Representations, convolution square roots and spherical vectors

We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras.     

Analysis of combined conduction and radiation heat transfer in presence of participating medium by the development of hybrid method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in the presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. A blended method where the concepts of modified differential approximation employed by combining discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The gray participating medium is bounded by isothermal walls of two-dimensional enclosure which are considered to be opaque, diffuse and gray. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The adaptability of the present method has also been addressed.     

Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts

A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fraction 1 for a1 (where is the Debye–Hückel parameter and a is the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditions 1 and a1are both satisfied.     

HITTING TIME AND PLACE TO A SPHERE OR SPHERICAL SHELL FOR BROWNIAN MOTION

61.IntroductionLetX~{X,(w),t20}beastandardd-dimensionalBrownianmotioninR'(d22).ThefirsthittingtimeofXforaBorelsetBinRdisdefinedtobeThefirsthittingplaceisX(TB).InthispapergwemainlyconsiderthesphereZ'--,(0,r)~{x:xERd,lxl~r}andthesphericalshellZ'--,(0,a)UZ'--,(0,b)~{x.xER',lxl=aorlxl~b},wherer>0,a>0,b>0anda相似文献   

纵振驱动球面弯曲振动超声聚焦系统的聚焦特性*

为了将超声聚焦效应应用于工业加工中的冷却技术中,该文提出一种由夹心式换能器纵向振动驱动球面弯曲振动超声聚焦系统。基于基尔霍夫-亥姆霍兹声场理论分析了由换能器中心面纵向振动和球面弯曲振动组成的复合超声振动条件下的声场聚焦特性,并通过实验进行验证。研究结果表明,该聚焦系统具有显著的聚焦特性,球面弯曲振动将声能汇聚在声场焦区;当声场相位相同时,换能器中心面纵向振动和球面弯曲振动产生的声场在焦区发生叠加,可以进一步提高焦区声压;减小换能器中心面半径和球面曲率半径、增加球面开口半径可以增强复合超声振动的聚焦效果。     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Structural and magnetic properties of self-assembled Sm-Co spherical aggregates

Self-assembled Sm-Co nanoparticles in the form of spherical aggregates (referred as nanospheres) with diameter ranging from 50 to 180 nm were achieved by means of polyol technique. The size distribution of the Sm-Co nanospheres can be regulated close to ∼100 nm by controlling the molar ratio of Sm:Co precursor. The spherical aggregates exhibited Sm₂Co₇ phase as a major constituent; while the aggregates obtained at higher Co concentration showed co-existence of Co-phase with Sm₂Co₇ phase. Upon annealing, the biphasic nature of nanospheres (Sm₂Co₇/Co) transformed into Sm₂Co₁₇ structure. By varying the Sm:Co precursor ratio from 1:5 to 1:9, the coercivity (H_c) and magnetization (M_s) values of the as-synthesized nanospheres can be tuned from 336 to 140 Oe and from 63.7 to 108 emu/g, respectively, and these values significantly improved after annealing. Maximum values of H_c (1050 Oe) at the Sm:Co molar ratio of 1:5 and M_s of 184.6 emu/g at the Sm:Co molar ratio of 1:9 were achieved in the annealed samples.     

Limit analysis and numerical modeling of spherically porous solids with Coulomb and Drucker-Prager matrices

The first goal of this work was to develop efficient limit analysis (la) tools to investigate the macroscopic criterion of a porous material on the basis of the hollow sphere model used by Gurson, here with a Coulomb matrix. Another goal was to give the resulting rigorous lower and upper bounds to the macroscopic criterion to enable comparisons and validations with further analytical or numerical studies on this micro-macro problem. In both static and kinematic approaches of la, a quadratic formulation was used to represent the stress and displacement velocity fields, in triangular finite elements. A significant improvement of the quality of the results was obtained by superimposing, on the fem fields, analytical fields which are the solutions to the problem under isotropic loadings.The final problems result in conic optimization, or linear programming after linearization of the criterion, so as to determine the “Porous Coulomb” criterion. A fine iterative post-analysis strictly restores the admissibility of the static and kinematic solutions. After presenting the results for various values of the porosity and internal friction angle, a comparison with a heuristic Cam-Clay-like criterion shows that this criterion cannot be considered a precise general approximation. Then a comparison with the “Porous Drucker-Prager” criterion treated by specific 3D codes is presented. With the same numerical tools, a final analysis of recent results in the literature is detailed, and tables of selected numerical data are presented in the appendices.     

球面介质作用下的测度值分枝过程

我们考虑空间上一粒子系统，当其受到分布于求面上的介质作进行粒子分枝和衍生，产生新了体，而新粒子仍按原粒子的运动规则继续空间运动。通过合理的假设和极限过程，粒子在空间的散布一测度值分枝过程来刻划。