2,481 research outputs found
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
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
Block partitions: an extended view
Given a sequence , a block of is a
subsequence . The size of a block is the sum
of its elements. It is proved in [1] that for each positive integer , there
is a partition of into blocks with for every . In this paper, we consider a generalization of the problem
in higher dimensions
Environmentally conscious consumption patterns in Hungarian households
This article provides a comprehensive review of the literature on the theoretical aspects of sustainable consumption. The conditions for consumers’ social responsibility and the formation of environmentally conscious behavior patterns will also be discussed, along with possible methods for motivating behavioral changes. The authors have completed a primary research study with the purpose of surveying environmentally conscious consumption patterns in Hungary. They also examined how the provision of appropriate information and the raising of awareness might encourage sustainable consumption. According to their findings, the respondents’ knowledge on environmentally conscious behavior was rather limited, and reinforcement was needed in identifying appropriate activity alternatives. This paper provides a summary of the qualitative research phase which employed in-depth interviews, logging and focus groups. The consecutive application of these methods enabled the authors to keep track of the process and the consequences of raising awareness
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 .
While the maximum free energy corresponds to the
orientation for all values, the minimum is realized by the direction for small , and by the orientation for higher . 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 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
Sums of products of Ramanujan sums
The Ramanujan sum is defined as the sum of -th powers of the
primitive -th roots of unity. We investigate arithmetic functions of
variables defined as certain sums of the products
, where are polynomials with
integer coefficients. A modified orthogonality relation of the Ramanujan sums
is also derived.Comment: 13 pages, revise
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