Solitary Waves in Relativistic Electromagnetic Plasma
XIE Bai-Song; HUA Cun-Cai
2005-01-01
Solitary waves in relativistic electromagnetic plasmas are obtained numerically. The longitudinal momentum of electrons has been taken into account in the problem. It is found that in the moving frame with electromagnetic field propagating the solitary waves can exist in both cases, where the vector potential frequency is larger or smaller than the plasma characteristic frequency.
Quantum ion-acoustic solitary waves in weak relativistic plasma
Biswajit Sahu
2011-06-01
Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized twospecies relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive perturbation method. A linear dispersion relation is also obtained taking into account the relativistic effect. The properties of quantum ion-acoustic solitary waves, obtained from the deformed KdV equation, are studied taking into account the quantum mechanical effects in the weak relativistic limit. It is found that relativistic effects signiﬁcantly modify the properties of quantum ion-acoustic waves. Also the effect of the quantum parameter on the nature of solitary wave solutions is studied in some detail.
Rehman, M. A.; Qureshi, M. N. S. [Department of Physics, GC University, Kachery Road, Lahore 54000 (Pakistan); Shah, H. A. [Department of Physics, Forman Christian College, Ferozepur Road, Lahore 54600 (Pakistan); Masood, W. [COMSATS, Institute of Information Technology, Park Road, Chak Shehzad, Islamabad 44000 (Pakistan); National Centre for Physics (NCP) Shahdra Valley Road, Islamabad (Pakistan)
2015-10-15
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Modeling of modified electron-acoustic solitary waves in a relativistic degenerate plasma
Hossen, M. R.; Mamun, A. A. [Jahangirnagar University, Savar, Dhaka (Bangladesh)
2014-12-15
The modeling of a theoretical and numerical study on the nonlinear propagation of modified electron-acoustic (mEA) solitary waves has been carried out in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non-relativistic degenerate inertial cold electrons, both non-relativistic and ultra-relativistic degenerate hot electron and inertial positron fluids, and positively-charged static ions). A reductive perturbation technique is used to derive the planar and the nonplanar Korteweg-de Vries (K-dV) equations, which admit a localized wave solution for the solitary profile. The solitary wave's characteristics are found to have been influenced significantly for the non-relativistic and the ultra-relativistic limits. The mEA solitary waves are also found to have been significantly modified due to the effects of the degenerate pressure and the number densities of this dense plasma's constituents. The properties of the planar K-dV solitary wave are quite different from those of the nonplanar K-dV solitary wave. The relevance of our results to astrophysical objects (like white dwarfs and neutron stars), which are of scientific interest, is briefly mentioned.
Hafez, M. G.; Talukder, M. R.
2015-09-01
This work investigates the theoretical and numerical studies on nonlinear propagation of ion acoustic solitary waves (IASWs) in an unmagnetized plasma consisting of nonextensive electrons, Boltzmann positrons and relativistic thermal ions. The Korteweg-de Vries (KdV) equation is derived by using the well known reductive perturbation method. This equation admits the soliton like solitary wave solution. The effects of phase velocity, amplitude of soliton, width of soliton and electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves have been discussed with graphical representation found in the variation of the plasma parameters. The obtained results can be helpful in understanding the features of small but finite amplitude localized relativistic ion-acoustic waves for an unmagnetized three component plasma system in astrophysical compact objects.
Hafez, M. G.; Talukder, M. R.; Sakthivel, R.
2016-05-01
The theoretical and numerical studies have been investigated on nonlinear propagation of weakly relativistic ion acoustic solitary waves in an unmagnetized plasma system consisting of nonextensive electrons, positrons and relativistic thermal ions. To study the characteristics of nonlinear propagation of the three-component plasma system, the reductive perturbation technique has been applied to derive the Korteweg-de Vries equation, which divulges the soliton-like solitary wave solution. The ansatz method is employed to carry out the integration of this equation. The effects of nonextensive electrons, positrons and relativistic thermal ions on phase velocity, amplitude and width of soliton and electrostatic nonlinear propagation of weakly relativistic ion acoustic solitary waves have been discussed taking different plasma parameters into consideration. The obtained results can be useful in understanding the features of small amplitude localized relativistic ion acoustic solitary waves in an unmagnetized three-component plasma system for hard thermal photon production with relativistic heavy ions collision in quark-gluon plasma as well as for astrophysical plasmas.
Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma
Saberian, E; Akbari-Moghanjoughi, M
2011-01-01
Propagation of large amplitude ion-acoustic solitary waves (IASWs) in a fully relativistic plasma consisting of cold ions and ultrarelativistic hot electrons and positrons is investigated using the Sagdeev's pseudopotential method in a relativistic hydrodynamics model. Effects of streaming speed of plasma fluid, thermal energy, positron density and positron temperature on large amplitude IASWs are studied by analysis of the pseudopotential structure. It is found that in regions that the streaming speed of plasma fluid is larger than that of solitary wave, by increasing the streaming speed of plasma fluid the depth and width of potential well increases and resulting in narrower solitons with larger amplitude. This behavior is opposite for the case where the streaming speed of plasma fluid is smaller than that of solitary wave. On the other hand, increase of the thermal energy results in wider solitons with smaller amplitude, because the depth and width of potential well decreases in that case. Additionally, th...
Lu, Ding; Xie, Bai-Song
2013-01-01
Effects of ion mobility and positron fraction on solitary waves of envelop of laser field and potential of electrostatic field in weak relativistic electron-positron-ion plasma are investigated. The parameter region for the existence of solitary waves is obtained analytically, and the reasonable choice of parameters is clarified. Both cases of mobile and immobile ions are considered. It is found that the amplitudes of solitary waves in the former case are larger compared to the latter case. For small plasma density, the localized solitary wave solutions in terms of approximate perturbation analytical method are consistent well with that by exact numerical calculations. However as the plasma density increases the analytical method loses its validity more and more. The influence of the positron fraction on the amplitudes of solitary waves shows a monotonous increasing relation. Implication of our results to the particle acceleration is also discussed briefly.
Lu, Ding; Li, Zi-Liang; Xie, Bai-Song
2013-09-01
The effects of ion mobility and positron fraction on the solitary waves of the laser field envelope and the potential of the electrostatic field in weak relativistic electron-positron-ion plasma are investigated. The parameter region for the existence of solitary waves is obtained analytically, and a reasonable choice of parameters is clarified. Both cases of mobile and immobile ions are considered. It is found that the amplitudes of solitary waves in the former case are larger compared to the latter case. For small plasma density, the localized solitary wave solutions in terms of the approximate perturbation analytical method are very consistent with those by exact numerical calculations. However, as the plasma density increases the analytical method loses its validity more and more. The influence of the positron fraction on the amplitudes of solitary waves shows a monotonous increasing relation. The implications of our results to particle acceleration are also discussed briefly.
Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions
Kalita, B. C., E-mail: bckalita123@gmail.com [Gauhati University, Department of Mathematics (India); Choudhury, M., E-mail: choudhurymamani@gmail.com [Handique Girls’ College, Department of Mathematics (India)
2016-10-15
Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z{sub d} and ion-to-dust mass ratio Q’ = m{sub i}/m{sub d} are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N{sub d} to yield rarefactive relativistic solitons of maximum amplitude.
Saini, N. S.; Singh, Kuldeep
2016-10-01
A head-on collision between two dust ion acoustic solitary waves (DIASWs) travelling in the opposite direction in a weakly relativistic plasma composed of four distinct particle populations, namely, weakly relativistic ion fluid, superthermal electrons as well as positrons, and immobile dust, is investigated. By employing extended Poincaré-Lighthill-Kuo method, two Korteweg-de Vries (KdV) equations are derived. The analytical phase shift after a head-on collision of two dust ion acoustic (DIA) solitary waves is also obtained. The combined effects of relativistic factor (β), electron to positron temperature ratio (α), ion to electron temperature ratio (σ), positron to electron density ratio (P), dust density ratio (d), and superthermality of electrons as well as positrons (via κ) on the phase shifts are numerically studied. All these physical parameters have also changed the potential amplitude and the width of colliding solitary waves. It is found that the presence of superthermal electrons as well as positrons and dust grains has emphatic influence on the phase shifts and potential pulse profiles of compressive DIA solitons. Our results are general and may be helpful in understanding a head-on collision between two DIASWs in astrophysical and laboratory plasmas, especially the interaction of pulsar relativistic winds with supernova ejecta that produces the superthermal particles and relativistic ions.
Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2016-01-01
The Korteweg-de Vries Burgers (KdVB) -like equation is derived to study the characteristics of nonlinear propagation of ion acoustic solitions in a highly relativistic plasma containing relativistic ions and nonextensive distribution of electrons and positrons using the well known reductive perturbation technique. The KdVB-like equation is solved employing the Bernoulli's equation method taking unperturbed positron to electron concentration ratio, electron to positron temperature ratio, strength of nonextensivity, ion kinematic viscosity, and highly relativistic streaming factor. It is found that these parameters significantly modify the structures of the solitonic excitation. The ion acoustic shock profiles are observed due to the influence of ion kinematic viscosity. In the absence of dissipative term to the KdVB equation, compressive and rarefactive solitons are observed in case of superthermality, but only compressive solitons are found for the case of subthermality.
Alam, M. S.; Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2017-07-01
A comparative study of the interactions between nonlinear ion acoustic solitary waves (IASWs) propagating toward each other, and the electrostatic nonlinear propagation of IASWs, both for the weakly and relativistic regimes consisting of relativistic warm ions, nonthermal electrons, and positrons, is carried out. Two-sided Korteweg-de Vries (KdV) equations are derived using the extended Poincaré-Lighthill-Kuo (PLK) method to reveal the physical issues concerned. The effects of positron concentration, ion-electron temperature ratio, electron-positron temperature ratio, relativistic streaming factor, the population of electron, and positron nonthermality on the electrostatic resonances and their phase shifts are investigated for both regimes. It is found that the plasma parameters significantly modify the phase shifts, electrostatic resonances, hump-shaped electrostatic potential profiles, and the electric fields on the nonlinear propagation characteristics of IASWs. The results obtained may be useful for clarifications of interaction between IASWs in astrophysical and laboratory plasmas, especially in pulsar magnetosphere, laser produced, inertial confinement plasmas, and pulsar relativistic winds with supernova ejecta that produce nonthermal electrons, positrons, and relativistic ions.
Relativistic spherical plasma waves
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Shallow Water Waves and Solitary Waves
Hereman, Willy
2013-01-01
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow Water Wave Equations of Geophysical Fluid Dynamics; Computation of Solitary Wave Solutions; Numerical Methods; Water Wave Experiments and Observations; Future Directions, and Bibliography.
Solitary waves and homoclinic orbits
Balmforth, N.J.
1994-03-01
The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids. More specifically, it centres around the mathematical description of solitary waves in a single spatial dimension. Moreover, it concentrates on strongly dissipative dynamics, rather than integrable systems like the KdV equation. One-dimensional solitary waves, or pulses and fronts as they are also called, are the simplest kinds of coherent structure (at least from a geometrical point of view). Nevertheless, their dynamics can be rich and complicated. In some circumstances this leads to the formation of spatio-temporal chaos in the systems giving birth to the solitary waves, and understanding that phenomenon is one of the major goals in the theory outlined in this review. Unfortunately, such a goal is far from achieved to date, and the author assess its current status and incompleteness.
Relativistic spherical plasma waves
Bulanov, S S; Schroeder, C B; Zhidkov, A G; Esarey, E; Leemans, W P
2011-01-01
Tightly focused laser pulses as they diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we report on theoretical study of relativistic spherical wake waves and their properties, including wave breaking. These waves may be suitable as particle injectors or as flying mirrors that both reflect and focus radiation, enabling unique X-ray sources and nonlinear QED phenomena.
Multi-component optical solitary waves
Kivshar, Y. S.; Sukhorukov, A. A.; Ostrovskaya, E. A.
2000-01-01
We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for highperformance computer networks......, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices. (C) 2000 Elsevier Science B.V. All rights reserved....
Transversally periodic solitary gravity–capillary waves
Milewski, Paul A.; Wang, Zhan
2014-01-01
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
T.Akhter; M.M.Hossain; A.A.Mamun
2013-01-01
Cylindrical and spherical (nonplanar) solitary waves (SWs) and double layers (DLs) in a multi-ion plasma system (containing inertial positively as well as negatively charged ions,non-inertial degenerate electrons,and negatively charged static dust) are studied by employing the standard reductive perturbation method.The modified Gardner (MG) equation describing the nonlinear propagation of the dust ion-acoustic (DIA) waves is derived,and its nonplanar SWs and DLs solutions are numerically analyzed.The parametric regimes for the existence of SWs,which are associated with both positive and negative potential,and DLs which are associated with negative potential,are obtained.The basic features of nonplanar DIA SWs,and DLs,which are found to be different from planar ones,are also identified.
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Conservative numerical methods for solitary wave interactions
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
Exact solitary wave solutions of nonlinear wave equations
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
From solitary wave to traveling surge
宋礼庭
1995-01-01
The solution of kinetic Alfven wave under action of anomalous resistance has two branches: the slow wave, VP
Colloidal solitary waves with temperature dependent compressibility
Azmi, A.; Marchant, T. R.
