Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

AFM nanooxidation process - Technology perspective for mesoscopic structures

We study the technology of local anodic oxidation (LAO) by the AFM tip applied to semiconductor heterostructures with two-dimensional electron gas. The aim is to design mesoscopic rings with persistent current and one subband occupied. For this purpose the need is to oxidize narrow lines that represent energy barriers high enough. Using the electrostatic model, we explain the electric field distribution in the system tip-sample just before LAO starts. We study the influence of the conductivity of the cap layer on LAO and explain the origin of the saddle-like profile lines, observed in the experiment. Using Monte Carlo simulation we show that the carrier redistribution in the system with LAO energy barriers effectively lowers the barrier height. In the experimental part we have grown InGaP/AlGaAs/GaAs heterostructures by organometalic vapor phase epitaxy with an active layer only 31 nm below the surface. We have prepared oxide lines on the heterostructures by LAO and characterized them by the temperature-dependent transport measurement.     

A geometric characterisation of resonance in Hopf bifurcation from relative equilibria

We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.     

太赫兹波光子晶体光纤传输特性分析

利用矢量有限元法分析了太赫兹波光子晶体光纤单模截止频率和波导色散随光纤结构的变化特性．结果表明，太赫兹波光子晶体光纤的单模截止频率随着光纤空气孔占空比的变大而降低，零波导色散点频率随着空气孔占空比变大而增加，约束损耗随着空气孔的圈数增加而降低．     

Finite element modelling of the elastic-plastic stress and strain state and lifetime of the belt chamber

Abstract

A special finite element method (FEM) programme has been developed, reflected all significant phenomena connected with assembly and exploration of the Belt chamber. A nonhomogeneous temperature field is taken into account. Isotropic, kinematic and mixed hardening rules can be considered.     

Abelian Subgroups of Garside Groups

In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ^?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.     

Cavitation in elastomeric solids: I—A defect-growth theory

It is by now well established that loading conditions with sufficiently large triaxialities can induce the sudden appearance of internal cavities within elastomeric (and other soft) solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. This paper introduces a new theory to study the phenomenon of cavitation in soft solids that: (i) allows to consider general 3D loading conditions with arbitrary triaxiality, (ii) applies to large (including compressible and anisotropic) classes of nonlinear elastic solids, and (iii) incorporates direct information on the initial shape, spatial distribution, and mechanical properties of the underlying defects at which cavitation can initiate. The basic idea is to first cast cavitation in elastomeric solids as a homogenization problem of nonlinear elastic materials containing random distributions of zero-volume cavities, or defects. This problem is then addressed by means of a novel iterated homogenization procedure, which allows to construct solutions for a specific, yet fairly general, class of defects. These include solutions for the change in size of the defects as a function of the applied loading conditions, from which the onset of cavitation — corresponding to the event when the initially infinitesimal defects suddenly grown into finite sizes — can be readily determined. In spite of the generality of the proposed approach, the relevant calculations amount to solving tractable Hamilton-Jacobi equations, in which the initial size of the defects plays the role of “time” and the applied load plays the role of “space”. When specialized to the case of hydrostatic loading conditions, isotropic solids, and defects that are vacuous and isotropically distributed, the proposed theory recovers the classical result of Ball (1982) for radially symmetric cavitation. The nature and implications of this remarkable connection are discussed in detail.     

The bond force constants and elastic properties of boron nitride nanosheets and nanoribbons using a hierarchical modeling approach

A hierarchical approach bridging the atomistic and nanometric scales is used to compute the elastic properties of boron nitride nanosheets and nanoribbons, examining the effect of sheet size, aspect ratio and anisotropy. The approach consists in obtaining the bond force (force field) constants by dedicated computations based on density functional theory (DFT) and using such constants as input for larger scale structural models solved by finite element analysis (FEA). The bond force constants calculated by DFT are 616.9 N/m for stretching, 6.27×10⁻¹⁹ Nm/rad² for in-plane rotation and 1.32×10⁻¹⁹ Nm/rad² for dihedral rotation. Using these constants, the elastic properties of boron nitride nanosheets and nanoribbons predicted by FEA are almost independent of the sheet size, but strongly dependent on their aspect ratio. The sheet anisotropy increases with increased aspect ratio, with nanoribbons of aspect ratios of 10 exhibiting a ratio of elastic moduli along both in-plane directions of 1.7.