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.

Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the system of shallow water wave equations and modified Liouville equation which play an important role in mathematical physics.

Research on Vibration Suppression of the Finite Plate with Square Steel Beams Using Traveling Wave Method

The vibration suppression of the finite plate with square steel beams is studied using traveling wave method. The finite plate with square beams is modeled as the coupling systems between the plate flexural motion and the flexural and torsional motions for the square beams. The vibration response at any position of the coupling structure can be obtained by wave method. Numerical results show that comparing to finite element method (FEM), not only the low frequency but also the medium-high frequency vibration response of the finite plate with square beam can be effectively calculated by wave method. The suppression effect can be increased as the square beam is located at one-third of the length of plate or increasing the height of the beam. The study provides reference for arranged square beams applying to vibration suppression of ship and train structures.

Exact Traveling Wave Solutions for Generalized Camassa-Holm Equation by Polynomial Expansion Methods

We formulate efficient polynomial expansion methods and obtain the exact traveling wave solutions for the generalized Camassa-Holm Equation. By the methods, we obtain three types traveling wave solutions for the generalized Camassa-Holm Equation: hyperbolic function traveling wave solutions, trigonometric function traveling wave solutions, and rational function traveling wave solutions. At the same time, we have shown graphical behavior of the traveling wave solutions.

Exact Traveling Wave Solutions of Nano-Ionic Solitons and Nano-Ionic Current of MTs Using the exp(-φ (ξ ))-Expansion Method

In this work, the exp(-φ (ξ )) -expansion method is used for the first time to investigate the exact traveling wave solutions involving parameters of nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. The validity and reliability of the method are tested by its applications to Nano-ionic solitons wave’s propagation along microtubules in living cells and Nano-ionic currents of MTs which play an important role in biology.

The Traveling Wave Solutions of Space-Time Fractional Partial Differential Equations by Modified Kudryashov Method

In this paper, the modified Kudryashov method is employed to find the traveling wave solutions of two well-known space-time fractional partial differential equations, namely the Zakharov Kuznetshov Benjamin Bona Mahony equation and Kolmogorov Petrovskii Piskunov equation, and as a helping tool, the sense of modified Riemann-Liouville derivative is also used. The propagation properties of obtained solutions are investigated where the graphical representations and justifications of the results are done by mathematical software Maple.

Exact Traveling Wave Solutions for the (1 + 1)-Dimensional Compound KdVB Equation via the Novel (G'/G)-Expansion Method

In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.

ASYMPTOTIC METHOD OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR REACTION DIFFUSION EQUATION

In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.

EXACT TRAVELING WAVE SOLUTIONS OF MODIFIED ZAKHAROV EQUATIONS FOR PLASMAS WITH A QUANTUM CORRECTION

In this article, the authors study the exact traveling wave solutions of modified Zakharov equations for plasmas with a quantum correction by hyperbolic tangent function expansion method, hyperbolic secant expansion method, and Jacobi elliptic function ex- pansion method. They obtain more exact traveling wave solutions including trigonometric function solutions, rational function solutions, and more generally solitary waves, which are called classical bright soliton, W-shaped soliton, and M-shaped soliton.

The (G'/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations

The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.

All Single Traveling Wave Solutions to （3＋1）-Dimensional Nizhnok-Novikov-Veselov Equation

Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.

A new auxiliary equation method for finding travelling wave solutions to KdV equation

In this paper, a new auxiliary equation method is used to find exact travelling wave solutions to the （1＋1）-dimensional KdV equation. Some exact travelling wave solu- tions with parameters have been obtained, which cover the existing solutions. Compared to other methods, the presented method is more direct, more concise, more effective, and easier for calculations. In addition, it can be used to solve other nonlinear evolution equations in mathematical physics.

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.

Novel Traveling Wave Sandwich Piezoelectric Transducer with Single Phase Drive:Theoretical Modeling,Experimental Validation,and Application Investigation

Most of traditional traveling wave piezoelectric transducers are driven by two phase different excitation signals,leading to a complex control system and seriously limiting their applications in industry.To overcome these issues,a novel traveling wave sandwich piezoelectric transducer with a single-phase drive is proposed in this study.Traveling waves are produced in two driving rings of the transducer while the longitudinal vibration is excited in its sandwich composite beam,due to the coupling property of the combined structure.This results in the production of elliptical motions in the two driving rings to achieve the drive function.An analytical model is firstly developed using the transfer matrix method to analyze the dynamic behavior of the proposed transducer.Its vibration characteristics are measured and compared with computational results to validate the effectiveness of the proposed analytical model.Besides,the driving concept of the transducer is investigated by computing the motion trajectory of surface points of the driving ring and the quality of traveling wave of the driving ring.Additionally,application example investigations on the driving effect of the proposed transducer are carried out by constructing and assembling a tracked mobile system.Experimental results indicated that 1)the assembled tracked mobile system moved in the driving frequency of 19410 Hz corresponding to its maximum mean velocity through frequency sensitivity experiments;2)motion characteristic and traction performance measurements of the system prototype presented its maximum mean velocity with 59 mm/s and its maximum stalling traction force with 1.65 N,at the excitation voltage of 500 V_(RMS).These experimental results demonstrate the feasibility of the proposed traveling wave sandwich piezoelectric transducer.

Classification of All Single Traveling Wave Solutions to (3 + 1)-Dimensional Breaking Soliton Equation

In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation.

Multi-Branch Fault Line Location Method Based on Time Difference Matrix Fitting

The distribution network exhibits complex structural characteristics,which makes fault localization a challenging task.Especially when a branch of the multi-branch distribution network fails,the traditional multi-branch fault location algorithm makes it difficult to meet the demands of high-precision fault localization in the multi-branch distribution network system.In this paper,the multi-branch mainline is decomposed into single branch lines,transforming the complex multi-branch fault location problem into a double-ended fault location problem.Based on the different transmission characteristics of the fault-traveling wave in fault lines and non-fault lines,the endpoint reference time difference matrix S and the fault time difference matrix G were established.The time variation rule of the fault-traveling wave arriving at each endpoint before and after a fault was comprehensively utilized.To realize the fault segment location,the least square method was introduced.It was used to find the first-order fitting relation that satisfies the matching relationship between the corresponding row vector and the first-order function in the two matrices,to realize the fault segment location.Then,the time difference matrix is used to determine the traveling wave velocity,which,combined with the double-ended traveling wave location,enables accurate fault location.

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation （ODE） method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.

Traveling Wave Solutions for Generalized Bretherton Equation

This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He＇s semi-inverse method （He＇s variational method）. Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.

Exact Traveling Wave Solutions of Nonlinear PDEs in Mathematical Physics

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

On Exact Traveling Wave Solutions for (1 + 1) Dimensional Kaup-Kupershmidt Equation

In this present paper, the Fan sub-equation method is used to construct exact traveling wave solutions of the (1 + 1) dimensional Kaup-Kupershmidt equation. Many exact traveling wave solutions are successfully obtained, which contain solitary wave solutions, trigonometric function solutions, hyperbolic function solutions and Jacobian elliptic function periodic solutions with double periods.