对薄层柱壳爆炸膨胀断裂过程的研究

 本文提出了一个用于描述动态破坏发展过程的损伤度函数。从这个损伤度函数出发,把材料特征性方程取为强化粘塑性本构方程形式,导出了薄层柱壳爆炸膨胀运动在两种近似下（恒定膨胀速度近似合恒定应变速率近似）断裂判据的解析表达式。结果分析表明,在上述条件下,存在着一个动态断裂“塑性峰”,在这个峰值条件的应变率下,柱壳出现贯穿断裂时刻的应变最大。以软钢为算例,本断裂判据可以比较好地解释Иванов和陈大年等给出的实验结果。这时,动态断裂“塑性峰”对应的应变率为4×10⁴ s^-1,相应的应变约为60%~80%。     

Superdegenerate point in FCC phase diagram: CVM and Monte Carlo investigations

We investigate the topology of the phase diagram of binary alloys on the fee lattice with first-neighbor antiferromagnetic interactions around the superdegenerate point, where the L1₀ and L1₂ phases meet. We treat the system as a hard-constraint lattice gas, following a procedure previously described by Lebowitzet al. We perform cluster variation method calculations in theT0 limit and Monte Carlo simulations directly atT=0 K on the ground states of the superdegenerate point. We find that: (i) there is no disordered phase in the neighborhood of this point; (ii) a phase L for which two of the four cubic sublattices have the same average occupancy and each of the two others are different appears between L1₀ and L1₂; (iii) the transition L/L1₂ is of first order.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Evaluation of Orbital- and Ground State Energies of Some Open- and Closed-Shell Atoms over Integer and Noninteger Slater Type Orbitals

Ab initio calculations of the orbital and the ground state energies of some open- and closed-shell atoms over Slater type orbitals with quantum numbers integer and Slater type orbitals with quantum numbers noninteger have been performed. In order to increase the efficiency of these calculations the atomic two-electron integrals were expressed in terms of incomplete beta function. Results were observed to be in good agreement with the literature.     

Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

Elektronenlokalisierung im Grundzustand und in angeregten Zuständen Pars-Orbital-Methode, 12. Mitt

UsingGleason's theorem the pars orbital concept is developed for excited states of conjugated systems described by CI-methods. A significance index is introduced to evaluate different patterns of fragmentation. The usefulness of this approach is illustrated for butadiene, biphenyl, naphthalene, and azulene.

11. Mitt.:H. Karpf, O. E. Polansky undM. Zander, Tetrahedron Lett.1978, 2069.     

Improved third-order Møller-Plesset perturbation theory

Based on a partitioning of the total correlation energy into contributions from parallel‐ and antiparallel‐spin pairs of electrons, a modified third‐order Møller–Plesset (MP) perturbation theory is developed. The method, termed SCS–MP3 (SCS for spin‐component‐scaled) continues previous work on an improved version of MP2 (S. Grimme, J Chem Phys 2003, 118, 9095). A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third‐order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C₂₀ isomers, transition states) demonstrate that the SCS–MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1529–1537, 2003     

Impact Responses of Prismatic Lithium-Ion Battery Based on the Membrane Factor Method北大核心CSCD

Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.