Turbulence over arrays of obstacles in low temperature helium gas

Turbulence produced in low temperature helium gas flowing over arrays of rectangular- and triangular-shaped blunt obstacles is investigated experimentally. The set-up allows both low fluctuation rates (down to 8%), and high microscale Reynolds numbers, (up to 1 150). The forced Kolmogorov equation is found to apply accurately. Similar to another flow configuration (counter rotating flow case [1]), the analysis of the flatness factor evolution with the Reynolds number reveals a transitional behavior around 650. Received 26 August 1999 and Received in final form 28 August 2000     

Nonperturbative renormalization group approach to turbulence

We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not to try to construct an elimination procedure based on some assumed statistical distribution, but to make an ansatz for possible RG transformations and to pose constraints upon those, which guarantee the invariance of the nonlinear term in the Navier-Stokes equation, the invariance of the energy dissipation, and other basic properties of the velocity field. The role of length scales is taken to be inverse to that in the theory of critical phenomena; thus possible intermittency corrections are connected with the outer length scale. Depending on the specific type of flow, we find different sets of admissible transformations with distinct scaling behaviour: for the often considered infinite, isotropic, and homogeneous system K41 scaling is enforced, but for the more realistic plane Couette geometry no restrictions on intermittency exponents were obtained so far. Received: 28 December 1997 / Accepted: 6 August 1998     

A statistical estimator of turbulence intermittency in physical and numerical experiments

The velocity increments statistic in various turbulent flows is analysed through the hypothesis that different scales are linked by a multiplicative process, of which multiplier is infinitely divisible. This generalisation of the Kolmogorov-Obukhov theory is compatible with the finite Reynolds number value of real flows, thus ensuring safe extrapolation to the infinite Reynolds limit. It exhibits a estimator universally depending on the Reynolds number of the flow, with the same law either for Direct Numerical Simulations or experiments, both for transverse and longitudinal increments. As an application of this result, the inverse dependence is used to define an unbiased value for a Large Eddy Simulation from the resolved scales velocity statistics. However, the exact shape of the multiplicative process, though independent of the Reynolds number for a given experimental setup, is found to depend significantly on this setup and on the nature of the increment, longitudinal or transverse. The asymmetry of longitudinal velocity increments probability density functions exhibits similarly a dependence with the experimental setup, but also systematically depends on the Reynolds number. Received 7 January 2000 and Received in final form 17 March 2000     

Affine turbulence

We present a generalization of the multiplicative model for velocity increments involving an affine process. The consequences on the shape of the probability distribution functions for the velocity increments are explored, and shown to be better compatible with the existence of a scale variation of the skewness. Received 29 March 1999 and Received in final form 14 September 1999     

Large scale correlations for energy injection mechanisms in swirling turbulent flows

We report an experimental study of large scale correlations in the power injected in turbulent swirling flows generated in the gap between two coaxial rotating disks. We measure the pressure fluctuations on the blades of one disk, as well as the pressure drop between the leading and the trailing edges of the rotating blades, i.e. the local drag force. Measurements at different positions on one blade and on two successive blades display a correlation length much larger than the ones usually expected in turbulent flows. The time lag for which the correlation between two points is maximum, strongly depends on the global flow configuration. These results help us to understand the statistical properties of the injected power fluctuations in turbulent swirling flows. Received 2 September 1999     

Persistency of material element deformation in isotropic flows and growth rate of lines and surfaces

We explore the consequence of isotropy on the growth of material lines and surfaces in complex flows. We show that the key parameter is the persistency , defined as the product of a typical stretching rate to its associated coherence time . In particular, we derive the dependence of the net growth rate of both lines and surfaces on . Their growth rates increase strongly with increasing persistencies for small , and then saturate for . Making use of measurements of Girimaji and Pope [1], we estimate the persistency to be of order 1 in isotropic turbulence. We then comment on the evolution of the shape of an initially spherical material blob. While its length increases, one of its tranverse dimension increases slowly and the other one decreases. This quasi-two-dimensional deformation leads a final ribbon-shape. Received 10 November 1999 and Received in final form 14 August 2000     

Power law distributions and dynamic behaviour of stock markets

A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation = F ϕ + G ϕ t where t is the usual Gaussian white noise, i.e.: t t ^′ = 2Dδ t-t ^′ and t = 0. Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as P ϕ = exp{ - Ψϕ - ln G(ϕ)} where Ψϕ = - F/ G dϕ and Z is a normalization factor. This is explored for the simple case where F ϕ = Jϕ + bϕ² - cϕ³ and fluctuations characterised by the amplitude G ϕ = ϕ + ɛ when it readily yields for ϕ≫ɛ, a distribution function with power law tails, viz: P ϕ = exp{2bϕ-cϕ² /D}. The parameter c ensures convergence of the distribution function for large values of ϕ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J < 0 and D≈ | J|. Received 25 July 2000     

Efficient option pricing with path integral

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of options, including those with path-dependent and early exercise features. As examples, the application of the method to European and American options in the Black-Scholes model is illustrated. The results of the algorithm are compared with those obtained with the standard procedures known in the literature and found to be in good agreement. Received 31 December 2001     

