Econophysics and Quantum Statistics

In this paper, we associate notions of entropy, temperature, free energy, and Hamiltonian occuring in problems in probability theory with a system of identical objects so that modern methods of quantum statistics can be applied to problems in mathematical finance.     

常数速度梯度时均匀湍流的二元速度关联函数

在湍流脉动速度比较小的条件下,本文得到了富氏变换过后脉动速度方程的解.它所代表的涡旋,在平均速度梯度为小量时,化为具有常数平均速度梯度的、组成后期均匀各向同性湍流场的涡旋和组成后期各向异性湍流场的涡旋.利用不同时刻的这种涡旋解,组成定常的有常数平均速度梯度的湍流场,这个湍流场可以近似地表达槽流和管流近中心区域的湍流场.我们求得了这种湍流场的二元速度关联函数,包括纵向的关联系数f(γ/λ)和横向的关联系数g(γ/λ).并且和均匀各向同性湍流实验中的前期和后期的f(γ/λ)和g(γ/λ)进行了比较.并且弄清楚了速度梯度对关联系数f(γ/λ)所产生的影响,最后还得到了雷诺应力和涡旋粘性系数的表达式.     

Non-classical polar unitals in finite Figueroa planes

The finite Figueroa planes are non-Desarguesian projective planes of order q ³ for all prime powers q > 2. These planes were constructed algebraically in 1982 by Figueroa, and Hering and Schaeffer, and synthetically in 1986 by Grundh?fer. All Figueroa planes of finite square order are shown to possess a unitary polarity by de Resmini and Hamilton in 1998, and hence admit unitals. Using the result of O??Nan in 1971 on the non-existence of his configuration in a classical unital, and the intrinsic characterization by Taylor in 1974 of the notion of perpendicularity induced by a unitary polarity in the classical plane (introduced by Dembowski and Hughes in 1965), we show that these Figueroa polar unitals do not satisfy a necessary condition, introduced by Wilbrink in 1983, for a unitary block design to be classical, and hence they are not classical.     

Non-classical polar unitals in finite Dickson semifield planes

We give three proofs, two intrinsic and one extrinsic, that every Dickson–Ganley unital ${\mathcal{U}(\sigma)}$ , parametrized by a field automorphism σ, is non-classical if σ is not the identity, extending a result of Ganley’s (Math Z 128:34–42, 1972); we prove that ${\mathcal{U}(\sigma_1)}$ is isomorphic to ${\mathcal{U}(\sigma_2)}$ if and only if σ ₁ = σ ₂ or σ ₁ = σ ₂ ^?1 ; and we determine the (design) automorphism group of ${\mathcal{U}(\sigma)}$ as the collineation subgroup of the ambient Dickson semifield plane stabilizing the unital. This contains as a special case the corresponding result of O’Nan’s (J Algebra 20:495–511, 1965) on the classical unital.     

三涡旋模式理论中小涡旋的二元和三元速度关联函数和网格湍流的衰变*

在三种涡旋分开考虑的湍流模式[1,2]里,我们用到了小涡旋的二元和三元速度关联函数。本文对小涡旋的二元和三元速度关联函数进行了讨论,并且对它们展开式的头几项中常用到的系数给出了表达式,最后,用它们讨论了网格湍流的衰减问题.计算结果与G.K.Batchelor和A.A.Townsend的实验[3]相符合得很好.     

Turbulent Superfluid Profiles and Vortex Density Waves in a Counterflow Channel

In this paper we study the two-dimensional profiles of the superfluid component velocity and the quantized vortex-points density in a counterflow channel where the influence of the walls cannot be neglected. The numerical results obtained show the presence of vortex density waves in the channel, as shown in a recent paper by means of the one-fluid model.     

