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Journal articles on the topic 'Travelling wave linear accelerators'

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Author: Grafiati

Published: 11 March 2023

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1

Quanfeng, Li, Yan Huiyong, Du Taibin, and Wang Peiqing. "Irradiation of semiconductor devices using a 10 MeV travelling wave electron linear accelerator." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 174, no. 1-2 (March 2001): 194–98. http://dx.doi.org/10.1016/s0168-583x(00)00438-9.

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2

Longuet-Higgins, M. S. "The propagation of short surface waves on longer gravity waves." Journal of Fluid Mechanics 177 (April 1987): 293–306. http://dx.doi.org/10.1017/s002211208700096x.

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To understand the imaging of the sea surface by radar, it is useful to know the theoretical variations in the wavelength and steepness of short gravity waves propagated over the surface of a train of longer gravity waves of finite amplitude. Such variations may be calculated once the orbital accelerations and surface velocities in the longer waves have been accurately determined – a non-trivial computational task.The results show that the linearized theory used previously for the longer waves is generally inadequate. The fully nonlinear theory used here indicates that for longer waves having a steepness parameter AK = 0.4, for example, the short-wave steepness can be increased at the crests of the longer waves by a factor of order 8, compared with its value at the mean level. (Linear theory gives a factor less than 2.)The calculations so far reported are for free, irrotational gravity waves travelling in the same or directly opposite sense to the longer waves. However, the method of calculation could be extended without essential difficulty so as to include effects of surface tension, energy dissipation due to short-wave breaking, surface wind-drift currents, and to arbitrary angles of wave propagation.

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3

Liu, Shikuo, Zuntao Fu, Shida Liu, and Zhanggui Wang. "Combinability of Travelling Wave Solutions to Nonlinear Evolution Equation." Zeitschrift für Naturforschung A 59, no. 10 (October 1, 2004): 623–28. http://dx.doi.org/10.1515/zna-2004-1001.

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First, applying the Jacobi elliptic sine function expansion, basic travelling wave solutions of some nonlinear evolution equations are obtained. Second, according to the formal invariance of nonlinear evolution equations, the sister travelling wave solutions, which have the same wave speed as the basic ones, are derived. Finally, we show that a suitable linear combination of these two solutions results in a combined travelling wave solution, whose wave speed is different from those of the basic and sister travelling wave solutions. The combination of travelling wave solutions to nonlinear evolution equations must satisfy certain conditions. - PACS: 03.65.Ge.

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4

McDonald, Fleur, Robert I. McLachlan, Brian E. Moore, and G. R. W. Quispel. "Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations." Journal of Difference Equations and Applications 22, no. 7 (March 28, 2016): 913–40. http://dx.doi.org/10.1080/10236198.2016.1162161.

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5

Holden, A. J., I. Davies, P. Medhurst, and C. H. Oxley. "New wideband GaAs travelling-wave device: linear gate transistor." Electronics Letters 22, no. 15 (1986): 777. http://dx.doi.org/10.1049/el:19860533.

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6

Khrushchev, I. Yu, E. M. Dianov, and V. A. Tanko. "Tunable travelling-wave laser with a linear cavity configuration." Electronics Letters 31, no. 11 (May 25, 1995): 895–96. http://dx.doi.org/10.1049/el:19950630.

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7

Jeffrey, Alan, and Siqing Xu. "Travelling wave solutions to certain non-linear evolution equations." International Journal of Non-Linear Mechanics 24, no. 5 (January 1989): 425–29. http://dx.doi.org/10.1016/0020-7462(89)90029-2.

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8

Filatov, Aleksandr Nikolaevich, and Vladimir Kuz'mich Shilov. "Radial dynamics of electrons in two-section linear accelerator." International Journal of Electrical and Computer Engineering (IJECE) 9, no. 1 (February 1, 2019): 215. http://dx.doi.org/10.11591/ijece.v9i1.pp215-220.

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This article discusses possibility of harness wiring with the use of focusing system of high frequency eigenfields of accelerating resonators in standing wave linear accelerators on the basis of biperiodic slowing systems. The scopes of business activities and specificity of existing engineering processes applied in industry, especially in chemistry and metallurgy, require for special measures on environmental protection. At present electron linear accelerators operating in pulse mode are used for application purposes. Such accelerators can be characterized by sufficient beam power for efficient industrial use and for environmental protection. The results of numerical analysis of electron dynamics in two-section accelerator upon various initial conditions are presented. The obtained results are applied for development of actual accelerator, calculated and experimental data are given. The performed experimental study confirmed possibility of development of standing wave linear accelerator without external magnetic focusing system with output beam diameter of not higher than . The results of calculations of beam dynamics are experimentally verified.