2014-05-01
Spatial solitary waves which form in colloidal suspensions of dielectric nanoparticles are considered. The interactions, or compressibility, of the colloidal particles, is modelled using a series in the particle density, or packing fraction, where the virial, or series, coefficients depend on the type of particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results show that particle interactions can be temperature dependent and either repulsive or attractive in nature, so we model the second virial coefficient using a physically realistic temperature power law. One- and two-dimensional semi-analytical colloidal solitary wave solutions are found. Trial functions, based on the form of the nonlinear Schrödinger equation soliton, are used, together with averaging, to develop the semi-analytical solutions. When the background packing fraction is low, the one-dimensional solitary waves have three solutions branches (with a bistable regime) while the two-dimensional solitary waves have two solution branches, with a single stable branch. The temperature dependent second virial coefficient results in changes to the solitary wave properties and the parameter space, in which multiple solutions branches occur. An excellent comparison is found between the semi-analytical and numerical solutions.
Adjustable solitary waves in electroactive rods
Wang, Y. Z.; Zhang, C. L.; Dai, H.-H.; Chen, W. Q.
2015-10-01
This paper presents an asymptotic analysis of solitary waves propagating in an incompressible isotropic electroactive circular rod subjected to a biasing longitudinal electric displacement. Several asymptotic expansions are introduced to simplify the rod governing equations. The boundary conditions on the lateral surface of the rod are satisfied from the asymptotic point of view. In the limit of finite-small amplitude and long wavelength, a set of ten simplified one-dimensional nonlinear governing equations is established. To validate our approach and the derivation, we compare the linear dispersion relation with the one directly derived from the three-dimensional linear theory in the limit of long wavelength. Then, by the reductive perturbation method, we deduce the far-field equation (i.e. the KdV equation). Finally, the leading order of the electroelastic solitary wave solution is presented. Numerical examples are provided to show the influences of the biasing electric displacement and material constants on the solitary waves. It is found that the biasing electric displacement can modulate the velocity of solitary waves with a prescribed amplitude in the electroactive rod, a very interesting result which may promote the particular application of solitary waves in solids with multi-field coupling.
Solitary waves on nonlinear elastic rods. I
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...
Solitary wave interactions of the GRLW equation
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n 29013 Malaga (Spain)]. E-mail: jirs@lcc.uma.es
2007-07-15
An approximate quasilinearization method for the solution of the generalized regularized long-wave (GRLW) equation based on the separation of the temporal and spatial derivatives, three-point, fourth-order accurate, compact difference equations, is presented. The method results in a system of linear equations with tridiagonal matrices, and is applied to determine the effects of the parameters of the GRLW equation and initial conditions on the formation of undular bores and interactions/collisions between two solitary waves. It is shown that the method preserves very accurately the first two invariants of the GRLW equation, the formation of secondary waves is a strong function of the amplitude and width of the initial Gaussian conditions, and the collision between two solitary waves is a strong function of the parameters that appear in the GRLW equation and the amplitude and speed of the initial conditions. It is also shown that the steepening of the leading and trailing waves may result in the formation of multiple secondary waves and/or an undular bore; the former interacts with the trailing solitary wave which may move parallel to or converge onto the leading solitary wave.
Two-color walking Peregrine solitary waves.
Baronio, Fabio; Chen, Shihua; Mihalache, Dumitru
2017-09-15
We study the extreme localization of light, evolving upon a non-zero background, in two-color parametric wave interaction in nonlinear quadratic media. We report the existence of quadratic Peregrine solitary waves, in the presence of significant group-velocity mismatch between the waves (or Poynting vector beam walk-off), in the regime of cascading second-harmonic generation. This finding opens a novel path for the experimental demonstration of extreme rogue waves in ultrafast quadratic nonlinear optics.
Solitary Wave Propagation Influenced by Submerged Breakwater
王锦; 左其华; 王登婷
2013-01-01
The form of Boussinesq equation derived by Nwogu (1993) using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method (WCCM) was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.
On the solitary wave paradigm for tsunamis
Madsen, Per A.; Fuhrman, David R.; Schäffer, Hemming Andreas
2008-01-01
Since the 1970s, solitary waves have commonly been used to model tsunamis especially in experimental and mathematical studies. Unfortunately, the link to geophysical scales is not well established, and in this work we question the geophysical relevance of this paradigm. In part 1, we simulate...... of finite amplitude solitary wave theory in laboratory studies of tsunamis. We conclude that order-of-magnitude errors in effective temporal and spatial duration occur when this theory is used as an approximation for long waves on a sloping bottom. In part 3, we investigate the phenomenon of disintegration...... of long waves into shorter waves, which has been observed e.g. in connection with the Indian Ocean tsunami in 2004. This happens if the front of the tsunami becomes sufficently steep, and as a result the front turns into an undular bore. We discuss the importance of these very short waves in connection...
Asymptotic Linear Stability of Solitary Water Waves
Pego, Robert L.; Sun, Shu-Ming
2016-12-01
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Solitary waves on nonlinear elastic rods. II
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results...
Solitary Wave Solutions for Zoomeron Equation
Amna IRSHAD
2013-04-01
Full Text Available Tanh-Coth Method is applied to find solitary wave solutions of the Zoomeron equation which is of extreme importance in mathematical physics. The proposed scheme is fully compatible with the complexity of the problem and is highly efficient. Moreover, suggested combination is capable to handle nonlinear problems of versatile physical nature.
Study on Solitary Waves of a General Boussinesq Model
无
2007-01-01
In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.
Uphill solitary waves in granular flows
Martínez, E.; Pérez-Penichet, C.; Sotolongo-Costa, O.; Ramos, O.; Måløy, K. J.; Douady, S.; Altshuler, E.
2007-03-01
We have experimentally observed uphill solitary waves in the surface flow on a granular material. A heap is constructed by injecting sand between two vertical glass plates separated by a distance much larger than the average grain size, with an open boundary. As the heap reaches the open boundary, solitary fluctuations appear on the flowing layer and move “up the hill” (i.e., against the direction of the flow). We explain the phenomenon in the context of stop-and-go traffic models.
The lifecycle of axisymmetric internal solitary waves
J. M. McMillan
2010-09-01
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r^{-p} with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r^{-1}.
Bulk solitary waves in elastic solids
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
Partial Differential Equations and Solitary Waves Theory
Wazwaz, Abdul-Majid
2009-01-01
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...
