparing the various methods proposed for approximate reconciliation.

A new proposition on the martingale representation theorem and on the approximate hedging of contingent claim in mean-variance criterion

In this work we revisit the problem of the hedging of contingent claim using mean-square criterion. We prove that in incomplete market, some probability measure can be identified so that becomes -martingale under .This is in fact a new proposition on the martingale representation theorem. The new results also identify a weight function that serves to be an approximation to the Radon-Nikodým derivative of the unique neutral martingale measure.

Nuclear ingredients for cross section calculation of exotic nuclei

The increasing need for cross sections far from the valley of stability, especially for applications such as nuclear astrophysics, poses a challenge for nuclear reaction models. So far, predictions of cross sections have relied on more or less phenomenological approaches, depending on parameters adjusted to available experimental data or deduced from systematic relations. While such predictions are expected to be reliable for nuclei not too far from the experimentally known regions, it is clearly preferable to use more fundamental approaches, based on sound physical bases, when dealing with very exotic nuclei. Thanks to the high computer power available today, all major ingredients required to model a nuclear reaction can now be (and have been) microscopically (or semi-microscopically) determined starting from the information provided by an effective nucleon-nucleon interaction. All these microscopic ingredients have been included in the latest version of the TALYS nuclear reaction code (http://www.talys.eu/).

Letter to the Editor: Calculation of photoionized plasmas with an average-atom model

We use a simple average-atom model (NIMP) to calculate the distribution of ionization in a photoionization-dominated plasma, for comparison with recent experimental measurements undertaken on the Z-machine at the Sandia National Laboratory. The agreement between theory and experiment is found to be as good for calculations with an average-atom model as for those generated by more detailed models.

Ion-Atom/Argon - Calculation of ionization cross sections by fast ion impact for neutral target atoms ranging from hydrogen to argon

A FORTRAN 90 program is presented which calculates the total cross sections, and the electron energy spectra of the singly and doubly differential cross sections for the single target ionization of neutral atoms ranging from hydrogen up to and including argon. The code is applicable for the case of both high and low Z projectile impact in fast ion-atom collisions. The theoretical models provided for the program user are based on two quantum mechanical approximations which have proved to be very successful in the study of ionization in ion-atom collisions. These are the continuum-distorted-wave (CDW) and continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximations. The codes presented here extend previously published. codes for single ionization of. target hydrogen [Crothers and McCartney, Comput. Phys. Commun. 72 (1992) 288], target helium [Nesbitt, O'Rourke and Crothers, Comput. Phys. Commun. 114 (1998) 385] and target atoms ranging from lithium to neon [O'Rourke, McSherry and Crothers, Comput. Phys. Commun. 131 (2000) 129]. Cross sections for all of these target atoms may be obtained as limiting cases from the present code. Title of program: ARGON Catalogue identifier: ADSE Program summary URL: http://cpc.cs.qub.ac.uk/cpc/summaries/ADSE Program obtainable from: CPC Program Library Queen's University of Belfast, N. Ireland Licensing provisions: none Computer for which the program is designed and others on which it is operable: Computers: Four by 200 MHz Pro Pentium Linux server, DEC Alpha 21164; Four by 400 MHz Pentium 2 Xeon 450 Linux server, IBM SP2 and SUN Enterprise 3500 Installations: Queen's University, Belfast Operating systems under which the program has been tested: Red-hat Linux 5.2, Digital UNIX Version 4.0d, AIX, Solaris SunOS 5.7 Compilers: PGI workstations, DEC CAMPUS Programming language used: FORTRAN 90 with MPI directives No. of bits in a word: 64, except on Linux servers 32 Number of processors used: any number Has the code been vectorized or parallelized? Parallelized using MPI No. of bytes in distributed program, including test data, etc.: 32 189 Distribution format: tar gzip file Keywords: Single ionization, cross sections, continuum-distorted-wave model, continuum- distorted-wave eikonal-initial-state model, target atoms, wave treatment Nature of physical problem: The code calculates total, and differential cross sections for the single ionization of target atoms ranging from hydrogen up to and including argon by both light and heavy ion impact. Method of solution: ARGON allows the user to calculate the cross sections using either the CDW or CDW-EIS [J. Phys. B 16 (1983) 3229] models within the wave treatment. Restrictions on the complexity of the program: Both the CDW and CDW-EIS models are two-state perturbative approximations. Typical running time: Times vary according to input data and number of processors. For one processor the test input data for double differential cross sections (40 points) took less than one second, whereas the test input for total cross sections (20 points) took 32 minutes. Unusual features of the program: none (C) 2003 Elsevier B.V All rights reserved.

2D-drop model applied to the calculation of step formation energies on a (111) substrate

A model is presented for obtaining the step formation energy for metallic islands on (1 1 1) surfaces from Monte Carlo simulations. This model is applied to homo (Cu/Cu(1 1 1), Ag/Ag(1 1 1)) and heteroepitaxy (Ag/Pt(1 1 1)) systems. The embedded atom method is used to represent the interaction between the particles of the system, but any other type of potential could be used as well. The formulation can also be employed to consider the case of other single crystal surfaces, since the higher barriers for atom motion on other surfaces are not a hindrance for the simulation scheme proposed.