Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Mean Motion in Stochastic Plasmas With a Space-Dependent Diffusion Coefficient

Radial transport in the tokamap, which has been proposed as a simple model for the motion in a stochastic plasma, is investigated. A theory for previous numerical findings is presented. The new results are stimulated by the fact that the radial diffusion coefficients is space-dependent. The space-dependence of the transport coefficient has several interesting effects which have not been elucidated so far. Among the new findings are the analytical predictions for the scaling of the mean radial displacement with time and the relation between the Fokker-Planck diffusion coefficient and the diffusion coefficient from the mean square displacement. The applicability to other systems is also discussed. (c) 2009 WILEY-VCH GmbH & Co. KGaA, Weinheim

Genesis of quantum nonlocality

We revisit the problem of an otherwise classical particle immersed in the zero-point radiation field, with the purpose of tracing the origin of the nonlocality characteristic of Schrodinger`s equation. The Fokker-Planck-type equation in the particles phase-space leads to an infinite hierarchy of equations in configuration space. In the radiationless limit the first two equations decouple from the rest. The first is the continuity equation: the second one, for the particle flux, contains a nonlocal term due to the momentum fluctuations impressed by the field. These equations are shown to lead to Schrodinger`s equation. Nonlocality (obtained here for the one-particle system) appears thus as a property of the description, not of Nature. (C) 2011 Elsevier B.V. All rights reserved.

Probing the Large Magellanic Cloud age gap at intermediate cluster masses

The Large Magellanic Cloud (LMC) has a rich star cluster system spanning a wide range of ages and masses. One striking feature of the LMC cluster system is the existence of an age gap between 3 and 10 Gyr. But this feature is not clearly seen among field stars. Three LMC fields containing relatively poor and sparse clusters whose integrated colours are consistent with those of intermediate-age simple stellar populations have been imaged in BVI with the Optical Imager (SOI) at the Southern Telescope for Astrophysical Research (SOAR). A total of six clusters, five of them with estimated initial masses M < 104 M(circle dot), were studied in these fields. Photometry was performed and colour-magnitude diagrams (CMDs) were built using standard point spread function fitting methods. The faintest stars measured reach V similar to 23. The CMD was cleaned from field contamination by making use of the three-dimensional colour and magnitude space available in order to select stars in excess relative to the field. A statistical CMD comparison method was developed for this purpose. The subtraction method has proven to be successful, yielding cleaned CMDs consistent with a simple stellar population. The intermediate-age candidates were found to be the oldest in our sample, with ages between 1 and 2 Gyr. The remaining clusters found in the SOAR/SOI have ages ranging from 100 to 200 Myr. Our analysis has conclusively shown that none of the relatively low-mass clusters studied by us belongs to the LMC age gap.

A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Clitia`s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking, numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis. (C) 2007 Elsevier Ltd. All rights reserved.

Integer and fractional microwave induced resistance oscillations in a 2D system with moderate mobility

We report on integer and fractional microwave-induced resistance oscillations in a 2D electron system with high density and moderate mobility, and present results of measurements at high microwave intensity and temperature. Fractional microwave-induced resistance oscillations occur up to fractional denominator 8 and are quenched independently of their fractional order. We discuss our results and compare them with existing theoretical models. (C) 2009 Elsevier B.V. All rights reserved.

VACUUM POLARIZATION EFFECTS ON QUASINORMAL MODES IN ELECTRICALLY CHARGED BLACK HOLE SPACE-TIMES

We investigate the influence of vacuum polarization of quantum massive fields on the scalar sector of quasinormal modes in spherically symmetric black holes. We consider the evolution of a massless scalar field on the space-time corresponding to a charged semiclassical black hole, consisting of the quantum-corrected geometry of a Reissner-Nordstrom black hole dressed by a quantum massive scalar field in the large mass limit. Using a sixth order WKB approach we find a shift in the quasinormal mode frequencies due to vacuum polarization.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Second-order negative-curvature methods for box-constrained and general constrained optimization

A Nonlinear Programming algorithm that converges to second-order stationary points is introduced in this paper. The main tool is a second-order negative-curvature method for box-constrained minimization of a certain class of functions that do not possess continuous second derivatives. This method is used to define an Augmented Lagrangian algorithm of PHR (Powell-Hestenes-Rockafellar) type. Convergence proofs under weak constraint qualifications are given. Numerical examples showing that the new method converges to second-order stationary points in situations in which first-order methods fail are exhibited.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.