Phonons and photons in crystals

The simultaneous propagation of phonons and photons in an insulator is discussed from both phenomenological and quantum mechanical points of view. A phenomenological form of the energy of an insulator is first supposed from which is obtained the equation of propagation of modes involving nuclei displacements and an electric field. This equation is then studied, mainly in the vicinity of q=0, in order to show how various limits lead to different types of propagation. The phenomenological equations are then justified from a microscopic point of view. The proof goes in two steps. A linear screened response function of the electrons in a solid is first assumed; one then proves that all the coefficients entering into the phenomenological equations may be obtained from the sole knowledge of this response function and of the charge of the nuclei. The existence of the response function is then justified from a many-body point of view. Finally, the necessary relations between the phenomenological coefficients are proved. Some other possible applications of the microscopic equations are also discussed at the end of the paper.     

Cubic phases of amphiphilic molecular aggregates

Stability and geometry of the lyotropic periodic cubic mesophases are considered in the framework of a general symmetry based phenomenological approach. A limited number of cubic structural types is shown to be formed by amphiphilic molecular aggregates due to the specific nature of self-organizing units. The related thermodynamic models predict topology of phase diagrams and specific features of transitions between isotropic, lamellar, cubic bicontinuous and cubic micellar phases. Received 25 February 1999 and Received in final form 29 June 1999     

On the phenomenological rate equation in a model exchange reaction

The limits of validity of the phenomenological rate equation, and the phenomenological rate constant k_f and k_b are found for the exchange reaction $\text{A + BC}\textcolor{red}{}\text{AB + C}$ within the framework of simple multistate models. The possibility of macroscopically long transient times is discussed. The rate constants are shown to depend on the total densities n_A, n_B and n_C of the chemical species present in the mixture, when nonequilibrium effects are important. The distinction between a rate constant and a flux coefficient is illustrated. Differences among exchange, dissociation-recombination, and isomerization reactions in that regard are discussed.     

Various kinds of two-dimensional rheological models

Two-dimensional rheological models consisting of two-dimensional elastic, viscous, and plastic elements are introduced in order to represent more closely the real rheological behavior of various isotropic and orthotropic viscoelastic, elastoplastic, viscoplastic, and elastoviscoplastic bodies in the plane-stress or plane-strain state, respectively. These models represent schematically the unit area of a body and consist of plane elastic, viscous, and plastic regions with rectangular straight boundaries lying in the principal direction of orthotropy.

The two-dimensional rheological models may be considered either from the phenomenological or from the structural point of view. They may also represent rheological structures with variously oriented multiphase systems having elastic, viscous, and plastic properties. The configuration of such models may correspond to the rheological nonhomogeneity of bodies and to both kinds of orthotropy arising either from the orthotropic properties of elastic, plastic, and viscous phases or from various configurations of phases. These models may also represent nonsymmetrical shear effects which are analogous to those arising in elastic Cosserat media.

The main differences between the presented two-dimensional models and the usual rheological models, which are one-dimensional, consist of the possibilities of representing directly two-dimensional rheological behavior, the anisotropy of rheological processes, and nonsymmetrical shear effects in rheological bodies.     

Phase diagram of transitions from an isotropic phase to nematic and smectic (uniaxial,biaxial) phases in liquid crystals with achiral molecules

The phase diagrams of transitions from an isotropic phase to nematic and smectic phases are investigated within a simple phenomenological model of the Landau thermodynamic potential. The conditions of the isomorphic phase transition between two uniaxial smectic phases and the direct transition from the isotropic phase to the uniaxial and biaxial smectic phases are determined. The behavior of the order parameters is described along different thermodynamic paths. The theoretical results are discussed using the example of liquid-crystal phases in compounds with banana-shaped achiral molecules.     

Functional-integral study of spin fluctuations in small Fe clusters

Finite temperature magnetic properties of small Fe_N clusters (N ≤6) are determined in the framework of a spin-fluctuation itinerant-electron theory based on a functional integral formulation of the canonical partition function and derived statistical averages. The free energy associated to each configuration of the exchange fields throughout the cluster are calculated by using Haydock-Heine-Kellys recursion method. The statistical averages of physical interest are obtained by performing parallel-tempering Monte Carlo simulations. Representative results are discussed for the average magnetization per atom as a function of temperature. The interplay between local environment and magnetization curves is analyzed by considering the low-temperature limit of the local spin-fluctuations energies ΔF_l(ξ) at different atoms l. The electronic calculations are contrasted with the predictions of simple of phenomenological Heisenberg-like models.     

Structural study of the ferroelectric instability in SnPSe

The structural change occurring in between the paraelectric and the ferroelectric phases is investigated by means of X-ray diffraction. Details of the structure in both phases are obtained and the role of the lone pair is discussed in the light of structural data. In agreement with the 2/ m to m symmetry lowering, polar displacements are found within the m plane away from a particular crystallographic direction but antiparallel displacements occur also. These results are discussed in the frame of the phenomenological theory which predicts a particular temperature dependence of the dielectric polarization in this crystal. Received: 10 July 1998     

On the phenomenological theory of diffusion

A phenomenological theory of diffusion is given along the lines of the treatment of De Groot and Mazur¹). Simple relations between the diffusion matrices of the various kinds of composition variables are established. In linear approximation all kinds of composition variables obey Fick's second law. The special role of the mean volume velocity is discussed and attention is given to Onsager coefficients and mobilities (friction coefficients).     

