Weighted isoperimetric inequalities in warped product manifolds

We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We also relate them to inequalities involving the higher order mean-curvature integrals. Applications include some sharp eigenvalue estimates, Pólya-Szegö inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces.     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.     

Neutrino emissivity of quark matter at finite temperatures

We evaluate the emissivity rates for d-decay and s-decay by exactly solving the angular integrals involved and without assuming the degeneracy of electrons. We have also studied the effects of QCD coupling constant as well as the s-quark mass on the emissivity rates. We find that these parameters are important in determining the threshold and extinction densities for d- and s-decays.     

Effect of size and charge on ordering of a highly charged concentrated macroions in suspension

An efficient fast Fourier transform method has been employed to determine correlation function [g(r*)] using the structure factor [S(Q*)] calculated with the rescaled mean spherical approximation (RMSA) and the DLVO potential. Based on this function a parametric (size and charge) study of the ordering in a highly charged and concentrated macroions (an ideal colloid) has been made. The strength of the correlation increases with the increase in the charge on macroions and it saturates after acertain value. Similarly, a critical diameter of the particle depending on the charge on it has been found at which normal feature of the ordering disappears.     

再谈"小球与均质自由杆的碰撞"

讨论了小球在杆上任一点的碰撞问题,并指出《大学物理》2006年第5期《小球与均质自由杆的碰撞》一文中"完全非弹性碰撞后两物体不一定粘在一起共同运动"的说法是错误的.     

真值、随机误差、系统误差的新定义

我国计量技术规范《JJF1001—1998通用计量术语及定义》对真值、随机误差和系统误差给予了新的定义,对过去的定义作了原则上的改变.本文对新定义的科学性和合理性进行了讨论,并建议在大学物理实验教学和教材中采用.     

Couette流能量的演变

利用Green函数法解析求得Couette流流函数的精确解,通过定义Couette能量、相对能量和能量增长率讨论了初始场结构对Couette流能量演变的影响、能量达到最大值时对应的时间与初始场的关系、最有利于Couette流能量在有限时段快速增长的初始场结构,并对Farrell的研究结果进行了补充和完善.在此基础上,进一步探讨了初值扰动对Couette流能量演变的影响.     

Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called ‘verification theorems’ and ‘viscosity solutions’ provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.     

Proof of a universal lower bound on the shear viscosity to entropy density ratio

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/4π$1/4\pi$ in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.