Influence of hydrodynamic fluctuations on the phase transition in the E and F models of critical dynamics

We use the renormalization group method to study the E model of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using the Martin-Siggia-Rose theorem, we obtain a field theory model that allows a perturbative renormalization group analysis. By direct power counting and an analysis of ultraviolet divergences, we show that the model is multiplicatively renormalizable, and we use a two-parameter expansion in ∈ and δ to calculate the renormalization constants. Here, ∈ is the deviation from the critical dimension four, and δ is the deviation from the Kolmogorov regime. We present the results of the one-loop approximation and part of the fixedpoint structure. We briefly discuss the possible effect of velocity fluctuations on the arge-scale behavior of the model.     

Rheological properties of rubbery polymers at low shear stresses

The rheological behavior of the rubbery amorphous polymers SKB-35 (sodium-butadiene rubber), SKN-26M(butadiene-nitrile rubber), and PIB-85 (polyisobutylene) has been investigated in relation to the creep process. The tests were conducted at low shear stresses, in the constant shear stress regime, on the temperature interval from 0 to 100°C using a parallel-plate viscometer. We have shown, for the first time, by a viscometric method that in the high-elastic state rubbery polymers have a particular equilibrium structure corresponding to each temperature. A reduction in temperature leads to molecular ordering processes associated with an increase in the viscosity of the polymer. A temperature rise leads to molecular disordering and a gradual fall in viscosity. At a given temperature the two processes converge to the same value of the equilibrium viscosity. The rate of the process of equilibrium structure formation is determined not only by the temperature but also by the nature of the polymer. The higher the polarity, the more slowly the equilibrium structure is established.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 6, pp. 970–974, November–December, 1969.     

On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations

We study the degrees of freedom of several conservative computational turbulence models that are derived via a non-dissipative regularizations of the Navier-Stokes equations. For the Navier-Stokes-α, the Leray-α and the Navier-Stokes-ω equations we prove that the longtime behavior of their respective solutions is completely determined by a finite set of grid values and by a finite set of Fourier modes. For each turbulence model the number of determining nodes and of determining modes is estimated in terms of flow parameters, such as viscosity, smoothing length, forcing and domain size. These estimates are global as they do not depend on an individual solution.     

Extension of a simplified Baldwin–Lomax model to nonequilibrium turbulence: Model,analysis and algorithms

Complex turbulence not at statistical equilibrium is impossible to simulate using eddy viscosity models due to a backscatter. This research presents the way to correct the Baldwin–Lomax model for nonequilibrium effects and gives an analysis of the energy evolution in the corrected model. Furthermore, a finite element approximation of the corrected eddy model with first‐order and second‐order time discretization is also presented. A numerical test is given to support the theory.     

A spectroscopic investigation of turbulence in magnetized plasmas

We present a spectroscopic investigation of turbulence in the Tore-Supra edge plasma, where deuterium spectral lines are found to exhibit a power-law behavior in their wings. Such a feature is not predicted by the equilibrium line broadening theory in the conditions of the edge plasma, where the thermal Stark effect is negligible. Therefore, the possible role of turbulence is investigated along two separate paths. Indeed, both the Stark and the Doppler profiles may differ significantly from the equilibrium profiles.     

Intermittency in flux driven kinetic simulations of trapped ion turbulence

Flux driven kinetic transport is analysed for deeply trapped ion turbulence with the code GYSELA. The main observation is the existence of a steady state situation with respect to the statistics, in particular the balance between the injected energy and the time averaged energy flowing out through the outer edge boundary layer. The temperature is characterised by a very bursty behaviour with a skewed PDF. Superimposed to these short time scale fluctuations, one finds a regime with a strong increase of the zonal flows and a quenching of the turbulent energy. During this phase of such a predator-prey cycle, the core temperature rapidly increases while the edge temperature gradually decreases. The end of this reduced transport regime is governed by the onset of turbulence that governs large relaxation events, and a strong modification of the zonal flow pattern.     

交易者行为倾向与股市波动形态

分析一个具有基础价值均衡、非基础价值均衡、周期和混沌等四种市场波动形态的随机多主体股市模型,利用理论分析和数值实验的方法研究交易者模仿学习、价格追踪和策略转移三种行为倾向对股市场波动形态的影响,得出结论:当三类行为倾向都很小时,股市处于基础价值均衡形态;随着价格追踪和模仿学习倾向逐渐增大,股市进入周期形态;当模仿学习倾向足够大时,系统处于非基础价值均衡形态;混沌形态出现在周期和非基础价值均衡形态中间很窄的参数范围.     

Path-space moderate deviations for a class of Curie–Weiss models with dissipation

We modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic approach based on the convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase we are considering and, moreover, their behavior may be influenced by the choice of the rates.     

