Classical scaling theory of quantum resonances

The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion and the classical resonances of a related system. A scaling law which characterizes the structure of the resonant peaks is derived and numerically demonstrated.     

Control of multiple filamentation in air

In this Letter we provide what is believed to be the first experimental evidence of suppression of the number of filaments for high-intensity laser pulses propagating in air by beam astigmatism. We also show that the number, pattern, and spatial stability of the filaments can be controlled by varying the angle that a focusing lens makes with the axial direction of propagation. This new methodology can be useful for applications involving atmospheric propagation, such as remote sensing.     

An Adaptive Algorithm for Vector Partitioning

The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part. Here all parameters d, p, n are considered variables. In this paper, we study the adjacency of vertices in the associated partition polytopes. Using our adjacency characterization for these polytopes, we are able to develop an adaptive algorithm for the vector partition problem that runs in time O(q(L)v) and in space O(L), where q is a polynomial function, L is the input size and v is the number of vertices of the associated partition polytope. It is based on an output-sensitive algorithm for enumerating all vertices of the partition polytope. Our adjacency characterization also implies a polynomial upper bound on the combinatorial diameter of partition polytopes. We also establish a partition polytope analogue of the lower bound theorem, indicating that the output-sensitive enumeration algorithm can be far superior to previously known algorithms that run in time polynomial in the size of the worst-case output.     

Generating uniform random vectors over a simplex with implications to the volume of a certain polytope and to multivariate extremes

A uniform random vector over a simplex is generated. An explicit expression for the first moment of its largest spacing is derived. The result is used in a proposed diagnostic tool which examines the validity of random number generators. It is then shown that the first moment of the largest uniform spacing is related to the dependence measure of random vectors following any extreme value distribution. The main result is proved by a geometric proof as well as by a probabilistic one.     

The effect of mechanochemical treatments of sepiolite with CsCl on the calcination products

Calcination of sepiolite and of two sepiolite/CsCl mixtures, unground and air-ground was investigated by thermo-XRD-analysis. At 200 °C sepiolite, neat, mixed or air-ground with CsCl lost interparticle and zeolitic water. The framework of sepiolite persisted during the dehydration but became defected, mainly in the air-ground mixture, less in the unground mixture and little in the neat clay. At 500 °C, with the loss of bound water, the neat clay was folded and transformed into sepiolite anhydride. In sepiolite/CsCl mixtures the dehydrated variety persisted but the degree of crystal-imperfection increased in the air-ground mixture more than in the unground mixture. At 700 °C the neat clay remained crystallized, but the CsCl mixtures became amorphous. Some crystalline dehydrated sepiolite or sepiolite anhydride persisted in the unground and air-ground CsCl mixtures, respectively. At 850 °C, the neat clay crystallized into protoenstatite with some enstatite and clinoenstatite. The amorphous fraction of sepiolite in the unground sepiolite/CsCl mixtures crystallized into pollucite and forsterite and the crystalline fraction was transformed into enstatite, protoenstatite, and clinoenstatite. In the air-ground mixture, the amorphous phase was transformed into pollucite with some forsterite and the crystalline fraction into enstatite.     

Finding the Homology of Submanifolds with High Confidence from Random Samples

Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high-dimensional spaces. We consider the case where data are drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide learning-theoretic complexity bounds. Our bounds are obtained in terms of a condition number that limits the curvature and nearness to self-intersection of the submanifold. We are also able to treat the situation where the data are “noisy” and lie near rather than on the submanifold in question. The main results of this paper were first presented at a conference in honor of John Franks and Clark Robinson at Northwestern University in April 2003. These results were formally written as Technical Report No. TR-2004-08, Department of Computer Science, University of Chicago.     

Mechanics of composites with two families of finitely extensible fibers undergoing large deformations

Motivated by experimental measurements of the uniaxial response of collagen fibers, a new strain energy-density function for a solid which is finitely extensible along a preferred direction is proposed. Next, by application of a homogenization technique, the macroscopic strain energy-density function of composites with one and two families of fibers of this material embedded in a neo-Hookean matrix are determined. The resulting explicit expressions for the macroscopic strain energy-density functions are given in terms of the behaviors of the individual phases and their volume fractions. The responses of a few specific composites are investigated, revealing the lock-up surfaces of these composites. Finally, we examine the ability of the macroscopic model to capture experimentally measured stress-strain curves for the medial layer of a human abdominal aorta.     

β-Amino alcohol selectors for enantioselective separation of amino acids by ligand-exchange capillary zone electrophoresis in a low molecular weight organogel

A new family of copper ligand-exchange selectors, L- or D-β-amino alcohols, is employed for the chiral separation of D,L-dansyl-amino acids, unmodified amino acid racemates, phenylalanine and tryptophan, and β-blocker L,D-propranolol by SDS-micellar electrokinetic chromatography and by electrophoretic chromatography in a low molecular weight organogel (LMOG)-filled capillary. The LMOG comprised a self-assembled fibrillar gel of trans-(1S,2S)-1,2-bis-(dodecylamido) cyclohexane in methanol. The di-L-valinol-copper complex exhibited the best performance on LMOG-CE compared with all other β-amino alcohol-copper selectors. The dependence of chiral resolution on the pH*, the ratio between the copper and the L-valinol ligand and the concentration of added selector complex in the run buffer were investigated revealing a marked difference between the activity of the copper-valinol and the previously studied copper-valine selector. The optimal separation conditions were achieved using a 2:1 valinol/copper ratio, in accordance with the 2:1 structure of the complex, which was proven by single crystal and powder X-ray diffractions and by elemental analysis. Unlike the copper-valine selectors that could be used only under acidic conditions (pH* 3.5), the copper-valinol selectors could be used under near-neutral conditions and even at pH* 9.1. A comparison between SDS-micellar electrokinetic chromatography and LMOG-CE under otherwise identical conditions revealed a significant superior separation on the LMOG-filled capillaries.