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.

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.

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.

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 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.

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.

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.

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.

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.

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 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 for parallel transmission lines using one-terminal current traveling waves

With proper phase module transformation,parallel lines can be decomposed to the same directional net and the reverse directional net. The propagation characteristics of traveling waves in the reverse directional net were analyzed,and the refraction coefficient at the fault point for a single phase fault was derived. In addition,the module selection was discussed. Simulation results show that satisfying accuracy can be achieved with the proposed method. Moreover,it is immune to fault types,fault resistances,and outside system parameters.

Traveling Waves for an Epidemic Model with Vaccination and Nonlocal Diffusion

An epidemic model with vaccination and nonlocal diffusion is proposed, and the existence of traveling wave solutions of this model is studied. By the cross-iteration scheme companied with a pair of upper and lower solutions and Schauder's fixed point theorem,sufficient conditions are obtained for the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.

Traveling Waves for an Epidemic Model with Spatio-Temporal Delays

This paper is concerned with traveling waves for an epidemic model with spatio-temporal delays. It is shown that the traveling wave solutions are still persistently existing in the model when the non-locality is caused by small average time delays via the geometric singular perturbation theory and the center manifold theorems.

Existence of Traveling Waves in Lattice Dynamical Systems

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c*>0 such that for each c≥c*, the systems under consideration admit monotonic nondecreasing traveling waves.

Traveling Waves in Degenerate Diffusion Equations

In this survey,we present a literature review on the study of travel-ing waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy.The main results on wave exis-tence and stability are presented for the typical degenerate equations,including porous medium equations,flux limited diffusion equations,delayed degener-ate diffusion equations,and other strong degenerate diffusion equations.

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.

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.

Traveling waves for a diffusive SEIR epidemic model with standard incidences

This paper is devoted to the existence of the traveling waves of the equations describing a diffusive susceptible-exposed-infected-recovered(SEIR) model. The existence of traveling waves depends on the basic reproduction rate and the minimal wave speed. We obtain a more precise estimation of the minimal wave speed of the epidemic model, which is of great practical value in the control of serious epidemics. The approach in this paper is to use the Schauder fixed point theorem and the Laplace transform. We also give some numerical results on the minimal wave speed.