Asymptotic expansions for the coupled wavenumbers in an infinite orthotropic flexible fluid-filled cylindrical shell

Analytical expressions are found for the coupled wavenumbers in flexible, fluid-filled, circular cylindrical orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders. The Donnell-Mushtari shell theory is used to model the shell and the effect of the fluid is introduced through the fluid-loading parameter μ. The orthotropic problem is posed as a perturbation on the corresponding isotropic problem by defining a suitable orthotropy parameter ε, which is a measure of the degree of orthotropy. For the first study, an isotropic shell is considered (by setting ε=0) and expansions are found for the coupled wavenumbers using a regular perturbation approach. In the second study, asymptotic expansions are found for the coupled wavenumbers in the limit of small orthotropy (ε?1). For each study, isotropy and orthotropy, expansions are found for small and large values of the fluid-loading parameter μ. All the asymptotic solutions are compared with numerical solutions to the coupled dispersion relation and the match is seen to be good. The differences between the isotropic and orthotropic solutions are discussed. The main contribution of this work lies in extending the existing literature beyond in vacuo studies to the case of fluid-filled shells (isotropic and orthotropic).     

Multiscale Basis Functions for Singular Perturbation on Adaptively Graded Meshes

We apply the multiscale basis functions for the singularly perturbed reaction-diffusion problem on adaptively graded meshes, which can provide a good balance between the numerical accuracy and computational cost. The multiscale space is built through standard finite element basis functions enriched with multiscale basis functions. The multiscale basis functions have abilities to capture originally perturbed information in the local problem, as a result, our method is capable of reducing the boundary layer errors remarkably on graded meshes, where the layer-adapted meshes are generated by a given parameter. Through numerical experiments we demonstrate that the multiscale method can acquire second order convergence in the L² norm and first order convergence in the energy norm on graded meshes, which is independent of ε. In contrast with the conventional methods, our method is much more accurate and effective.     

THEORY OF RAMAN SCATTERING FROM CHARGE DENSITY-WAVE SUPERCONDUCTORS

A theory is developed for the Raman scattering of light from a charge-density-wave (CDW) superconductor on the basis of a modified Balseiro-Falicov interactibn pro.posed by the authors and including renormalization of both the Coulomb interaction at the small q limit, and the residual coupling between electrons. Both the electron-photon and electron-phonon vertices are taken into account. It is shown that there always exist poles at frequency ω=2Δ (Δ is superconducting gap) in the effective electron polarization and in the phonon self-energy, and these poles survive the Coulomb screening and the renormalization of the residual electron interactions if the coupling parameter g₂(k) is anisotropic, in contrast with an isotropic electron gas. The effect of the Littlewood-Varma interaction in a coexistent CDW-siiperconductcr is also discussed.     

极性晶体的表面或界面极化子

本文用动量和位置的线性组合作为算符,计算了极性晶体的表面或界面极化子的基态能量,结果表明,线性组合算符对于研究极性晶体的表面或界面极化子的性质也是适用的。 关键词：     

Spatial anisotropy: a method to study anisotropic flow in heavy ion collisions

We introduce a method to study anisotropic flow parameter v<,n> as a collective probe to Quark Gluon Plasma in relativistic heavy ion collisions. The emphasis is put on the use of the Fourier expansion of initial spatial azimuthal distributions of participant nucleons in the overlapped region. The coefficients ε<,n> of Fourier expansion are called the spatial anisotropy parameter for the n-th harmonic. We propose that collective dynamics can be studied by v<,n>/ε<,n>. In this paper, we will discuss in particular the second (n=2) and the fourth (n=4) harmonics.     

金刚石晶格上的对角无序与非对角无序非晶量子点

报道金刚石晶格上对角无序与非对角无序非晶量子点的理论研究，用简单的紧束缚哈密顿量描述模型的电子结构，用ｒｅｃｕｒｓｉｏｎ方法求解哈密顿方程，用边界条件对本征值的影响判断局域化，研究发现，带边为扩展态时，带宽的变化趋势与晶态量子点类似；带边为局域态时，尺寸超过某一临界长度后，带宽不变，但带边态密度随尺寸增大而增大。还研究了非晶量子点的介电函数虚部ε₂（?ω）。与扩展态对应的ε₂（?ω），对尺寸变化较敏感。与局域态对应的ε₂（?ω），当尺寸大于 关键词：     

On the Friedrichs inequality in a domain perforated aperiodically along the boundary. Homogenization procedure. Asymptotics for parabolic problems

This paper is devoted to the asymptotic analysis of functions depending on a small parameter characterizing the microinhomogeneous structure of the domain on which the functions are defined. We derive the Friedrichs inequality for these functions and prove the convergence of solutions to corresponding problems posed in a domain perforated aperiodically along the boundary. Moreover, we use numerical simulation to illustrate the results. The work of the first author was partially supported by RFBR. The work of the first and the second authors was partially supported by the program “Leading Scientific Schools” (NSh-1698.2008.1).     

