Dynamical stability and pure thermodynamic phases

A notion of stability of dynamics under distant perturbations is introduced. It is demonstrated, for quasi-local systems, that the stability of an equilibrium state under the same perturbations implies the state is factorial, i.e. strongly clustering in space. We also characterize the set of perturbations necessary to ensure the equivalence of stability and factorialness.     

Statistical thermodynamic formalism in the solution of information theory problems

This is the first of several papers dealing with the application of statistical thermodynamic methodology to the solution of coding and communication theory problems. Emphasis is placed on the various ensemble techniques of statistical mechanics, the words or samples of a message taking the place of molecules in the prototype physical system. Analogs of temperature, internal energy, pressure, chemical potential, volume, entropy, etc., are developed. The isomorphism with thermodynamics is complete and these quantities transform (for example, by partial differentiation) in exactly the same way as the prototype physical quantities. The methods are nicely applicable to coding cases involving sources with memory, in which case, correlation can be discussed in terms of analog coupling energies between signals or words so that the store of many-body-problem techniques can be used. In addition, the manipulative freedom stemming from the possibility of choosing from a multiplicity of ensembles constrained by intensive parameters proves a distinct advantage. A concrete example dealing with the choice of a compact code for a nonextended source with memory is presented. The compact code is derived, and some discussion is given concerning the breadth of its power spectrum. In a following paper, its autocorrelation function within the framework of pulse code modulation is derived and transformed by Wiener theory so that the power spectrum is directly exhibited (along with the spectra for several other cases).Research supported under AFOSR Grant No. 70-1877. The present work is contribution No. 2643 of the Department of Chemistry, University of California-Los Angeles.     

Statistical mechanics and stability of random lattice field theory

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities.     

Stress anisotropy in liquid crystalline phases

Monte Carlo simulations of bulk liquid crystals in the isotropic, nematic and smectic phases were performed. The simulations were carried out using different box shapes. The diagonal components of the pressure tensor were calculated to verify that the system is in mechanical equilibrium. For simulations in cubic boxes it was found that the three components of the pressure tensor had the same values in the isotropic and nematic phases but they were different in the smectic phase, i.e. the system seemed to be under anisotropic stress. NVT and NPT simulations in the smectic phase were performed by allowing the box sides to fluctuate independently; in this case, the average diagonal components of the pressure tensor had the same value. Inaccurate calculation of the total pressure produces incorrect equilibrium boundaries in the phase diagram. Microphases and poorly defined layering can be found in simulations of smectic phases when they are performed on cubic boxes. Although the pressure anisotropy is relaxed out, the layering structure in smectic phases seems to depend on the initial configuration, regardless of the simulation method.     

Molecular structure and chiral liquid crystalline phases

We describe briefly some results obtained on both chiral and achiral compounds exhibiting chiral mesophases. We report the first example of a single component system exhibiting the undulated twist grain boundary C* or UTGB _C* phase. Preliminary results concerning a few achiral compounds composed of banana-shaped molecules exhibiting a mesophase is reported. They have been investigated by polarized light optical microscopy, differential scanning calorimetry and x-ray diffraction studies.     

Stellar stability by thermodynamic instability

For gravity-dominated systems the three features shrinking <=> energy decrease <=> temperature increase are dynamically linked together. So are their inverses: expansion <=> energy increase <=> temperature decrease. We exhibit these features by one classical particle in a suitable environment, and by many particles with purely attractive interactions. We then show how the ensuing negative heat capacity tames an explosive energy input.     

Non-equilibrium and crystalline phases on the Mg-Ga-Sn system

Samples in the eutectic composition were obtained with the piston and anvil technique and the crystallization towards a metastable phase was observed upon annealing at room temperature. Small amounts of Sn were added to the binary MgGa in order to analyze its influence on the glass forming ability. Cast and rapid quenched ternary samples were studied employing X-ray diffraction, Mössbauer spectroscopy and electron probe microanalysis. The solubility of the third element was analyzed in the equilibrium phases Mg₅Ga₂, Mg₂Ga and Mg₂Sn. As far as we know, these are the first contributions to the knowledge of the MgGaSn system.     

Magnetostatic properties of heterogeneous Co-based amorphous/crystalline phases

Using the magneto-optical Kerr effect, magnetic hysteresis loops are measured on annealed amorphous Co₆₆Fe₄B₁₅Si₁₅ samples, to characterize the magnetostatic properties of the heterogeneous crystalline/amorphous phases. A gradual change, on microscale inhomogeneous, change of the magnetic properties with respect to thickness is revealed on HCP-Co, FCC-Co crystalline phases near the surface. The inner amorphous phase exhibits an irregular variation of the local magnetic properties, presumably due to the occurrence and distribution of microcrystallites. The effective field, exerted by the crystalline layer on the amorphous phase, is opposite to the surface magnetization, indicating that there is an antiferromagnetic coupling between surface and inner amorphous phases.     

Radiation stability of ionic crystalline materials

An analysis of the processes determining radiation stability of ionic compounds is performed. It is shown that the resistance of ionic crystalline compounds to the action of radiation is determined primarily by the degree of ionization of the bond, and the values of defect formation energy, effective dielectric constant, and primary defect mobility.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 85–90, August, 1977.     

Geometric theory of diblock copolymer phases

We analyze the energetics of spherelike micellar phases in diblock copolymers in terms of well-studied, geometric quantities for their lattices. We argue that the A15 lattice with Pm3;n symmetry should be favored as the blocks become more symmetric and corroborate this through a self-consistent field theory. Because phases with columnar or bicontinuous topologies intervene, the A15 phase, though metastable, is not an equilibrium phase of symmetric diblocks. We investigate the phase diagram of branched diblocks and find that the A15 phase is stable.     

Composition and thermodynamic properties of thermal plasma with condensed phases

The initial relations of a method for calculating the composition and thermodynamic properties of a closed heterogeneous system in thermodynamic equilibrium at constant pressure and temperature are given. The gaseous phase is always present in the system, and substances in the condensed state can also be present, which are divided into several condensed phases. The essence of the method consists in the minimizing the Gibbs energy of a system in ideal state. The application possibilities of the method described are discussed in detail. The main aim of the article is to provide solutions to problems arising in the calculations of composition and thermodynamic properties. These problems are not only of physico-chemical nature but they also relate to the numerical calculations and stability. The nature of the problems is general and independent of computation method.     

On the thermodynamic stability of odd-frequency superconductors

The thermodynamic stability of odd-frequency pairing states is investigated within an Eliashberg-type framework. We find the rigorous result that in the weak coupling limit a continuous transition from the normal state to a spatially homogeneous odd-in-ω superconducting state is forbidden, irrespective of details of the pairing interaction and of the spin symmetry of the gap function. For isotropic systems, it is shown that the inclusion of strong coupling corrections does not invalidate this result. We discuss a few scenarios that might escape these thermodynamic constraints and permit stable odd-frequency pairing states.     

Generalized thermodynamic stability of systems under shear

Starting from the extended irreversible thermodynamics (EIT) theory, some corrections to the specific heat and to the thermal compressibility of a nonequilibrium system are obtained. We study the subsequent modifications of the static stability conditions of a system under shear. In some situations, a shear-induced melting transition can be present.