Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zeroth-mode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.Comment: 26 pages, 5 figures; submitted to Phys. Rev.

Results of an investigation of hypersonic viscous interaction effects of the space shuttle orbiter using a 0.010 scale model (51-0) in the AEDC-VKF tunnel F (OA160)

An experimental aerodynamic investigation was conducted in the AEDC-VKF Hypervelocity Wind Tunnel (Tunnel F) at a nomial Mach number of 19 to determine hypersonic viscous interaction effects on the space shuttle orbiter. The tests were conducted at an angle of attack of 30 degrees over a free-stream Reynolds number (based on fuselage length) variation from 0.1 to 0.4 million. Viscous interaction parameter was varied from 0.02 to 0.06. Six component static stability force and moment data were measured by an internally compensated internal strain gage balance. Resulting data are presented

The Application of Molecular Orbital Calculations to Wood Chemistry. II. The Protonation of Beta-Methyl Glucopyranoside

The protonation step in the acid hydrolysis reaction of beta-methyl glucopyranoside was studied by molecular orbital techniques. The semi-empirical, self-consistent fields method of modified neglect of diatomic overlap (MNDO) was used to calculate energetic and electronic information in an attempt to determine the site of initial protonation

Ordering kinetics of stripe patterns

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure

On groups and counter automata

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of rank n; this result, which answers a question of Gilman, is in a very precise sense an abelian analogue of the Muller-Schupp theorem. More generally, if G is a virtually abelian group then every group with word problem recognised by a G-automaton is virtually abelian with growth class bounded above by the growth class of G. We consider also other types of counter automata.Comment: 18 page

Properties of pattern formation and selection processes in nonequilibrium systems with external fluctuations

We extend the phase field crystal method for nonequilibrium patterning to stochastic systems with external source where transient dynamics is essential. It was shown that at short time scales the system manifests pattern selection processes. These processes are studied by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed by means of numerical simulations.Comment: 15 poages, 8 figure

Human amylase gene copy number variation as a determinant of metabolic state

Introduction Humans have multiple genes encoding amylase that are broadly divided into salivary (AMY1) and pancreatic (AMY2) genes. They exhibit some of the greatest copy numbers of any human gene, an expansion possibly driven by increased dietary starch intake. Within the population, amylase gene copy number is highly variable and there is evidence of an inverse association between AMY1 copy number and BMI. Areas covered We examine the evidence for the link between AMY1 and BMI, its potential mechanisms, and the metabolic effects of salivary and pancreatic amylase, both in the gastrointestinal tract and the blood. Expert commentary Salivary amylase may influence postprandial ‘cephalic phase’ insulin release, which improves glucose tolerance, while serum amylase may have insulin-sensitizing properties. This could explain the favorable metabolic status associated with higher AMY1 copy number. The association with BMI is harder to explain and is potentially mediated by increased flux of undigested starch into the ileum, with resultant effects on short-chain fatty acids (SCFAs), changes in gut microbiota and effects on appetite and energy expenditure in those with low copy number. Future research on the role of amylase as a determinant of metabolic health and BMI may lead to novel therapies to target obesity

Grain boundary motion in layered phases

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as $\epsilon^{-1/2}$, where $\epsilon$ is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time dependent traveling velocity of the boundary, and especially their dependence on wavenumber. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain boundary motion through curved rolls is the dominant coarsening mechanism.Comment: 16 pages, 5 figure