Magnetic ordering in granular system

The conditions of the formation of different magnetic structures with ferromagnetic (FM) and antiferromagnetic (AFM) ordering in granular materials containing a subsystem of ferromagnetic granules are considered within the phenomenological approach. It is supposed that the magnetostatic field and the exchange interaction between conduction electrons and magnetic ions are responsible for the formation of magnetic structure.     

Thermal behavior for a nanoscale two ferromagnetic phase system based on random anisotropy model

Advances in theory that explain the magnetic behavior as function of temperature for two phase nanocrystalline soft magnetic materials are presented. The theory developed is based on the well known random anisotropy model, which includes the crystalline exchange stiffness and anisotropy energies in both amorphous and crystalline phases. The phenomenological behavior of the coercivity was obtained in the temperature range between the amorphous phase Curie temperature and the crystalline phase one.     

On the description of noise in quantum systems

A formalism of probability operators which generalizes the notion of density operator is introduced into the theory of noisy quantum systems. The Markov property and the connexion between Heisenberg and Schrödinger picture for systems undergoing an irreversible change are discussed in detail. The probability-operator treatment of noise is related to the Langevin method discussed byLax through a generalized Einstein-relation. The master equation for the quantum mechanical oscillator with linear damping is written down in a Fokker-Planck-type approximation. By means of the Einstein-relation the coefficients in the Fokker-Planck-equation are related to the parameters in the phenomenological equations.     

An upper limit on the mass of exotic fermions in superstring inspired E(6) models

We show that in a large class of superstring inspired E(6) models considered in the literature the requirement of perturbative unification implies that the lightest neutral exotic fermion (≠ ν^c) is lighter than 115 GeV. In many models this fermion may be considerably lighter and may even be the lightest supersymmetric particle. It is argued that such a particle is compatible with all known experiments and with cosmology. Some phenomenological implications are also discussed.     

Theoretical pressure-temperature phase diagram for [N(CH3)4]2CuCl4

The pressure-temperature phase diagram for a [N(CH₃)₄]₂CuCl₄ crystal has been theoretically constructed using the phenomenological approach developed earlier. The relationships for the thermodynamic potentials of different phases and the boundaries between these phases are derived. The theoretical and experimental diagrams are in reasonable agreement. The approximations and assumptions made in the construction of the diagrams are discussed.     

Baryon exchange processes

The theory and phenomenology of baryon exchange processes are critically reviewed. As regards theory the main topics are the parity doublet problem and the patterns of exchange degenerate baryon trajectories implied by duality. In the phenomenological part, all baryon exchange reactions are considered, with the emphasis being on seeing how far simple ideas of pole exchange with the constraints implied by duality and broken SU(3) can be taken in forming an understanding of the data.     

Phenomenological approach on wave propagation in dielectric media with two relaxation times

In this paper dielectric phenomena with two relaxation times are discussed. By assuming a sinusoidal form for induction vector D a sinusoidal electric field is generated and it depends on unknown phenomenological coefficients whose expressions together to their numerical values as functions of frequency are obtained. Moreover, electromagnetic wave propagation is analysed obtaining wave vector as function of the aforementioned coefficients. The results are applied to a Vinylidene Chloride-Vinyl Chloride (VDC-VC) to test the applicability of the model.     

Violation of CP invariance in the two-doublet higgs sector of the MSSM

Problems of substantiation and investigation of CP violation in models with the extended Higgs sector are discussed. The general form of the effective two-doublet Higgs potential with complex parameters whose CP invariance is violated both explicitly and spontaneously is considered. For the special case of the two-doublet Higgs sector of the minimum supersymmetric model in which the CP invariance of the effective potential is violated by the interaction of Higgs fields with third generation scalar quarks, the physical states of Higgs bosons, their masses and interaction constants are obtained. The basic phenomenological scenarios and predictions for investigation of the properties of the Higgs sector are considered.     

Transmissivity and reflectivity of spatially dispersive thin films

We calculate the transmission and reflection coefficients for electromagnetic radiation incident normally on the surfaces of thin, spatially dispersive, absorbing, dielectric films. Results are obtained for four models of spatially dispersive dielectrics and for the case in which spatial dispersion is neglected. For each model the effects of spatial dispersion are to introduce additional fine structure into the transmission and reflection coefficients, regarded either as functions of frequency or of the thickness of the film. In addition, the results reveal an interleaving between the maxima and minima of the spectra for different models, which may provide a basis for an experimental discrimination between different phenomenological models for the nonlocal dielectric constant of a spatially dispersive dielectric medium.     

An aspect on relaxor behaviours and phase boundaries in ferroelectric mixed crystals

In order to search for Pb-free relaxor substances and to define relaxor behaviour, a theoretical aspect is presented from not only microscopic but also phenomenological viewpoint. In order–disorder type mixed crystals, the microscopic approach is attempted under conditions similar to those for relaxor perovskite-type oxides. Basing on the theory for the precursor to glass state, two kinds of technique of X-ray diffuse scattering (static properties) and quadrupole perturbed nuclear magnetic resonance (NMR-NQR) (dynamic properties) are discussed in ferroelectric (FE) -- antiferroelectric (AFE) mixed crystals of Rb_1?x(NH₄)_xH₂PO₄. After investigating both boundary regions between FE and glass (G) phases, and between AFE and G phases, relaxor-like behaviours as a large dispersion in dielectric constants are found in the AFE-G phase boundary region where the gradual growth of wave number to make the energy minimum and a discontinuous broad NMR-NQR spectrum appear in quite different forms from those of the FE-G phase boundary region. On the other hand, in perovskite-oxides, the conditions for relaxor appearance are discussed within the phenomenological theory by comparing with the microscopic analysis in hydrogen-bonded systems.