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 $q$-Eulerian polynomials for Weyl groups of type $D$, 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 $q$-Eulerian polynomials of type $D$, 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 $q$, and hence prove Brenti's conjecture. For $q=1$, our result reduces to the real-rootedness of the Eulerian polynomials of type $D$, 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 $D$. 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 $D$. 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

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

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