ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE p-LAPLACIAN DIFFUSION

We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.

Coexisting fast–slow dendritic traveling waves in a 3D-array electric field coupled neuronal network

Coexistence of fast and slow traveling waves without synaptic transmission has been found in hhhippocampal tissues,which is closely related to both normal brain activity and abnormal neural activity such as epileptic discharge. However, the propagation mechanism behind this coexistence phenomenon remains unclear. In this paper, a three-dimensional electric field coupled hippocampal neural network is established to investigate generation of coexisting spontaneous fast and slow traveling waves. This model captures two types of dendritic traveling waves propagating in both transverse and longitude directions: the N-methyl-D-aspartate(NMDA)-dependent wave with a speed of about 0.1 m/s and the Ca-dependent wave with a speed of about 0.009 m/s. These traveling waves are synaptic-independent and could be conducted only by the electric fields generated by neighboring neurons, which are basically consistent with the in vitro data measured experiments. It is also found that the slow Ca wave could trigger generation of fast NMDA waves in the propagation path of slow waves whereas fast NMDA waves cannot affect the propagation of slow Ca waves. These results suggest that dendritic Ca waves could acted as the source of the coexistence fast and slow waves. Furthermore, we also confirm the impact of cellular spacing heterogeneity on the onset of coexisting fast and slow waves. The local region with decreasing distances among neighbor neurons is more liable to promote the onset of spontaneous slow waves which, as sources, excite propagation of fast waves. These modeling studies provide possible biophysical mechanisms underlying the neural dynamics of spontaneous traveling waves in brain tissues.

Measurement of very low-molecular weight metabolites by traveling wave ion mobility and its use in human urine samples

The collision cross-sections(CCS)measurement using ion mobility spectrometry(IMS)in combination with mass spectrometry(MS)offers a great opportunity to increase confidence in metabolite identification.However,owing to the lack of sensitivity and resolution,IMS has an analytical challenge in studying the CCS values of very low-molecular-weight metabolites(VLMs250 Da).Here,we describe an analytical method using ultrahigh-performance liquid chromatography(UPLC)coupled to a traveling wave ion mobility-quadrupole-time-of-flight mass spectrometer optimized for the measurement of VLMs in human urine samples.The experimental CCS values,along with mass spectral properties,were reported for the 174 metabolites.The experimental data included the mass-to-charge ratio(m/z),retention time(RT),tandem MS(MS/MS)spectra,and CCS values.Among the studied metabolites,263 traveling wave ion mobility spectrometry(TWIMS)-derived CCS values(TWCCSN2)were reported for the first time,and more than 70%of these were CCS values of VLMs.The TWCCSN2 values were highly repeatable,with inter-day variations of<1%relative standard deviation(RSD).The developed method revealed excellent TWCCSN2 accuracy with a CCS difference(DCCS)within±2%of the reported drift tube IMS(DTIMS)and TWIMS CCS values.The complexity of the urine matrix did not affect the precision of the method,as evidenced by DCCS within±1.92%.According to the Metabolomics Standards Initiative,55 urinary metabolites were identified with a confidence level of 1.Among these 55 metabolites,53(96%)were VLMs.The larger number of confirmed compounds found in this study was a result of the addition of TWCCSN2 values,which clearly increased metabolite identification confidence.

Harmonic balance simulation of the influence of component uniformity and reliability on the performance of a Josephson traveling wave parametric amplifier

A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.

Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay

In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.

Propagation and Pinning of Travelling Wave for Nagumo Type Equation

In this paper, we study the propagation and its failure to propagate (pinning) of a travelling wave in a Nagumo type equation, an equation that describes impulse propagation in nerve axons that also models population growth with Allee effect. An analytical solution is derived for the traveling wave and the work is extended to a discrete formulation with a piecewise linear reaction function. We propose an operator splitting numerical scheme to solve the equation and demonstrate that the wave either propagates or gets pinned based on how the spatial mesh is chosen.

Parameter Identification in Traveling Wave Solutions of a Modified Fisher’s Equation

In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes a relaxation time in relating the flux to the gradient of the density and an added cubic non-linearity. We show that such equations still possess traveling wave solutions by using standard methods for nonlinear dynamical systems in which fixed points in the phase plane are found and their stability characteristics are classified. A heteroclinic orbit in the phase plane connecting a saddle point to a node represents the traveling wave solution. We then design parameter estimation/discovery algorithms for this system including a few based on machine learning methods and compare their performance.

Adaptive Reclosing Scheme Based on Traveling Wave Injection For Multi-Terminal dc Grids

The hybrid dc circuit breaker(HCB)has the advantages of fast action speed and low operating loss,which is an idealmethod for fault isolation ofmulti-terminal dc grids.Formulti-terminal dc grids that transmit power through overhead lines,HCBs are required to have reclosing capability due to the high fault probability and the fact that most of the faults are temporary faults.To avoid the secondary fault strike and equipment damage that may be caused by the reclosing of the HCB when the permanent fault occurs,an adaptive reclosing scheme based on traveling wave injection is proposed in this paper.The scheme injects traveling wave signal into the fault dc line through the additionally configured auxiliary discharge branch in the HCB,and then uses the reflection characteristic of the traveling wave signal on the dc line to identify temporary and permanent faults,to be able to realize fast reclosing when the temporary fault occurs and reliably avoid reclosing after the permanent fault occurs.The test results in the simulation model of the four-terminal dc grid show that the proposed adaptive reclosing scheme can quickly and reliably identify temporary and permanent faults,greatly shorten the power outage time of temporary faults.In addition,it has the advantages of easiness to implement,high reliability,robustness to high-resistance fault and no dead zone,etc.

