Many models have been developed to study the role of branching actin networks in motility. One important component of those models is the distribution of filament orientations relative to the cell membrane. Two mean-field models previously proposed are generalized and analyzed. In particular, we find that both models uniquely select for a dominant orientation pattern. In the linear case, the pa...

Abstract: In this paper, we present a novel method for computation of eigenvalues and eigenfunctions for a class of singular Sturm-Liouville boundary value problems using modified Adomian decomposition method. The proposed method can be applied to any type of regular as well as singular Sturm-Liouville problems. This current method is capable of finding any n-th eigenvalues and eigenfunctions o...

Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange f...

The perturbation analysis of an ideal acoustical duct was first made by Rayleigh in 1878 and the result has since stood in the literature. However, the analysis is based on the assumption of potential and kinetic energy densities that remain constant as a change in cross section occurs, whereas, in fact, they may fluctuate significantly in comparison to the slowly varying "wave function," Psi(x...

New elements of the dual cone of the set of fermion N -representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N -representability is obtained for N = 3. In this case the new condition is stronger than the known Band C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N -repre...

In earlier work, we developed a Monte Carlo method to compute the principal eigenvalue of linear operators, which was based on the simulation of exit times. In this paper, we generalize this approach by showing how to use a branching method to improve the efficacy of simulating large exit times for the purpose of computing eigenvalues. Furthermore, we show that this new method provides a natura...

The two-dimensional sloshing problem is considered in a half-plane covered by a rigid dock with two symmetric gaps. It is proved that the antisymmetric (symmetric) sloshing eigenvalues are monotonically decreasing (increasing) functions of spacing between gaps and formulae for their derivatives are obtained. sloshing problem / eigenvalue / eigenfunction / integral operator / asymptotic formula ...

Let u be an eigenfunction of the Laplacian on a compact manifold with boundary, with Dirichlet or Neumann boundary conditions, and let −λ2 be the corresponding eigenvalue. We consider the problem of estimating maxM u in terms of λ, for large λ, assuming ∫ M u 2 = 1. We prove that maxM u ≤ CMλ (n−1)/2, which is optimal for some M . Our proof simplifies some of the arguments used before for such ...

Let M be a closed Riemannian manifold of dimension n. Let φλ be an eigenfunction of the Laplace–Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {φλ > 0} ∩B is ≥ C|B|/λ , where B is any ball centered at a point of the nodal set. We apply this result to prove that each nodal domain contains a ball of radius ≥ C/λ. The results in this paper extend previous results of...

The Dafermos regularization of a system of n conservation laws in one space dimension admits smooth self-similar solutions of the form u= u(X/T ). In particular, there are such solutions near a Riemann solution consisting of n possibly large Lax shocks. In Lin and Schecter (2004, SIAM. J. Math. Anal. 35, 884–921), eigenvalues and eigenfunctions of the linearized Dafermos operator at such a solu...