Effects of Patterned Substrate on Thin Films Simulated by Family Model

Patterned substrate growth has been a subject of much interest. In this work, characteristics of some statistical properties of a film grown on triangular and vicinal substrates using the Family model are studied. Substrate size and tilt angle are varied. It is found that the interface width and the correlation function increase as the roughness of the pattern is increased. The new scaling exponents are calculated and anomalous scaling is obtained. The transient persistence probability does not show a power law relation when the initial surface is sufficiently rough. The initial rough surface also causes multifractal behavior in the model.

Homogeneous isotropic superfluid turbulence in two dimensions: Inverse and forward cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the simplified, Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normalfluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli.

Calculations of longitudinal and transverse velocity structure functions using a vortex model of isotropic turbulence

The longitudinal structure function (LSF) and the transverse structure function (TSF) in isotropic turbulence are calculated using a vortex model. The vortex model is composed of the Rankine and Burgers vortices which have the exponential distributions in the vortex Reynolds number and vortex radii. This model exhibits a power law in the inertial range and satisfies the minimal condition of isotropy that the second-order exponent of the LSF in the inertial range is equal to that of the TSF. Also observed are differences between longitudinal and transverse structure functions caused by intermittency. These differences are related to their scaling differences which have been previously observed in experiments and numerical simulations.

A Simple Model For Predicting The Void Fraction Of Gas/Non-Newtonian Fluid Intermittent Flows In Upward Inclined Pipes

In this work, a simple correlation, which incorporates the mixture velocity, drift velocity, and the correction factor of Farooqi and Richardson, was proposed to predict the void fraction of gas/non-Newtonian intermittent flow in upward inclined pipes. The correlation was based on 352 data points covering a wide range of flow rates for different CMC solutions at diverse angles. A good agreement was obtained between the predicted and experimental results. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase intermittent flows.

Magnetic shielding properties of high- Tc superconducting hollow cylinders: Model combining experimental data for axial and transverse magnetic field configurations

Magnetic shielding efficiency was measured on high- Tc superconducting hollow cylinders subjected to either an axial or a transverse magnetic field in a large range of field sweep rates, dBapp/dt. The behaviour of the superconductor was modelled in order to reproduce the main features of the field penetration curves by using a minimum number of free parameters suitable for both magnetic field orientations. The field penetration measurements were carried out on Pb-doped Bi-2223 tubes at 77K by applying linearly increasing magnetic fields with a constant sweep rate ranging between 10νTs-1 and 10mTs-1 for both directions of the applied magnetic field. The experimental curves of the internal field versus the applied field, Bin(Bapp), show that, at a given sweep rate, the magnetic field for which the penetration occurs, Blim, is lower for the transverse configuration than for the axial configuration. A power law dependence with large exponent, n′, is found between Blim and dBapp/dt. The values of n′ are nearly the same for both configurations. We show that the main features of the curves B in(Bapp) can be reproduced using a simple 2D model, based on the method of Brandt, involving a E(J) power law with an n-exponent and a field-dependent critical current density, Jc(B), (following the Kim model: Jc = Jc0(1+B/B1)-1). In particular, a linear relationship between the measured n′-exponents and the n-exponent of the E(J) power law is suggested by taking into account the field dependence of the critical current density. Differences between the axial and the transverse shielding properties can be simply attributed to demagnetizing fields. © 2009 IOP Publishing Ltd.

Strain gradient theory based on a new framework of non-local model

A new framework of non-local model for the strain energy density is proposed in this paper. The global strain energy density of the representative volume element is treated as a non-local variable and can be obtained through a special integral of the local strain energy density. The local strain energy density is assumed to be dependent on both the strain and the rotation-gradient. As a result of the non-local model, a new strain gradient theory is derived directly, in which the first and second strain gradients, as well as the triadic and tetradic stress, are introduced in the context of work conjugate. For power law hardening materials, size effects in thin metallic wire torsion and ultra-thin cantilever beam bend are investigated. It is found that the result predicted by the theoretical model is well consistent with the experimental data for the thin wire torsion. On the other hand, the calculation result for the micro-cantilever beam bend clearly shows the size effect.

Temperature dependence of the distribution of the first passage time: Results from discontinuous molecular dynamics simulations of an all-atom model of the second beta-hairpin fragment of protein G

More than 22 000 folding kinetic simulations were performed to study the temperature dependence of the distribution of first passage time (FPT) for the folding of an all-atom Go-like model of the second beta-hairpin fragment of protein G. We find that the mean FPT (MFPT) for folding has a U (or V)-shaped dependence on the temperature with a minimum at a characteristic optimal folding temperature T-opt*. The optimal folding temperature T-opt* is located between the thermodynamic folding transition temperature and the solidification temperature based on the Lindemann criterion for the solid. Both the T-opt* and the MFPT decrease when the energy bias gap against nonnative contacts increases. The high-order moments are nearly constant when the temperature is higher than T-opt* and start to diverge when the temperature is lower than T-opt*. The distribution of FPT is close to a log-normal-like distribution at T* greater than or equal to T-opt*. At even lower temperatures, the distribution starts to develop long power-law-like tails, indicating the non-self-averaging intermittent behavior of the folding dynamics. It is demonstrated that the distribution of FPT can also be calculated reliably from the derivative of the fraction not folded (or fraction folded), a measurable quantity by routine ensemble-averaged experimental techniques at dilute protein concentrations.

