Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

A Ferroelectric Frequency-Doubling Material-Potassium Lithium Niobate

The potassium lithium niobate crystals have been grown up. The shapes of solid-melt interfaces which maintaining the steady growth of the potassium lithium niobate crystals have been described. The optical transmission spectrum of the crystal has been surveyed. The perfected crystals showed good Second Harmonic Generation properties.     

s-wave bound and scattering state wave functions for a velocity-dependent Kisslinger potential

A relation linking the normalized s-wave scattering and the corresponding bound state wave functions at bound state poles is derived. This is done in the case of a non-local, velocity-dependent Kisslinger potential. Using formal scattering theory, we present two analytical proofs of the validity of the theorem. The first tackles the non-local potential directly, while the other transforms the potential to an equivalent local but energy-dependent one. The theorem is tested both analytically and numerically by solving the Schr?dinger equation exactly for the scattering and bound state wave functions when the Kisslinger potential has the form of a square well. A first order approximation to the deviation from the theorem away from bound state poles is obtained analytically. Furthermore, a proof of the analyticity of the Jost solutions in the presence of a non-local potential term is also given. Received: 3 March 2001 / Accepted: 9 June 2001     

The First in Vivo Observation of C–N Coupling in Mammalian Brain

[5-¹³C,¹⁵N]Glutamine, with ¹J(¹³C–¹⁵N) of 16 Hz, was observed in vivo in the brain of spontaneously breathing rats by ¹³C MRS at 4.7 T. The brain [5-¹³C]glutamine peak consisted of the doublet from [5-¹³C,¹⁵N]glutamine and the center [5-¹³C,¹⁴N]glutamine peak, resulting in an apparent triplet with a separation of 8 Hz. The time course of formation of brain [5-¹³C,¹⁵N]glutamine was monitored in vivo with a time resolution of 20–35 min. This [5-¹³C,¹⁵N]glutamine was formed by glial uptake of released neurotransmitter [5-¹³C]glutamate and its reaction with ¹⁵NH₃ catalyzed by the glia-specific glutamine synthetase. The neurotransmitter glutamate C5 was selectively¹³C-enriched by intravenous [2,5-¹³C]glucose infusion to ¹³C-label whole-brain glutamate C5, followed by [¹²C]glucose infusion to chase ¹³C from the small and rapidly turning-over glial glutamate pool, leaving ¹³C mainly in the neurotransmitter [5-¹³C]glutamate pool, which is sequestered in vesicles until release. Hence, the observed [5-¹³C,¹⁵N]glutamine arises from a coupling between ¹³C of neuronal origin and ¹⁵N of glial origin. Measurement of the rate of brain [5-¹³C,¹⁵N]glutamine formation provides a novel noninvasive method of studying the kinetics of neurotransmitter uptake into glia in vivo, a process that is crucial for protecting the brain from glutamate excitotoxicity.     

Molecular dynamics simulations of the freezing of gold nanoparticles

A set of molten gold clusters, each with 1157 gold atoms, was studied by molecular dynamics simulations as the clusters underwent freezing at three different temperatures. Most of the clusters attained an icosahedral structure upon freezing, a structure found to be stable to mild annealing. Other structures observed were imperfect truncated decahedral, truncated octahedral and hexagonal close packed structures. The role of kinetics in the process of cluster solidification is discussed. Received 6 November 2000     

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the lamellar and L₃ sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface. Received 4 November 1998     

Statistical mechanics of money: how saving propensity affects its distribution

We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. Analogous to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the saving propensity of the agents on the stationary or equilibrium probability distribution of money. When the agents do not save, the equilibrium money distribution becomes the usual Gibb's distribution, characteristic of non-interacting agents. However with saving, even for individual self-interest, the dynamics becomes cooperative and the resulting asymmetric Gaussian-like stationary distribution acquires global ordering properties. Intriguing singularities are observed in the stationary money distribution in the market, as functions of the marginal saving propensity of the agents. Received 2 May 2000     

Raman scattering of Ge dot superlattices

Self-organised Ge dot superlattices grown by molecular beam epitaxy of Ge and Si layers utilizing Stranski-Krastanov growth mode were investigated by Raman spectroscopy. An average size of Ge quantum dots was obtained from transmission electron microscopy measurements. The strain and interdiffusion of Ge and Si atoms in Ge quantum dots were estimated from the analysis of frequency positions of optical phonons observed in the Raman spectra. Raman scattering by folded longitudinal acoustic phonons in the Ge dot superlattices was observed and explained using of elastic continuum theory. Received 25 January 2000     

Critical properties of the double-frequency sine-Gordon model with applications

We study the properties of the double-frequency sine-Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalized lattice quantum Ashkin–Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential.     

The Kolmogorov–Riesz compactness theorem

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly's theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.