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Far distant wind farms are integrated nowadays with the help of Voltage Source Converter (VSC)-based HVDC grids. Rapid fault current is very common in VSC-based HVDC grids and, therefore, quick fault detection and fast executing protection methods are critical for the existence of the HVDC grids. This paper proposes a rise time-based fault detection method using local measurement data and Travelling Wave (TW) characteristics of incoming fault TW. Dominating frequency of the primary wavefront is computed by the rise time of incoming fault TW. With the help of auto-updating transmission line parameters and the dominating frequency of incoming TW, the fault location is identified. The performance of the proposed method has been observed in PSCAD Simulation with a 4-Terminal HVDC test grid in multiple scenarios and compared with the existing fault detection methods on multiple levels. The results show that the proposed method is very fast, and accurate and can complete the whole Fault Location process within a few microseconds just after the Inception of the fault. [ABSTRACT FROM AUTHOR]

The type of symmetry exhibited by a travelling wave can have important implications for its behaviour and properties, such as its polarization, dispersion, and interactions with other waves or boundaries. The fractional differential Duffing problem refers to the mathematical modelling of nonlinear, damped oscillations of a system with fractional derivatives. It is a generalization of the classical Duffing equation, which describes the behaviour of a nonlinear, damped oscillator (the equation becomes symmetric under time-reversal). The fractional derivatives allow for a more accurate description of the system's memory and hereditary properties. The solution of the fractional Duffing equation can provide insight into the complex dynamic behaviour of various physical, biological, and engineering systems. We are concerned with studying a new differential Duffing fractional problem. It involves some sequential Caputo derivatives with an infinite series of Riemann-Liouville integrals and some other functions. We begin by proving a first existence and uniqueness result, then we discuss two types of stability for the obtained uniqueness result. An illustrative examples is given to show the applicability of the result. We are also concerned with applying the Tanh method to obtain new classes of travelling wave solutions for three important classes of (Khalil) fractional conformable problems; the generalized equation of Duffing, the Landau-Ginzburg-Higgs equation and the Sine-Gordon one. Some numerical simulations are plotted and a conclusion is given at the end. [ABSTRACT FROM AUTHOR]

The electrical curtain board (ECB) is constituted of parallel linear electrodes deposited on a dielectric layer plate and supplied by a poly-phase electrical voltage. This paper reports a study of the movement of Polyvinyl Chloride (PVC) µm-size particles on such an ECB. The experimental setup comprised three ECB plates of different inter-electrodes spacing, and a homemade electric supply. Obtained results show that it is possible to move the quasi-totality of the particles on the ECB if adequate values are given to the voltage, the frequency and the inter-electrodes spacing. [ABSTRACT FROM AUTHOR]

Given any positive speed, we prove the existence of a travelling wave solution for a viscous incompressible thin dilatant liquid film coated with an insoluble surfactant. Relying on first principles of fluid mechanics, lubrication theory leads to a coupled system of second-order partial differential equations for the film's height and the surfactant's concentration where a second-order approximation of the viscosity function is used. The travelling wave solution is C 2 -regular and generates a heteroclinic orbit which connects two distinct equilibrium points of the associated plane dynamical system. [ABSTRACT FROM AUTHOR]

The concept of the Phase Field is currently widely used in the Theory of Phase Transitions and Material science. The Penrose-Fife phase field model is now a well-established model in these fields. In the course of study of this model both the rigorous mathematical results and approximate solutions were obtained. However, to the best of our knowledge, no exact solutions were given in the literature. In the present paper we give exact travelling wave solutions for this system. While the functional form of the solutions is rather simple, the dependence of solutions on the parameters of the model is quite complicated. Also, an interesting link between this model and the Convective-Viscous Cahn-Hilliard equation is established. [ABSTRACT FROM AUTHOR]

In this short note we apply the nonlinear Green's function method for the solution of the Tzitzéica type equation hierarchies arising in nonlinear science. Using the travelling wave ansatz, we first transform the nonlinear partial differential equations to nonlinear ordinary differential equations. Then, we establish a general representation formula for nonlinear Green's function of these equations. Eventually, using Frasca's short time expansion, we obtain the exact solution to these equations. Numerical analysis shows that the obtained Green's function solution is sufficiently close to the numerical solution obtained by the well-known method of lines. Finally, we involve the inverse transform and study the full nature of the Tzitzéica equation. [ABSTRACT FROM AUTHOR]

