Active and passive scalar intermittent statistics in turbulent atmospheric convection

We study the small-scale statistics of active and passive scalar fields, obtained from 3D large-eddy simulations of the atmospheric boundary layer turbulence. The velocity field is anisotropic and inhomogeneous, due to the action of both buoyancy and shear. We focus on scalar field rare fluctuations dominated by the so-called fronts. Temperature, coupled to the velocity field by the Boussinesq equations, exhibits anomalous scaling and saturation of the scaling exponents to a constant value, due to the presence of thermal fronts. Although qualitatively similar, the small-scale statistics of a passive tracer advected by the convective flow shows quantitative differences: the large fluctuations of the tracer concentration field distribute differently and appear to be less intermittent than the temperature ones. To better understand these results, the role of boundaries in this problem is discussed.     

Multiscale SOC in turbulent convection

Using data obtained in a laboratory thermal convection experiment at high Rayleigh numbers, it is shown that the multiscaling properties of the observed mean wind reversals are quantitatively consistent with analogous multiscaling properties of the Bak–Tang–Wiesenfeld prototype model of self-organized criticality in two dimensions.     

Multilayer modeling of radiative transfer by SLW and CW methods in non-isothermal gaseous medium

Non-isothermal gaseous medium is modeled using the multilayer approach, breaking the one-dimensional system into a series of isothermal layers. Spectral integration of the radiative transfer equation (RTE) is performed for the spectral line weighted-sum-of-gray-gases and cumulative wavenumber approaches to modeling the spectral nature of the gas radiation. An exact analytical solution of RTE is obtained for the layers with both black and gray walls. Predictions show high accuracy, even with surprisingly few layers.     

Chaotic diffusion for particles moving in a time dependent potential well

The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and; (ii) by the solution of the diffusion equation. The dynamic of the diffusing particles is made by the use of a two dimensional, nonlinear area preserving map for the variables energy and time. The phase space of the system is mixed containing both chaos, periodic regions and invariant spanning curves limiting the diffusion of the chaotic particles. The chaotic evolution for an ensemble of particles is treated as random particles motion and hence described by the diffusion equation. The boundary conditions impose that the particles can not cross the invariant spanning curves, serving as upper boundary for the diffusion, nor the lowest energy domain that is the energy the particles escape from the time moving potential well. The diffusion coefficient is determined via the equation of the mapping while the analytical solution of the diffusion equation gives the probability to find a given particle with a certain energy at a specific time. The momenta of the probability describe qualitatively the behavior of the average energy obtained by numerical simulation, which is investigated either as a function of the time as well as some of the control parameters of the problem.     

Recent fluid deformation closure for velocity gradient tensor dynamics in turbulence: Timescale effects and expansions

In order to model pressure and viscous terms in the equation for the Lagrangian dynamics of the velocity gradient tensor in turbulent flows, Chevillard & Meneveau [L. Chevillard, C. Meneveau, Lagrangian dynamics and geometric structure of turbulence, Phys. Rev. Lett. 97 (174501) (2006) 1-4] introduced the Recent Fluid Deformation closure. Using matrix exponentials, the closure allows us to overcome the unphysical finite-time blow-up of the well-known Restricted Euler model. However, it also requires the specification of a decorrelation timescale of the velocity gradient along the Lagrangian evolution, and when the latter is chosen too short (or, equivalently, the Reynolds number is too high), the model leads to unphysical statistics. In the present paper, we explore the limitations of this closure by means of numerical experiments and analytical considerations. We also study the possible effects of using time-correlated stochastic forcing instead of the previously employed white-noise forcing. Numerical experiments show that reducing the correlation timescale specified in the closure and in the forcing does not lead to a commensurate reduction of the autocorrelation timescale of the predicted evolution of the velocity gradient tensor. This observed inconsistency could explain the unrealistic predictions at increasing Reynolds numbers. We perform a series expansion of the matrix exponentials in powers of the decorrelation timescale, and we compare the full original model with a linearized version. The latter is not able to extend the limits of applicability of the former but allows the model to be cast in terms of a damping term whose sign gives additional information about the stability of the model as a function of the second invariant of the velocity gradient tensor.     

