Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation

This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor.The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed,and this circuit is implemented digitally using ARM-based MCU.Firstly,the mathematical model of the memristor is designed,which is nonvolatile,locally-active and bi-stable.Secondly,the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained.Thirdly,complex dynamics of the novel system are analyzed using phase diagram,Lyapunov exponential spectrum,bifurcation diagram,basin of attractor,and coexisting bifurcation,coexisting attractors are observed.All of these results indicate that this simple system contains the abundant dynamic characteristics.Moreover,transient transition behaviors of the system are analyzed,and it is found that the behaviors of transient chaotic and transient period transition alternately occur.Finally,the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies.However,the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis.This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions.The pressure-dependent length shrinkage coefficients,which quantify the length changes of the inner zone and propped fractures,are modified and incorporated into this multi-zone semi-analytical model.With simultaneous numerical iterations and numerical inversions in Laplace and real-time space,the transient solutions to pressure and rate behavior are determined in just a few seconds.The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods:fracture bilinear flow(FR1),dynamic PFs flow(FR2),inner-area linear flow(FR3),dynamic inner boundary flow(FR4),and outer-area dominated linear flow(FR5).The early hump during FR2 period and a positive upward shift during FR4period are captured on the log-log pressure transient curves,reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary.The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly.The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves.If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected,the flow rate will be overestimated in the later production period.

Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production,the fluid in the vicinity of the directional well enters the wellbore with different rates,leading to non-uniform flux distribution along the directional well.However,in all existing studies,it is oversimplified to a uniform flux distribution,which can result in inaccurate results for field applications.Therefore,this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution.Specifically,the direction well is discretized into a carefully chosen series of linear sources,such that the complex well trajectory can be captured and the nonuniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior.By using the finite difference method,we can obtain the numerical solutions of the transient flow within the wellbore.With the aid of Green's function method,we can obtain the analytical solutions of the transient flow from the matrix to the wellbore.The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow.Subsequently,on the basis of the proposed model,we conduct a comprehensive analysis of the pressure transient behavior of a directional well.The computation results show that the flux variation along the direction well has a significant effect on pressure responses.In addition,the directional well in an infinite reservoir may exhibit the following flow regimes:wellbore afterflow,transition flow,inclined radial flow,elliptical flow,horizontal linear flow,and horizontal radial flow.The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length.Furthermore,a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

Numerical Investigations on the Transient Behavior of Sand Waves in Beibu Gulf Under Normal and Extreme Sea Conditions

In this study, a morphodynamic numerical model is established with the Regional Ocean Modeling System(ROMS)to investigate the transient behavior of sand waves under realistic sea conditions. The simulation of sand wave evolution comprises two steps: 1) a regional-scale model is configured first to simulate the ocean hydrodynamics, i.e., tides and tidal currents, and 2) the transient behavior of sand waves is simulated in a small computational domain under the time-variant currents extracted from the large model. The evolution of sand waves on the continental shelf in the Beibu Gulf is specifically investigated. The numerical results of the two-year evolution of sand waves under normal sea conditions compare well with the field survey data. The transient behavior of sand waves in individual months shows that the sand waves are more stable in April and October than that in other months, which can be selected as the windows for seabed operations. The effects of sediment properties, including settling velocity, critical shear stress and surface erosion rate, on sand wave evolution are also analyzed. Then, the typhoon-induced currents are further superimposed on the tidal currents as the extreme weather conditions. Sand waves with the average wavelength generally have more active behavior than smaller or larger sand waves. The characteristics of the evolution of sand waves in an individual typhoon process are quite different for different hydrodynamic combinations. For the storm conditions, i.e., the real combination and maximum combination cases, the sand waves experience a significant migration together with a damping in height due to the dominant suspended sediment transport. For the mild conditions, i.e., the pure tidal current and minimum combination cases, the sand waves migrate less, but the heights continue growing due to the dominant bedload transport.

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.

The transient fracture behavior for a functionally graded layered structure subjected to an in-plane impact load

The transient fracture behavior of a functionally graded layered structure subjected to an in-plane impact load is investigated. The studied structure is composed of two homogeneous layers and a functionally gradedinterlayer with a crack perpendicular to the boundaries. The impact load is applied on the face of the crack. Fourier transform and Laplace transform methods are used to formulate the present problem in terms of a singular integral equation in Laplace transform domain. Considering variations of parameters such as the nonhomogeneity constant, the thickness ratio and the crack length, the dynamic stress intensity factors （DSIFs） in time domain are studied and some meaningful conclusions are obtained.

