Matching Boundary Conditions for a Heterogeneous Atomic Chain

We propose accurate boundary treatments for a heterogeneous atomic chain, in terms of matching boundary conditions （MBCs）. The main challenge lies in reproducing the physical reflection across the boundary to a correct amount. With reflection coefficients we demonstrate that the accuracy is improved when more atoms are used under the boundary condition. The inclusion of an atom in the embedded sublattice B may considerably enhance the performance. Numerical testing illustrates the effectiveness of the proposed MBCs.

Controller design for stochastic nonlinear systems with matched conditions

This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.

Robust exponential control of a class of systems with uncertainties

The robust exponential stabilization problem for uncertain systems isstudied. Based on the solution for a nominal linear quadratic regulator problem with a prescribeddegree of stability, the methods of constructing state feedback controllers are developed to ensurethe robust stability of the closed loop system under the conditions weaker than the matchingcondition. Also, the cases where the matching condition is satisfied are considered in detail. Someexamples are included to show the solution methods.

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE Ⅱ PLANE STRESS CRACK

The near crack line field analysis method has been used io investigate into theexact elastic-plastic solutions of a mode II crack under plane stress condilion in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theory.hare been completely. dbandoned and the correct formulations of matching conditionsat the elaslic-plastic boundary. have been given. By, matching the general solution ofthe plastic slress field (bul not the special solution used to be adopted) with the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary, near the crack line, the plastic stresses. the length of the plastic =one and theunit normal vector of the elastic-plastic boundary.which are sufficiently precise near the crack line region ,have been given.

THE EXACT SOLUTIONS OF ELASTIC－PLASTIC CRACK LINE FIELD FOR MODE Ⅱ PLANE STRESS CRACK

The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱ crack under plane stress condition in anelastic-perfectly plastic solid. The assumptions of the usual small scale yielding theoryhave been completely. dbandoned and the correct .formulations of matching conditionsat the elastic-plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopted) will the exactelastic stress field (but not the crack tip K-dominant field) at the elastic-plasticboundary. near the crack line, the plastic .stresses, the length of the plastic zone and theunit normal vector of the elaslic-plastic boundary. which sufficiently precise nearthe crack line region, hare been given.

Matching Boundary Conditions for Scalar Waves in Body-Centered-Cubic Lattices

Matching boundary conditions(MBC’s)are proposed to treat scalar waves in the body-centered-cubic lattices.By matching the dispersion relation,we construct MBC’s for normal incidence and incidence with an angle a.Multiplication of MBC operators then leads to multi-directional absorbing boundary conditions.The effectiveness are illustrated by the reflection coefficient analysis and wave packet tests.In particular,the designed M1M1 treats the scalar waves in a satisfactory manner.

Novel Ship Propulsion System

As the development tends towards high-speed, large-scale and high-power, power of the ship main engine becomes larger and larger. This make the engine design and cabin arrangement become more and more difficult. Ship maneuverability becomes bad. A new ship propulsion system, integrated hydraulic propulsion （IHP）, is put forward to meet the development of modem ship. Principle of IHP system is discussed. Working condition matching characteristic of IHP ship is studied based on its matching characteristic charts. According to their propulsion principle, dynamic mathematic models of IHP ship and direct propulsion （DP） ship are developed. These two models are verified by test sailing and test stand data. Based on the software Matlab/Simulink, comparison research between IHP ship and DP ship is conducted. The results show that cabin arrangement of IHP ship is very flexible, working condition matching characteristic of IHP ship is good, the ratio of power to weight of IHP ship is larger than DP ship, and maneuverability is excellent. IHP system is suitable for engineering ship, superpower ship and warship, etc.

Stability of Atomic Simulations with Matching Boundary Conditions

.We explore the stability of matching boundary conditions in one space dimension,which were proposed recently for atomic simulations(Wang and Tang,Int.J.Numer.Mech.Eng.,93(2013),pp.1255–1285).For a finite segment of the linear harmonic chain,we construct explicit energy functionals that decay along with time.For a nonlinear atomic chain with its nonlinearity vanished around the boundaries,an energy functional is constructed for the first order matching boundary condition.Numerical verifications are also presented.

Matching Preclusion for Augmented k-ary n-cubes

The （conditional） matching preclusion number of a graph is the minimum number of edges whose deletion leaves a resulting graph （with no isolated vertices） that has neither perfect matchings nor almost perfect matchings. In this paper, we find this number and classify all optimal sets for the augmented k-ary n-cubes with even k ≥ 4.

Controller design for 2-DOF underactuated mechanical systems based on controlled Lagrangians and application to Acrobot control

On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their property.As a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic forces.Further,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general solutions.Benefiting from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general form.Specifically,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms involved.Unlike what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)method.As a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.

Asymptotic Behavior of Global Classical Solutions to the Cauchy Problem on a Semi-Bounded Initial Axis for Quasilinear Hyperbolic Systems

In this paper we study the asymptotic behavior of global classical solutions to the Cauchy problem with initial data given on a semi-bounded axis for quasilinear hyperbolic systems. Based on the existence result on the global classical solution, we prove that, when t tends to the infinity, the solution approaches a combination of C1 travelling wave solutions with the algebraic rate （1 ＋ t）^-u, provided that the initial data decay with the rate （1 ＋ x）^-（l＋u） （resp. （1 - x）^-（1＋u）） as x tends to ＋∞ （resp. -∞）, where u is a positive constant.

High contrast ratio,high uniformity multiple quantum well spatial light modulators

Our latest research results on GaAs-A1GaAs multiple quantum well spatial light modulators are presented. The thickness uniformity of the epitaxial layers across the 3-inch wafer grown by our molecular beam epitaxy is better than 0.1% and the variation of cavity resonance wavelength within the wafer is only 0.9 nm. A contrast ratio （CR） of 102 by varying bias voltage from 0 to 6.7 V is achieved after fine tuning the cavity by etching an adjust layer. Both theoretical and experimental results demonstrate that incorporating an adjust layer is an effective tuning method for obtaining high CR.