Single-scale wavelet representation of turbulence dynamics: Formulation and Navier-Stokes regularity

The ‘triad interactions’, arising from the spectral resolution of the nonlinear terms in the Navier-Stokes equations, have so far not been substantially modified in the wavelet representation. In this paper, the multiscale interactions are captured by exact expressions evaluated at a single scale of the Mexican hat wavelet coefficients: the larger-scale terms as a volume integral of nearby wavelet coefficients, and the smaller-scale contributions as iterated Laplacians of the coefficient at the point of interest. As a result, the Navier-Stokes equations are expressed exactly at a single scale. This facilitates the evaluation of the dominant Hölder exponent near singularities. From the scaling properties of wavelet coefficients, it is shown that Euler dynamics would generate stronger singularities for any h<1, but that viscous dynamics would not unless h<−1 (a discontinuous case). We discuss how this conclusion could be affected by boundary conditions.     

永磁体在磁流体中的磁力学建模及自悬浮位置可控性

以球形永磁体和球形容器为对象,推导出永磁体磁浮力模型,分析磁导率、永磁体的剩余磁化强度和永磁体半径、容器半径以及永磁体相对于容器中心位置的位移对磁场力的影响,结论具有一定普遍性.计算结果表明各参数均遵循一定规律对磁场力产生影响,始终有满足自悬浮现象的条件存在.通过对悬浮平衡位置特征分析,论述各变化参数与自悬浮位置的关系,并讨论实现自悬浮位置的可控性途径. 关键词： 磁流体 磁场力模型 自悬浮     

Scaling laws and the modern city

The inter-relations and the complexity of modern urban spaces are difficult to analyse in a way that allows improving living conditions or help to ascertain optimal decisions for saving energy or improving sustainability. Carefully designed decisions and guidelines might produce unexpected results because of particularities, or complex sets of reactions from residents or economic counterparts. Complexity tends to increase with size, such as when, for instance, services tend to concentrate in large agglomerations, and transportation needs take on critical importance. Complex systems such as living organisms are known to follow approximate relationships as scaling laws between the variables that describe them. Some of these kinds of relationships are tested in relation to modern developed urban spaces, in which it is possible to find a reasonable continuity with the types of scales seen in living organisms, and some preliminary conclusions are drawn.     

Scaling analysis of the magnetocaloric effect in Gd5Si2Ge1.9X0.1 (X=Al, Cu, Ga, Mn, Fe, Co)

The field dependence of the magnetic entropy change has been studied for a series of doped Gd₅Si₂Ge₂ alloys, which possess a magnetic phase transition that is either entirely second order or a combination of primarily second-order mixed to a very minor degree with a first-order transition arising from a magneto-structural phase change. By analyzing the field scaling of the refrigerant capacity as well as of the reference temperatures used for constructing a universal scaling curve, a procedure for estimating the values of the critical exponents for the alloys was developed. For the cases where the transition is entirely second order, the results obtained from this procedure are comparable to the values obtained from the Kouvel–Fisher method. For the case of Fe-doped alloys which partially possess a first-order phase change, the Kouvel–Fisher method is inapplicable. However, their critical exponents determined by our developed procedure can be used to estimate the Curie temperature of the orthorhombic majority phase.     

The modeling of small scales in two-dimensional turbulent flows: A statistical mechanics approach

In previous work we have defined statistical equilibrium states for 2D incompressible Euler equations. We study here the relaxation process toward equilibrium. This leads to a natural modeling of the small scales in turbulent flows, which might be relevant for meteorological and oceanographic applications. Numerical simulations illustrating the performance of these new models are presented.     

Perturbation,symmetry analysis,Bäcklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain B?cklund transformation associated with truncated Painlevéexpansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal B?cklund transformations of the derived conservation laws for the first time.     

A (2+1)-dimensional KdV equation and mKdV equation: Symmetries,group invariant solutions and conservation laws

In this paper, we analyse the (2+1)-dimensional KdV and mKdV equations. Firtly, on the basis of the extended Lax pair, we derive these equations. Thereafter, the symmetry generators are determined followed by the application of the mCK method. Finally, conservation laws (including higher order) are studied.     

Log-Poisson statistics and extended self-similarity in driven dissipative systems

The Bak–Chen–Tang forest fire model [Phys. Lett. A 147 (1990) 297] was proposed as a toy model of turbulent systems, where energy (in the form of trees) is injected uniformly and globally, but is dissipated (burns) locally. We review our previous results on the model [Phys. Rev. E 62 (2000) 1613; Phys. Rev. Lett. 86 (2000) 4215] and present our new results on the statistics of the higher-order moments for the spatial distribution of fires. We show numerically that the spatial distribution of dissipation can be described by Log-Poisson statistics which leads to extended self-similarity [Phys. Rev. E. 48 (1993) R29; Phys. Rev. Lett. 73 (1994) 959]. Similar behavior is also found in models based on directed percolation; this suggests that the concept of Log-Poisson statistics of (appropriately normalized) variables can be used to describe scaling not only in turbulence but also in a wide range of driven dissipative systems.     