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9

Oliveras, K. L., and C. W. Curtis. "Nonlinear travelling internal waves with piecewise-linear shear profiles." Journal of Fluid Mechanics 856 (October 12, 2018): 984–1013. http://dx.doi.org/10.1017/jfm.2018.679.

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In this work, we study the nonlinear travelling waves in density stratified fluids with piecewise-linear shear currents. Beginning with the formulation of the water-wave problem due to Ablowitz et al. (J. Fluid Mech., vol. 562, 2006, pp. 313–343), we extend the work of Ashton & Fokas (J. Fluid Mech., vol. 689, 2011, pp. 129–148) and Haut & Ablowitz (J. Fluid Mech., vol. 631, 2009, pp. 375–396) to examine the interface between two fluids of differing densities and varying linear shear. We derive a systems of equations depending only on variables at the interface, and numerically solve for periodic travelling wave solutions using numerical continuation. Here, we consider only branches which bifurcate from solutions where there is no slip in the tangential velocity at the interface for the trivial flow. The spectral stability of these solutions is then determined using a numerical Fourier–Floquet technique. We find that the strength of the linear shear in each fluid impacts the stability of the corresponding travelling wave solutions. Specifically, opposing shears may amplify or suppress instabilities.

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10

Krylovas, Aleksandras, and Rima Kriauzienė. "ASYMPTOTICAL ANALYSIS OF SOME COUPLED NONLINEAR WAVE EQUATIONS." Mathematical Modelling and Analysis 16, no. 1 (April 8, 2011): 97–108. http://dx.doi.org/10.3846/13926292.2011.560618.

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We consider coupled nonlinear equations modelling a family of travelling wave solutions. The goal of our work is to show that the method of internal averaging along characteristics can be used for wide classes of coupled non-linear wave equations such as Korteweg-de Vries, Klein – Gordon, Hirota – Satsuma, etc. The asymptotical analysis reduces a system of coupled non-linear equations to a system of integro – differential averaged equations. The averaged system with the periodical initial conditions disintegrates into independent equations in non-resonance case. These equations describe simple weakly non-linear travelling waves in the non-resonance case. In the resonance case the integro – differential averaged systems describe interaction of waves and give a good asymptotical approximation for exact solutions.

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11

MÜNCH, A., and B. A. WAGNER. "Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination." European Journal of Applied Mathematics 10, no. 3 (June 1999): 297–318. http://dx.doi.org/10.1017/s0956792599003769.

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We model a thin liquid film moving down a slope using the lubrication approximation with a slip condition. The travelling-wave solution is derived for small inclination angle α, using singular perturbation methods, and compared to the numerical solution. For the linear stability analysis we combine numerical methods with the long-wave approximation and find a small but finite critical α* below which the flow remains linearly stable to spanwise perturbations. This is contrasted with the vanishing of the hump of the travelling-wave solution. Finally, the prevailing linear stability of the travelling-wave at small inclination angles is compared with recent related results using a precursor model. Here, though, a strong dependence on the magnitude of the contact angle is found, which we think has not been observed before.

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12

Tian, Yi, and Zai-Zai Yan. "Travelling wave solutions for a surface wave equation in fluid mechanics." Thermal Science 20, no. 3 (2016): 893–98. http://dx.doi.org/10.2298/tsci1603893t.

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This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

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13

Fusco, V. F. "Broad-band linear polarization sensor using a travelling-wave antenna." IEEE Transactions on Antennas and Propagation 51, no. 4 (April 2003): 908–12. http://dx.doi.org/10.1109/tap.2003.811111.

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14

NAKAGAWA, Yosuke, Akira SAITO, and Takashi MAENO. "Non-linear Dynamic Analysis of Travelling-Wave-Type Ultrasonic Motors." Transactions of the Japan Society of Mechanical Engineers Series C 73, no. 727 (2007): 708–15. http://dx.doi.org/10.1299/kikaic.73.708.

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15

Sánchez-Garduño, Faustino, and Philip K. Maini. "Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations." Journal of Mathematical Biology 35, no. 6 (June 2, 1997): 713–28. http://dx.doi.org/10.1007/s002850050073.

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16

Li, Yifei, Peter van Heijster, Robert Marangell, and Matthew J. Simpson. "Travelling wave solutions in a negative nonlinear diffusion–reaction model." Journal of Mathematical Biology 81, no. 6-7 (November 20, 2020): 1495–522. http://dx.doi.org/10.1007/s00285-020-01547-1.

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AbstractWe use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, $$c^*$$ c ∗ , and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

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17

Lesinhovski, W. C., and A. Ruiz de Zárate. "Numerical Analysis and Approximate Travelling Wave Solutions for a Higher Order Internal Wave System." Trends in Computational and Applied Mathematics 23, no. 1 (March 25, 2022): 79–100. http://dx.doi.org/10.5540/tcam.2022.023.01.00079.