Exact propagator of the Fokker-Planck equation with a space-dependent diffusion coefficient and a time-dependent mean-reverting force

We have investigated the algebraic structure of the Fokker-Planck equation with a variable diffusion coefficient and a time-dependent mean-reverting force. Such a model could be useful to study the general problem of a Brownian walker with a space-dependent diffusion coefficient. We also show that this model is related to the Fokker-Planck equation with a constant diffusion coefficient and a time-dependent anharmonic potential of the form V(x, t) = ?a(t)x ² + b ln x, which has been widely applied to model different physical and biological phenomena, e.g. the study of neuron models and stochastic resonance in monostable nonlinear oscillators. Using the Lie algebraic approach we have derived the exact diffusion propagators for the Fokker-Planck equations associated with different boundary conditions, namely (i) the case of a single absorbing barrier, and (ii) the case of two absorbing barriers. These exact diffusion propagators enable us to study the time evolution of the corresponding stochastic systems. Received 23 October 2001 and Received in final form 24 December 2001     

Local multifractal thermodynamics of 3D turbulence

Using results of a direct numerical simulation (DNS) of 3D turbulence we show that the observed generalized scaling (i.e. scaling moments versus moments of different orders) is consistent with a lognormal-like distribution of turbulent energy dissipation fluctuations with moderate amplitudes for all space scales available in this DNS (beginning from the molecular viscosity scale up to largest ones). Local multifractal thermodynamics has been developed to interpret the data obtained using the generalized scaling, and a new interval of space scales with inverse cascade of generalized energy has been found between dissipative and inertial intervals of scales for sufficiently large values of the Reynolds number. Received 21 July 2000     

Onsager-Machlup Theory and Work Fluctuation Theorem for a Harmonically Driven Brownian Particle

We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.     

Finite size scale invariance

We develop a new approach to scale symmetry, which takes into account the possible finite cut-offs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similarity as a limiting case, when the cut-offs are set to infinity (infinite size-system); ii) is consistent with the traditional finite size scaling approach already used in critical phenomena; iii) enables the computation of some of the universal functions appearing in the finite size scaling formulation; iv) allows scale transformations leaving the cut-offs invariant, like in the traditional renormalization approach; v) can be formulated to allow for positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical findings. Received 26 January 1999 and Received in final form 25 October 1999     

Lie algebraic approach for Fokker-Planck dynamics with space-dependent diffusion and mean-reverting drift

Using the Lie algebraic approach we have derived the exact diffusion propagator of the Fokker-Planck equation with a time-dependent variable diffusion coefficient and a time-dependent mean-reverting force between two absorbing boundaries. The exact diffusion propagator not only enables us to study the time evolution of the corresponding stochastic system, but the knowledge of the propagator can also provide a benchmark for testing approximate numerical or analytical procedures. Furthermore, the Lie algebraic method is very simple and could be easily extended to the more general Fokker-Planck equations with well-defined algebraic structures. Received 18 December 2002 / Received in final form 3 March 2003 Published online 24 April 2003     

Potential symmetry and invariant solutions of Fokker-Planck equation in cylindrical coordinates related to magnetic field diffusion in magnetohydrodynamics including the Hall current

Lie groups involving potential symmetries are applied in connection with the system of magnetohydrodynamic equations for incompressible matter with Ohm's law for finite resistivity and Hall current in cylindrical geometry. Some simplifications allow to obtain a Fokker-Planck type equation. Invariant solutions are obtained involving the effects of time-dependent flow and the Hall-current. Some interesting side results of this approach are new exact solutions that do not seem to have been reported in the literature.     

Charge density plateaux and insulating phases in the $\mathsf{t-J}$ model with ladder geometry

We discuss the occurrence and the stability of charge density plateaux in ladder-like t-J systems (at zero magnetization M = 0) for the cases of 2- and 3-leg ladders. Starting from isolated rungs at zero leg coupling, we study the behaviour of plateaux-related phase transitions by means of first order perturbation theory and compare our results with Lanczos diagonalizations for t-J ladders (N = 2 × 8) with increasing leg couplings. Furthermore we discuss the regimes of rung and leg couplings that should be favoured for the appearance of the charge density plateaux.Received: 28 July 2003, Published online: 8 December 2003PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.-b General theory and models of magnetic ordering - 75.10.Jm Quantized spin models     

Mean magnetic field and noise cross-correlation in magnetohydrodynamic turbulence: results from a one-dimensional model

We show that a recently proposed [J. Fleischer, P.H. Diamond, Phys. Rev. E 58, R2709 (1998)] one-dimensional Burgers-like model for magnetohydrodynamics (MHD) is in effect identical to existing models for drifting lines and sedimenting lattices. We use the model to demonstrate, contrary to claims in the literature, that the energy spectrum of MHD turbulence should be independent of mean magnetic field and that cross-correlations between the noise sources for the velocity and magnetic fields cannot change the structure of the equations under renormalisation. We comment on the scaling and the multiscaling properties of the stochastically forced version of the model. Received 29 October 1998 and Received in final form 8 December 1998     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.