Transient thermal behavior of radial fins of rectangular,triangular and hyperbolic profiles with temperature-dependent properties using DTM-FDM

This work focuses on transient thermal behavior of radial fins of rectangular,triangular and hyperbolic profiles with temperature-dependent properties.A hybrid numerical algorithm which combines differential transformation(DTM) and finite difference(FDM) methods is utilized to theoretically study the present problem.DTM and FDM are applied to the time and space domains of the problem,respectively.The accuracy of this method solution is checked against the numerical solution.Then,the effects of some applicable parameters were studied comparatively.Since a broad range of governing parameters are investigated,the results could be useful in a number of industrial and engineering applications.

An efficient algorithm to compute transient pressure responses of slanted wells with arbitrary inclination in reservoirs

Compared with vertical and horizontal wells, the solution and computation of transient pressure responses of slanted wells are more complex. Vertical and horizontal wells are both simplified cases of slanted wells at particular inclination, so the model for slanted wells is more general and more complex than other models for vertical and horizontal wells. Many authors have studied unsteady-state flow of fluids in slanted wells and various solutions have been proposed. However, until now, few of the published results pertain to the computational efficiency. Whether in the time domain or in the Laplace domain, the computation of integration of complex functions is necessary in obtaining pressure responses of slanted wells, while the computation of the integration is complex and time-consuming. To obtain a perfect type curve the computation time is unacceptable even with an aid of high-speed computers. The purpose of this paper is to present an efficient algorithm to compute transient pressure distributions caused by slanted wells in reservoirs. Based on rigorous derivation, the transient pressure solution for slanted wells of any inclination angle is presented. Assuming an infinite-conductivity wellbore, the location of the equivalent-pressure point is determined. More importantly, according to the characteristics of the integrand in a transient pressure solution for slanted wells, the whole integral interval is partitioned into several small integral intervals, and then the method of variable substitution and the variable step-size piecewise numerical integration are employed. The amount of computation is significantly reduced and the computational efficiency is greatly improved. The algorithm proposed in this paper thoroughly solved the difficulty in the efficient and high-speed computation of transient pressure distribution of slanted wells with any inclination angle.

Multistability and coexisting transient chaos in a simple memcapacitive system

The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper.The critical parameter of stable and unstable states is calculated by identifying the eigenvalues of Jacobian matrix.Besides,complex dynamical behaviors are investigated in the system,such as coexisting attractors,hidden attractors,coexisting bifurcation modes,intermittent chaos,and multistability.From the theoretical analyses and numerical simulations,it is found that there are four different kinds of transient transition behaviors in the memcapacitive system.Finally,field programmable gate array(FPGA)is used to implement the proposed chaotic system.

ELECTROMECHANICAL COUPLING MODEL AND ANALYSIS OF TRANSIENT BEHAVIOR FOR INERTIAL RECIPROCATION MACHINES

The dynamical equations for a inertial reciprocating machine excited by two rotating eccentric weights were built by the matrix methodology for establishing dynamical equations of discrete systems. A mathematical model of electromechanical coupling system for the machine was formed by combining the dynamical equations with the state equations of the two motors. The computer simulation to the model was performed for several values of the damping coefficient or the motor power, respectively. The substance of transient behavior of the machine is unveiled by analyzing the results of the computer simulation, and new methods are presented for diminishing the transient amplitude of the vibrating machine and improving the transient behavior. The reliable mathematical model is provided for intelligent control of the transient behavior and engineering design of the equipment.

Transient Analysis of Bandwidth Allocation Strategies in Broadband ISDN

We study the transient behavior of B-ISDN bandwidth allocation strategies in tills paper. First, we present the united state transition equations and obtain the steady-state probability distribution vector by the matrixgeometric solution method. Second, we treat the problem in a uniform way that establishing the coupled differential equations describing the dynamic flow process of B-ISDN channel with the steady state probability as its initial condition and solve it numerically based on the fourth-order Runge-kutta procedure which allows a good balance between computing time and accuracy. Finally, experiment results and discussion are given to illustrate the effectes of the method presented in this paper and show that the idea and analysis way can be extended to all dynamic traffic controlling and management in B-ISDN systems.

Electromechanical coupling model and analysis of transient behavior for inertial vibrating machines

A mathematical model of electromechanical coupling system for a planar inertial vibrating machine is built by setting up dynamical equations of discrete systems with a matrix methodology proposed. The substance of the transient behavior of the machine is unveiled by analyzing the results of the computer simulation to the model, and new methods are presented for diminishing the transient amplitude of the vibrating machine and improving the transient behavior. The reliable mathematical model is provided for intelligent control of the transient behavior of the equipment.

LONG-TIME BEHAVIOR OF TRANSIENT SOLUTIONS FOR CELLULAR NEURAL NETWORK SYSTEMS

By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.