Total Routhian Surface Calculations on Hf Isotopes

The two-dimensional total routhian surface calculations have been carried out to study the triaxial superdeformed structure of a neutron-rich nucleus ¹⁷³Hf firstly. In particular the effects of the rotational frequency ω and pairing-energy gap parameter Δ are discussed in detail in the course of shaping its triaxial superdeformation; additionally the neutron-shell correction energy is analyzed with emphasis in the confirmed triaxial superdeformed nucleus ¹⁷³Hf. Finally, more systematical results have been investigated for some confirmed superdeformed nuclei experimentally and a few predicted triaxial superdeformed nuclei theoretically with quadropole deformation ε₂≈0.4 and triaxial deformation γ≈20^º or 30^º in the Z=72 region.     

Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities

The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r^-(d-p). The asymptotic scaling law is studied in the framework of the expansion in e = 4 - d. In d ~ 4, the dynamic exponent z .is calculated up to the second order in p with ρ= O(ε^1/2). The shape function is obtained in one-loop calculation. When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.     

Probability distribution of Majorana end-state energies in disordered wires

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.     

Short—Time Critical Behavior Affected by Weakly Long—Range Interactions

The theoretic renormalization group approach is applied to the study of short-time critical behavior of the Ginzburg-Landau model with weakly long-range interactions pσsps-p,The system initially at a high temperature is firstly quenched to the critical temperature Tc and then released to an evolution with a model A dynamics,A double expansion in ε=2σ-d and α=1-σ/2 with α of order ε of order ε is employed,where d is the spatial dimension.The asymptotic scaling laws and the initial slip exponents θ′and θ for the order parameter and the response function respectively are calculated to the second order in ε for σ close to 2.     

强电场作用下反铁电锆钛酸铅的介电行为研究

采用电滞回线方法和偏置直流电场中叠加小交变电场方法研究了锆钛酸铅反铁电陶瓷材料在强电场作用下的介电行为.测量结果显示，锆钛酸铅反铁电材料的介电常数随外加电场强度呈非线性变化，在反铁电 铁电转变的电场区间形成介电峰.表征极化强度随电场强度变化率的微分介电常数εd峰值出现在反铁电 铁电转换电场强度处，最高达到41000.随着偏置电场增加反铁电向铁电体转变过程中，小信号介电常数εc减小；在电场降低铁电回复成反铁电过程中，小信号介电常数εc增大，小信号介电常数εc峰先于微分介电常数εd峰出现.根据电场作用下反铁电 关键词： 锆钛酸铅反铁电陶瓷 介电行为 强电场条件     

Emptiness Formation Probability

We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix \({\mathcal{T}_0}\). Focusing on the eigenvalues of \({\mathcal{T}_0}\) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required \({\mathcal{T}_0}\) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work.     

On the onset condition of fast-time instability in Liñán's premixed-flame regime

The fast-time instability of Liñán's premixed-flame regime is revisited in order to resolve the unrealistic result, previously obtained by Peters, that the inner reaction zone becomes unstable under all subadiabatic conditions. The problem is posed as that of finding the stable range of the heat-loss parameter, defined as the ratio of the downstream heat loss to the total chemical energy influx, near the adiabatic condition. Central to the analysis is rescaling near the adiabatic condition by employing a distinguished limit that the heat-loss parameter is of the order of the inverse of the Zel'dovich number, which enables us to take into account the stabilizing effect of the outer diffusive layers on the inner reaction zone. For a general diffusion flamelet model, the critical value of the heat-loss parameter at the neutral-stability condition is obtained to form a bound for the stable subadiabatic range of the heat–loss parameter.     

