Identification,characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in vis-cous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian struc-tures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.     

Sensitivity analysis of composite piecewise smooth equations

This paper is a contribution to the sensitivity analysis of piecewise smooth equations. A piecewise smooth function is a Lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible B-derivative at this point. We emphasise the role of functions of the typef=g °h whereg is piecewise smooth andh is smooth and present verifiable conditions which ensure that the functionf=g ° is a Lipschitzian homeomorphism near a given point for every sufficiently close toh with respect to theC ¹-topology. Revised version of part of the paper “Sensitivity analysis and Newton’s method for composite piecewise smooth equations”.     

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return-risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.     

Action of the Cremona group on a noncommutative ring

The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a noncommutative algebra that is an analog of a noncommutative field of two independent variables and prove that the Cremona group embeds in a group of outer automorphisms of this algebra. We give two proofs of it, the first proof is technical, the second one is conceptual and proceeds through a construction of a birational invariant of an algebraic variety from its bounded derived category of coherent sheaves.     

Distortion-free magnetic resonance imaging in the zero-field limit

MRI is a powerful technique for clinical diagnosis and materials characterization. Images are acquired in a homogeneous static magnetic field much higher than the fields generated across the field of view by the spatially encoding field gradients. Without such a high field, the concomitant components of the field gradient dictated by Maxwell’s equations lead to severe distortions that make imaging impossible with conventional MRI encoding. In this paper, we present a distortion-free image of a phantom acquired with a fundamentally different methodology in which the applied static field approaches zero. Our technique involves encoding with pulses of uniform and gradient field, and acquiring the magnetic field signals with a SQUID. The method can be extended to weak ambient fields, potentially enabling imaging in the Earth’s field without cancellation coils or shielding. Other potential applications include quantum information processing and fundamental studies of long-range ferromagnetic interactions.     

Separation of velocity distribution and diffusion using PFG NMR

Pulsed field gradient (PFG) NMR is applied to investigate flow processes. In this case the NMR signal experiences phase modulation due to flow and signal attenuation due to the distribution of velocities. The velocity distribution consists of one part originating from diffusion and of a second part, the distribution of the directed motion. The usual PFG-experiment in which the gradient strength is incremented cannot distinguish between both. Incrementing velocity at constant gradient strength keeps the contribution from diffusion constant but changes the absolute width of the velocity distribution. So the signal is attenuated again, but only due to the distribution of the directed motion. The phase modulation as a signature of flow is not affected by this strategy, because velocity and gradient strength are Fourier conjugated. The key advantage of this approach is the possibility of measuring very low velocities, which only cause a very slight phase modulation that is easily covered by diffusion. The method is discussed here for very slow flow in a rheometer cell.