A Numerical Model for Nonlinear Wave Propagation on Non-uniform Current

On the basis of the new type Boussinesq equations （Madsen et al., 2002）, a set of equations explicitly including the effects of currents on waves are derived. A numerical implementation of the present equations in one dimension is described. The numerical model is tested for wave propagation in a wave flume of uniform depth with current present. The present numerical results are compared with those of other researchers. It is validated that the present numerical model can reasonably reflect the nonlinear influences of currents on waves. Moreover, the effects of inputting different incident boundary conditions on the calculated results are studied.

THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

In this article, the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered. Using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = a. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

A Quasilinear Parabolic System with Nonlocal Boundary Conditions and Localized Sources

This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow- up rate estimates are also derived.

EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.

Simulations of thermal conductance across tilt grain boundaries in graphene

Non-equilibrium molecular dynamics （MD） method was performed to simulate the thermal transporta- tion process in graphene nanoribbons （GNRs）. A convenient way was conceived to introduce tilt grain boundaries （GBs） into the graphene lattice by repetitive removing C atom rows along certain directions. Comprehensive MD simulations reveal that larger-angle GBs are effective thermal barriers and substantially reduce the average thermal conductivity of GNRs. The GB thermal conductivity is ~ 10 W-m-1 .K-l for a bicrystal GNR with a misorientation of 21.8%, which is -97 % less than that of a prefect GNR with the same size. The total thermal resistance has a monotonic dependence on the den- sity of the 5-7 defects along the GBs. A theoretical model is proposed to capture this relation and resolve the contribu- tions by both the reduction in the phonon mean free path and the defect-induced thermal resistance.

A new SINS/GPS sensor fusion scheme for UAV localization problem using nonlinear SVSF with covariance derivation and an adaptive boundary layer

The state estimation strategy using the smooth variable structure filter （SVSF） is based on the variable structure and sliding mode concepts. As presented in its standard form with a fixed boundary layer limit, the value of the boundary layer width is not precisely known at each step and may be selected based on a priori knowledge. The boundary layer width reflects the level of uncertainty in the model parameters and disturbance characteristics, where large values of the boundary layer width lead to robustness without optimality and small values of the boundary layer width provide optimality with poor robustness. As a solution and to overcome these limitations, an adaptive smoothing boundary layer is required to achieve greater robustness and suitable accuracy. This adapted value of the boundary layer width is obtained by minimizing the trace of the a posteriori covariance matrix. In this paper, the proposed new approach will be considered as another alternative to the extended Kalman filters （EKF）, nonlinear H∞ and standard SVSF-based data fusion techniques for the autonomous airborne navigation and self-localization problem. This alternative is based on strapdown inertial navigation system （SINS） and GPS data using the nonlinear SVSF with a covariance derivation and adaptive boundary layer width. Furthermore, the full mathematical model of the SINS/GPS navigation system considering the unmanned aerial vehicle （UAV） position, velocity and Euler angle as well as gyro and accelerometer biases will be used in this paper to estimate the airborne position and velocity with better accuracy.

A FIRST-ORDER NUMERICAL SCHEME FOR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN BOUNDED DOMAINS

We propose a novel numerical scheme for decoupled forward-backward stochastic differ- ential equations （FBSDEs） in bounded domains, which corresponds to a class of nonlinear parabolic partial differential equations with Dirichlet boundary conditions. The key idea is to exploit the regularity of the solution （Yt,Zt） with respect to Xt to avoid direct ap- proximation of the involved random exit time. Especially, in the one-dimensional case, we prove that the probability of Xt exiting the domain within At is on the order of O（（△t）ε exp（--1/（△t）2ε））, if the distance between the start point X0 and the boundary is 1 g at least on the order of O（△t）^1/2-ε ） for any fixed c 〉 0. Hence, in spatial discretization, we set the mesh size △x - （9（（At）^1/2-ε ）, so that all the interior grid points are sufficiently far from the boundary, which makes the error caused by the exit time decay sub-exponentially with respect to △t. The accuracy of the approximate solution near the boundary can be guaranteed by means of high-order piecewise polynomial interpolation. Our method is developed using the implicit Euler scheme and cubic polynomial interpolation, which leads to an overall first-order convergence rate with respect to △t.

Internal friction peak associated with dislocations in Mg-0.6%Zr alloy

The internal friction （IF） of Mg-0.6%Zr alloy is measured in the present study and two IF peaks of （PI （97 ℃, 1 Hz） and P2 （230 ℃, 1Hz）） are found, respectively. It is shown that the novel P1 peak is frequency independent and the peak temperature increased with the increase of strain amplitude or heating rate. P1 peak could be repressed by the reheating-up measurements and represented by heat treatment. The mechanism of PI peak is clarified by optical microscope （OM） and transmission electron microscope （TEM） observation, and considered to be caused by the creation and expansion of dislocations during plastic deformation. The P2 peak is a thermally activated relaxation IF peak, and activation energy is 1.46 eV, which is caused by the relaxation of the grain boundaries in Mg-0.6%Zr alloy.