Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory （ITP） of the dynamical mean field theory （DMFT） and coherentpotential approximation （CPA） is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tij^mn（m ≠ n） are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.

Feynman Perturbation Series for the Morse Potential

In this paper we give an alternative treatment of the Schrodinger equation with the Morse potential, which based on the exact summation of the Feynman perturbation series in its original form. Using Fourier transform we establish a recurrence equation between terms of the perturbation series. Finally, by the inverse Fourier transform and some technical tools of the ordinary differential equations of the second order, we can compute the exact sum of the perturbation series which is the Green’s function of the problem.

Effect of Potential Perturbation Polarization on the Stress Corrosion Cracking of Type 321 Stainless Steel

The SCC susceptibility of type 321 stainless steel in acidic chloride solution has been studied by slow strain rate testing (SSRT) and SEM. During the slow rate tensile process, the specimen was polarized with different potential perturbation modes such as cyclic potential scan and cyclic potential step methods. The results indicated that the potential scan rate or step frequency played an essential role in the initiation and propagation of crack.

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

A batch-to-batch optimal iterative learning control （ILC） strategy for the tracking control of product quality in batch processes is presented. The linear time-varying perturbation （LTVP） model is built for product quality around the nominal trajectories. To address problems of model-plant mismatches, model prediction errors in the previous batch run are added to the model predictions for the current batch run. Then tracking error transition models can be built, and the ILC law with direct error feedback is explicitly obtained, A rigorous theorem is proposed, to prove the convergence of tracking error under ILC, The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.

Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations

This paper investigates the problem of robust exponential stability for neutral systems with time-varying delays and nonlinear perturbations. Based on a novel Lyapunov functional approach and linear matrix inequality technique, a new delay-dependent stability condition is derived. Since the model transformation and bounding techniques for cross terms are avoided, the criteria proposed in this paper are less conservative than some previous approaches by using the free-weighting matrices. One numerical example is presented to illustrate the effectiveness of the proposed results.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

Peculiar features of the interaction potential between hydrogen and antihydrogen at intermediate separations

This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.

Dissipation-Managed Bright Soliton in a 1D Bose-Einstein Condensate in an Optical-Lattice Potential

We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-onedimensional Bose-Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we demonstrate that the height （as well as width） of bright soliton may have little change through selecting experimental parameters.

Stability Analysis of Cyber-Physical Micro Grid Load Frequency Control System with Time-Varying Delay and Non-Linear Load Perturbations

In a cyber-physical micro-grid system,wherein the control functions are executed through open communication channel,stability is an important issue owing to the factors related to the time-delay encountered in the data transfer.Transfer of feedback variable as discrete data packets in communication network invariably introduces inevitable time-delays in closed loop control systems.This delay,depending upon the network traffic condition,inherits a time-varying characteristic;nevertheless,it adversely impacts the system performance and stability.The load perturbations in a micro-grid system are considerably influenced by the presence of fluctuating power generators like wind and solar power.Since these non-conventional energy sources are integrated into the power grid through power electronic interface circuits that usually works at high switching frequency,noise signals are introduced into the micro-grid system and these signals gets super-imposed to the load variations.Based on this back ground,in this paper,the delay-dependent stability issue of networked micro-grid system combined with time-varying feedback loop delay and uncertain load perturbations is investigated,and a deeper insight has been presented to infer the impact of time-delay on the variations in the system frequency.The classical Lyapunov-Krasovskii method is employed to address the problem,and using a standard benchmark micro-grid system,and the proposed stability criterion is validated.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.

Coupling Interactions and Trapped Effects for a Triple-Well Potential

Weak and strong coupling interactions and trapped effects have always played a significant role in understanding physical and chemical properties of materials. Triple-well anharmonic potential may be modeled for interpretation of energy spectra from the nuclear to macro molecular systems, and also crystalline systems. Exact periods of a trapped particle in each well of the potential are explicitly derived. For the extended Duffing system, it is predicted that infinite series of both frequency and spatial trajectory approach to exact results in the limit of weak-coupling cases (g→0).

