偶数维空间耗散波动方程解的衰减估计

研究偶数维空间带粘性的波动方程柯西问题解的逐点估计.通过对格林函数的精细分析,得到解的大时间状态.解呈现出惠更斯现象.     

提升钢丝绳动态分析的分段线性化解法

本文在研究提升机绳系动态特性过程中,建立了一类非齐次边界条件混合问题的波动方程;应用离散化方法将非齐次项分段线性化,得到了该类波动方程的半解析解.     

分光光度法同时测定铝(Ⅲ)和铁(Ⅱ)

以甲基百里酚蓝(MTB)为显色剂、CTMAB为增溶增敏剂,利用系数补偿和双峰双波长的两次分光光度法同时测定铝(Ⅲ)和铁(Ⅱ)的结果令人满意.     

Effective wave propagation along a rough thin-elastic beam

Two methods for computing the complex-valued effective wavenumber of a rough beam in the context of linear time-harmonic theory are presented. The roughness of the beam is modelled as a continuous random process of known characteristic length and root-mean-square amplitude for either the beam mass or the beam rigidity. The first method is based on a random sampling method, with the effective wave field calculated as the mean of a large ensemble of wave fields for individual realisations of the roughness. The individual wave fields are calculated using a step approximation, which is validated for a deterministic problem via comparison to results produced by an integral equation approach. The second method assumes a splitting of the length scale of the fluctuations and an observation scale, employing a multiple-scale approximation to derive analytical expressions for the effective attenuation rate and phase change. Numerical comparisons show agreement of the results of the random sampling method and the multiple-scale approximation for a wide range of parameters. It is shown that the effective wavenumbers only differ by a real constant between the cases of varying beam mass and rigidity.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.     

Mechanical wave momentum from the first principles

Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.     

Three-dimensional localization of atoms in the polychromatic optical superlattice

Quasiclassical kinetic theory of the light pressure force has been applied to describe the localization of atoms (or ions) with the transition F=1→F=0 in the three-dimensional (3D) dissipative optical superlattice of a new type. Its action is based on the effect of the gradient force rectification in the polychromatic field: superposition of the three color far-off-resonant field and partially coherent resonant field. An approximate explicit solution of the kinetic equation for 3D motion of atoms in such a (multicolor) field has been achieved. This solution demonstrates the capability of the polychromatic superlattice to provide efficient cooling and strong spatial localization of the particles and to form an atomic (or ionic) grating with highly controllable characteristics.     

Revealing sol-gel type main effects by exploring a molecular cluster behavior in model in-plane amphiphilic aggregations

In-plane (bio)matter aggregations of amphiphilic nature are modeled extensively by Monte Carlo simulation in their natural entropic contexts. The modeling starts by designing the aggregations at a molecular level, pointing to its well-known configuration vs conformation character. Then, the conformational behavior is distributed over the aggregations obtained, with the aim of revealing their main sol-gel type (viscoelastic) effects. The passage between the resulting sol and gel phases is not controlled by a scan in the temperature domain, on the contrary, the control parameter is selected to be the hydrophobic-interaction strength while the temperature remains unchanged. The distribution of ordered fringed micelles, and the overall crystalline inclusions of the gel phase, suggested a first-order phase change, reasonably conceivable in terms of Avrami-Kolmogorov formalism for such hydrophobic-force driven and percolation-in-nature systems. A phase transition diagram has been presented as a novel proposition to discern between sol vs gel phases. As specific results, also of high experimental value, a damped-oscillating cluster-involving effect on the resulting hydrophobic-polar matrices has been detected and analysed. Other additional intermolecular-sharing entropy-influenced effects on clustering, as seen in terms of chain-to-chain connectivities, have been addressed as being of sufficient relevance to the gelation mechanism described. The microcrystalline inclusions downgrade to some extent the overall picture of entropy-affected gelation, being all together suitable for experimental check-out.