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In this work we focus on the numerical solution of a higher order bidirectional nonlinear model of Boussinesq type involving a nonlocal operator. Based on a von Neumann stability analysis for the linearized problem, an efficient and stable scheme for the nonlinear system is proposed. Our method is based on a numerical scheme known from the literature that solves satisfactorily a lower order linear system. Additionally, approximate periodic travelling wave solutions profiles for the higher order nonlinear system are presented. Such approximate travelling wave solutions are obtained from a solitary wave family of solutions for the Intermediate Long Wave (ILW) equation and the regularized Intermediate Long Wave (rILW) equation.

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18

Yang, Z., and S. Leibovich. "Nonlinear dynamics near the stability margin in rotating pipe flow." Journal of Fluid Mechanics 233 (December 1991): 329–47. http://dx.doi.org/10.1017/s0022112091000502.

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The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and we explore the entire marginal stability boundary. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a travelling wave. The envelope of the wave system is governed by a complex Ginzburg–Landau equation. The Ginzburg–Landau equation admits Stokes waves, which correspond to standing modulations of the linear travelling wavetrain, as well as travelling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

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19

Konstantinov, Stanislav. "Linear acceleration of protons on a backward wave (Bogomolov’s accelerator)." Physics & Astronomy International Journal 6, no. 3 (2022): 105–7. http://dx.doi.org/10.15406/paij.2022.06.00261.

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The article proposes to consider fundamentally new way of accelerating charged particles: linear acceleration (LA) of protons on a backward wave (Professor Bogomolov's Accelerator). The article discusses the advantages and scope of the new accelerator. The European Strategic Group (ESG) is considering fundamentally new projects to create more efficient and less expensive accelerators and colliders for research.

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20

Rahman, S., J. L. Díaz Palencia, and J. Roa González. "Analysis and profiles of travelling wave solutions to a Darcy-Forchheimer fluid formulated with a non-linear diffusion." AIMS Mathematics 7, no. 4 (2022): 6898–914. http://dx.doi.org/10.3934/math.2022383.

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<abstract><p>The intention along the presented analysis is to explore existence, uniqueness, regularity of solutions and travelling waves profiles to a Darcy-Forchheimer fluid flow formulated with a non-linear diffusion. Such formulation is the main novelty of the present study and requires the introduction of an appropriate mathematical treatment to deal with the introduced degenerate diffusivity. Firstly, the analysis on existence, regularity and uniqueness is shown upon definition of an appropriate test function. Afterwards, the problem is formulated within the travelling wave domain and analyzed close the critical points with the Geometric Perturbation Theory. Based on this theory, exact and asymptotic travelling wave profiles are obtained. In addition, the Geometric Perturbation Theory is used to provide evidences of the normal hyperbolicity in the involved manifolds that are used to get the associated travelling wave solutions. The main finding, which is not trivial in the non-linear diffusion case, is related with the existence of an exponential profile along the travelling frame. Eventually, a numerical exercise is introduced to validate the analytical solutions obtained.</p></abstract>

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21

Ruiz-Díez, Víctor, Jorge Hernando-García, Javier Toledo, Abdallah Ababneh, Helmut Seidel, and José Luis Sánchez-Rojas. "Piezoelectric MEMS Linear Motor for Nanopositioning Applications." Actuators 10, no. 2 (February 18, 2021): 36. http://dx.doi.org/10.3390/act10020036.

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This paper reports the design, fabrication, and performance of piezoelectric bidirectional conveyors based on microelectromechanical systems (MEMS) and featuring 3D-printed legs in bridge resonators. The structures consisted of aluminum-nitride (AlN) piezoelectric film on top of millimeter-sized rectangular thin silicon bridges and two electrode patches. The position and size of the patches were analytically optimized for travelling or standing wave generation, while the addition of 3D-printed legs allowed for a controlled contact and amplified displacement, a further step into the manufacturing of efficient linear motors. Such hybrid devices have recently demonstrated the conveyance of sliders of several times the motor weight, with speeds of 1.7 mm/s by travelling waves generated at 6 V and 19.3 kHz. In this paper both travelling and standing wave motors are compared. By the optimization of various aspects of the device such as the vibrational modes, leg collocation and excitation signals, speeds as high as 35 mm/s, and payloads above 10 times the motor weight were demonstrated. The devices exhibited a promising positional resolution while actuated with only a few sinusoidal cycles in an open-loop configuration. Discrete steps as low as 70 nm were measured in the conveyance of 2-mg sliders.