Investigation on Transient Dynamic Behaviors of Low-Tension Undersea Cables

This paper presents a numerical analysis of the dynamic transient behaviors of undersea cables.In this numerical study,the governing equations based on Euler-Bernoulli beam theory are adopted,and they can satisfy many applications no matter what the magnitude of the cable tension is.The nonlinear coupled equations are solved by a popular central finite difference method,and the numerical results of transient behaviors are presented when several kinds of surrounding conditions,such as different towing speeds of surface vessel,different currents and waves with various frequencies and amplitudes,are exerted.Then a detailed comparison of the results,including the upper end tension and cable shape in time-domain,is made under the above external excitations,and finally the possible reasons for these are further explained.

Hydraulic fluctuations during the pump power-off runaway transient process of a pump turbine with consideration of cavitation effects

A runaway transition after the pump power interruption and the simultaneous guide vane servomotor failure is one of the most dangerous and complex transitions for a pumped storage power system(PSPS).This paper analyzes the fluctuation behavior and mechanism of a PSPS during a runaway transition caused by the pump power interruption.The transient cavitation flow in the PSPS is simulated by using a one-dimensional and three-dimensional coupling flow simulation method for the runaway transition.Subsequently,the effects of the transient fluctuation of the radial hydraulic thrust on the runner and transient pressures are analyzed using the short-time Fourier transform method.Finally,the mechanisms are analyzed based on the analysis of the internal flow field.This study suggests that the extreme fluctuation generally occurs near the critical transformation points between the two operation modes.In addition,the extreme fluctuation behavior is primarily related to the local backflow near the runner inlet and the unstable cavitation phenomena in the runner and the draft tube.This finding helps for optimizing the runner design to resolve the instability problems of a PSPS.

A multiphysics model for studying transient crevice corrosion of stainless steel

The transient crevice corrosion behavior of 304 stainless steel in NaCl solution has been investigated by a multiphysics coupling model.The model considers local electrochemical reactions,transport of diffe rent species,and homogeneous reactions.The moving mesh method is used to obtain the geometrical change of the crevice wall with time due to corrosion.The level set method is employed to quantitatively describe the influence of the precipitation process on electrochemical reactions.The transient crevice corrosion morphology,potential and current distributions,and pH and chloride ion concentration distributions are obtained by simulation.The effect of crevice geometry factors on the corrosion process is also discussed.The simulation results are in good agreement with the experiments,showing that the model has high reliability.

A Mixed-finite Volume Element Coupled with the Method of Characteristic Fractional Step Difference for Simulating Transient Behavior of Semiconductor Device of Heat Conductor And Its Numerical Analysis

The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.

Experimental Study on a Centrifugal Pump with an Open Impeller during Startup Period

Transient performance of fluid machinery during transient operating periods, such as startup and stopping, has been drawn more attentions recently due to the growing engineering needs. In this paper, the transient behavior of a prototype centrifugal pump with an open impeller during rapid startup period is studied experimentally. The variations of the rotational speed, flow rate, head, and shaft power during rapid startup period are recorded in ex- periments at different discharge valve openings. In addition, the non-dimensional flow rate and head are also used to analyze the transient behavior. The research result shows that the rise characteristic of the rotational speed is not basically changed by working points, while mainly depends on the startnp characteristics of the driving motor. Compared with the rapid rise of the rotational speed, the flow rate rises slowly in the initial stage of startup. Moreover, the flow rate lags behind the rotational speed to rise to final stable value, and the delay becomes more severe with the increase of the discharge valve opening. The shaft power impact phenomenon generally exists in the process of startup. The non-dimensional analysis shows that the non-dimensional head is very high at the very beginning of startup, and quickly falls to the minimum, then gradually rises to final stable value, while the non-dimensional flow rate always shows the rise tendency during whole startup period. In conclusion, it is found from the non-dimensional results that the quasi-steady analysis is unable to accurately assess the transient flow during startup period.

Sigma-delta modulator modeling analysis and design

This paper introduces a new method for SC sigma-delta modulator modeling.It studies the integrator＇s different equivalent circuits in the integrating and sampling phases.This model uses the OP-AMP input pair＇s tail current（I_0） and overdrive voltage（v_（on）） as variables.The modulator＇s static and dynamic errors are analyzed.A group of optimized I0 and von for maximum SNR and power x area ratio can be obtained through this model.As examples, a MASH21 modulator for digital audio and a second order modulator for RFID baseband are implemented and tested, and they can achieve 91 dB and 72 dB respectively,which verifies the modeling and design criteria.

AVAILABILITY ANALYSIS OF THE QUEUEING SYSTEM GI/PH/I WITH SERVER BREAKDOWNS

In the existing literature of Repairable Queueing Systems (RQS), i.e., queueing systems with server breakdowns, it is almost all assumed that interarrival times of successive customers are independent, identically exponentially distributed. In this paper, we deal with more generic system GI/PH/1 with server's exponential uptime and phase-type repair time. With matrix analysis theory, we establish the equilibrium condition and the characteristics of the system, derive the transient and stationary availability behavior of the system.