227,175 research outputs found
Solid-liquid interfacial premelting
We report the observation of a premelting transition at chemically sharp
solid-liquid interfaces using molecular-dynamics simulations. The transition is
observed in the solid-Al/liquid-Pb system and involves the formation of a
liquid interfacial film of Al with a width that grows logarithmically as the
bulk melting temperature is approached from below, consistent with current
theories of premelting. The premelting behavior leads to a sharp change in the
temperature dependence of the diffusion coefficient in the interfacial region,
and could have important consequences for phenomena such as particle
coalescence and shape equilibration, which are governed by interfacial kinetic
processes.Comment: 6 pages, 4 figure
Solvable Lattice Gas Models with Three Phases
Phase boundaries in p-T and p-V diagrams are essential in material science
researches. Exact analytic knowledge about such phase boundaries are known so
far only in two-dimensional (2D) Ising-like models, and only for cases with two
phases. In the present paper we present several lattice gas models, some with
three phases. The phase boundaries are either analytically calculated or
exactly evaluated.Comment: 5 pages, 6 figure
The fuzzy boundary: the spatial definition of urban areas
Cities seem to have some kind of area structure, usually distinguished in terms of land use types, socio-economic variables, physical appearance or historical and culturalcharacteristics. Is there any possibility that urban areas could in general be differentiated from the spatial perspective? What is the nature of boundaries between areas in terms of space? These questions could be approached by the analysis of internal or contextual spatial structure, or the relation between the two. Most studies on area structure however had focused in the main on the internal area with a secondaryrole for the context. Is there any way in which we could give more explicit attention to the context, following the clue that had come out of the earlier studies?This paper is to try to develop spatial techniques for identifying area boundaries, and looking at their performance in both the traditional areas, such as the Central London and the Inner City of Beijing, and the new development of the London Docklands. It focuses on explicitly exploring the properties of contextual structure in the formation ofarea boundaries rather than simply the properties of internal structure. After much experimentation, a new technique was arrived at for exploring properties of the context. Each axial line or segment in the whole map is taken as the root of a graph, and the numbers of axial lines, or segments, found with increasing radius from the root is calculated, and expressed as a rate of change. This rate of change value is thenassigned to the original axial line and expressed through bands of color. The results show strong areal effects, in that groups of neighbouring lines tend to have similar coloring, and in many cases, these suggest natural areas.Through the case studies, this paper suggests that historic areas typically have what we will call fuzzy boundaries. Fuzzy boundaries arise from the way space is structured internally and how this relates to the external structure of space. Such boundaries can be effective in supporting functional differentiation of areas or the growth of areal identities and characters, but do not depend on the area being either spatially self contained or geometrically differentiated, or having clear spatial limits. It is the relation of urban areas and their further surroundings that determine fuzzy boundaries of these urban areas
Mutual Interlacing and Eulerian-like Polynomials for Weyl Groups
We use the method of mutual interlacing to prove two conjectures on the
real-rootedness of Eulerian-like polynomials: Brenti's conjecture on
-Eulerian polynomials for Weyl groups of type , and Dilks, Petersen, and
Stembridge's conjecture on affine Eulerian polynomials for irreducible finite
Weyl groups.
For the former, we obtain a refinement of Brenti's -Eulerian polynomials
of type , and then show that these refined Eulerian polynomials satisfy
certain recurrence relation. By using the Routh--Hurwitz theory and the
recurrence relation, we prove that these polynomials form a mutually
interlacing sequence for any positive , and hence prove Brenti's conjecture.
For , our result reduces to the real-rootedness of the Eulerian
polynomials of type , which were originally conjectured by Brenti and
recently proved by Savage and Visontai.
For the latter, we introduce a family of polynomials based on Savage and
Visontai's refinement of Eulerian polynomials of type . We show that these
new polynomials satisfy the same recurrence relation as Savage and Visontai's
refined Eulerian polynomials. As a result, we get the real-rootedness of the
affine Eulerian polynomials of type . Combining the previous results for
other types, we completely prove Dilks, Petersen, and Stembridge's conjecture,
which states that, for every irreducible finite Weyl group, the affine descent
polynomial has only real zeros.Comment: 28 page
Bayesian Conditional Tensor Factorizations for High-Dimensional Classification
In many application areas, data are collected on a categorical response and
high-dimensional categorical predictors, with the goals being to build a
parsimonious model for classification while doing inferences on the important
predictors. In settings such as genomics, there can be complex interactions
among the predictors. By using a carefully-structured Tucker factorization, we
define a model that can characterize any conditional probability, while
facilitating variable selection and modeling of higher-order interactions.
Following a Bayesian approach, we propose a Markov chain Monte Carlo algorithm
for posterior computation accommodating uncertainty in the predictors to be
included. Under near sparsity assumptions, the posterior distribution for the
conditional probability is shown to achieve close to the parametric rate of
contraction even in ultra high-dimensional settings. The methods are
illustrated using simulation examples and biomedical applications
Field-ionization threshold and its induced ionization-window phenomenon for Rydberg atoms in a short single-cycle pulse
We study the field-ionization threshold behavior when a Rydberg atom is
ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are
considered. The required threshold field amplitude is found to scale
\emph{inversely} with the binding energy when the pulse duration becomes
shorter than the classical Rydberg period, and, thus, more weakly bound
electrons require larger fields for ionization. This threshold scaling behavior
is confirmed by both 3D classical trajectory Monte Carlo simulations and
numerically solving the time-dependent Schr\"{o}dinger equation. More
surprisingly, the same scaling behavior in the short pulse limit is also
followed by the ionization thresholds for much lower bound states, including
the hydrogen ground state. An empirical formula is obtained from a simple
model, and the dominant ionization mechanism is identified as a nonzero spatial
displacement of the electron. This displacement ionization should be another
important mechanism beyond the tunneling ionization and the multiphoton
ionization. In addition, an "ionization window" is shown to exist for the
ionization of Rydberg states, which may have potential applications to
selectively modify and control the Rydberg-state population of atoms and
molecules
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