反映强流动曲率效应的非线性湍流模型

首先定性地分析了流线曲率效应对流场湍流结构的影响,然后以U型槽道流为典型算例,对多种湍流模型进行了评估．评估的模型包括:线性涡粘性模型,二阶和三阶非线性涡粘性模型,二阶显式代数应力模型和Reynolds应力模型．评估结果表明,性能良好的三阶非线性涡粘性模型,如黄于宁等人发展的HM模型以及CLS模型,可以较好地描述流线的曲率效应对湍流结构的影响,如凸曲率作用下内壁附近湍流强度的衰减和凹曲率作用下外壁附近湍流的增强,并且较好地确定了管道下游的分离点位置和分离泡长度,其预测的结果和实验符合较好,与Reynolds力模型的结果十分接近,因此可以较好地应用于具有曲率效应的工程湍流的计算．     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Boundary layer problem: Navier–Stokes equations and Euler equations

This work is concerned with the boundary layer turbulence, which is an outstanding problem in fluid mechanics. We consider an incompressible viscous fluid in 2D domains with permeable walls. The permeability is described by the Yudovich condition. The goal of the article is to study the fluid behavior at vanishing viscosity (large Reynold’s numbers). We show that the vanishing viscous limit is a solution of the Euler equations with the Yudovich condition on the inflow region of the boundary.     

Numerical calculation of turbulent corner flows

Numerical predictions are presented of the hydrodynamic characteristics of developing and fully-developed turbulent flow in a square duct. The turbulent stresses in the plane of the cross-section, gradients of which cause the familiar secondary flows, are approximated by gradients in the axial mean velocity. Two distinct approximations are investigated, one of which specifies some of the model ‘constants’ as functions of the gradient of the length scale to account for wall effects. The stresses in the axial momentum equation are calculated from an eddy viscosity deduced from the K-W model of turbulence, K being the turbulence energy and W, a measure of the time-mean-square-vorticity fluctuations. The approximation incorporating wall effects generally performs better than the other when compared with fully-developed flow-data. This same approximation also compares favourably with data for developing flow and predictions based on K-? models in the literature.     

Temperature Green’s functions in Fermi systems: The superconducting phase transition

We consider the model of an equilibrium Fermi system of arbitrary-spin particles with the density-densitytype interaction. Based on the microscopic Hamiltonian in the formalism of temperature Green’s functions, we find critical modes and construct an effective action describing a neighborhood of the phase transition point. A renormalization group analysis of the obtained model leads to the standard critical behavior indices for spin-1/2 fermions but shows that in the system of higher-spin fermions, a first-order phase transition occurs whose temperature exceeds the standard estimates for the temperature of a second-order phase transition.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Plastic flow in very low temperature regime within annular micropores

The rate of deformation for glassy (amorphous) matter confined in microscopic domain at very low temperature regime was investigated using a rate-state-dependent model considering the shear thinning behavior which means, once material being subjected to high shear rates, the viscosity diminishes with increasing shear rate. The preliminary results show that there might be the enhanced rate of deformation and (shear) yield stress due to the almost vanishing viscosity in micropores subjected to some surface conditions: The relatively larger roughness (compared to the macroscopic domain) inside micropores and the slip. As the pore size decreases, the surface-to-volume ratio increases and therefore, surface roughness will greatly affect the (plastic) flow in micropores. By using the boundary perturbation method, we obtained a class of microscopic fields for the rate of deformation and yield stress at low temperature regime with the presumed small wavy roughness distributed along the walls of an annular micropore.     

Fractals in the open quantum kicked top model

Fractals are one of the most important features of the classically chaotic systems. We analyze the fractal phenomena in a quantum chaos system in terms of its fidelity and dynamical localization properties in the paper. We show that, even in the open and dissipative quantum kicked top model, the fidelity displays fractal fluctuations if the underlying dynamics is in the classically chaotic regime. Moreover, the fluctuations of the inverse participation ratio which characterize the dynamical localization behavior also exhibit fractality. The relations between the fractal dimensions and the decoherence rates are explored.     

Numerical Investigation of the Interaction of Turbulent Wind Flow and Elastic Structures

The Interaction between wind flow and structures plays an important role in the computation of civil engineering application. In case of gravity prestressed membrane roofs, the wind lifting forces may exceed the dead load leading to high amplitude structural oscillations, which interact with the flow field. To investigate the interaction a consistent discretization method based on stabilized space‐time finite elements is applied. The flow field is modeled with the incompressible Reynolds Averaged Navier‐Stokes (RANS) equations with an anisotropic eddy‐viscosity turbulence model. The structural motion is described with the theory for geometrically nonlinear elastic deformation behavior, a strong coupling algorithm for the time‐dependent fluid‐structure interaction is implemented. Two applications show the capability of the turbulence model in representing the anisotropic turbulence structure, the differences in the flow field over a bluff body between two configurations representing a rigid and an elastic membrane roof, discusses the structural responses of the roof at a high Reynolds number. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems

We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a φ ³ critical dynamics model describing universal properties of metastable states in the vicinity of a firstorder phase transition and a reaction-diffusion system near the point of a second-order transition between fluctuation and absorption states (a simple epidemic process or the Gribov process). In both cases, we demonstrate the existence of a new strongly nonequilibrium, anisotropic scaling regime (universality class) for which both the mixing and the nonlinearity in the order parameter are relevant. We evaluate the corresponding critical dimensions in the one-loop approximation of the renormalization group.