A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Adhesive bonding of glassy polymer surfaces by an ultrathin layer of a semicrystalline polymer

To develop a greater understanding of interfacial interactions between a semicrystalline polymer and a glassy polymer, adhesion tests were performed on very thin layers of poly(ethylene oxide) (PEO) sandwiched between two layers of poly(tetramethyl bisphenol A polycarbonate) (TMPC). The tests were designed to provide intimate contact between the surfaces while they were heated above the melting point of the PEO and cooled back to room temperature. A contact mechanics approach, based on the Johnson, Kendall, and Roberts theory, was used to determine values of the energy release rate describing the energetic driving force for crack propagation within the interfacial region. The ability to measure crack propagation at large values of the energy release rate was limited by rupture of the silicone elastomer that was used to provide a sufficiently compliant matrix for the adhesion experiment. By cycling the tensile stress at relatively low loading levels, we were able to measure fatigue crack propagation at values of the energy release rate that did not result in failure of the elastomer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3809–3821, 2004     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

Monte Carlo Hamiltonian: Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.     

氢原子的固有电偶极矩

用经典力学和双波量子力学计算了氢原子的固有电偶极矩。双波量子理论算得的结果在经典极限下与经典力学的结果一致。普通量子力学对氢原子Stark效应中表现出来的电偶极矩难以做出很好的解释，因为一个波函数描述的是系综而不是单个粒子。经典力学和双波量子力学可描述单个粒子的行为，对永久电偶极矩的计算和解释显得自然而合理。     

Structural optimization with parameter-transfer finite element

A mathematical method to solve structural problems, using parameter-transfer finite elements (P-TFE) was recently proposed by the authors [1] [2] [3]. The proposed transfer finite element approach is able to create a mathematical model of a structure, taking into account directly the whole behaviour of the structure under dynamic, aerodynamic, and thermal actions, and not by assembling, in a separate fashion, the stiffness and the mass matrix on one side and the external load vector as performed by the classical finite element procedure.The purpose of this paper is to apply the above methodology to optimization problems, in particular to obtain the minimum structural weight for a beam, under primary constraints on buckling load or natural frequencies.The use of P-TFE in the field of structural optimization overcomes most difficulties of the usual techniques of solution and the element is particularly useful in the evaluation of the sensitivity matrix.The formulation of the optimization problem based on P-TFE is presented and some applications are studied. The numerical results obtained are compared with other existing methodologies and briefly discussed.

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Sommario Gli autori hanno già proposto un metodo per studiare problemi strutturali [1] [2] [3], introducendo una nuova metodologia di discretizzazione, basata sull'impiego di elementi finiti di trasferimento, funzioni esplicite di un parametro, indicati come P-TFE. Tali elementi sono in grado di rappresentare, in similitudine alla funzione di trasferimento, il comportamento completo dell'elemento strutturale in esame, soggetto ad azioni dinamiche, aerodinamiche e termiche; sono parimenti in grado di produrre, in similitudine al metodo degli elementi finiti, un modello matematico discreto di un continuo.Scopo del presente lavoro è di applicare detta metodologia a problemi di ottimizzazione, in particolare alla ricerca del minimo peso per una trave che mantenga inalterate le sue caratteristiche di carico critico o le frequenze naturali di vibrazione.Vengono quindi presentati alcuni risultati numerici dei casi esaminati e confrontati con quelli ottenuti da altri autori con l'impiego di altre metodologie.

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List of Symbols {B} _m vector of the generalized state variables - {C} _m vector of integration constants - [I] unit matrix - EI bending stiffness - A cross-sectional area - u adimensional thickness - l beam length - M,M bending moment - [N] _m shape function ofm-th order - [N*] shape function atx ₀ - P axial load - [R] _i transfer matrix of thei-th element - T,T shear force - w transverse displacement - x adimensional independent variable - x ₀ value ofx at the left of the element - {Y} vector of state variables - {Y*} imposed condition atx ₀ - _0m Kronecker delta with the first pedix always set equal to zero - normalized eigenfrequency - normalized buckling load - mass density     

Conformational analysis of 5,6-dihydropyrimidine and its derivatives

The equilibrium geometry and inversion barriers of 5,6-dihydropyrimidine, 6,7-dihydroazolopyrimidines with node nitrogen atoms and their alkyl (Me, Et, Prⁱ, Bu^t) and phenyl derivatives were calculated using a molecular mechanics approach. Annelation with azole cycles and the introduction of substituents have a slight effect on the equilibrium conformation of the dihydrocycle (distorted sofa). Alkyl substutuents at saturated carbons have an essentially equatorial orientation in 5,6-dihydropyridimine derivatives and are axial in the annelated analogs. On the other hand, the equatorial conformers are more stable in phenyl derivatives of dihydroazolopyrimidines. Factors determining the relative stability of conformers were analyzed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 487–491, March, 1995.     

The complete symmetrization of quantum operators: new thoughts on an old problem

The complete symmetrization with respect to x, p _x,... of the operators associated with dynamical properties can sometimes lead to results different from those obtained by the conventional quantum formalism based on the rule op (A ²)=(op A)². For example, angular momentum operators M _z ² and M ² are modified by the additive constants ²/2 and 3 ²/2 respectively (M ²0 for electron in the ground state of H atom, rotator never at rest, but spectra unchanged); the average quadratic dispersion of energy is different from zero. These results can be interpreted by assuming that the system is never strictly isolated but communicates with the other systems of the universe by means of electromagnetic interactions. Quantum mechanics would give only average values over a sufficiently long time and would exhibit a quasi-ergodic character. Examples supporting this possibility are given, in particular that of arsines for which quantum forecasts correspond to average values over one year.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Alcohols,ethers, carbohydrates,and related compounds. II. The anomeric effect

The anomeric effect has been studied for a variety of compounds using the MM4 force field, and also using MP2/6-311++G(2d,2p) ab initio calculations and experimental data for reference purposes. Geometries and energies, including conformational, rotational barriers, and heats of formation were examined. Overall, the agreement of MM4 with the experimental and ab initio data is good, and significantly better than the agreement obtained with the MM3 force field. The anomeric effect is represented in MM4 by various explicit terms in the force constant matrix. The bond length changes are accounted for with torsion-stretch elements. The angle changes are accounted for with torsion-bend elements. The energies are taken into account with a number of torsional terms in the usual way. A torsion-torsion interaction is also of some importance. With all of these elements included in the calculation, the MM4 results now appear to be adequately accurate. The heats of formation were examined for a total of 12 anomeric compounds, and the experimental values were fit by MM4 with an RMS error of 0.42 kcal/mol.     

Molecular mechanics (MM2) calculations and cone angles of phosphine ligands

Molecular mechanics (MM2) calculations were performed on 54 conformations of 18 phosphines (PH₃; PH_3−nR_n, where n = 1,…3, and R = Me and Et, n = 1 or 2 and R =ⁱPr, and n = 1 and R =^tBu, PMe₂Et, PMeEt₂, and PPhMe₂, and PPh₂R where R = Me, Et, ⁱPr, ^tBu and Ph). The results are compared to those previously obtained from MINDO/3 and MNDO calculations, and to experimental data. Single conformer cone angles and weighted average cone angles were calculated from MM2 optimized geometries employing Tolman's general definition, and they are compared to Tolman's values, MINDO/3 results, and T.L. Brown's E_R values. Of the cone angle definitions used, the weighted average values are suggested as the best single representation of phosphine ligand sizes. The steric parameters (cone angle and E_R values) alone, and in conjunction with electronic parameters, are correlated with experimental data.