Shape equations for two-dimensional manifolds with nonempty boundary based on a variational method

A smooth surface is considered which has a curved boundary. A system of exterior differential forms is introduced which describes the surface and boundary curves completely in the moving frame approach. A total free energy functional is defined based on these forms for which an equilibrium equation and boundary conditions of the surface are derived by calculating the variation of the total free energy. These results can be applied to a surface with several freely exposed edges.

Investigation of thermodynamic properties of single-layer two-component coatings

The results of studying the dynamics of disordered alloys by the method of collective variables are presented. The densities of phonon states of disordered alloys with BCC structure of the kxrb1-x system are calculated. The contribution of phonons to the free energy and entropy of the alloy at different temperatures is determined. It is shown that the contribution of phonons to the total free energy of the alloy decreases with decreasing temperature. The contribution of phonons to the entropy of alloys at 300 K is crucial.

The Temperature-sensitivity of a Critical Electric Field Induced Magnetic Easy-axis Reorientation Ferromagnetic/ferroelectric Layered Heterostructures

We have investigated the effects of temperature on the magnetic easy axis reorientation (EARs) in polycrystalline ferromagnetic (FM) nano-scale thin films, i.e. (001)-oriented cubic films such as Fe, Ni, CFO and (0001)-oriented hexagonal films such as Co, grown on ferroelectric (FE) substrates, for example PZT, BTO substrates. The model of FM/FE bilayered heterostructures has been applied to study the total free energy of the FM films. By minimizing this energy, we have shown that temperature has a significant effect on a critical electric field induced magnetic reorientation.

DIRECTOR FIELD OF DISCLINATION LINE IN UNIAXIAL NEMATIC LIQUID CRYSTAL IN THE PRESENCE OF MAGNETIC FIELD

Using the Oseen–Zöcher–Frank theory, in the steady state, I study the distortion energy of a disclination line in nematic liquid crystal in the presence of an external magnetic field. The director field around a disclination line is exactly calculated by minimizing the total free energy. The behavior of total free energy as a function of magnetic field for two kinds of nematic material (positive and negative magnetic anisotropy) are discussed. In the short distance limit, the total free energy per unit length is calculated. In this case, the magnetic dependence of total free energy is discussed.

B2 Phases and their Defect Structures: Part I.I. Ab initio Vibrational and Electronic Free Energy in the Al-Ni-Pt-Ru System

ABSTRACTIn this work, we calculate the finite temperature thermodynamic properties of the binary B2 phases in the Al-Ni-Pt-Ru system, particularly the B2 RuAl phase in the Pt-Al-Ru ternary, through the incorporation of the vibrational and electronic contributions to the total free energy. The harmonic approximation is used to consider the atomic vibrations, with the quasi-harmonic correction to account for volume expansion effects on the vibrational entropy as the temperature increases. The vibrational entropy calculations are incorporated through the supercell approach. The calculated phonon dispersion curves show that the B2 PtRu structure is mechanically unstable at low temperatures, while B2 PtAl is marginally stable. The thermal electronic contribution is added to the total free energy. Finally, the formation enthalpies and entropies of B2 RuAl are calculated as a function of temperature.

On the thermodynamic stability of clathrate hydrates

The thermodynamic stability of clathrate hydrates is investigated by theoretically examining the free energy of formation of clathrate hydrates encaging propane and argon. The total free energy is divided into several contributions: the interaction between water and guest molecules, the entropic contribution arising from the combinations of cage occupancy, and the free energy due to intermolecular vibrations. The method introduced here removes some of the assumptions of the van der Waals and Platteeuw theory. It is shown that the shift of the vibrational frequency of the host lattice destabilizes the clathrate hydrates thermodynamically. PACS No.: 61.50Ah

Fully-Finite Two-Dimensional Critical Systems: Casimir Terms and Instabilities

We review recent results for the universal part of the free energy of fully-finite two-dimensional regions at criticality. Their effect on the total free energy is considered. Including non-universal edge free energy terms leads to various Casimir instabilities toward elongation, sharp corners on the boundary, and other behavior. Universal features of certain matrix elements of the transfer matrix and corner transfer matrix are also obtained.