An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Application of similarity aggregation techniques to a population of paraplegic patients

We studied a population of paraplegic patients in order to give prominence to a possible relationship between the topography of their spinal lesion and the occurrence of special articular diseases (P.O.A.). According to the motor and sensory state of their spinal cord, we first tried to obtain a classification of these lesions (the usual one schematically separates ‘flaccid’ and ‘rigid’ paraplegics). We mainly put the emphasis on this clustering step of the study:

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Fermionic perturbation theory for the statistical mechanics of the nonlinear Schrödinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrödinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the function of Yang and Yang: It represents a fermion energy at finite temperatures.     

Three-body interactions,rotational invariance and the elastic consistency of lattice dynamical models for face-centred tetragonal indium

The origin of the elastic inconsistency ofdaf, mas andgtf models for non-cubic solids and the failure of their force constants to comply with all the rotational invariance conditions are analysed by resolving the atomic displacements of face-centred tetragonal indium along three mutually perpendicular directions. It is shown that a lattice dynamical model suffers from these deficiencies as a consequence of its neglect of three-body interactions as well as the mixed neighbour interactions associated with the angular forces, while thecgw model which incorporates both these interactions is elastically consistent and its potential energy rotationally invariant. The degree of equivalence that exists among the force constants ofdaf, mas, gtf andcgw models, the distortions introduced by the elastic inconsistency into the phonon dispersion curves of fct indium as well as the consequences of imposing the rotational invariance conditions on the force constants of a lattice dynamical model are discussed.     

Gas chromatographic retention indices for alkenes on OV-101 and squalane capillary columns

Summary Gas chromatographic retention indices for 47 C₅ to C₈ alkenes on OV-101 dimethylsilicone at 50 and 70 °C were determined within a standard deviation of 0.3i.u. Data obtained on OV-101 are compared with those measured on squalane. The comparison of the retention index and dl/dT values from both columns is presented as linear regression equations with correlation coefficients greater than 0.98.     

Quantum chemical study on the one-carbon unit transfer of imidazolinium

One-carbon unit transfer reaction of folate cofactor model compound, 1-acetyl-2-methyl-imidazolinium, with 1,2-diaminobenzene has been studied theoretically with ONIOM method. The result shows that there are two pathways to complete this reaction because the imidazolinium ring has two breaking patterns. Both the two pathways have six steps. They are combination of two reactants, proton migration, break of five-membered ring, formation of benzimidazole derivate, another proton migration, and formation of final products. In each of the above pathways, the two proton migration steps have higher energy, which illuminate that the reaction is catalyzed by general acid-base. This fact agrees with the experimental results of enzymatic one-carbon unit transfer at oxidation level of formate.     

有机链状分子的定域分子轨道的研究

利用Foster-Boys定域化程序和STO-3G ab initio方法,对含有C、H、O、N原子的100多个有机链状分子进行了研究,得到定域分子轨道能量及其相互作用参数。应用这些参数和定域分子轨道模型,对于众多的含有C、H、O、N原子的有机链状分子,可得到相应的正则分子轨道能量及其与定域分子轨道的关系。以此预测它们的电离能,结果与实验值符合较好。