Fractional diffusion equation for an n-dimensional correlated Lévy walk.

Lévy walks define a fundamental concept in random walk theory that allows one to model diffusive spreading faster than Brownian motion. They have many applications across different disciplines. However, so far the derivation of a diffusion equation for an n-dimensional correlated Lévy walk remained elusive. Starting from a fractional Klein-Kramers equation here we use a moment method combined with a Cattaneo approximation to derive a fractional diffusion equation for superdiffusive short-range auto-correlated Lévy walks in the large time limit, and we solve it. Our derivation discloses different dynamical mechanisms leading to correlated Lévy walk diffusion in terms of quantities that can be measured experimentally

Mechanical and kinetic effects of shortened tropomyosin reconstituted into myofibrils

The effects of tropomyosin on muscle mechanics and kinetics were examined in skeletal myofibrils using a novel method to remove tropomyosin (Tm) and troponin (Tn) and then replace these proteins with altered versions. Extraction employed a low ionic strength rigor solution, followed by sequential reconstitution at physiological ionic strength with Tm then Tn. SDS-PAGE analysis was consistent with full reconstitution, and fluorescence imaging after reconstitution using Oregon-green-labeled Tm indicated the expected localization. Myofibrils remained mechanically viable: maximum isometric forces of myofibrils after sTm/sTn reconstitution (control) were comparable (~84%) to the forces generated by non-reconstituted preparations, and the reconstitution minimally affected the rate of isometric activation (kact), calcium sensitivity (pCa50), and cooperativity (nH). Reconstitutions using various combinations of cardiac and skeletal Tm and Tn indicated that isoforms of both Tm and Tn influence calcium sensitivity of force development in opposite directions, but the isoforms do not otherwise alter cross-bridge kinetics. Myofibrils reconstituted with Δ23Tm, a deletion mutant lacking the second and third of Tm’s seven quasi-repeats, exhibited greatly depressed maximal force, moderately slower kact rates and reduced nH. Δ23Tm similarly decreased the cooperativity of calcium binding to the troponin regulatory sites of isolated thin filaments in solution. The mechanisms behind these effects of Δ23Tm also were investigated using Pi and ADP jumps. Pi and ADP kinetics were indistinguishable in Δ23Tm myofibrils compared to controls. The results suggest that the deleted region of tropomyosin is important for cooperative thin filament activation by calcium

Implicit Differential Equation Arising In The Steady Flow Of A Sisko Fluid

Consideration is given to the thin film flow of a Sisko fluid on a moving belt. Using the implicit function theorem, an existence result for the solution of the resulting non-linear differential equation is established. Also, the homotopy analysis method is used to obtain approximate analytical solution of the problem for non-integer values of the power index. The numerical results thus obtained are presented graphically and the salient features of the solution are discussed for various values of the power index parameter. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress. © 2009 Elsevier Inc. All rights reserved

Orbital Stability for Stationary Solutions of the Wadati–Konno–Ichikawa–Shimizu Equation

We determine the orbital stability properties of the space-periodic stationary solutions to the Wadati-Konno- Ichikawa-Shimizu (WKIS) equation previously obtained in R. A. Van Gorder: Prog. Theor. Phys. 128 (2012) 993. The stability result is completely analytic, whereas most results for similar equations are numerical. The method is concise and can be applied to a number of other derivative nonlinear Schrödinger (NLS) type equations admitting spaceperiodic stationary solutions. © 2013 The Physical Society of Japan

A Jacobi rational pseudospectral method for Lane–Emden initial value problems arising in astrophysics on a semi-infinite interval

We derive an operational matrix representation for the differentiation of Jacobi rational functions, which is used to create a new Jacobi rational pseudospectral method based on the operational matrix of Jacobi rational functions. This Jacobi rational pseudospectral method is implemented to approximate solutions to Lane–Emden type equations on semi-infinite intervals. The advantages of using the Jacobi rational pseudospectral method over other techniques are discussed. Indeed, through several numerical examples, including the Lane–Emden problems of first and second kind, we evaluate the accuracy and performance of the proposed method. We also compare our method to other approaches in the literature. The results suggest that the Jacobi rational pseudospectral method is a useful tool for studying Lane–Emden initial value problems, as well as related problems which have regular singular points and are nonlinear

Orbital Stability for Rotating Planar Vortex Filaments in the Cartesian and Arclength Forms of the Local Induction Approximation

The local induction approximation (LIA) is commonly used to study the motion of a vortex filament in a fluid. The fully nonlinear form of the LIA is equivalent to a type of derivative nonlinear Schrödinger (NLS) equation, and stationary solutions of this equation correspond to rotating planar vortex filaments. Such solutions were first discussed in the plane by Hasimoto [J. Phys. Soc. Jpn. 31 (1971) 293], and have been described both in Cartesian three-space and in the arclength formulation in subsequent works. Despite their interest, fully analytical stability results have been elusive. In the present paper, we present elegant and simple proofs of the orbital stability for the stationary solutions to the derivative nonlinear Schrödinger equations governing the self-induced motion of a vortex filament under the LIA, in both the extrinsic (Cartesian) and intrinsic (arclength) coordinate representations. Such results constitute an exact criterion for the orbital stability of rotating planar vortex filament solutions for the vortex filament problem under the LIA