A Logarithmic-Quadratic Proximal Method for Variational Inequalities

We present a new method for solving variational inequalities on polyhedra. The method is proximal based, but uses a very special logarithmic-quadratic proximal term which replaces the usual quadratic, and leads to an interior proximal type algorithm. We allow for computing the iterates approximately and prove that the resulting method is globally convergent under the sole assumption that the optimal set of the variational inequality is nonempty.     

Laser-induced thermal stresses on steel surface

In laser heat treatment of steels, a thin surface layer of austenite forms during heating and subsequent phase change process in the cooling period. However, thermal stress develops due to high-temperature gradient attainment in the surface vicinity which in turn results in microcrack development at the surface. The present study is carried out to compute the temperature profiles due to step input pulse laser radiation and determine the resulting thermal stresses. The study is extended to include three-step input pulses having the same energy content. This provides the comparison for the influence of the pulse length on the resulting thermal stresses. To validate the theoretical predictions, an experiment is conducted to irradiate the AISI 4142 steel surface by an Nd–YAG laser. Microphotography and EDS analysis of the heated regions are carried out. It is found that considerable thermal stress is eveloped at the workpiece surface due to attainment of high-temperature gradient in this region. In addition, microcracks are observed at the surface of the irradiated spot.     

Integrability of det▽u and Evolutionary Wente's Problem Associated to Heat Operator

In this note,the authors resolve an evolutionary Wente's problem associated to heat equation,where the special integrability of det▽u for u∈H~1(R~2,R~2)is used.     

Marches aléatoires sur certains groupes unimodulaires p-adiques

We give central and off-diagonal estimates for the transition kernels corresponding to simple random walks on certain unimodular solvable p-adic groups. To cite this article: S. Mustapha, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Extended entanglement to quantum networks

Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms–fields entanglement to atoms–atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.     

Vortex pump for dilute bose-einstein condensates

The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.     

Exact solutions of the Klein—Gordon equation with ring-shaped oscillator potential by using the Laplace integral transform

We present exact solutions for the Klein-Gordon equation with a ring-shaped oscillator potential. The energy eigenvalues and the normalized wave functions are obtained for a particle in the presence of non-central oscillator potential. The angular functions are expressed in terms of the hypergeometric functions. The radial eigenfunctions have been obtained by using the Laplace integral transform. By means of the Laplace transform method, which is efficient and simple, the radial Klein-Gordon equation is reduced to a first-order differential equation.     

Quantitative two-dimensional HSQC experiment for high magnetic field NMR spectrometers

The finite RF power available on carbon channel in proton–carbon correlation experiments leads to non-uniform cross peak intensity response across carbon chemical shift range. Several classes of broadband pulses are available that alleviate this problem. Adiabatic pulses provide an excellent magnetization inversion over a large bandwidth, and very recently, novel phase-modulated pulses have been proposed that perform 90° and 180° magnetization rotations with good offset tolerance. Here, we present a study how these broadband pulses (adiabatic and phase-modulated) can improve quantitative application of the heteronuclear single quantum coherence (HSQC) experiment on high magnetic field strength NMR spectrometers. Theoretical and experimental examinations of the quantitative, offset-compensated, CPMG-adjusted HSQC (Q-OCCAHSQC) experiment are presented. The proposed experiment offers a formidable improvement to the offset performance; ¹³C offset-dependent standard deviation of the peak intensity was below 6% in range of ±20 kHz. This covers the carbon chemical shift range of 150 ppm, which contains the protonated carbons excluding the aldehydes, for 22.3 T NMR magnets. A demonstration of the quantitative analysis of a fasting blood plasma sample obtained from a healthy volunteer is given.     

Oscillation threshold of a clarinet model: a numerical continuation approach

This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. Previous works have shown interesting tendencies, using analytical expressions with simplified models. In the present study, a more elaborated physical model is considered. The influence of several parameters, depending on the reed properties, the design of the instrument or the control operated by the player, are studied. Previous results on the influence of the reed resonance frequency are confirmed. New results concerning the simultaneous influence of two model parameters on oscillation threshold, regime selection and playing frequency are presented and discussed. The authors use a numerical continuation approach. Numerical continuation consists in following a given solution of a set of equations when a parameter varies. Considering the instrument as a dynamical system, the oscillation threshold problem is formulated as a path following of Hopf bifurcations, generalizing the usual approach of the characteristic equation, as used in previous works. The proposed numerical approach proves to be useful for the study of musical instruments. It is complementary to analytical analysis and direct time-domain or frequency-domain simulations since it allows to derive information that is hardly reachable through simulation, without the approximations needed for analytical approach.     

Slip flow of MHD Casson fluid in an inclined channel with variable transport properties

Due to the instructive role of the peristaltic phenomenon in the human body, interests have been developed in recent years towards peristaltic transport with various thermo-physical features. The current investigation reveals the effects of the magnetic field and variable transport properties on the peristaltic transport of a Casson fluid slip flow through an inclined channel. Nonlinear coupled partial differential equations regulate the fluid flow. Through the perturbation method, the momentum and energy equations are solved for small values of variable viscosity and thermal conductivity, and the closed-form solution is obtained for mass transfer. The impact on physiological quantities of related parameters of interest is evaluated and discussed via graphs. The results obtained for the current flow represent some interesting behaviors which have applications in the biomedical field.