A high-order finite volume method for systems of conservation laws—Multi-dimensional Optimal Order Detection (MOOD)

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.     

Does the Electrical Conductivity of W/O Microemulsions Follow a Percolative Behaviour?

Abstract

The conductivities of different microemulsions prepared with triethanolamine were measured as a function of concentration for several temperatures. The goal of this work has been to test the degree of accuracy of the application of the scaling laws used in the literature. Our conclusion is that there is no general validity even though the abrupt variation of conductivity with concentration may be seen as a percolative phenomenon.     

Volatility return intervals analysis of the Japanese market

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.     

Domains of Geometric Partial Attraction of Max-Semistable Laws: Structure, Merge and Almost Sure Limit Theorems

Max-semistable laws arise as non-degenerate weak limits of suitably centered and normed maxima of i.i.d. random variables along subsequences {k(n)} such that k(n+1)/k(n)c1, in which case the common distribution function F of the i.i.d. random variables is said to belong to the domain of geometric partial attraction of the max-semistable law. We give a necessary and sufficient condition for F to belong to the domain of geometric partial attraction of a max-semistable law and investigate the structure of these domains. We show that although weak convergence does not take place along {n}=, the distributions of the maxima merge together along the entire {n} with a suitably chosen family of limiting laws. The use of merge is demonstrated by almost sure limit theorems, which are also valid along the whole {n}.     

ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

1.IntrodnctionWegiveaproofofthestrongconvergenceinofthesolutionoftheparabolicapproximationtowardstheentropicsolutiontothescalarconservationlawwhereuo(RN),udenotessomeapproximationofuosuchthatandthefluxfsatisfiesTheconvergenceoftheapproximatesolutions...     

Derivation of a new class of distributions for the microcanonical ensemble

A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137.     

Neighboring extremals of dynamic optimization problems with path equality constraints

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique. This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC-2-106. The author is indebted to Professor A. E. Bryson, Jr., Department of Aeronautics and Astronautics, Stanford University, for many stimulating discussions.     

The dynamics of random interfaces in phase transitions

A review is given of recent developments involving the dynamics of random interfaces formed in the evolution of metastable and unstable systems. Topics which are discussed include interface growth and nonequilibrium dynamical scaling. The possibility of there being dynamical universality classes in first-order phase transitions is also discussed. There are a large number of systems of experimental interest which include binary alloys, binary fluids, and polymer mixtures. Other systems studied by computer simulation include the kinetic Ising, Potts, andZ _N models.Work supported by NSF grant No. DMR-8013700.     

A Bahadur efficiency comparison between one and two sample rank statistics and their sequential rank statistic analogues

One and two sample rank statistics are shown in general to be more efficient in the Bahadur sense than their sequential rank statistic analogues as defined by Mason (1981, Ann. Statist.9 424–436) and Lombard (1981, South African Statist. J.15 129–152), even though the two families of statistics (those based on full ranks and those based on sequential ranks) have the same Pitman efficiency against local alternatives. In the process, general results on large deviation probabilities and laws of large numbers for statistics based on sequential ranks are obtained.