Tension and stiffness of the hard sphere crystal-fluid interface

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kT/\sigma^2 with a small anisotropy of about 0.025 kT and stiffnesses with e.g. 0.53 kT/\sigma^2 for the (001) orientation and 1.03 kT/\sigma^2 for the (111) orientation. Here kT is denoting the thermal energy and \sigma the hard sphere diameter. We compare our results with existing experimental findings

A 2-Component Generalization of the Camassa-Holm Equation and Its Solutions

An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.Comment: 15 pages, 16 figures, some typos correcte

On Soliton-type Solutions of Equations Associated with N-component Systems

The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink transitions and multi-peaked soliton solutions is carried out. Transformations are used to connect these solutions to several other equations that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure

Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions

We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new.Comment: 15 page

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe

シンサイ ニツイテ タイワスル コドモ ノ テツガク ノ カノウセイ

International audienc

Local atomic order, electronic structure and electron transport properties of Cu-Zr metallic glasses

We studied atomic and electronic structures of binary Cu-Zr metallic glasses (MGs) using combined experimental and computational methods including X-ray absorption fine structure spectroscopy, electrical resistivity, thermoelectric power (TEP) measurements, molecular dynamics (MD) simulations, and ab-initio calculations. The results of MD simulations and extended X-ray absorption fine structure analysis indicate that atomic order of Cu-Zr MGs and can be described in terms of interpenetrating icosahedral-like clusters involving five-fold symmetry. MD configurations were used as an input for calculations of theoretical electronic density of states (DOS) functions which exhibits good agreement with the experimental X-ray absorption near-edge spectra. We found no indication of minimum of DOS at Fermi energy predicted by Mott's nearly free electron (NFE) model for glass-forming alloys. The theoretical DOS was subsequently used to test Mott's model describing the temperature variation of electrical resistivity and thermoelectric power of transition metal-based MGs. We demonstrate that the measured temperature variations of electrical resistivity and TEP remain in a contradiction with this model. On the other hand, the experimental temperature dependence of electrical resistivity can be explained by incipient localization of conduction electrons. It is shown that weak localization model works up to relatively high temperatures when localization is destroyed by phonons. Our results indicate that electron transport properties of Cu-Zr MGs are dominated by localization effects rather than by electronic structure. We suggest that NFE model fails to explain a relatively high glass-forming ability of binary Cu-Zr alloy

De novo lipogenesis alters the phospholipidome of esophageal adenocarcinoma

The incidence of esophageal adenocarcinoma is rising, survival remains poor, and new tools to improve early diagnosis and precise treatment are needed. Cancer phospholipidomes quantified with mass spectrometry imaging can support objective diagnosis in minutes using a routine frozen tissue section. However, whether mass spectrometry imaging can objectively identify primary esophageal adenocarcinoma is currently unknown and represents a significant challenge, as this microenvironment is complex with phenotypically similar tissue-types. Here we used desorption electrospray ionisation mass spectrometry imaging (DESI-MSI) and bespoke chemometrics to assess the phospholipidomes of esophageal adenocarcinoma and relevant control tissues. Multivariable models derived from phospholipid profiles of 117 patients were highly discriminant for esophageal adenocarcinoma both in discovery (area-under-curve = 0.97) and validation cohorts (AUC = 1). Among many other changes, esophageal adenocarcinoma samples were markedly enriched for polyunsaturated phosphatidylglycerols with longer acyl chains, with stepwise enrichment in pre-malignant tissues. Expression of fatty acid and glycerophospholipid synthesis genes was significantly upregulated, and characteristics of fatty acid acyls matched glycerophospholipid acyls. Mechanistically, silencing the carbon switch ACLY in esophageal adenocarcinoma cells shortened GPL chains, linking de novo lipogenesis to the phospholipidome. Thus, DESI-MSI can objectively identify invasive esophageal adenocarcinoma from a number of pre-malignant tissues and unveils mechanisms of phospholipidomic reprogramming. These results call for accelerated diagnosis studies using DESI-MSI in the upper gastrointestinal endoscopy suite as well as functional studies to determine how polyunsaturated phosphatidylglycerols contribute to esophageal carcinogenesis

Binary Nonlinearization of Lax pairs of Kaup-Newell Soliton Hierarchy

Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense, which also provides us with new examples of finite dimensional integrable Hamiltonian systems. A sort of involutive solutions to the Kaup-Newell hierarchy are exhibited through the obtained finite dimensional integrable systems and the general involutive system engendered by binary nonlinearization is reduced to a specific involutive system generated by mono-nonlinearization.Comment: 15 pages, plain+ams tex, to be published in Il Nuovo Cimento

On Separation of Variables for Integrable Equations of Soliton Type

We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$. In particular, we illustrate the scheme by application to modified Korteweg--de Vries (MKdV), sin(sinh)-Gordon, nonlinear Schr\"odinger, and Heisenberg magnetic equations.Comment: 22 page