Hyperpolarizabilities of Chelidamic Acid Complexes M_m(C_7H_3O_5N)_n (M=Cu, Ag): Theoretical Analysis

The frequency‐dependent hyperpolarizabilities of chelidamic acid complexes M_m(C₇H₃O₅N)_n (M?Cu, Ag) were investigated under the time dependent density functional theory (TDDFT) combined with the sum‐over‐states method (SOS). The relationship between molecular orbitals and nonlinear optical (NLO) properties has been explored. The results show that the charge transitions of π‐π* and 3d_M‐π* are very important to the second‐order polarizabilities, and the largest component of dynamic β is 3.84×10^?25 cm⁵·esu^?1 at 0.74 eV for Ag₂Cu₂(C₇H₃O₅N)₄. The charge transition between π‐π* is also highly crucial to the third‐order polarizabilities, and the largest component of dynamic γ is ?4.46×10^?29 esu at 0.50 eV for Ag₂Cu₂(C₇H₃O₅N)₄. The central Cu ion, as electron bridge, extends the range of delocalization and leads to an interesting phenomenon of spiroconjugation.     

非线性非完整转动相对论系统的新型Vacco动力学方程

建立了非线性非完整转动相对论系统的新型Vacco 动力学方程     

Prediction of polyimide materials with high glass‐transition temperatures

The prediction of chemical structures that possess higher glass‐transition temperatures (T_g's) is crucial for designing polyimides. Because of a lack of suitable parameters, several estimation methods cannot be used for this purpose. In this study, therefore, we used molecular dynamic simulation with the DREIDING II force field to predict T_g's for polyimides. Simulated results indicated a good agreement with experimental observations. A barrier analysis of the bridging bonds between moieties along the main‐chain backbone showed a correlation between T_g and the barrier height. This proved to be helpful in a preliminary selection before the molecular dynamic simulation for accelerating the process of research and development on new polyimides. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2243–2251, 2001     

Intensive variables in the framework of the non-extensive thermostatistics

By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner consistent with the thermostatistics structure of the theory. We show that the definitions of these quantities are sensitive to the composition law of entropy and internal energy governing the system. In this way, we can clarify some questions raised about the possible introduction of intensive variables in the context of non-extensive statistical mechanics.     

Mathematical analogy of a beam on elastic supports as a beam on elastic foundation

This paper presents the mathematical hypothesis that a beam on equidistant elastic supports (BOES) can be considered as a beam on an elastic foundation (BOEF) in static and free vibration problems. This modeling of BOES as BOEF is presumed to be applicable to a limited range of support stiffness, spacing and flexural rigidity of the beam. The authors investigate the applicability of the modeling of BOEF from the property of characteristic solutions obtained from governing equations of both BOES and BOEF. In this study, the formulation of BOES leads to governing difference equations, and the motions of BOEF are expressed by differential equations. This is because exact solutions must be employed in order to verify their analogy accurately. The characteristic solutions obtained from these two governing equations are compared to each other in order to investigate the relationship between them.     

Anisotropy of the angle resolved electron attenuation at crystal surfaces

Photoemission multiple scattering theory is used to describe the electron transport in the surface region of a crystal. Intensities of photoemission from core levels of atoms situated in subsurface atomic layers are calculated as a function of the emitter distance from the surface. The electron angle resolved attenuation length (ARAL) is extracted from the exponential fitting of the intensity decays of photoemission into different directions. Substantial anisotropy of the electron ARAL is found for the Cu(1 1 1) surface in Mg Kα photoexcitation of Cu 2p_3/2 levels and correlated with the orientation of highly packed atomic rows. Enhanced photoemission contributions from specific subsurface layers, caused by electron forward focusing effects, are reported.     

General Analytic Solutions and Complementary Variational Principles for Large Deformation Nonsmooth Mechanics

This paper presents a nonlinear dual transformation method and general complementary energy principle for solving large deformation theory of elastoplasticity governed by nonsmooth constitutive laws. It is shown that by using this method and principle, the nonconvex and nonsmooth total potential energy is dual to a smooth complementary energy functional, and fully nonlinear equilibrium equations in finite deformation problems can be converted into certain tensor equations. The algebraic relation between the first and the second Piola–Kirchhoff stresses are revealed. A closed form solution for general three-dimensional large deformation boundary value problems is obtained. The properties of this general solution are clarified by a triality extremum principle. This triality theory reveals an important phenomenon in nonconvex variational problems. Applications are illustrated by nonlinear, nonsmooth equilibrium problems in Hencky's plasticity, 3D cylindrical structures and post buckling analysis of elastoplastic bar with jumping and hardening effects. The idea and methods presented in this paper can be used and generalized to solve many nonlinear boundary value problems in finite deformation theory.Sommario. Il lavoro presenta un metodo di trasformazione duale nonlineare ed un principio generale di energia complementare per la soluzione di problemi di teoria elastoplastica in grandi deformazioni governati da leggi costitutive con discontinuità. Si mostra come, usando il metodo ed il principio proposti, l' energia potenziale totale discontinua e nonconvessa duale di un funzionale energia complementare continuo, e le equazioni di equilibrio nonlineare in problemi di deformazione finita, possano essere convertite in equazioni tensoriali. Vengono mostrate le relazioni algebriche fra il primo ed il secondo tensore delle tensioni di Piola–Kirchhoff. Si ottiene una soluzione in forma chiusa per problemi al contorno generali tridimensionali in grandi deformazioni. Le proprietà di tale soluzione generale vengono chiarite per mezzo di un principio estremale di trialità. La eoria della trialità evidenzia un fenomeno importante in problemi variazionali nonconvessi. Vengono presentate applicazioni a problemi di equilibrio nonlineare con discontinuità in situazioni di plasticità alla Hencky, strutture cilindriche in 3D, e nell'analisi postcritica di una barra elastoplastica con effetti hardening e di jumping. L'idea ed i metodi presentati in questo lavoro possono essere usati e generalizzati per risolvere molti problemi al contorno nonlineari nella teoria delle deformazioni finite.     

FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.     

Algorithm of orbit determination using one or two GPS satellites

The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary state of satellite orbit with a certain precision in short time.