Turbulence Phenomena in Real Analysis

The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and stands for the one-point compactification of X, while E^X is the equivalence relation which is defined on the Polish group C(X,R₊*) by where f, g are in C(X,R₊*), then E^X is induced by a turbulent Polish group action. Second we show that given any if we identify the n-dimensional unit sphere Sⁿ with the one-point compactification of Rⁿ via the stereographic projection, while E_n,r is the equivalence relation which is defined on the Polish group C^r(Rⁿ,R₊*) by where f, g are in C^r(Rⁿ,R₊*), then E_n,r is also induced by a turbulent Polish group action. Dedicated to my sister Alexandra and to her daughter Marianthi.     

Non-classical regimes of colloid-facilitated impurity transport in statistically homogeneous double porosity media

In the context of impurity transport study it is shown how complexity of the system leads to emergence of anomalous transport regimes, moreover the power-law behavior of which changes with time. Specifically, a model of nonequillibrium colloid-facilitated transport in statistically homogeneous double porosity media is presented and possible transport regimes are simulated. Depending on the medium and colloids characteristics different sequences of transport regimes can realize. Temporal interval exists where anomalous transport regimes (sub-diffusion and quasi-diffusion) occur. At asymptotically large times the transport is described by the classical advection-diffusion with modified parameters.     

Non-classical preference models in combinatorial problems: Models and algorithms for graphs

This is a summary of the most important results presented in the authors PhD thesis (Spanjaard 2003). This thesis, written in French, was defended on 16 December 2003 and supervised by Patrice Perny. A copy is available from the author upon request. This thesis deals with the search for preferred solutions in combinatorial optimization problems (and more particularly graph problems). It aims at conciliating preference modelling and algorithmic concerns for decision aiding.Received: March 2004, MSC classification: 91B06, 90C27, 90B40, 16Y60     

Quantum Inequalities in Quantum Mechanics

We study a phenomenon occurring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise non-negative may assume arbitrarily negative expectation values after quantization, even though the spatially integrated density remains non-negative. Two prominent examples which have previously been studied are the energy density (in quantum field theory) and the probability flux of rightwards-moving particles (in quantum mechanics). However, in the quantum field context, it has been shown that the magnitude and space-time extension of negative energy densities are not arbitrary, but restricted by relations which have come to be known as quantum inequalities. In the present work, we explore the extent to which such quantum inequalities hold for typical quantum mechanical systems. We derive quantum inequalities of two types. The first are kinematical quantum inequalities where spatially averaged densities are shown to be bounded below. Specifically, we obtain such kinematical quantum inequalities for the current density in one spatial dimension (imposing constraints on the backflow phenomenon) and for the densities arising in Weyl–Wigner quantization. The latter quantum inequalities are direct consequences of sharp Gårding inequalities. The second type are dynamical quantum inequalities where one obtains bounds from below on temporally averaged densities. We derive such quantum inequalities in the case of the energy density in general quantum mechanical systems having suitable decay properties on the negative spectral axis of the total energy.Furthermore, we obtain explicit numerical values for the quantum inequalities on the one-dimensional current density, using various spatial averaging weight functions. We also improve the numerical value of the related backflow constant previously investigated by Bracken and Melloy. In many cases our numerical results are controlled by rigorous error estimates.submitted 27/01/04, accepted 05/05/04     

Knots and Unknots in Superfluid Turbulence

The study of vortex lines in a inviscid, incompressible Euler fluid dates back to the times of Lord Kelvin. Vortex lines are highly idealised mathematical objects which at first sight do not seem relevant to vortices and turbulence in real fluids. In this article I show that superfluid vortices are good physical realizations of these classical mathematical objects, and provide us with a convenient context to investigate topological aspects of turbulence. Received: March 2007     

On Turbulence in Nonlinear Schrödinger Equations

We consider the small-dispersion and small-diffusion nonlinear Schr?dinger equation , , where the space-variable x belongs to the unit n-cube () and u satisfies Dirichlet boundary conditions. Assuming that the force is a zero-meanvalue random field, smooth in x and stationary in t with decaying correlations, we prove that the C ^m -norms in x with of solutions u, averaged in ensemble and locally averaged in time, are larger than , . This means that the length-scale of a solution u decays with as its positive degree (at least, as and - in a sense - proves existence of turbulence for this equation. Submitted: August 1996, revised version: May 1997