关于《Existence and Multiplicity of Traveling Waves in a lattice Dynamical System》的注记

文章《Existence and Multiplicity of Traveling Waves in a lattice Dynamical System》利用单调迭代格式和上下解方法研究了一个格动力系统小于临界波速的行波解的存在性,而当波速等于临界波速时不易通过构造上下解来证明其行波解的存在性,该文利用极限方法证明了原格动力系统的具有临界波速的行波解。

Exact Traveling Wave Solutions of the Generalized Fractional Differential mBBM Equation

By using the fractional complex transform and the bifurcation theory to the generalized fractional differential mBBM equation, we first transform this fractional equation into a plane dynamic system, and then find its equilibrium points and first integral. Based on this, the phase portraits of the corresponding plane dynamic system are given. According to the phase diagram characteristics of the dynamic system, the periodic solution corresponds to the limit cycle or periodic closed orbit. Therefore, according to the phase portraits and the properties of elliptic functions, we obtain exact explicit parametric expressions of smooth periodic wave solutions. This method can also be applied to other fractional equations.

NONLINEAR TRAVELING WAVES IN A COMPRESSIBLE MOONEY-RIVLIN ROD I.LONG FINITE-AMPLITUDE WAVES

In literature,nonlinear traveling waves in elastic circular rods have only been studied based on single partial differential equation(pde)models,and here we consider such a problem by using a more accurate coupled-pde model.We derive the Hamiltonian from the model equations for the long finite-amplitude wave approximation,analyze how the number of singular points of the system changes with the parameters,and study the features of these singular points qualitatively.Various physically acceptable nonlinear traveling waves are also discussed,and corresponding examples are given.In particular,we find that certain waves,which cannot be counted by the single-equation model,can arise.

ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx＋（ζθ）x＋aθxx,ζt=-θx＋βζxx;with initial data and end states （ζθ）（x,0）=（ζ0,θ0）（x）→（ζ±,θ±）as x→∞.We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coeffi- cients a and v by the method of energy estimates.

STABILITY OF TRAVELING WAVES IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE

This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.

Complex modes and traveling waves in axially moving Timoshenko beams

Complex modes and traveling waves in axially moving Timoshenko beams are studied. Due to the axially moving velocity, complex modes emerge instead of real value modes. Correspondingly, traveling waves are present for the axially moving material while standing waves dominate in the traditional static structures. The analytical results obtained in this study are verified with a numerical differential quadrature method.

Traveling Waves for 2-1 Dimension Lattice Difference Equations

A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results.

TRAVELING WAVES IN A SIRH MODEL WITH SPATIO-TEMPORAL DELAY AND NONLOCAL DISPERSAL

This paper deals mainly with the existence and asymptotic behavior of traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal based on Schauder’s fixed-point theorem and analysis techniques,which generalize the results of nonlocal SIRH models without relapse and delay.In particular,the difficulty of obtaining the asymptotic behavior of traveling waves for the appearance of spatio-temporal delay is overcome by the use of integral techniques and analysis techniques.Finally,the more general nonexistence result of traveling waves is also included.

INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL

This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.

Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

This paper is devoted to the study of a three-dimensional delayed system with nonlocal diffusion and partial quasi-monotonicity. By developing a new definition of upper-lower solutions and a new cross iteration scheme, we establish some existence results of traveling wave solutions. The results are applied to a nonlocal diffusion model which takes the three-species Lotka-Volterra model as its special case.

Fault location method for transmission line based on traveling waves

The single phase grounding fault location is the focus which researchers pay attention to and study in power system. The accurate fault location can lighten the patrolling burden, and enhance the reliability of the power network. It adopts A/D which has high speed, and uses TMS320VC5402 DSP chip as the system core. This paper presented theory of operation based on traveling waves and achieved software and hardware in detail.

Influence of the Domain Boundary on the Speeds of Traveling Waves

Let H > 0 be a constant, g ≥ 0 be a periodic function and Ω ={(x, y) ||x| H + g (y), y ∈R}. We consider a curvature flow equation V = κ + A in Ω, where for a simple curve γt Ω, V denotes its normal velocity, κ denotes its curvature and A > 0 is a constant. [1] proved that this equation has a periodic traveling wave U, and that the average speed c of U is increasing in A and H, decreasing in max g' when the scale of g is sufficiently small. In this paper we study the dependence of c on A, H, max g' and on the period of g when the scale of g is large. We show that similar results as [1] hold in certain weak sense.