Long solitary internal waves in stable stratifications
W. B. Zimmerman
2004-01-01
Full Text Available Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994 demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak nonlinear theories that have been applied to stable stratifications all begin with perturbations of simple long waves, with corrections for weak nonlinearity and dispersion resulting in nonlinear wave equations (Korteweg-deVries (KdV or Benjamin-Davis-Ono that admit localized propagating solutions. It is shown that these theories are apparently inappropriate when the Scorer parameter, which gives the lowest wavenumber that does not radiate vertically, is positive. In this paper, a new nonlinear evolution equation is derived for an arbitrary wave packet thus including one bounded below by the Scorer parameter. The new theory shows that solitary internal waves excited in high Richardson number waveguides are predicted to have a halfwidth inversely proportional to the Scorer parameter, in agreement with atmospheric observations. A localized analytic solution for the new wave equation is demonstrated, and its soliton-like properties are demonstrated by numerical simulation.
Numerical Study on Breaking Criteria for Solitary Waves
Chung-ren CHOU; Ruey-syan SHIH; John Z. YIM
2003-01-01
Studies of the breaking criteria for solitary waves on a slope are presented in this paper. The boundary element method is used to model the processes of shoaling and breaking of solitary waves on various slopes. Empirical formulae that can be used to characterize the breaking of solitary waves are presented. These include the breaking index, the wave height, the water depth, and the maximum particle velocity at the point of breaking. Comparisons with the results of other researches are given.
Solitary Wave and Wave Front as Viewed From Curvature
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; LIANG Fu-Ming; XIN Guo-Jun
2004-01-01
The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometri cally, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s), which varies with arc length s. For solitary wave when s →±∞, then its curvature c(s) approaches zero, and when s = 0, the curvature c(s) reaches its maximum. For wave front, when s →±∞, then its curvature c(s) approaches zero, and when s = 0, the curvature c(s) is still zero, but c'(s) ≠ 0. That is, s = 0 is a turning point. When c(s) is given, the variance at some point (x, y) in stream line with arc length s satisfies a 2-order linear variable-coefficient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.
Solitary Wave and Wave Front as Viewed From Curvature
LIUShi-Kuo; FUZun-Tao; LIUShi-Da; LIANGFu-Ming; XINGuo-Jun
2004-01-01
The solitary wave and wave front are two important behaviors of nonlinear evolution equations. Geometrically, solitary wave and wave front are all plane curve. In this paper, they can be represented in terms of curvature c(s),which varies with arc length s. For solitary wave when s→±∞, then its curvature c(s) approaches zero, and whens = 0, the curvature c(s) reaches its maximum. For wave front, when s→±∞, then its curvature c(s) approaches zero,and when s = 0, the curvature c(s) is still zero, but c'(s)≠0. That is, s = 0 is a turning point. When c(s) is given,the variance at some point (x, y) in stream line with arc length s satisfies a 2-order linear variable-coeffcient ordinary differential equation. From this equation, it can be determined qualitatively whether the given curvature is a solitary wave or wave front.
Stable complex solitary waves of Sasa Satsuma equation
Sasanka Ghosh
2001-11-01
Existence of a new class of complex solitary waves is shown for Sasa Satsuma equation. These solitary waves are found to be stable in a certain domain of the parameter and become chaotic if the parameter exceeds the value 2.4. Signiﬁcantly, the complex solitary waves propagate at higher bit rate over the most stable solitons under the same conditions of the input parameters.
Stability of Solitary Waves for Three Coupled Long Wave - Short Wave Interaction Equations
Borluk, H.; Erbay, S.
2009-01-01
In this paper we consider a three-component system of one dimensional long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods.
Localization and solitary waves in solid mechanics
Champneys, A R; Thompson, J M T
1999-01-01
This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classi
Microtubules: A network for solitary waves
Zdravković Slobodan
2017-01-01
Full Text Available In the present paper we deal with nonlinear dynamics of microtubules. The structure and role of microtubules in cells are explained as well as one of models explaining their dynamics. Solutions of the crucial nonlinear differential equation depend on used mathematical methods. Two commonly used procedures, continuum and semi-discrete approximations, are explained. These solutions are solitary waves usually called as kink solitons, breathers and bell-type solitons. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. III45010
Houlrik, Jens Madsen
2009-01-01
The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…
Solitary waves of the splitted RLW equation
Zaki, S. I.
2001-07-01
A combination of the splitting method and the cubic B-spline finite elements is used to solve the non-linear regularized long wave (RLW) equation. This approach involves a Bubnov-Galerkin method with cubic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution region. Time integration of the resulting systems is effected using a Crank-Nicholson approximation. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent splitting difference scheme based on cubic spline interpolation functions, for different amplitudes ranging from a very small ( ⩾0.03) to a considerably high amplitudes ( ⩽0.3). The development of an undular bore is modeled.
Numerical Simulation of Solitary Kinetic Alfven Waves
DING Jian; LI Yi; WANG Shui
2008-01-01
Using the two-fluid model in the case of α1 (α=β/2Q, β is the ratio of thermal pressure to magnetic pressure, and Q=m,e/m,I), we numerically investigate the interactions between two solitary kinetic Alfven waves (SKAWs) and between an SKAW and a density discontinuity. The results show that the two SKAWs would remain in their original shapes and propagate at their initiating speeds, which indicates that SKAWs behave just like standard solitons. The simulation also shows that SKAWs will reflect and refract when crossing a discontinuity and propagating into a higher density region. The transmission wave is an SKAW with increasing density, and the reverberation is a disturbance with lower amplitude.
Hossen, M. R.; Nahar, L.; Mamun, A. A. [Jahangirnagar University,Savar, Dhaka (Bangladesh)
2014-12-15
The properties of time-dependent cylindrical and spherical, modified ion-acoustic (mIA) solitary structures in relativistic degenerate multi-ion plasmas (containing degenerate electron fluids, inertial positively-, as well as negatively-, charged light ions, and positively-charged static heavy ions) have been investigated theoretically. This investigation is valid for both non-relativistic and ultrarelativistic limits. The well-known reductive perturbation method has been used to derive the Korteweg-de Vries (K-dV) and the mK-dV equations for studying the basic features of solitary waves. The fundamental characteristics of mIA solitary waves are found to be significantly modified by the effects of the degenerate pressures of the electron and the ion fluids, their number densities, and the various charge states of heavy ions. The relevance of our results in astrophysical compact objects like white dwarfs and neutron stars, which are of scientific interest, is briefly discussed.
