PREDICTION BY EÖTVÖS´ TORSION BALANCE DATA IN HUNGARY

Possible geodetic applications of Eötvös´ torsion balance gravity gradient data were investigated in the present study. As a practical example gravity data have been predicted for two test areas in Hungary with the method of least squares collocation. By evaluating the results with gridded data interpolated from gravity measurements the standard deviation of differences ± 1-1.7 mGal was found which proves the usability of such gradient data for geodetic applications

Nonlinear hydrodynamic theory of crystallization

We present an isothermal fluctuating nonlinear hydrodynamic theory of crystallization in molecular liquids. A dynamic coarse-graining technique is used to derive the velocity field, a phenomenology, which allows a direct coupling between the free energy functional of the classical Density Functional Theory and the Navier-Stokes equation. Contrary to the Ginzburg-Landau type amplitude theories, the dynamic response to elastic deformations is described by parameter-free kinetic equations. Employing our approach to the free energy functional of the Phase-Field Crystal model, we recover the classical spectrum for the phonons and the steady-state growth fronts. The capillary wave spectrum of the equilibrium crystal-liquid interface is in a good qualitative agreement with the molecular dynamics simulations

A statistical mechanical approach to fluid dynamics: Thermodynamically consistent equations for simple dissipative fluids

In this paper, a statistical mechanical derivation of thermodynamically consistent fluid dynamical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on the combination of key concepts from earlier works, including the Dirac-delta formalism of Irving and Kirkwood, the identity of statistical physical ensemble averages by Khinchin, and a first-order Taylor expansion around the leading-order solution of the Chapman-Enskog theory. The non-equilibrium thermodynamic quantities and constitutive relations directly emerge in the proposed coarse-graining process, which results in a completion of the phenomenological theory. We show that (i) the variational form of the thermodynamic part of the reversible stress is already encoded on the level of the Hamiltonian many-body problem, (ii) the dynamics monotonically maximizes the entropy at constant energy, and (iii) that the phenomenological energy balance equation obtained in the adiabatic approximation lacks the contribution of non-local interactions, which is crucial in modelling the gas-liquid transition in near-critical fluids

Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region

The official version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsIn the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.This work has been supported by the Hungarian Academy of Sciences under contract No. OTKA-K-62588 and by the ESA PECS Nos. 98021 and 98043

Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model

The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range $\epsilon\in\left[0,0.5\right]$. While the maximum free energy corresponds to the $\left\{ 100\right\}$ orientation for all $\epsilon$ values, the minimum is realized by the $\left\{ 111\right\}$ direction for small $\epsilon\,(<0.13)$, and by the $\left\{ 211\right\}$ orientation for higher $\epsilon$. The predicted dependence on the reduced temperature is consistent with the respective mean field critical exponent. The results are fitted with an eight-term Kubic harmonic series, and are used to create stereographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing $\epsilon$ from sphere to a polyhedral form that differs from the rhombo-dodecahedron obtained previously by growing a bcc seed until reaching equilibrium with the remaining liquid