Self-organized Criticality Model for Ocean Internal Waves

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality (SOC). The oscillations of the water blocks in the model display power-law behavior with an exponent of -2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2(1972) 225; J. Geophys. REs. 80 (1975) 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed.

A Quantitative Evaluation of the AVITEWRITE Model of Handwriting Learning

Much sensory-motor behavior develops through imitation, as during the learning of handwriting by children. Such complex sequential acts are broken down into distinct motor control synergies, or muscle groups, whose activities overlap in time to generate continuous, curved movements that obey an intense relation between curvature and speed. The Adaptive Vector Integration to Endpoint (AVITEWRITE) model of Grossberg and Paine (2000) proposed how such complex movements may be learned through attentive imitation. The model suggest how frontal, parietal, and motor cortical mechanisms, such as difference vector encoding, under volitional control from the basal ganglia, interact with adaptively-timed, predictive cerebellar learning during movement imitation and predictive performance. Key psycophysical and neural data about learning to make curved movements were simulated, including a decrease in writing time as learning progresses; generation of unimodal, bell-shaped velocity profiles for each movement synergy; size scaling with isochrony, and speed scaling with preservation of the letter shape and the shapes of the velocity profiles; an inverse relation between curvature and tangential velocity; and a Two-Thirds Power Law relation between angular velocity and curvature. However, the model learned from letter trajectories of only one subject, and only qualitative kinematic comparisons were made with previously published human data. The present work describes a quantitative test of AVITEWRITE through direct comparison of a corpus of human handwriting data with the model's performance when it learns by tracing human trajectories. The results show that model performance was variable across subjects, with an average correlation between the model and human data of 89+/-10%. The present data from simulations using the AVITEWRITE model highlight some of its strengths while focusing attention on areas, such as novel shape learning in children, where all models of handwriting and learning of other complex sensory-motor skills would benefit from further research.

The VITEWRITE Model of Handwriting Production

This article describes the VITEWRITE model for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in the outflow command to a given synergy occurs. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. Each synergy exhibits a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

A Neural Network Model for Cursive Script Production

This article describes a neural network model, called the VITEWRITE model, for generating handwriting movements. The model consists of a sequential controller, or motor program, that interacts with a trajectory generator to move a. hand with redundant degrees of freedom. The neural trajectory generator is the Vector Integration to Endpoint (VITE) model for synchronous variable-speed control of multijoint movements. VITE properties enable a simple control strategy to generate complex handwritten script if the hand model contains redundant degrees of freedom. The proposed controller launches transient directional commands to independent hand synergies at times when the hand begins to move, or when a velocity peak in a given synergy is achieved. The VITE model translates these temporally disjoint synergy commands into smooth curvilinear trajectories among temporally overlapping synergetic movements. The separate "score" of onset times used in most prior models is hereby replaced by a self-scaling activity-released "motor program" that uses few memory resources, enables each synergy to exhibit a unimodal velocity profile during any stroke, generates letters that are invariant under speed and size rescaling, and enables effortless. connection of letter shapes into words. Speed and size rescaling are achieved by scalar GO and GRO signals that express computationally simple volitional commands. Psychophysical data concerning band movements, such as the isochrony principle, asymmetric velocity profiles, and the two-thirds power law relating movement curvature and velocity arise as emergent properties of model interactions.

A material model for multiaxial stretching and stress relaxation of polypropylene under process conditions

Polypropylene sheets have been stretched at 160 °C to a state of large biaxial strain of extension ratio 3, and the stresses then allowed to relax at constant strain. The state of strain is reached via a path consisting of two sequential planar extensions, the second perpendicular to the first, under plane stress conditions with zero stress acting normal to the sheet. This strain path is highly relevant to solid phase deformation processes such as stretch blow moulding and thermoforming, and also reveals fundamental aspects of the flow rule required in the constitutive behaviour of the material. The rate of decay of stress is rapid, and such as to be highly significant in the modelling of processes that include stages of constant strain. A constitutive equation is developed that includes Eyring processes to model both the stress relaxation and strain rate dependence of the stress. The axial and transverse stresses observed during loading show that the use of a conventional Levy-Mises flow rule is ineffective, and instead a flow rule is used that takes account of the anisotropic state of the material via a power law function of the principal extension ratios. Finally the constitutive model is demonstrated to give quantitatively useful representation of the stresses both in loading and in stress relaxation.

A review of power laws in real life phenomena

Power law distributions, also known as heavy tail distributions, model distinct real life phenomena in the areas of biology, demography, computer science, economics, information theory, language, and astronomy, amongst others. In this paper, it is presented a review of the literature having in mind applications and possible explanations for the use of power laws in real phenomena. We also unravel some controversies around power laws.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.