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22

Miloh, Touvia, and Jacob Nagler. "Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles." Micromachines 12, no. 2 (January 22, 2021): 114. http://dx.doi.org/10.3390/mi12020114.

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We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized ‘standard’ model (Poisson–Nernst–Planck formulation) and on the assumptions of a ‘weak’ field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

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23

He, Fang-ming, Wen-qiu Xie, Ji-run Luo, Min Zhu, and Wei Guo. "Linear theory of beam–wave interaction in double-slot coupled cavity travelling wave tube." Chinese Physics B 25, no. 3 (March 2016): 038401. http://dx.doi.org/10.1088/1674-1056/25/3/038401.

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24

Zhao, Xiaoshan, Huabing Jia, Hongxian Zhou, and Yaning Tang. "Bifurcations of travelling wave solutions in a non-linear dispersive equation." Chaos, Solitons & Fractals 37, no. 2 (July 2008): 525–31. http://dx.doi.org/10.1016/j.chaos.2006.09.028.

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25

Manceau, J. F., and F. Bastien. "Linear motor using a quasi-travelling wave in a rectangular plate." Ultrasonics 34, no. 2-5 (June 1996): 257–60. http://dx.doi.org/10.1016/0041-624x(95)00080-m.

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26

DUCROT, ARNAUD, and MICHEL LANGLAIS. "TRAVELLING WAVES IN INVASION PROCESSES WITH PATHOGENS." Mathematical Models and Methods in Applied Sciences 18, no. 03 (March 2008): 325–49. http://dx.doi.org/10.1142/s021820250800270x.

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This work is devoted to the study of a singular reaction–diffusion system arising in modelling the introduction of a lethal pathogen within an invading host population. In the absence of the pathogen, the host population exhibits a bistable dynamics (or Allee effect). Earlier numerical simulations of the singular SI model under consideration have exhibited stable travelling waves and also, under some circumstances, a reversal of the wave front speed due to the introduction of the pathogen. Here we prove the existence of such travelling wave solutions, study their linear stability and give analytical conditions yielding a reversal of the wave front speed, i.e. the invading host population may eventually retreat following the introduction of the lethal pathogen.

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27

Waters, S. L., and C. Guiot. "Flow in an Elastic Tube Subject to Prescribed Forcing: A Model of Umbilical Venous Flow." Journal of Theoretical Medicine 3, no. 4 (2001): 287–98. http://dx.doi.org/10.1080/10273660108833081.

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We investigate the fluid flow through a finite length, axisymmetric tube when the elastic wall is subject to either a prescribed external pressure or a prescribed motion. The prescribed wall forcing is assumed to consist of a forward travelling wave together with a reflected travelling wave. The dimensionless diameter variation of the tube is taken to be small and perturbation techniques are used to solve the weakly non-linear problem. Particular attention is given to the steady streaming flow that is induced through the non-linear convective acceleration terms. The results are applied to the flow of blood in the umbilical vein (UV), which has important physiological implications.

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28

DECONINCK, BERNARD, and KATIE OLIVERAS. "The instability of periodic surface gravity waves." Journal of Fluid Mechanics 675 (March 17, 2011): 141–67. http://dx.doi.org/10.1017/s0022112011000073.

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Euler's equations describe the dynamics of gravity waves on the surface of an ideal fluid with arbitrary depth. In this paper, we discuss the stability of periodic travelling wave solutions to the full set of nonlinear equations via a non-local formulation of the water wave problem, modified from that of Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, p. 313), restricted to a one-dimensional surface. Transforming the non-local formulation to a travelling coordinate frame, we obtain a new formulation for the stationary solutions in the travelling reference frame as a single equation for the surface in physical coordinates. We demonstrate that this equation can be used to numerically determine non-trivial travelling wave solutions by exploiting the bifurcation structure of this new equation. Specifically, we use the continuous dependence of the amplitude of the solutions on their propagation speed. Finally, we numerically examine the spectral stability of the periodic travelling wave solutions by extending Fourier–Floquet analysis to apply to the associated linear non-local problem. In addition to presenting the full spectrum of this linear stability problem, we recover past well-known results such as the Benjamin–Feir instability for waves in deep water. In shallow water, we find different instabilities. These shallow water instabilities are critically related to the wavelength of the perturbation and are difficult to find numerically. To address this problem, we propose a strategy to estimate a priori the location in the complex plane of the eigenvalues associated with the instability.

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29

Shilov, Vladimir Kuz'mich, Aleksandr Nikolaevich Filatov, and Aleksandr Evgen'evich Novozhilov. "Focusing Properties of a Modified Retarding Structure for Linear Electron Accelerators." International Journal of Electrical and Computer Engineering (IJECE) 7, no. 2 (April 1, 2017): 741. http://dx.doi.org/10.11591/ijece.v7i2.pp741-747.