Ponderomotive Acceleration by Relativistic Waves
Lau, Calvin; Yeh, Po-Chun; Luk, Onnie; McClenaghan, Joseph; Ebisuzaki, Toshikazu; Tajima, Toshiki
2014-01-01
In the extreme high intensity regime of electromagnetic (EM) waves in plasma, the acceleration process is found to be dominated by the ponderomotive acceleration (PA). While the wakefields driven by the ponderomotive force of the relativistic intensity EM waves are important, they may be overtaken by the PA itself in the extreme high intensity regime when the dimensionless vector potential $a_0$ of the EM waves far exceeds unity. The energy gain by this regime (in 1D) is shown to be (approximately) proportional to $a_0^2$. Before reaching this extreme regime, the coexistence of the PA and the wakefield acceleration (WA) is observed where the wave structures driven by the wakefields show the phenomenon of multiple and folded wave-breakings. Investigated are various signatures of the acceleration processes such as the dependence on the mass ratio for the energy gain as well as the energy spectral features. The relevance to high energy cosmic ray acceleration and to the relativistic laser acceleration is conside...
Generation of Solitary Rossby Waves by Unstable Topography
YANG Hong-Wei; YIN Bao-Shu; DONG Huan-He
2012-01-01
The effect of topography on generation of the solitary Rossby waves is researched. Here, the topography, as a forcing for waves generation, is taken as a function of longitude variable x and time variable t, which is called unstable topography. With the help of a perturbation expansion method, a forced mKdv equation governing the evolution of amplitude of the solitary Rossby waves is derived from quasi-geostrophic vortieity equation and is solved by the pseudo-spectral method. Basing on the waterfall plots, the generational features of the solitary Rossby waves under the influence of unstable topography and stable topography are compared and some conclusions are obtained.
Transparent lattices and their solitary waves.
Sadurní, E
2014-09-01
We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.
Weak bond detection in composites using highly nonlinear solitary waves
Singhal, Taru; Kim, Eunho; Kim, Tae-Yeon; Yang, Jinkyu
2017-05-01
We experimentally investigate a diagnostic technique for identifying a weak bond in composites using highly nonlinear solitary waves (HNSWs). We set up a one-dimensional chain of granular crystals, consisting of spherical particles with nonlinear interactions, to generate HNSWs. These solitary wave packets are transmitted into an inspection area of composites by making a direct contact with the chain. We demonstrate that a strong type of solitary waves injected to the weak bond area can break the weak bond of laminates, thereby causing delamination. Then, to identify the creation of the delamination, we transmit a weak type of solitary waves by employing the same apparatus, and measure the solitary waves reflected from the specimens. By analyzing these reflected solitary waves, we differentiate the weak bond samples with the pristine bond ones in an efficient and fast manner. The diagnostic results based on the proposed method are compared with the strength and energy release rate at bond interfaces, which are measured via standard testing methods such as three point bending and end notched flexure tests. This study shows the potential of solitary wave-based detection of weak bonds for hot spot monitoring of composite-based structures.
On cusped solitary waves in finite water depth
Liao, Shijun
2013-01-01
It is well-known that the Camassa-Holm (CH) equation admits both of the peaked and cusped solitary waves in shallow water. However, it was an open question whether or not the exact wave equations can admit them in finite water depth. Besides, it was traditionally believed that cusped solitary waves, whose 1st-derivative tends to infinity at crest, are essentially different from peaked solitary ones with finite 1st-derivative. Currently, based on the symmetry and the exact water wave equations, Liao [1] proposed a unified wave model (UWM) for progressive gravity waves in finite water depth. The UWM admits not only all traditional smooth progressive waves but also the peaked solitary waves in finite water depth: in other words, the peaked solitary progressive waves are consistent with the traditional smooth ones. In this paper, in the frame of the linearized UWM, we further give, for the first time, the cusped solitary waves in finite water depth, and besides reveal a close relationship between the cusped and p...
Solitary Wave in One-dimensional Buckyball System at Nanoscale
Xu, Jun; Zheng, Bowen; Liu, Yilun
2016-01-01
We have studied the stress wave propagation in one-dimensional (1-D) nanoscopic buckyball (C60) system by molecular dynamics (MD) simulation and quantitative modeling. Simulation results have shown that solitary waves are generated and propagating in the buckyball system through impacting one buckyball at one end of the buckyball chain. We have found the solitary wave behaviors are closely dependent on the initial temperature and impacting speed of the buckyball chain. There are almost no dispersion and dissipation of the solitary waves (stationary solitary wave) for relatively low temperature and high impacting speed. While for relatively high temperature and low impacting speed the profile of the solitary waves is highly distorted and dissipated after propagating several tens of buckyballs. A phase diagram is proposed to describe the effect of the temperature and impacting speed on the solitary wave behaviors in buckyball system. In order to quantitatively describe the wave behavior in buckyball system, a simple nonlinear-spring model is established, which can describe the MD simulation results at low temperature very well. The results presented in this work may lay a solid step towards the further understanding and manipulation of stress wave propagation and impact energy mitigation at nanoscale. PMID:26891624
Shoaling Large Amplitude Internal Solitary Waves in a Laboratory Tank
Allshouse, Michael; Larue, Conner; Swinney, Harry
2014-11-01
The shoaling of internal solitary waves onto the continental shelf can change both the wave dynamics and the state of the environment. Previous observations have demonstrated that these waves can trap fluid and transport it over long distances. Through the use of a camshaft-based wavemaker, we produce large amplitude shoaling waves in a stratified fluid in a laboratory tank. Simulations of solitary waves are used to guide the tuning of the wave generator to approximate solitary waves; thus nonlinear waves can be produced within the 4m long tank. PIV and synthetic schlieren measurements are made to study the transport of fluid by the wave as it moves up a sloping boundary. The results are then compared to numerical simulations and analyzed using finite time Lyapunov exponent calculations. This Lagrangian analysis provides an objective measure of barriers surrounding trapped regions in the flow. Supported by ONR MURI Grant N000141110701 (WHOI).
Transverse relativistic effects in paraxial wave interference
Bliokh, Konstantin Y; Nori, Franco
2013-01-01
We consider relativistic deformations of interfering paraxial waves moving in the transverse direction. Owing to superluminal transverse phase velocities, noticeable deformations of the interference patterns arise when the waves move with respect to each other with non-relativistic velocities. Similar distortions also appear on a mutual tilt of the interfering waves, which causes a phase delay analogous to the relativistic time delay. We illustrate these observations by the interference between a vortex wave beam and a plane wave, which exhibits a pronounced deformation of the radial fringes into a fork-like pattern (relativistic Hall effect). Furthermore, we describe an additional relativistic motion of the interference fringes (a counter-rotation in the vortex case), which become noticeable at the same non-relativistic velocities.
Simple waves in relativistic fluids.
