Three Dimensional Laser Simulation Code on a Desktop Personal Computer

We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.     

Falling ball viscosimetry of giant vesicle membranes: Finite-size effects

We study the general problem of the friction felt by a spherical solid particle which moves parallel to the membrane of a spherical vesicle. Experiments are carried out with SOPC vesicles at room temperature, with different particle and vesicle sizes. Experimental data show considerable finite-size effects whenever the particle is not very small compared to the vesicle. These effects are found consistent with the hydrodynamical theory of the vesicle-particle problem. This agreement allows for a “robust” determination of membrane viscosity, independently of particle and vesicle sizes. Received 4 January 1999 and Received in final form 11 May 1999     

A Robust and Efficient Method for the Computation of Equilibrium Composition in Gaseous Mixtures

This paper presents in detail a robust, efficient and accurate methodology for the computation of equilibrium composition in gaseous mixtures. The methodology is founded on the concept of the chemical basis, which is defined and formalized using a powerful matricial approach. The method is specially designed to be general, thus providing basic thermodynamic data in several areas, such as combustion, plasma chemistry and, more generally speaking, computational fluid dynamics. The performance of the method is given in terms of CPU usage and the computed results are compared with those in the published literature. The method is shown to yield results of very high quality in terms of accuracy and smoothness.     

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

Computation of Galois groups over function fields

Symmetric function theory provides a basis for computing Galois groups which is largely independent of the coefficient ring. An exact algorithm has been implemented over in Maple for degree up to 8. A table of polynomials realizing each transitive permutation group of degree 8 as a Galois group over the rationals is included.

     

Stability criterion for small perturbations for a quasi-gasdynamic system of equations

The stability of small perturbations against a constant background is studied for a system of quasi-gasdynamic equations in an arbitrary number of space variables. It is established that, for a fixed adiabatic exponent γ, the stability is determined only by the background Mach number, and a necessary and sufficient condition for stability at any Mach number is $\gamma \leqslant \bar \gamma $ , where $\bar \gamma \approx 6.2479$ . The proof is based on a direct analysis of the corresponding complex characteristic numbers depending on several parameters. The multidimensional case is successfully reduced to the one-dimensional one. Then, the generalized Routh-Hurwitz criterion is applied in conjunction with analytical calculations based on Mathematica.     

Two efficient algorithms for the computation of ideal sums in quadratic orders

This paper deals with two different asymptotically fast algorithms for the computation of ideal sums in quadratic orders. If the class number of the quadratic number field is equal to 1, these algorithms can be used to calculate the GCD in the quadratic order. We show that the calculation of an ideal sum in a fixed quadratic order can be done as fast as in up to a constant factor, i.e., in where bounds the size of the operands and denotes an upper bound for the multiplication time of -bit integers. Using Schönhage-Strassen's asymptotically fast multiplication for -bit integers, we achieve

     

Speeding up Exponentiation using an Untrusted Computational Resource

We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of over the square-and-multiply algorithm, where k is the bitlength of the exponent. One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform variable-base variable- exponent exponentiation, which also has this feature. Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller. Our protocols are unconditionally secure.