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When using accelerators in industry and medicine, important are the dimensions of the device used, especially the radial ones. In the linear electron accelerators based on a biperiodic retarding structure, which operates in the standing wave mode, there is a possibility to provide focusing of the accelerated particles with the help of high-frequency fields without the use of external focusing elements. In the accelerating cell, due to the presence of the far protruding drift sleeves, the electric field lines become strongly curved, which leads to the appearance in the regions adjacent to these sleeves of a substantial in magnitude radial component of the electric field. The particles entering the accelerating gap experience the action of a force directed toward the axis of the system, and at the exit, of a force directed away from the axis. Under certain conditions, alternation of the focusing and defocusing fields can lead to a general focusing effect. In the paper we study the focusing properties of a modified biperiodic structure with standing wave. The main attention is paid to the possibility of using the focusing properties of the electromagnetic accelerating field for guiding the electron beam through the aperture of the accelerating system, which will lead to a significant reduction in the accelerator sizes. The proposed method can be applied in the calculation and design of linear electron accelerators.

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30

Sato, Naoki, and Michio Yamada. "Superharmonic instability of nonlinear travelling wave solutions in Hamiltonian systems." Journal of Fluid Mechanics 876 (August 8, 2019): 896–911. http://dx.doi.org/10.1017/jfm.2019.565.

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The problem of linear instability of a nonlinear travelling wave in a canonical Hamiltonian system with translational symmetry subject to superharmonic perturbations is discussed. It is shown that exchange of stability occurs when energy is stationary as a function of wave speed. This generalizes a result proved by Saffman (J. Fluid Mech., vol. 159, 1985, pp. 169–174) for travelling wave solutions exhibiting a wave profile with reflectional symmetry. The present argument remains true for any non-canonical Hamiltonian system that can be cast in Darboux form, i.e. a canonical Hamiltonian form on a submanifold defined by constraints, such as a two-dimensional surface wave on a constant shearing flow, revealing a general feature of Hamiltonian dynamics.

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31

Nishida, Yasushi. "Electron linear accelerator based on cross field acceleration principle." Laser and Particle Beams 7, no. 3 (August 1989): 561–79. http://dx.doi.org/10.1017/s0263034600007540.

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Powerful lasers have the potential to be used for power sources of the high energy particle accelerators. However, we have to convert the transverse wave into a longitudinal one which can trap the charged particles in the wave trough to accelerate them. In order to obtain a high field-gradient in an accelerator, several new concepts have been proposed. One of them is a beat wave accelerator (BWA) which uses a nonlinear optical mixing of two laser beams. Another concept is a Cross Field Acceleration (or a Vp × B acceleration) scheme, in which the trapped particles in the wave trough are accelerated along the wavefront and across the static magnetic field applied externally. An overview is presented including some new results.

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32

Wong, W. M., and K. J. Blow. "Travelling-wave model of semiconductor optical amplifier based non-linear loop mirror." Optics Communications 215, no. 1-3 (January 2003): 169–84. http://dx.doi.org/10.1016/s0030-4018(02)02179-x.

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33

Shakeel, Muhammad. "Travelling Wave Solution of the Fisher-Kolmogorov Equation with Non-Linear Diffusion." Applied Mathematics 04, no. 08 (2013): 148–60. http://dx.doi.org/10.4236/am.2013.48a021.

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34

Scalo, Carlo, Sanjiva K. Lele, and Lambertus Hesselink. "Linear and nonlinear modelling of a theoretical travelling-wave thermoacoustic heat engine." Journal of Fluid Mechanics 766 (February 5, 2015): 368–404. http://dx.doi.org/10.1017/jfm.2014.745.

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AbstractWe have carried out three-dimensional Navier–Stokes simulations, from quiescent conditions to the limit cycle, of a theoretical travelling-wave thermoacoustic heat engine (TAE) composed of a long variable-area resonator shrouding a smaller annular tube, which encloses the hot (HHX) and ambient (AHX) heat exchangers, and the regenerator (REG). Simulations are wall-resolved, with no-slip and adiabatic conditions enforced at all boundaries, while the heat transfer and drag due to the REG and HXs are modelled. HHX temperatures have been investigated in the range 440–500 K with the AHX temperature fixed at 300 K. The initial exponential growth of acoustic energy is due to a network of travelling waves thermoacoustically amplified by looping around the REG/HX unit in the direction of the imposed temperature gradient. A simple analytical model demonstrates that such instability is a localized Lagrangian thermodynamic process resembling a Stirling cycle. An inviscid system-wide linear stability model based on Rott’s theory is able to accurately predict the operating frequency and the growth rate, exhibiting properties consistent with a supercritical Hopf bifurcation. The limit cycle is governed by acoustic streaming – a rectified steady flow resulting from high-amplitude nonlinear acoustics. Its key features are explained with an axially symmetric incompressible model driven by the wave-induced stresses extracted from the compressible calculations. These features include Gedeon streaming, Rayleigh streaming in the resonator, and mean recirculations due to flow separation. The first drives the mean advection of hot fluid from the HHX to a secondary heat exchanger (AHX2), in the thermal buffer tube (TBT), necessary to achieve saturation of the acoustic energy growth. The direct evaluation of the nonlinear energy fluxes reveals that the efficiency of the device deteriorates with the drive ratio and that the acoustic power in the TBT is balanced primarily by the mean advection and thermoacoustic heat transport.