Lyutikov, Maxim
2010-11-01
We consider the Riemann problem for relativistic flows of polytropic fluids and find relations for the flow characteristics. Evolution of physical quantities takes especially simple form for the case of cold magnetized plasmas. We find exact explicit analytical solutions for one-dimensional expansion of magnetized plasma into vacuum, valid for arbitrary magnetization. We also consider expansion into cold unmagnetized external medium both for stationary initial conditions and for initially moving plasma, as well as reflection of rarefaction wave from a wall. We also find self-similar structure of three-dimensional magnetized outflows into vacuum, valid close to the plasma-vacuum interface.
Obliquely propagating large amplitude solitary waves in charge neutral plasmas
F. Verheest
2007-01-01
Full Text Available This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not of the phase, since the amplitude or envelope graphs look very similar.
A plethora of generalised solitary gravity-capillary water waves
Clamond, Didier; Duran, Angel
2014-01-01
The present study describes, first, an efficient algorithm for computing gravity-capillary solitary waves solutions of the irrotational Euler equations and, second, provides numerical evidences of the existence of (likely) an infinite number of generalised solitary waves (i.e. solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain (which is to be determined) is mapped into a uniform strip of the complex plane. A Babenko-like equation is then derived from a Lagrangian expressed in the transformed domain. The Babenko equation is then solved numerically using a Levenberg-Marquardt algorithm. Various interesting solutions are computed, some of them being known, some seem to be new. The emergence of generalised solitary waves is shown when the Bond number is increased.
Oblique solitary waves in a five component plasma
Sijo, S.; Manesh, M.; Sreekala, G.; Venugopal, C., E-mail: cvgmgphys@yahoo.co.in [School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam, 686 560 Kerala (India); Neethu, T. W. [Department of Physics, CMS College, Mahatma Gandhi University, Kottayam, 686 001 Kerala (India); Renuka, G. [Kerala State Council for Science, Technology and Environment, Thiruvananthapuram, 695 004 Kerala (India)
2015-12-15
We investigate the influence of a second electron component on oblique dust ion acoustic solitary waves in a five component plasma consisting of positively and negatively charged dust, hydrogen ions, and hotter and colder electrons. Of these, the heavier dust and colder photo-electrons are of cometary origin while the other two are of solar origin; electron components are described by kappa distributions. The K-dV equation is derived, and different attributes of the soliton such as amplitude and width are plotted for parameters relevant to comet Halley. We find that the second electron component has a profound influence on the solitary wave, decreasing both its amplitude and width. The normalized hydrogen density strongly influences the solitary wave by decreasing its width; the amplitude of the solitary wave, however, increases with increasing solar electron temperatures.
Zhang, Heng; Duan, Wen-Shan; Qi, Xin; Yang, Lei
2016-02-12
Head-on collision and overtaking collision between a KdV solitary wave and an envelope solitary wave are first studied in present paper by using Particle-in-cell (PIC) method in a dusty plasma. There are phase shifts of the KdV solitary wave in both head-on collision and the overtaking collision, while no phase shift is found for the envelop solitary wave in any cases. The remarkable difference between head-on collision and the overtaking collision is that the phase shift of KdV solitary wave increases as amplitude of KdV solitary wave increases in head-on collision, while it decreases as amplitude of the KdV solitary wave increases in the overtaking collision. It is found that the maximum amplitude during the collision process is less than sum of two amplitudes of both solitary waves, but is larger than either of the amplitude.
Kazantseva E.V.
2015-01-01
Full Text Available In a model which describes asymmetric oppositely directed nonlinear coupler it was observed in numerical simulations a phenomenon of solitary wave generation from the input constant continuous wave set at the entrance of a waveguide with negative refraction. The period of solitary wave formation decreases with increase of the continuum wave amplitude.
Diffractons: Solitary Waves Created by Diffraction in Periodic Media
Ketcheson, David I.
2015-03-31
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically varying sound speed. They share some properties with known classes of solitary waves but possess important differences as well.
Exact Periodic Solitary Solutions to the Shallow Water Wave Equation
LI Dong-Long; ZHAO Jun-Xiao
2009-01-01
Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
Developing Serpent-Type Wave Generators to Create Solitary Wave Simulations with BEM
Wen-Kai WENG; Ruey-Syan SHIH; Chung-Ren CHOU
2013-01-01
Developing serpent-type wave generators to generate solitary waves in a 3D-basin was investigated in this study. Based on the Lagrangian description with time-marching procedures and finite differences of the time derivative, a 3D multiple directional wave basin with multidirectional piston wave generators was developed to simulate ocean waves by using BEM with quadrilateral elements, and to simulate wave-caused problems with fully nonlinear water surface conditions. The simulations of perpendicular solitary waves were conducted in the first instance to verify this scheme. Furthermore, the comparison of the waveform variations confirms that the estimation of 3D solitary waves is a feasible scheme.
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel
2013-07-14
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Measurement of velocity field in parametrically excited solitary waves
Gordillo, Leonardo
2014-01-01
Paramerically excited solitary waves emerge as localized structures in high-aspect-ratio free surfaces subject to vertical vibrations. Herein, we provide the first experimental characterization of the hydrodynamics of thess waves using Particle Image Velocimetry. We show that the underlying velocity field of parametrically excited solitary waves is mainly composed by an oscillatory velocity field. Our results confirm the accuracy of Hamiltonian models with added dissipation in describing this field. Remarkably, our measurements also uncover the onset of a streaming velocity field which is shown to be as important as other crucial nonlinear terms in the current theory. The observed streaming pattern is particularly interesting due to the presence of oscillatory meniscii.
Relativistic suppression of wave packet spreading.
Su, Q; Smetanko, B; Grobe, R
1998-03-30
We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the field's polarization direction as well as in the transverse directions is reduced.
INTERNAL TIDES, SOLITARY WAVES AND BORES IN SHALLOW SEAS
王涛; 高天赋
2001-01-01
Remote sensing and in situ observations of internal tides, solitary waves and bores in shallow water are briefly reviewed in this paper. The emphasis is laid on interpreting SAR images based on oceanographic measurements, and analyzing characteristics of internal waves in the China Seas. Direc-tions for future research are discussed.
INTERNAL TIDES, SOLITARY WAVES AND BORES IN SHALLOW SEAS
无
2001-01-01
Remote sensing and in situ observations of internal tides, solitary waves and bores in shallow water are briefly reviewed in this paper. The emphasis is laid on interpreting SAR images based on oceanographic measurements, and analyzing characteristics of internal waves in the China Seas. Directions for future research are discussed.
Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain
Truskinovsky, Lev; Vainchtein, Anna
2014-10-01
We present a family of exact solutions describing discrete solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. The family is sufficiently rich to cover the whole spectrum of known behaviors from delocalized quasicontinuum waves moving with near-sonic velocities to highly localized anticontinuum excitations with only one particle moving at a time.
