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.

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

DDFT calibration and investigation of an anisotropic phase-field crystal model

The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation. Further its morphology diagram is explored. In particular we investigated the influence of anisotropy and undercooling on the process of nucleation and microstructure formation from atomic to the microscale. To that end numerical simulations were performed varying those dimensionless parameters which represent anisotropy and undercooling in our anisotropic phase-field crystal (APFC) model. The results from these numerical simulations are summarized in terms of a morphology diagram of the stable state phase. These stable phases are also investigated with respect to their kinetics and characteristic morphological features.Comment: It contain 13 pages and total of 7 figure

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

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

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

Interviewing suspects: examining the association between skills, questioning, evidence disclosure, and interview outcomes

The interviewing of suspects is an important element in the investigation of crime. However, studies concerning actual performance of investigators when undertaking such interviews remain sparse. Nevertheless, in England and Wales, since the introduction of a prescribed framework over 20 years ago, field studies have generally shown an improvement in interviewing performance, notwithstanding ongoing concerns largely relating to the more demanding aspects (such as building/maintaining rapport, intermittent summarising and the logical development of topics). Using a sample of 70 real-life interviews, the present study examined questioning and various evidence disclosure strategies (which have also been found demanding), examining their relationships between interview skills and interview outcomes. It was found that when evidence was disclosed gradually (but revealed later), interviews were generally both more skilled and involved the gaining of comprehensive accounts, whereas when evidence was disclosed either early or very late, interviews were found to be both less skilled and less likely to involve this outcome. These findings contribute towards an increased research base for the prescribed framework

Evaluation of early and late presentation of patients with ocular mucous membrane pemphigoid to two major tertiary referral hospitals in the United Kingdom

PURPOSE: Ocular mucous membrane pemphigoid (OcMMP) is a sight-threatening autoimmune disease in which referral to specialists units for further management is a common practise. This study aims to describe referral patterns, disease phenotype and management strategies in patients who present with either early or established disease to two large tertiary care hospitals in the United Kingdom.\ud \ud PATIENTS AND METHODS: In all, 54 consecutive patients with a documented history of OcMMP were followed for 24 months. Two groups were defined: (i) early-onset disease (EOD:<3 years, n=26, 51 eyes) and (ii) established disease (EstD:>5 years, n=24, 48 eyes). Data were captured at first clinic visit, and at 12 and 24 months follow-up. Information regarding duration, activity and stage of disease, visual acuity (VA), therapeutic strategies and clinical outcome were analysed.\ud \ud RESULTS: Patients with EOD were younger and had more severe conjunctival inflammation (76% of inflamed eyes) than the EstD group, who had poorer VA (26.7%=VA<3/60, P<0.01) and more advanced disease. Although 40% of patients were on existing immunosuppression, 48% required initiation or switch to more potent immunotherapy. In all, 28% (14) were referred back to the originating hospitals for continued care. Although inflammation had resolved in 78% (60/77) at 12 months, persistence of inflammation and progression did not differ between the two phenotypes. Importantly, 42% demonstrated disease progression in the absence of clinically detectable inflammation.\ud \ud CONCLUSIONS: These data highlight that irrespective of OcMMP phenotype, initiation or escalation of potent immunosuppression is required at tertiary hospitals. Moreover, the conjunctival scarring progresses even when the eye remains clinically quiescent. Early referral to tertiary centres is recommended to optimise immunosuppression and limit long-term ocular damage.\ud \u

Oxygen cost of dynamic or isometric exercise relative to recruited muscle mass

BACKGROUND: Oxygen cost of different muscle actions may be influenced by different recruitment and rate coding strategies. The purpose of this study was to account for these strategies by comparing the oxygen cost of dynamic and isometric muscle actions relative to the muscle mass recruited via surface electrical stimulation of the knee extensors. METHODS: Comparisons of whole body pulmonary Δ [Formula: see text] O(2 )were made in seven young healthy adults (1 female) during 3 minutes of dynamic or isometric knee extensions, both induced by surface electrical stimulation. Recruited mass was quantified in T(2 )weighted spin echo magnetic resonance images. RESULTS: The Δ [Formula: see text] O(2 )for dynamic muscle actions, 242 ± 128 ml • min(-1 )(mean ± SD) was greater (p = 0.003) than that for isometric actions, 143 ± 99 ml • min(-1). Recruited muscle mass was also greater (p = 0.004) for dynamic exercise, 0.716 ± 282 versus 0.483 ± 0.139 kg. The rate of oxygen consumption per unit of recruited muscle ([Formula: see text]) was similar in dynamic and isometric exercise (346 ± 162 versus 307 ± 198 ml • kg(-1 )• min(-1); p = 0.352), but the [Formula: see text] calculated relative to initial knee extensor torque was significantly greater during dynamic exercise 5.1 ± 1.5 versus 3.6 ± 1.6 ml • kg(-1 )• Nm(-1 )• min(-1 )(p = 0.019). CONCLUSION: These results are consistent with the view that oxygen cost of dynamic and isometric actions is determined by different circumstances of mechanical interaction between actin and myosin in the sarcomere, and that muscle recruitment has only a minor role