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35

Yang, Zhao, Chen Yanyan, Yu Guoyao, Luo Ercang, and Zhou Yuan. "Experimental Investigation on a Linear-compressor Driven Travelling-wave Thermoacoustic Heat Pump." Energy Procedia 75 (August 2015): 1844–49. http://dx.doi.org/10.1016/j.egypro.2015.07.160.

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36

Pankaj, Ram Dayal, Arun Kumar, and Chandrawati Sindhi. "EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION." International Journal of Engineering Technologies and Management Research 5, no. 1 (February 7, 2020): 1–7. http://dx.doi.org/10.29121/ijetmr.v5.i1.2018.42.

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The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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37

Djomegni, P. M. Tchepmo, and K. S. Govinder. "Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth." Advances in Applied Mathematics and Mechanics 9, no. 5 (July 11, 2017): 1250–70. http://dx.doi.org/10.4208/aamm.oa-2016-0114.

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AbstractMass migration of cells (via wave motion) plays an important role in many biological processes, particularly chemotaxis. We study the existence of travelling wave solutions for a chemotaxis model on a microscopic scale. The interaction between nutrients and chemoattractants are considered. Unlike previous approaches, we allow for diffusion of substrates, degradation of chemoattractants and cell growth (constant and linear growth rate). We apply asymptotic methods to investigate the behaviour of the solutions when cells are highly sensitive to extracellular signalling. Explicit solutions are demonstrated, and their biological implications are presented. The results presented here extend and generalize known results.

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38

Lin, Guojian, and Rong Yuan. "Travelling waves for the population genetics model with delay." ANZIAM Journal 48, no. 1 (July 2006): 57–71. http://dx.doi.org/10.1017/s1446181100003412.

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AbstractUnder the assumptions that the spatial variable is one dimensional and the distributed delay kernel is the general Gamma distributed delay kernel, when the average delay is small, the existence of travelling wave solutions for the population genetics model with distributed delay is obtained by using the linear chain trick and geometric singular perturbation theory. On the other hand, for the population genetics model with small discrete delay, the existence of travelling wave solutions is obtained by employing a technique which is based on a result concerning the existence of the inertial manifold for small discrete delay equations.

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Aibarakati, Wafaa, Aly Seadaw, and Noufe Aljahdaly. "Application of mathematical methods for the non-linear seventh order Sawada-Kotera-Ito dynamical wave equation." Thermal Science 23, Suppl. 6 (2019): 2081–93. http://dx.doi.org/10.2298/tsci190705373a.

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This article deal with finding travelling wave solutions for the 7th order Sawada-Kotera-Ito dynamical wave equation which describes the evolution of steeper waves of shorter wavelength than KdV equations using modified extended direct algebraic method. The new solutions derived have various physical structure, we also give graphic representation of the exact and stable solutions.

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40

Babu, Avula Benerji, Gundlapally Shiva Kumar Reddy, and Nilam Venkata Koteswararao. "Nonlinear Magneto Convection in a Rotating Fluid due to Vertical Magnetic Field and Vertical Axis of Rotation." International Journal of Heat and Technology 39, no. 3 (June 30, 2021): 775–86. http://dx.doi.org/10.18280/ijht.390311.

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In the present paper, linear and weakly nonlinear analysis of magnetoconvection in a rotating fluid due to the vertical magnetic field and the vertical axis of rotation are presented. For linear stability analysis, the normal mode analysis is utilized to find the Rayleigh number which is the function of Taylor number, Magnetic Prandtl number, Thermal Prandtl number and Chandrasekhar number. Also, the correlation between the Rayleigh number and wave number is graphically analyzed. The parameter regimes for the existence of pitchfork, Takens-Bogdanov and Hopf bifurcations are reported. Small-amplitude modulation is considered to derive the Newell-Whitehead-Segel equation and using its phase-winding solution, the conditions for the occurrence of Eckhaus and zigzag secondary instabilities are obtained. The system of coupled Landau-Ginzburg equations is derived. The travelling wave and standing wave solutions for the Newell-Whitehead-Segel equation are also presented. For, standing waves and travelling waves, the stability regions are identified.