Solitary Wave in Linear ODE with Variable Coefficients
LIU Shi-Da; FU Zun-Tao; LIU Shi-Kuo; XIN Guo-Jun; LIANG Fu-Ming; FENG Bei-Ye
2003-01-01
In this paper, the linear ordinary differential equations with variable coefficients are obtained from thecontrolling equations satisfied by wavelet transform or atmospheric internal gravity waves, and these linear equationscan be further transformed into Weber equations. From Weber equations, the homoclinic orbit solutions can be derived,so the solitary wave solutions to linear equations with variable coefficients are obtained.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma
M G HAFEZ; M R TALUKDER; M HOSSAIN ALI
2016-11-01
This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries(KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influenceof plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequencywaves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.
Solitary and freak waves in superthermal plasma with ion jet
Abdelsalam, U. M.; Abdelsalam
2013-06-01
The nonlinear solitary and freak waves in a plasma composed of positive and negative ions, superthermal electrons, ion beam, and stationary dust particles have been investigated. The reductive perturbation method is used to obtain the Korteweg-de Vries (KdV) equation describing the system. The latter admits solitary wave solution, while the dynamics of the modulationally unstable wavepackets described by the KdV equation gives rise to the formation of freak/rogue excitation described by the nonlinear Schrödinger equation. In order to show that the characteristics of solitary and freak waves are influenced by plasma parameters, relevant numerical analysis of appropriate nonlinear solutions are presented. The results from this work predict nonlinear excitations that may associate with ion jet and superthermal electrons in Herbig-Haro objects.
Solitary waves of the EW and RLW equations
Ramos, J.I. [Room I-320-D, E.T.S. Ingenieros Industriales, Universidad de Malaga, Plaza El Ejido, s/n, 29013 Malaga (Spain)]. E-mail: jirs@lcc.uma.es
2007-12-15
Eight finite difference methods are employed to study the solitary waves of the equal-width (EW) and regularized long-wave (RLW) equations. The methods include second-order accurate (in space) implicit and linearly implicit techniques, a three-point, fourth-order accurate, compact operator algorithm, an exponential method based on the local integration of linear, second-order ordinary differential equations, and first- and second-order accurate temporal discretizations. It is shown that the compact operator method with a Crank-Nicolson discretization is more accurate than the other seven techniques as assessed for the three invariants of the EW and RLW equations and the L {sub 2}-norm errors when the exact solution is available. It is also shown that the use of Gaussian initial conditions may result in the formation of either positive or negative secondary solitary waves for the EW equation and the formation of positive solitary waves with or without oscillating tails for the RLW equation depending on the amplitude and width of the Gaussian initial conditions. In either case, it is shown that the creation of the secondary wave may be preceded by a steepening and an narrowing of the initial condition. The creation of a secondary wave is reported to also occur in the dissipative RLW equation, whereas the effects of dissipation in the EW equation are characterized by a decrease in amplitude, an increase of the width and a curving of the trajectory of the solitary wave. The collision and divergence of solitary waves of the EW and RLW equations are also considered in terms of the wave amplitude and the invariants of these equations.
NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP
LU Ji; YU Xi-ping
2008-01-01
Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.
The novel multi-solitary wave solution to the fifth-order KdV equation
Zhang Yi; Chen Deng-Yuan
2004-01-01
By using Hirota's method, the novel multi-solitary wave solutions to the fifth-order KdV equation are obtained.Furthermore, various new solitary wave solutions are also derived by a reconstructed bilinear Backlund transformation.
Exact Solitary Wave Solution in the ZK-BBM Equation
Juan Zhao
2014-01-01
Full Text Available The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
Single-peak solitary wave solutions for the variant Boussinesq equations
Hong Li; Lilin Ma; Dahe Feng
2013-06-01
This paper presents all possible smooth, cusped solitary wave solutions for the variant Boussinesq equations under the inhomogeneous boundary condition. The parametric conditions for the existence of smooth, cusped solitary wave solutions are given using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for smooth, cusped solitary wave solutions of the variant Boussinesq equations.
Existence,Orbital Stability and Instability of Solitary Waves for Coupled BBM Equations
Li-wei Cui
2009-01-01
This paper is concerned with the orbital stability/instability of solitary waves for coupled BBM equations which have Hamiltonian form.The explicit solitary wave solutions will be worked out first.Then by detailed spectral analysis and decaying estimates of solutions for the initial value problem,we obtain the orbital stability/instability of solitary waves.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Workshop on gravitational waves and relativistic astrophysics
Patrick Das Gupta
2004-10-01
Discussions related to gravitational wave experiments viz. LIGO and LISA as well as to observations of supermassive black holes dominated the workshop sessions on gravitational waves and relativistic astrophysics in the ICGC-2004. A summary of seven papers that were presented in these workshop sessions has been provided in this article.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Solitary plane waves in an isotropic hexagonal lattice
Zolotaryuk, Yaroslav; Savin, A.V.; Christiansen, Peter Leth
1998-01-01
Solitary plane-wave solutions in a two-dimensional hexagonal lattice which can propagate in different directions on the plane are found by using the pseudospectral method. The main point of our studies is that the lattice model is isotropic and we show that the sound velocity is the same for diff...
Internal solitary waves in the Red Sea: An unfolding mystery
da Silva, J.C.B.; Magalhães, J.M.; Gerkema, T.; Maas, L.R.M.
2012-01-01
The off-shelf region between 16.0 degrees and 16.5 degrees N in the southern Red Sea is identified as a new hotspot for the occurrence of oceanic internal solitary waves. Satellite observations reveal trains of solitons that, surprisingly, appear to propagate from the center of the Red Sea, where it
Numerical Modelling of Solitary Wave Experiments on Rubble Mound Breakwaters
Guler, H. G.; Arikawa, T.; Baykal, C.; Yalciner, A. C.
