Response to the Letter to the Editor

Journal of Nanoparticle Research -     

The need to certify products to CDRH Regulations

Laser products that are sold in the United States are required to comply with the regulations published by the Center for Devices and Radiological Health (CDRH) within the US Food and Drug Administration [1]. The need to certify products is straightforward in most instances, however, the applicability of the regulations is not as clear for: lasers sold only to Original Equipment Manufacturers (OEMs) as components for incorporation into end-use products, end-use products that contain lasers which have already been certified by their manufacturers, and end-use products that are being imported into the US and that already comply with international laser safety standards. This article will discuss these applications in an attempt to clarify the need for certification by laser product manufacturers and importers. The discussion applies equally for lasers and laser systems.     

Melting from one to two to three dimensions

The transformation of a crystalline solid into a liquid, seeming to have no precursor and no intermediate states, has challenged scientists for over a century. The search for the fundamental mechanism stimulated the development of quantum mechanics, concepts of the roles of dimensionality and topological order in condensed matter, and experimental techniques to test the theories. We now understand that the transition begins at lower temperatures than the melting point of the bulk. It starts at the edges of crystal planes, progresses across the surface, evolves into the successive melting of atomic layers, and ends in bulk phase coexistence. The memory of the process remains within a few molecular distances at the crystal-melt interface.     

端到端网络流量的混合估计方法(英文)

利用主成分分析法获取端到端网络流量的主要特征分量并获得其初始估计结果.为克服其初值敏感性将估计结果作为遗传算法的初始值、链路流量估计偏差作为遗传算法的适应度函数,通过构建合适的交叉和变异概率函数来控制遗传算法的交叉和变异过程.采用合适的约束迭代函数,利用遗传算法通过迭代寻优获得端到端流量的估计结果,仿真结果表明所提出的方法是可行的.     

An attempt to relate area-preserving diffeomorphisms to Kac-Moody algebras

In the same way as the Virasoro algebra can be connected with Kac-Moody algebras defined on the S ¹ circle, the area-preserving diffeomorphism algebra SDiff(), where is a two-dimensional surface, acts as a derivation algebra on super Kac-Moody algebras with one or two supersymmetries. Then a Sugawara-like construction with fermions of the nonextended SDiff() algebra is discussed.     

On the approach to kinetic theory due to Gross

A classical kinetic theory introduced by Gross is explored in further detail. The theory consists of a sequence of approximations to the Liouville distribution function, with each approximation leading to a truncation of the BBGKY hierarchy at successively higher order. We formulate the truncation scheme at general order in terms of a set of time-dependent equilibrium correlation functions. It has the correct symmetries and, as is implied by the work of Gross with the first two approximations, is such that the interparticle potential appears only implicitly via static equilibrium correlation functions. We arrange the theory as a sequence of linear kinetic equations for the phase-space density correlation function, and solve for the collision kernels which result in each order. The collision kernel of the second approximation, which involves only binary dynamics, is shown to be a mean-field generalization of the known low-density kernel. The third approximation gives a similar generalization of the triple-collision kernel. The nth approximation also reproduces the frequency moments of S(kω) through order ω²ⁿ. More generally, the approximations are shown to give a continued-fraction expansion of the collision kernel, with the levels governed by the dynamics of successively larger numbers of particles. This is a renormalized kinetic theory in the sense that the potential is eliminated and clusters of particles are never isolated.     

Corrections to deuterium hyperfine structure due to deuteron excitations

We consider the corrections to the deuterium hyperfine structure originating from the two-photon exchange between an electron and deuteron, with deuteron excitations in the intermediate states. In particular, the motion of the two intermediate nucleons as a whole is taken into account. The problem is solved in the zero-range approximation. The result is in good agreement with the experimental value of deuterium hyperfine splitting.