Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates Ω is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of Ω = 5 rad/s (with Rossby number much smaller than unity). Typically, the Taylor-scale Reynolds number in our experiments is around Re_λ ≈ 100. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see L.J.A. van Bokhoven, H.J.H. Clercx, G.J.F. van Heijst, and R.R. Trieling, Experiments on rapidly rotating turbulent flows, Phys. Fluids 21 (2009) 096601. Based on the full set of velocity derivatives, measured in a Lagrangian way by three-dimensional (3D) particle tracking velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. For the range of rotation rates considered, the experimental results show how the turbulence evolves from almost isotropic 3D turbulence (Ω ? 0.2 rad/s) to quasi-two-dimensional turbulence (Ω ≈ 5.0 rad/s), and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect of background rotation is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.     

Regular and chaotic dynamics of a neutral atom in a magnetic trap

In the framework of the nonlinear mechanics, we study the dynamics of a neutral atom confined in a magnetic quadrupolar trap. Owing to the axial symmetry of the system, the z-component of the angular momentum p _φ is an integral of motion and, in cylindrical coordinates, the dynamics of the atom is modeled by a two-degree of freedom Hamiltonian. The structure and evolution of the phase space as a function of the energy is explored extensively by means of numerical techniques of continuation of families of periodic orbits and Poincaré surfaces of section.     

On the uniqueness in gevrey spaces for degenerate elliptic operators

The uniqueness and the non–uniqueness of the Gevrey ultradifferentiable solutions to the Cauchy problem for a class of second order degenerate elliptic operators is studied. Some uniqueness results are proved and the necessity of the hypotheses is discussed by the construction of some counter-examples.     

A Hyperbolic Non Distributive Algebra in 1 + 2 Dimensions

We introduce a non distributive algebra over the reals in 1 + 2 dimensions that contains the hyperbolic complex algebra ${\mathbb{H}_2}$ . The algebra has divisors of zero that can be avoided by introducing the necessary conditions. Under these conditions, the proposed addition and product operations satisfy group properties. More stringent restrictions sufficient to satisfy group properties separate the algebra in two subspaces. As an application, the composition of velocities in a deformed Lorentz metric is presented. In this approach, Minkowski light cones are deformed into light bipyramids.     

Sequential Monte Carlo Methods for Option Pricing

In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.