2016-12-01
Performance of a rubble mound breakwater protecting Haydarpasa Port, Turkey, has been tested under tsunami attack by physical model tests conducted at Port and Airport Research Institute (Guler et al, 2015). It is aimed to understand dynamic force of the tsunami by conducting solitary wave tests (Arikawa, 2015). In this study, the main objective is to perform numerical modelling of solitary wave tests in order to verify accuracy of the CFD model IHFOAM, developed in OpenFOAM environment (Higuera et al, 2013), by comparing results of the numerical computations with the experimental results. IHFOAM is the numerical modelling tool which is based on VARANS equations with a k-ω SST turbulence model including realistic wave generation, and active wave absorption. Experiments are performed using a Froude scale of 1/30, measuring surface elevation and flow velocity at several locations in the wave channel, and wave pressure around the crown wall of the breakwater. Solitary wave tests with wave heights of H=7.5 cm and H=10 cm are selected which represent the results of the experiments. The first test (H=7.5 cm) is the case that resulted in no damage whereas the second case (H=10 cm) resulted in total damage due to the sliding of the crown wall. After comparison of the preliminary results of numerical simulations with experimental data for both cases, it is observed that solitary wave experiments could be accurately modeled using IHFOAM focusing water surface elevations, flow velocities, and wave pressures on the crown wall of the breakwater (Figure, result of sim. at t=29.6 sec). ACKNOWLEDGEMENTSThe authors acknowledge developers of IHFOAM, further extend their acknowledgements for the partial supports from the research projects MarDiM, ASTARTE, RAPSODI, and TUBITAK 213M534. REFERENCESArikawa (2015) "Consideration of Characteristics of Pressure on Seawall by Solitary Waves Based on Hydraulic Experiments", Jour. of Japan. Soc. of Civ. Eng. Ser. B2 (Coast. Eng.), Vol 71, p I
The frustrated Brownian motion of nonlocal solitary waves
Folli, Viola
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave-packets. The result is valid for any kind of nonlocality and in the presence of non-paraxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equation
Existence of solitary waves in dipolar quantum gases
Antonelli, Paolo
2011-02-01
We study a nonlinear Schrdinger equation arising in the mean field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some of their properties. This gives a rigorous argument for the possible existence of solitary waves in BoseEinstein condensates, which originate solely due to the dipolar interaction between the particles. © 2010 Elsevier B.V. All rights reserved.
Phase modulated solitary waves controlled by bottom boundary condition
Mukherjee, Abhik
2014-01-01
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently produce different forced kdV equations as the evolution equations for the free surface. Solitary wave solutions have been analytically obtained where phase gets modulated controlled by bottom boundary condition whereas amplitude remains constant.
Conjugate flows and amplitude bounds for internal solitary waves
N. I. Makarenko
2009-03-01
Full Text Available Amplitude bounds imposed by the conservation of mass, momentum and energy for strongly nonlinear waves in stratified fluid are considered. We discuss the theoretical scheme which allows to determine broadening limits for solitary waves in the terms of a given upstream density profile. Attention is focused on the continuously stratified flows having multiple broadening limits. The role of the mean density profile and the influence of fine-scale stratification are analyzed.
Corrugation of relativistic magnetized shock waves
Lemoine, M; Gremillet, L
2016-01-01
As a shock front interacts with turbulence, it develops corrugation which induces outgoing wave modes in the downstream plasma. For a fast shock wave, the incoming wave modes can either be fast magnetosonic waves originating from downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting through the shock. Using linear perturbation theory in relativistic MHD, this paper provides a general analysis of the corrugation of relativistic magnetized fast shock waves resulting from their interaction with small amplitude disturbances. Transfer functions characterizing the linear response for each of the outgoing modes are calculated as a function of the magnetization of the upstream medium and as a function of the nature of the incoming wave. Interestingly, if the latter is an eigenmode of the upstream plasma, we find that there exists a resonance at which the (linear) response of the shock becomes large or even diverges. This result may have profound consequences on the phenomenology of astrophys...
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Energetics of internal solitary waves in a background sheared current
K. G. Lamb
2010-10-01
Full Text Available The energetics of internal waves in the presence of a background sheared current is explored via numerical simulations for four different situations based on oceanographic conditions: the nonlinear interaction of two internal solitary waves; an internal solitary wave shoaling through a turning point; internal solitary wave reflection from a sloping boundary and a deep-water internal seiche trapped in a deep basin. In the simulations with variable water depth using the Boussinesq approximation the combination of a background sheared current, bathymetry and a rigid lid results in a change in the total energy of the system due to the work done by a pressure change that is established across the domain. A final simulation of the deep-water internal seiche in which the Boussinesq approximation is not invoked and a diffuse air-water interface is added to the system results in the energy remaining constant because the generation of surface waves prevents the establishment of a net pressure increase across the domain. The difference in the perturbation energy in the Boussinesq and non-Boussinesq simulations is accounted for by the surface waves.
Solitary wave shoaling and breaking in a regularized Boussinesq system
Senthilkumar, Amutha
2016-01-01
A coupled BBM system of equations is studied in the situation of water waves propagating over decreasing fluid depth. A conservation equation for mass and a wave breaking criterion valid in the Boussinesq approximation is found. A Fourier collocation method coupled with a 4-stage Runge-Kutta time integration scheme is employed to approximate solutions of the BBM system. The mass conservation equation is used to quantify the role of reflection in the shoaling of solitary waves on a sloping bottom. Shoaling results based on an adiabatic approximation are analyzed. Wave shoaling and the criterion of breaking solitary waves on a sloping bottom is studied. To validate the numerical model the simulation results are compared with those obtained by Grilli et al.[16] and a good agreement between them is observed. Shoaling of solitary waves of two different types of mild slope model systems in [8] and [13] are compared, and it is found that each of these models works well in their respective regimes of applicability.
SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD
LIU Zhi-fang; ZHANG Shan-yuan
2006-01-01
A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.
Effect of nonthermal ion distribution and dust temperature on nonlinear dust-acoustic solitary waves
K Annou; R Annou
2012-01-01
Dust-acoustic solitary waves in unmagnetized dusty plasma whose constituents are inertial charged dust grains, Boltzmannian electrons and nonthermal ions have been investigated by taking into account ﬁnite dust temperature. The pseudopotential has been used to study solitary solution. The existence of solitary waves having negative potential is reported.
WANG Qi; CHEN Yong; ZHANG Hong-Qing
2005-01-01
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
Orbital Stability of Solitary Waves of The Long Wave—Short Wave Resonance Equations
BolingGUO; LinCHEN
1996-01-01
This paper concerns the orbital stability for soliary waves of the long wave short wave resonance equations.By using a different method from[15] ,applying the abstract rsults of Grillakis et al.[8][9] and detailed spectral analysis.we obtain the necessary and sufficient condition for the stability of the solitary waves.
Colliding solitary waves in quark gluon plasmas
Rafiei, Azam; Javidan, Kurosh
2016-09-01
We study the head-on collision of propagating waves due to perturbations in quark gluon plasmas. We use the Massachusetts Institute of Technology bag model, hydrodynamics equation, and suitable equation of state for describing the time evolution of such localized waves. A nonlinear differential equation is derived for the propagation of small amplitude localized waves using the reductive perturbation method. We show that these waves are unstable and amplitude of the left-moving (right-moving) wave increases (decreases) after the collision, and so they reach the borders of a quark gluon plasma fireball with different amplitudes. Indeed we show that such arrangements are created because of the geometrical symmetries of the medium.
Flow and sediment transport induced by a plunging solitary wave
Sumer, B. Mutlu; Sen, M.Berke; Karagali, