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11.
Giuseppe Gaeta 《Annals of Physics》2004,312(2):511-540
In the Landau theory of phase transitions one considers an effective potential Φ whose symmetry group G and degree d depend on the system under consideration; generally speaking, Φ is the most general G-invariant polynomial of degree d. When such a Φ turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion (as stated by Gufan) and rigorously justify it on the basis of classical Lie-Poincaré theory as far as one deals with fixed values of the control parameter(s) in the Landau potential; when one considers a range of values, in particular near a phase transition, the criterion has to be accordingly partially modified, as we discuss. We consider some specific cases of group G as examples, and study in detail the application to the Sergienko-Gufan-Urazhdin model for highly piezoelectric perovskites. 相似文献
12.
13.
The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis
of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two
modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the
latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. Then we restrict our attention
to pairs of free modules. Our main results are that the theory of pairs of free Abelian groups is co-recursively enumerable,
and that a few remarkable extensions of this theory are decidable.
Work performed under the auspices of GNSAGA-INDAM 相似文献
14.
A new microwave dielectric method for studying photoinitiated chain radical polymerization processes
Carlo Carlini Francesco Ciardelli Pier Angelo Rolla Elpidio Tombari 《Journal of Polymer Science.Polymer Physics》1987,25(6):1253-1261
Measurements of both real and imaginary parts of the dielectric constant at a fixed microwave frequency have been performed on n-butyl acrylate/poly(n-butyl acrylate) mixtures. The dielectric constant of the mixtures has been compared with that of neat n-butyl acrylate during UV photoinitiated polymerization. The values of the imaginary part of the dielectric constant thus obtained have allowed determination of the instantaneous monomer concentration and verified the kinetic equation for the photoinitiated polymerization process. The limits of validity of the method as well as its capability of providing detailed kinetic information are also discussed. 相似文献
15.
Francesco Catoni Roberto Cannata Paolo Zampetti 《Advances in Applied Clifford Algebras》2006,16(2):85-101
It is known that complex numbers can be associated with plane Euclidean geometry and their functions are successfully used
for studying extensions of Euclidean geometry, i.e., non-Euclidean geometries and surfaces differential geometry.
In this paper we begin to study the constant curvature spaces associated with the geometry generated by commutative elliptic-quaternions
and we show how the “mathematics” they generate allows us to introduce these spaces and obtain the geodesic equations without
developing a complete mathematical apparatus as the one developed for Riemannian geometry. 相似文献
16.
17.
Nicola Fusco Michele Gori Francesco Maggi 《NoDEA : Nonlinear Differential Equations and Applications》2006,13(4):425-433
An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex
functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of
the Calculus of Variations by James Serrin is unified in one single statement. 相似文献
18.
We have investigated the distribution of conformations and orientations for a simple internal rotor molecule, 2,2'-bithienyl dissolved in liquid crystal solvents, by re-analysing published proton dipolar coupling data with the maximum entropy internal order method (MEIO). We show that detailed, model independent, conformational information can be obtained when data of sufficiently high quality are available. We also propose a novel and convenient representation method for the orientational-conformational coupling. 相似文献
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