Monocrystal elastic constants in the ultrasonic study of welds

For studying welds ultrasonically, the importance of knowing the material's single-crystal elastic constants, the C_ijs, is explained. Where these constants are not known, some guidelines are given for estimating them from polycrystalline elastic constants such as Young's modulus and the shear modulus.The important case of [001] fibre texture is considered. Being transversely isotropic, this case exhibits five macroscopic elastic constants, which are related to the three cubic elastic constants: C₁₁, C₁₂, C₄₄. From these five constants the angular variations of Young's modulus, the torsional modulus, and the sound velocities can be computed. For the same [001] fibre texture, results are given for a standard well-characterized material — copper, where the C_ijs are well known.     

Elastic,mechanical, electronic properties and hardness of Nb2AsC from first principles

The study aims at the elastic, mechanical, electronic properties and hardness of Nb₂AsC using first principles based on the density functional theory method within the generalised gradient approximation. The calculated lattice parameters of Nb₂AsC are in good agreement with the experimental data. The five independent elastic constants are firstly calculated as a function of pressure, and our results indicate that it is mechanically stable in the applied pressure. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. The pressure dependences of the bulk modulus, shear modulus, average velocity of acoustic waves and Debye temperature of Nb₂AsC are systematically investigated. The band structure and density of states are discussed, and the results show that the strong hybridisations C p–Nb d and As p–Nb d would be beneficial to the structure stability of Nb₂AsC. Based on the Mulliken population analysis, the hardness of Nb₂AsC is predicted.     

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.     

Elastic,electronic and thermal properties of topological insulator SmB6: first-principles calculations

Abstract

The pressure dependence of the structural, elastic, electronic and thermal properties of Kondo insulator SmB₆ have been systematically studied by density functional theory combined with the quasi-harmonic Debye model. The calculated structure at zero pressure is in good agreement with the available experimental results at low temperature. The obtained elastic constants, bulk modulus and shear modulus indicate that SmB₆ is mechanically stable and behaves in a brittle manner under the applied pressure 0–20 GPa, consistent with available experimental data. In addition, the elastic-relevant properties, Young’s modulus and the Poisson ratio manifest that increasing pressure results in an enhancement in the stiffness of the compound. It is found that unlike temperature, pressure has little effect on the heat capacity of SmB_6. What more important is that we observed an insulator to metal phase transition at about 5.5 GPa through the disappearance of the band gap, well consistent with the experimental data. This transition has little effect on the physical properties of SmB₆.     

A note on stability of some parametrically excited structural elastic systems

An analogue simulation study for the stability investigations of nonlinear parametrically excited structural systems, exhibiting hard and soft spring characteristics is undertaken as a feasible alternative to current asymptotic and other analytic methods. It is shown that this technique locates the position of an unstable limit cycle, identifying the point of change of equilibrium states, which is ordinarily obscured in using the other existing schemes.     

Skorokhod decomposition of reflected diffusions on bounded Lipschitz domains with singular non-reflection part

Let be a compact set with interior G. Let L ¹ (G,dx), >0 dx-a.e. on G, and m:=dx. Let A=(a _ij ) be symmetric, and globally uniformly strictly elliptic on G. Let be such that ; f, , is closable in L ² (G,m) with closure ( ^r ,D( ^r )). The latter is fulfilled if satisfies the Hamza type condition, or _i L ¹ _loc (G,dx), 1id. Conservative, non-symmetric diffusion processes X _t related to the extension of a generalized Dirichlet form where satisfies are constructed and analyzed. If G is a bounded Lipschitz domain, H ^1,1 (G), and a _ij D( ^r ), a Skorokhod decomposition for X _t is given. This happens through a local time that is uniquely associated to the smooth measure 1_{{ Tr ()>0}} d, where Tr denotes the trace and the surface measure on G.This research has been financially supported by TMR grant HPMF-CT-2000-00942 of the European Union. Mathematics Subject Classification (2000): 60J60, 60J55, 31C15, 31C25, 35J25     

Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

En route to Background Independence: Broken split-symmetry,and how to restore it with bi-metric average actions

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.     

UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…