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Ogata, Atsushi, and Kazuhisa Nakajima. "Recent progress and perspectives of laser–plasma accelerators." Laser and Particle Beams 16, no. 2 (June 1998): 381–96. http://dx.doi.org/10.1017/s0263034600011654.

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Recent progress in laser-plasma accelerators has matured a concept of particle acceleration as a possible next-generation particle accelerator promising ultrahigh accelerating gradients in a compact size. Four major concepts of laser-plasma accelerators—the plasma beat wave accelerator, the laser wakefield accelerator, the self-modulated laser wakefield accelerator, and the plasma wakefield accelerator—are reviewed on accelerator physics issues and experiments demonstrating the basic mechanisms of their concepts. As a perspective to the future practical application, a design of 5-TeV linear colliders based on the laser wakefield accelerator is discussed.

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Kang, J. "Dynamic surface characteristics during disc brake squeal: non-linear modelling and simulation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 6 (April 20, 2011): 1341–48. http://dx.doi.org/10.1177/0954406211399332.

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This article studies the non-linear dynamic behaviour of a disc brake system during squealing induced by a disc doublet mode. The disc brake system is modelled as a rotating annular plate in contact with annular sector-friction material. In order to investigate the possibility of detachment over the contact area between the disc surface and friction material during squealing, the lift-off condition is applied to this model. Also, the non-linearity arising from the contact stiffness is considered on the basis of the load–deflection test for the friction material. Numerical results show that the vibration after the onset of squeal reaches the limit cycle. In the steady-squealing response, several interesting phenomena are observed: the stick-slip and lift-off over the specific regime of the contact area. It is shown that the dynamic surface pattern rotates due to the forward travelling wave of the squealing surface. However, the mark of the surface pattern does not seem to move because the speed of the travelling wave fluctuates at a double frequency of squeal vibration.

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43

Cardoso, W. B., N. G. de Almeida, A. T. Avelar, and B. Baseia. "Splitting of quantum information in travelling wave fields using only linear optical elements." Journal of Physics B: Atomic, Molecular and Optical Physics 44, no. 4 (January 28, 2011): 045501. http://dx.doi.org/10.1088/0953-4075/44/4/045501.

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Ruiz-Díez, Víctor, Jorge Hernando-García, Javier Toledo, Abdallah Ababneh, Helmut Seidel, and José Luis Sánchez-Rojas. "Bidirectional Linear Motion by Travelling Waves on Legged Piezoelectric Microfabricated Plates." Micromachines 11, no. 5 (May 20, 2020): 517. http://dx.doi.org/10.3390/mi11050517.

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This paper reports the design, fabrication and performance of MEMS-based piezoelectric bidirectional conveyors featuring 3D printed legs, driven by linear travelling waves (TW). The structures consisted of an aluminium–nitride (AlN) piezoelectric film on top of millimetre-sized rectangular thin silicon bridges and two electrode patches. The position and size of the patches were analytically optimised for TW generation in three frequency ranges: 19, 112 and 420 kHz, by the proper combination of two contiguous flexural modes. After fabrication, the generated TW were characterized by means of Laser–Doppler vibrometry to obtain the relevant tables of merit, such as the standing wave ratio and the average amplitude. The experimental results agreed with the simulation, showing the generation of a TW with an amplitude as high as 6 nm/V and a standing wave ratio as low as 1.46 for a device working at 19.3 kHz. The applicability of the fabricated linear actuator device as a conveyor was investigated. Its kinetic performance was studied with sliders of different mass, being able to carry a 35 mg silicon slider, 18 times its weight, with 6 V of continuous sinusoidal excitation and a speed of 0.65 mm/s. A lighter slider, weighting only 3 mg, reached a mean speed of 1.7 mm/s at 6 V. In addition, by applying a burst sinusoidal excitation comprising 10 cycles, the TW generated in the bridge surface was able to move a 23 mg slider in discrete steps of 70 nm, in both directions, which is a promising result for a TW piezoelectric actuator of this size.

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Vladimir Kuzmich Shilov, Aleksandr Nikolaevich Filatov, and Aleksandr Evgenevich Novozhilov. "High frequency power supply to improve operation stability of linear electron accelerator." Nexo Revista Científica 34, no. 04 (October 28, 2021): 1515–20. http://dx.doi.org/10.5377/nexo.v34i04.12697.

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The use of linear electron accelerators in medicine and industry is explained by the simplicity of the input and output of accelerated electrons and adjusting the energy and dose rate, as well as the high dose rate of bremsstrahlung. The purpose of this work is to increase the stability of their work. A standing wave accelerator containing a high-frequency generator, a phase shifter, a waveguide bridge, a high-frequency load, and an accelerating system of two accelerating sections is equipped with two waveguide tees. Their inputs are connected to the output arms of the waveguide bridge, and the first and second output arms of each tee are connected to the first and last accelerating cells of each section, respectively. In this system, due to the introduction of several elements that do not require large costs for manufacturing and tuning, a significantly greater frequency separation of the operating mode of oscillations from neighboring ones is ensured, or even a single-frequency excitation mode is implemented, which makes it possible to significantly increase the stability of the accelerator operation. This technique can be used to increase the stability of operation in the design and calculation of linear accelerators of electrons with a standing wave.

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Audiard, Corentin. "Existence of multi-travelling waves in capillary fluids." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (August 19, 2019): 2905–36. http://dx.doi.org/10.1017/prm.2019.51.

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We prove the existence of multi-soliton and kink-multi-soliton solutions of the Euler–Korteweg system in dimension one. Such solutions behave asymptotically in time like several travelling waves far away from each other. A kink is a travelling wave with different limits at ±∞. The main assumption is the linear stability of the solitons, and we prove that this assumption is satisfied at least in the transonic limit. The proof relies on a classical approach based on energy estimates and a compactness argument.

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Jamal, Sameerah. "Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions." Mathematics 8, no. 11 (November 12, 2020): 2019. http://dx.doi.org/10.3390/math8112019.

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In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise. One solution to this is to minimise the total variation norm of the image, thus giving rise to non-linear equations. We investigate the variational properties of the Lagrange functionals associated with these minimisation problems.

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Barker, B., J. Humpherys, G. Lyng, and J. Lytle. "Evans function computation for the stability of travelling waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2117 (March 5, 2018): 20170184. http://dx.doi.org/10.1098/rsta.2017.0184.

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In recent years, the Evans function has become an important tool for the determination of stability of travelling waves. This function, a Wronskian of decaying solutions of the eigenvalue equation, is useful both analytically and computationally for the spectral analysis of the linearized operator about the wave. In particular, Evans-function computation allows one to locate any unstable eigenvalues of the linear operator (if they exist); this allows one to establish spectral stability of a given wave and identify bifurcation points (loss of stability) as model parameters vary. In this paper, we review computational aspects of the Evans function and apply it to multidimensional detonation waves. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

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Ruyer-Quil, C., S. Chakraborty, and B. S. Dandapat. "Wavy regime of a power-law film flow." Journal of Fluid Mechanics 692 (January 5, 2012): 220–56. http://dx.doi.org/10.1017/jfm.2011.508.

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AbstractWe consider a power-law fluid flowing down an inclined plane under the action of gravity. The divergence of the viscosity at zero strain rate is taken care of by introducing a Newtonian plateau at small strain rate. Two-equation models are formulated within the framework of lubrication theory in terms of the exact mass balance and an averaged momentum equation, which form a set of evolution equations for the film thickness $h$, a local velocity amplitude or the flow rate $q$. The models account for the streamwise diffusion of momentum. Comparisons with Orr–Sommerfeld stability analysis and with direct numerical simulation (DNS) show convincing agreement in both linear and nonlinear regimes. The influence of shear-thinning or shear-thickening on the primary instability is shown to be non-trivial. A destabilization of the base flow close to threshold is promoted by the shear-thinning effect, whereas, further from threshold, it tends to stabilize the base flow when the viscous damping of short waves becomes dominant. A reverse situation is observed in the case of shear-thickening fluids. Shear-thinning accelerates solitary waves and promotes a subcritical onset of travelling waves at larger wavenumber than the linear cut-off wavenumber. A conditional stability of the base flow is thus observed. This phenomenon results from a reduction of the effective viscosity at the free surface. When compared with DNS, simulations of the temporal response of the film based on weighted residual models satisfactorily capture the conditional stability of the film.

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Khalique, Chaudry Masood, and Innocent Simbanefayi. "Exact solutions and conservation laws for the modified equal width-Burgers equation." Open Physics 16, no. 1 (December 26, 2018): 795–800. http://dx.doi.org/10.1515/phys-2018-0099.

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AbstractIn this paper we study the modified equal width-Burgers equation, which describes long wave propagation in nonlinear media with dispersion and dissipation. Using the Lie symmetry method in conjunction with the (G'/G)− expansion method we construct its travelling wave solutions. Also, we determine the conservation laws by invoking the new conservation theorem due to Ibragimov. As a result we obtain energy and linear momentum conservation laws.

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