基于最小加速度原理的刚塑性动力问题

应用有限变形的最小加速度原理，推导出了小变形或有限变形构件受到刚性飞射物撞击时的刚塑性运动方程，指出该方法具有直接、简捷和可靠的特点。     

A pseudo active kinematic constraint for a biological living soft tissue: An effect of the collagen network

Recent studies in mammalian hearts show that left ventricular wall thickening is an important mechanism for systolic ejection, and that during contraction the cardiac muscle develops significant stresses in the muscular cross-fiber direction. We suggested that the collagen network surrounding the muscular fibers could account for these mechanical behaviors. To test this hypothesis we develop a model for large deformation response of active, incompressible, nonlinear elastic and transversely isotropic living soft tissue (such as cardiac or arteries tissues) in which we include a coupling effect between the connective tissue and the muscular fibers. Then, a three-dimensional finite element formulation including this internal pseudo-active kinematic constraint is derived. Analytical and finite element solutions are in a very good agreement. The numerical results show this wall thickening effect with an order of magnitude compatible with the experimental observations.     

Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

We present a general result of transverse nonlinear instability of 1d solitary waves for Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1-d model and the transverse perturbation “have the same sign”. Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Boussinesq system and the Zakharov–Kuznetsov equation and we hope that it may be useful in other contexts.     

A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

In this article, a novel numerical method is proposed for nonlinear partial differential equations with space- and time-fractional derivatives. This method is based on the two-dimensional differential transform method (DTM) and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented elsewhere. Results also show that the numerical scheme is very effective and convenient for solving nonlinear partial differential equations of fractional order.     

Earth surface effects on active faults: An eigenvalue asymptotic analysis

We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d^-2, where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.     

A Fourier spectral-discontinuous Galerkin method for time-dependent 3-D Schrödinger–Poisson equations with discontinuous potentials

In this paper, we propose a high order Fourier spectral-discontinuous Galerkin method for time-dependent Schrödinger–Poisson equations in 3-D spaces. The Fourier spectral Galerkin method is used for the two periodic transverse directions and a high order discontinuous Galerkin method for the longitudinal propagation direction. Such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures. As the derivative matrices are required for various time integration schemes such as the exponential time differencing and Crank Nicholson methods, explicit derivative matrices of the discontinuous Galerkin method of various orders are derived. Numerical results, using the proposed method with various time integration schemes, are provided to validate the method.     

On Ito-Kurzweil-Henstock Integral and Integration-by-Part Formula

In this paper we derive the Integration-by-Parts Formula using the generalized Riemann approach to stochastic integrals, which is called the Ito-Kurzweil-Henstock integral.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Electron scattering from an assembly of point scatterers in the presence of a quantizing magnetic field

Summary We have studied the scattering of electrons by a structured target in the presence of a quantizing static magnetic field, under the assumption that the presence of the field does not affect the behaviour of the massive target nuclei, but it influences only the motion of the incident electrons. In this case, the electron motion in the plane perpendicular to the magnetic field is confined within a typical distance given by the cyclotron radius ρ₀=(cℏ/|e|B)^1/2, that for particular values of the intensity of the magnetic field can be comparable with the distance between two scattering centres. The known field-free interference conditions are modified, depending both on the energy of the incident particle and on the intensity and the direction of the magnetic field. The general case of a three-dimensional scattering array has been derived in detail. Numerical results are given for the case of two scattering centres in perpendicular geometry. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.