Using the definition of algebraic travelling wave solution for general 2-th order differential equations given in [9], we provide the only possible algebraic travelling wave solutions for the celebrated generalized Burgers-Fisher equation. [ABSTRACT FROM AUTHOR]

This article studies existence and stability of travelling wave of unstirred Gray-Scott system in biological pattern formation which models an isothermal chemical reactioninvolving two chemical species, a reactantAand an auto-catalystB, and a linear decay, whereCis an inert product. Our result shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different travelling pulses than related models in the literature. In particular, the existence of multiple travelling waves which have distinctive number of local maxima is proved. Furthermore, the stability of travelling wave of the reaction–diffusion system of isothermal diffusion system, is also studied. [ABSTRACT FROM PUBLISHER]

We study the periodic lattice dynamical systems with bistable nonlinearity. We use Moser's theorem to show that there exist infinitely many stationary solutions when one of the migration coefficients is sufficiently small. Moreover, we prove that the propagation failure occurs when both migration coefficients are sufficiently small. [ABSTRACT FROM PUBLISHER]

In this paper, by using the integral bifurcation method, we study a nonlinear dispersive equation. Some new soliton-like solutions and some compacton-like periodic wave solutions are obtained. Their dynamic characters are investigated and the profiles are given by the mathematical software Maple. From the graphs of some soliton-like solutions, we find that their profiles are transformable. [ABSTRACT FROM AUTHOR]

Piezoelectric micro-pump should contain the physical running parts like check valves for acquiring the unilateral motion of fluid from the alternating motion of actuators. But the check valves raise many problems such as abrasion or exhaustive destruction by the recursive mechanical displacement. And the performances of micro pump are deteriorated by them. To solve these problems, we propose a novel type piezoelectric valveless micro-pump using peristaltic motion due to the travelling wave excitation. Proposed pump model consists of two piezoelectric ceramic plates, elastic metal body, caps for covering flow path, rubber rings for tight sealing and disk springs for the pressurization of pump body. The FEM simulation analysis of the proposed pump model was carried out to verify its operation mechanism. And a prototype pump was fabricated and evaluated to validate the proposed concepts. Maximum back pressure was 0.97kPa and flow rate was 640μl/min under 130Vrms, 67.5kHz of driving voltage. [ABSTRACT FROM AUTHOR]

Existence and bifurcation results are derived for quasi periodic travelling waves of discrete nonlinear Schrodinger equations with nonlocal interactions and with polynomial-type potentials. Variational tools are used. Several concrete nonlocal interactions are studied as well. [ABSTRACT FROM AUTHOR]

Linearizing nonlinear differential equations and finding exact solutions has been an interesting subject in the theory of differential equations. For many nonlinear differential equations, so far no general treatment on linearizing transformations and obtaining exact solutions has been formulated. In this article we use the generalized linearizing transformation to derive the first integral of a generalized reaction-diffusion equation with higher order nonlinear rate of growth, which enables us to linearize the associated second-order nonlinear ordinary differential equation to a linear case. Under certain parametric conditions we can also find travelling wave solutions explicitly for the generalized reaction-diffusion equation through using the derived first integral. [ABSTRACT FROM AUTHOR]

In a study (Szekely, Acta Physiol. Hung. 27 (1965), pp. 285-289) of the locomotion of salamanders, it is observed that a 'doubly periodic travelling wave solution' of a logical neural network can be used to explain a dynamic pattern of movements. We show here that a relatively simple (nonlogical) artificial neural network can also be built and necessary and sufficient conditions for the existence of doubly periodic travelling wave solutions can be found. It is hoped that our investigation will set some foundation in the future design of other artificial neural networks that also allow periodic travelling wave solutions. [ABSTRACT FROM AUTHOR]

The time-delayed Burgers equation is introduced and the improved tanh-function method is used to construct exact multiple soliton and triangular periodic solutions. For an understanding of the nature of the exact solutions that contained the time-delay parameter, we calculated the numerical solutions of this equation by using the Adomian decomposition method to the boundary value problem. [ABSTRACT FROM AUTHOR]

In this paper, we study the Korteweg-de Vries-Burgers equation with boundary conditions. After making a series of transformations, we convert the Korteweg-de Vries-Burgers equation into an Emden-Fowler equation. An approximate solution in series form is obtained by means of the Adomian decomposition method. The solution is illustrated to agree well with phase plane analysis. [ABSTRACT FROM AUTHOR]