Causality, symmetries and quantum mechanics

It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumptions that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to quantum mechanics. In particular, an argument is made for why there are probability amplitudes that are complex numbers. This argument generalizes the Feynman path integral formulation of quantum mechanics to include all possible terms in the action that are allowed by the symmetries, but only the lowest order terms are observable at the presently accessible energy scales, which is consistent with observation. The notion of relational reality is introduced in order to give physical meaning to probabilities. This appears to give rise to a new interpretation of quantum mechanics.     

Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters

In this paper a procedure for large-eddy simulation (LES) has been devised for fluid and magnetohydrodynamic turbulence in Fourier space using the renormalized parameters. The parameters calculated using field theory have been taken from recent papers by Verma [1,2]. We have carried out LES on 64³ grid. These results match quite well with direct numerical simulations of 128³. We show that proper choice of parameter is necessary in LES.     

A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands

Our purpose is to start understanding from a mathematical viewpoint experiments in which regularized structures with spatially distinct bands or rings of precipitated material are exhibited, with clearly visible scaling properties. Such patterns are known as Liesegang bands or rings. In this paper, we study a one-dimensional version of the Keller and Rubinow model and present conditions ensuring the existence of Liesegang bands.     

Quantum mechanics,relativity and time

A discussion on quantum mechanics, general relativity and their relations is introduced. The assumption of the absolute validity of conservation laws and the extension to a 5D-space lead to reconsider several shortcomings and paradoxes of modern physics under a new light without the necessity to take into account symmetry breakings. In this picture, starting from first principles, and after a reduction procedure from 5D to 4D, dynamics leads to the natural emergence of two time arrows and ofa scalar-tensor theory of gravity. In this framework, phenomena like entanglement of systems and topology changes can be naturally accounted and, furthermore, several experimental evidences as gamma ray bursts, sizes of astrophysical structures and the observed values of cosmological parameters can be explained. The identification, thanks to conservation laws, of a covariant symplectic structure as a general feature also for gravity can be seen as a deep link common to all the interactions.     

Scaling Limits of Waves in Convex Scalar Conservation Laws Under Random Initial Perturbations

We study waves in convex scalar conservation laws under noisy initial perturbations. It is known that the building blocks of these waves are shock and rarefaction waves, both are invariant under hyperbolic scaling. Noisy perturbations can generate complicated wave patterns, such as diffusion process of shock locations. However we show that under the hyperbolic scaling, the solutions converge in the sense of distribution to the unperturbed waves. In particular, randomly perturbed shock waves move at the unperturbed velocity in the scaling limit. Analysis makes use of the Hopf formula of the related Hamilton-Jacobi equation and regularity estimates of noisy processes. AMS subject classifications: 35L60, 35B40, 60H15     

基于新物性库的低温回热器REGEN模拟

REGEN程序是用于回热式低温制冷机中回热器部分的仿真模拟软件。在仅内嵌有氦元素工质的基础上,工作新增了包含N2、H2、Ne、Ar和甲烷等13种低温工质的物性库,介绍了其适用温度、压力区间及计算精度等情况。在保留原有氦-4(4He)的基础上补充了当前最新的4He状态方程的研究成果,以此验证了新物性库与原物性库的衔接性和复现性。使用基于新物性库的REGEN3.3a程序对He、H2和Ne为工质的斯特林型脉管制冷机,进行了模拟优化计算并比较了采用不同工质时制冷机的制冷系数。     

The local Hurst exponent of the financial time series in the vicinity of crashes on the Polish stock exchange market

We investigate the local fractal properties of the financial time series based on the whole history evolution (1991–2007) of the Warsaw Stock Exchange Index (WIG), connected with the largest developing financial market in Europe. Calculating the so-called local time-dependent Hurst exponent for the WIG time series we find the dependence between the behavior of the local fractal properties of the WIG time series and the crashes’ appearance on the financial market. We formulate the necessary conditions based on the behavior which have to be satisfied if the rupture or crash point is expected soon. As a result we show that the signal to sell or the signal to buy on the stock exchange market can be translated into evolution pattern. We also find a relation between the rate of the drop and the total correction the WIG index gains after the crash. The current situation on the market, particularly related to the recent Fed intervention in September ’07, is also discussed.