Characterizing Frictional Contact Loading via Isochromatics

Isochromatic patterns in the vicinity of frictional contacts furnish vital clues for characterizing friction. Though friction effects are evident in a diametrally loaded circular disk, three-point loading provides better results towards highlighting friction. In this paper, a new method of characterizing friction at loading contacts using photoelastic isochromatics patterns is presented. Location of isotropic points (IPs) formed in three-point and four-point loadings of circular disk is used as a main tool to quantify the friction component using theoretical analysis. Bifurcation of isochromatic fringe loops near the distributed loads is explained by the presence of anti-symmetric Hertzian shear traction in addition to Hertzian normal traction. The classical solution by Flamant for point load at the edge of half plane is used to derive stresses in circular disk for all required loading configurations. A semicircualr ring under three-point loading is examined using photoelasticity to understand the isochromatics pattern theoretically by considering normal and shear traction components at loaded regions.     

Oligopeptides and copeptides of homochiral sequence, via beta-sheets, from mixtures of racemic alpha-amino acids, in a one-pot reaction in water; relevance to biochirogenesis

As part of our studies on the biochirogenesis of peptides of homochiral sequence during early evolution, the formation of oligopeptides composed of 14-24 residues of the same handedness in the polymerization of dl-leucine (Leu), dl-phenylalanine (Phe), and dl-valine (Val) in aqueous solutions, by activation with N, N'-carbonyldiimidazole and then initiation with a primary amine, in a one-pot reaction, was demonstrated by MALDI-TOF MS using deuterium enantio-labeled alpha-amino acids. The formation of long isotactic peptides is rationalized by the following steps occurring in tandem: (i) creation of a library of short diasteroisomeric oligopeptides containing isotactic peptides in excess in comparison to a binomial kinetics, as a result of an asymmetric induction exerted by the N-terminal residue of a given handedness; (ii) precipitation of the less soluble racemic isotactic penta- and hexapeptides in the form of beta-sheets that are delineated by homochiral rims; (iii) regio-enantiospecific chain elongation occurring heterogeneously at the beta-sheets/solution interface. Polymerization of l-Leu with l-isoleucine (Ile) or l-Phe with l- (1) N-Me-histidine yielded mixtures of copeptides containing both residues. In contrast, in the polymerization of the corresponding mixtures of l- + d-alpha-amino acids, the long oligopeptides were composed mainly from oligo- l-Leu and oligo- d-Ile in the first system and oligo- d-Phe in the second. Furthermore, in the polymerization of mixtures of hydrophobic racemic alpha-amino acids dl-Leu, dl-Val, and dl-Phe and with added racemic dl-alanine and dl-tyrosine, copeptides of homochiral sequences are most dominantly represented. Possible routes for a spontaneous "mirror-symmetry breaking" process of the racemic mixtures of homochiral peptides are presented.     

On Polynomially Normal Lattice Configurations

In this paper we extend Champernowne’s construction of a normal sequence in base b to the case and obtain an explicit construction of the generic point of the shift transformation of the set . We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal sequence in base b.     

The Complete Differential Game of Active Target Defense

In the Target–Attacker–Defender differential game, an Attacker missile strives to capture a Target aircraft. The Target tries to escape the Attacker and is aided by a Defender missile which aims at intercepting the Attacker, before the latter manages to close in on the Target. The conflict between these intelligent adversaries is naturally modeled as a zero-sum differential game. The Game of Degree when the Attacker is able to win the Target–Attacker–Defender differential game has not been fully solved, and it is addressed in this paper. Previous attempts at designing the players’ strategies have not been proven to be optimal in the differential game sense. In this paper, the optimal strategies of the Game of Degree in the Attacker’s winning region of the state space are synthesized. Also, the value function is obtained, and it is shown that it is continuously differentiable, and it is the solution of the Hamilton–Jacobi–Isaacs equation. The obtained state feedback strategies are compared to recent results addressing this differential game. It is shown that the correct solution of the Target–Attacker–Defender differential game that provides a semipermeable Barrier surface is synthesized and verified in this paper.

     

A quasistatic contact problem with slip‐dependent coefficient of friction

We consider a mathematical model which describes the bilateral quasistatic contact of a viscoelastic body with a rigid obstacle. The contact is modelled with a modified version of Coulomb's law of dry friction and, moreover, the coefficient of friction is assumed to depend either on the total slip or on the current slip. In the first case, the problem depends upon contact history. We present the classical formulations of the problems, the variational formulations and establish the existence and uniqueness of a weak solution to each of them, when the coefficient of friction is sufficiently small. The proofs are based on classical results for elliptic variational inequalities and fixed point arguments. We also study the dependence of the solutions on the perturbations of the friction coefficient and obtain a uniform convergence result. Copyright © 1999 John Wiley & Sons, Ltd.     

Three-dimensional optical transfer of rotating beams

Systems in which the point spread function (PSF) is a rotating beam have increasing use in three-dimensional (3D) microscopy and depth estimation. We analyze in several ways the 3D optical transfer function (OTF) of Gauss Laguerre modes and rotating beams. This is based on analysis of 3D OTFs of general aperture functions. Consequently, we suggest a criterion for depth resolution based on an effective cutoff of the axial frequency response. This criterion can be used to optimize PSFs explicitly and directly, to maximize axial resolution.     

Indistinguishable photon pairs from independent true chaotic sources

Indistinguishability of events in quantum mechanics is manifested by interference between their probability amplitudes. We report a unique kind of interference occurring between indistinguishable events of photon-pair emission, where each photon of the pair is emitted from a distinct true chaotic light source and has a different energy. The indistinguishability results in an interference which is observed as an ultrafast modulation of the second-order coherence function, measured on a femtosecond time scale by two-photon absorption in a semiconductor photomultiplier tube.