The Pionic Deuterium and the Pion Tetrahedron Vacuum Polarization

A double-well potential model is proposed for the pionic deuterium that enables to calculate the energy split, the potential barrier height and estimate the pion tetrahedron edge length. We propose that pion tetrahedrons, πTd = ud~dũ, play a central role in the Yukawa interaction by enabling quark exchange reactions between protons and neutrons by tunneling through a potential barrier. A vacuum polarization Feynman diagram is proposed for the πTd having chains of fermion loops for the two valence quarks and anti-quarks connected by gluons. With a higher order vacuum polarization diagram, the d and u quark loops are interleaved and the chiral symmetry is broken dynamically. The proposed πTd vacuum polarization integral does not diverge in both the IR and UV limits and vanishes in the limit of an infinite pion tetrahedron condensate. We propose a new Delbruck scattering Feynman diagram that includes d and u quark and anti-quark interleaved loops. We further propose that conversion of gravitons to photons may occur via quark and anti-quark loops that describe the pion tetrahedrons dynamics in the vacuum and may also transfer gravitational waves.

Stability of nonlinearly-perturbed systems with time varying delay using LMIs

This paper studies delay dependent robust stability and the stabilization problem of nonlinear perturbed systems with time varying delay. A new set of sufficient conditions for the stability of open as well as close loop systems are obtained in the sense of Lyapunov-Krasovskii. To reduce the conservatism, the work exploits the idea of splitting the delay interval into multiple equal regions so that less information on the time delay can be imposed to derive the results. The derived criterion not only improves the upper bounds of the time delay but also does not require the derivative of the delay to be known at prior. Easily testable sufficient criteria are presented in terms of linear matrix inequalities. It is shown that the derived conditions are very less conservative while comparing the maximum allowable upper bound of delay with the existing results in literature.

Analytic perturbation solutions to the Venusian orbiter due to the nonspherical gravitational potential

The analytic perturbation solutions to the motions of a planetary orbiter given in this paper are effective for 0e1, where e is the orbital eccentricity of the orbiter. In the solution, it is assumed that the rotation of the central body is slow, and its astronomical background is clear. Examples for such planets in the solar system are Venus and Mercury. The perturbation solution is tested numerically on two Venusian orbiters with eccentric orbits, PVO and Magellan, and found to be effective.

Bound States of the Perturbed Schrödinger Systems

A bound state of the Schrödinger system is disturbed by an additional potential.It is shown that the system is still in a bound state if and only if its energy correction is restricted to the corresponding value.This infers some previous series solutions in quantum mechanics to be unbound states for the order i>1 of perturbation.The corrected bound states of the system are given and their physical meaning is discussed simply.Application of the method to Stark effect reveals its advantage for researches of quantum chaos.

Investigation of Bose-Einstein Condensates in q-Deformed Potentials with First Order Perturbation Theory

The Gross-Pitaevskii equation, which is the governor equation of Bose-Einstein condensates, is solved by first order perturbation expansion under various q-deformed potentials. Stationary probability distributions reveal one and two soliton behavior depending on the type of the q-deformed potential. Additionally a spatial shift of the probability distribution is found for the dark soliton solution, when the q parameter is changed.

电化学分散法制备PtRh纳米粒子

将纯PtRh丝放置在NaOH溶液中,采用方波电势法可制备PtRh水溶胶。PtRh原子在方波电势搅动下被快速-氧化还原而发生重排,同时,在氢气的推动力下,PtRh丝得以分散。采用这种方法可在温和的条件下绿色合成清洁的PtRh纳米粒子(NPs),制备过程中无需任何前驱体金属离子和还原剂。采用扫描电子显微镜(SEM)、能谱分析(EDS)、高分辨透射电镜(HR-TEM)、X射线衍射(XRD)和X射线光电子能谱(XPS)对PtRh纳米溶胶进行了表征。PtRh纳米粒对甲醇氧化具有较高的电催化活性。

L^p-L^q ESTIMATES FOR HIGHER ORDER PERTURBED HYPERBOLIC EQUATION

In this paper Lp Lq estimates for the solution u(x,t) to the following perturbed higher order hyperbolic equation are considered,(οtt-aΔ)(οtt-bΔ)u+V(x)u=0,\ x∈Rn,n≥6, οjtu(x,0)=0,\ ο3tu(x,0)=f(x),\ (j=0,1,2).We assume that the potential V(x) and the initial data f(x) are compactly supported, and V(x) is sufficiently small, then the solution u(x,t) of the above problem satisfies the same Lp Lq estimates as that of the unperturbed problem. Received November 25,1996. Revised April 14,1997.1991 MR Subject Classification:35L05,35B20,35B45.