Equivariant maps and bimodule projections

We construct a counterexample to Solel's [B. Solel, Contractive projections onto bimodules of von Neumann algebras, J. London Math. Soc. 45 (2) (1992) 169–179] conjecture that the range of any contractive, idempotent, MASA bimodule map on is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana's theory [M. Hamana, Injective envelopes of C^*-dynamical systems, Tohoku Math. J. 37 (1985) 463–487] of G-injective operator spaces and G-injective envelopes.     

A DLM/FD/IB Method for Simulating Cell/Cell and Cell/Particle Interaction in Microchannels

A spring model is used to simulate the skeleton structure of the red blood cell （RBC） membrane and to study the red blood cell （RBC） rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. The authors also combine the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of cells and neutrally buoyant particles in a microchannel for studying the margination of particles.     

Closed-form solutions of a general inequality-constrained lq optimal control problem

A general linear quadratic (LQ) optimal control problem, with the dynamic system being governed by a higher-order vector-valued ordinary differential equation and with inequality-constraints on the state vector and/or the control input, is studied. Based on an explicit characterization result, optimal solutions are obtained in closed-form. A constructive method for finding the closed-form optimal solutions is proposed, and two illustrative examples are included     

Shearlet Smoothness Spaces

The shearlet representation has gained increasingly more prominence in recent years as a flexible and efficient mathematical framework for the analysis of anisotropic phenomena. This is achieved by combining traditional multiscale analysis with a superior ability to handle directional information. In this paper, we introduce a class of shearlet smoothness spaces which is derived from the theory of decomposition spaces recently developed by L. Borup and M. Nielsen. The introduction of these spaces is motivated by recent results in image processing showing the advantage of using smoothness spaces associated with directional multiscale representations for the design and performance analysis of improved image restoration algorithms. In particular, we examine the relationship of the shearlet smoothness spaces with respect to Besov spaces, curvelet-type decomposition spaces and shearlet coorbit spaces. With respect to the theory of shearlet coorbit space, the construction of shearlet smoothness spaces presented in this paper does not require the use of a group structure.     

Central Limit Theorems for the Shrinking Target Problem

Suppose B _i :=B(p,r _i ) are nested balls of radius r _i about a point p in a dynamical system (T,X,μ). The question of whether T ⁱ x∈B _i infinitely often (i.o.) for μ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if $E_{n}:=\sum_{i=1}^{n} \mu(B_{i})$ diverges then there is a quantitative rate of entry and $\lim_{n\to\infty} \frac{1}{E_{n}} \sum_{j=1}^{n} 1_{B_{i}} (T^{i} x) \to1$ for μ a.e. x∈X. This is a self-norming type of strong law of large numbers. We establish self-norming central limit theorems (CLT) of the form $\lim_{ n\to\infty} \frac{1}{a_{n}} \sum_{i=1}^{n} [1_{B_{i}} (T^{i} x)-\mu(B_{i})] \to N(0,1)$ (in distribution) for a variety of hyperbolic and non-uniformly hyperbolic dynamical systems, the normalization constants are $a^{2}_{n} \sim E [\sum_{i=1}^{n} 1_{B_{i}} (T^{i} x)-\mu(B_{i})]^{2}$ . Dynamical systems to which our results apply include smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps and, in higher dimensions, piecewise expanding maps. For such central limit theorems the main difficulty is to prove that the non-stationary variance has a limit in probability.     

On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev′e Equation: an Operator-Splitting Approach

The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevé transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang’s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows: (i) The first Painlevé ordinary differential equation, (ii) a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather “violent” phenomenon.     

The influence of surface preparation on the electrochemistry of boron doped diamond: A study of the reduction of 1,4-benzoquinone in acetonitrile

The reduction, at boron doped diamond electrodes, of 1,4-benzoquinone dissolved in acetonitrile is investigated. It is shown that the mechanism of reduction is dependent on electrode pre-treatment. Whilst the response at an oxygenated diamond electrode surface resembles that at platinum and carbon electrodes, the i–E curve at a hydrogenated diamond surface is indicative of protonation of intermediates. The cyclic voltammograms obtained suggest that the sub-surface hydrogen present in the hydrogenated diamond lattice is able to participate in electrochemical processes.     

Processing,microstructure and properties of bulk metallic glass composites

A Zr-Nb-Cu-Ni-Al bulk metallic glass was reinforced with up to 80 volume-percent (% V_f) continuous fibers, short fibers or particles. Characterization based on X-ray diffraction, differential scanning calorimetry, electron microprobe and scanning electron microscopy is presented. The metallic glass matrix remains amorphous after adding reinforcements. Reactions at the matrix/reinforcement interfaces were examined using transmission electron microscopy. A narrow band of crystalline particles typically forms adjacent to the reinforcement. The composites were tested in compression. Compressive strain-to-failure increased by up to factor of 12 compared to the unreinforced bulk metallic glass. The increase in compressive strain-to-failure is due to the particles restricting shear band propagation, promoting the generation of multiple shear bands and additional fracture surface area.     

Assessment of electronic properties of InNxSb1−x for long-wavelength infrared detector applications

This work assesses theoretically the potential of dilute nitride alloys of InN_xSb_1−x for long-wavelength IR applications. A 10-band k.p approximation modified to account for conduction/valence band coupling is implemented to extract the bandgap as a function of the nitrogen concentration in the alloy and the temperature. The calculations show the possibility to obtain a band closure at ∼2% of nitrogen for InSbN at 300 K. The absorption coefficient, and its temperature dependence, is then determined using an Elliot-like formalism, predicting stronger absorption properties associated with the enhancement of conduction band effective masses. This enhancement yields over an order of magnitude increase in the non-radiative Auger recombination lifetimes suggesting the potential of InNSb for significantly enhancing detectivity limits and operation temperatures of long-wavelength IR detectors.