Integrable Structure of the Dirichlet Boundary Problem in Two Dimensions

We study how the solution of the two-dimensional Dirichlet boundary problem for smooth simply connected domains depends upon variations of the data of the problem. We show that the Hadamard formula for the variation of the Dirichlet Green function under deformations of the domain reveals an integrable structure. The independent variables corresponding to the infinite set of commuting flows are identified with harmonic moments of the domain. The solution to the Dirichlet boundary problem is expressed through the tau-function of the dispersionless Toda hierarchy. We also discuss a degenerate case of the Dirichlet problem on the plane with a gap. In this case the tau-function is identical to the partition function of the planar large N limit of the Hermitian one-matrix model. Received: 18 September 2001 / Accepted: 18 December 2001     

Contribution of Electromagnetic Field to Atomic Spin

We examine the contribution of electromagnetic field to the atomic spin, by adopting two different, both gauge invariant definitions of the electromagnetic angular momentum: \vec{J}_I ≡ ∫d³ x ε₀ \vec{r} X (\vec{E} X \vec{B}) and \vec{J}_II ≡ ∫d³ x ( ε₀ \vec{E} X \vec{A}^\bot + ε₀ E_i \vec{r} X \vec{\nabla }A^{\bot}_i ). Notably, at the classical level, \vec{J}_II gives an exactly null result while \vec{J}_I gives a finite value. This suggests that \vec{J}_II leads to a simpler and more reasonable picture of the atomic spin, therefore qualifies as a more appropriate definition of the electromagnetic angular momentum. Our observation gives important hint on the delicate issue of gluon contribution to the nucleon spin.     

用椭圆偏振光法四相模型研究Si SOI光学性质

用椭圆偏振光谱仪在波长为3000到5000?范围内,测量了绝缘衬底上低压CVD生长的多晶Si薄膜(LPCVD Si SOI)及其激光退火和高频感应高温石墨棒热退火后的椭圆偏振光谱参数。以矩阵乘积形式表示了椭偏光谱四相模型,用Monte Carlo统计模拟法求得Si SOI表面多晶Si薄膜的光学参数ε₁和ε₂,并对退火后出Si SOI的晶格完整性进行了讨论。 关键词：     

皮肤含水量对太赫兹光谱参数的影响规律研究

太赫兹时域光谱技术已经用于皮肤癌、皮肤烧伤以及皮肤疤痕治疗效果的诊断和过程监测,通常采用太赫兹时域和频域光谱参数作为区分皮肤组织不同状态的诊断参量。目前最常用的皮肤活体反射式太赫兹测量装置需将皮肤放置于介质窗上来提高测量的准确性,这使得皮肤表层水分含量因为阻塞而发生变化,从而影响太赫兹诊断皮肤的精确性。随着太赫兹生物应用从离体检测到活体测量方向发展,需要分析阻塞情况下皮肤太赫兹光谱参数的变化规律。采用太赫兹反射系统对手臂皮肤在石英介质窗上的阻塞过程进行了连续测量,然后对不同时刻时域波形的峰峰值、半波脉宽等13个特征量进行了分析。结果表明：时域信号和传递函数的峰峰值、最大值与最小值之间的拟合斜率等参量随阻塞时间而呈指数衰减;传递函数的最大值与最小值时间差、最大值与最小值的斜率等随阻塞时间呈指数增加;时域波形的半峰全宽、对数频谱等保持不变。然后用双德拜模型来模拟皮肤组织在0.2～1 THz频段的介电常数,采用遗传算法和Levenberg-Marquardt相结合的优化算法得到了皮肤阻塞情况下不同时刻的双德拜参数,结果表明：ε_∞和ε_s均随着时间呈指数上升,5 min内增幅分别达到了27.8%和12.5%;ε₂、弛豫时间常数τ₁和τ₂基本保持不变。将皮肤组织视为多层媒质结构,基于Bruggeman有效介质模型,将计算得到的太赫兹反射率和测量得到的反射率作为目标函数,再采用上述混合优化算法得出了皮肤含水量随时间的变化规律。结果表明：随着阻塞时间的增加,皮肤角质层中的水分以指数函数的形式增加,5 min的阻塞时间即可增加23.8%。因此,在进行临床应用和研究时,必须谨慎考虑皮肤与介质窗接触阻塞而导致的参数变化。该研究有利于提高太赫兹活体检测的准确性和推动太赫兹时域光谱技术的临床应用。     

Activated tunneling decay of metastable state: Solution of the Kramers problem

At sufficiently low friction the Fokker-Planck equation for Brownian motion in a potential well is reduced to an integral equation for the energy variable. The basic small parameter of the problem is the ratio of the temperature T to the depth U₀ of the well. Quantum tunneling effects are naturally incorporated into the calculations. An explicit solution for Kramers' problem of the lifetime of the Brownian particle in the potential well is given.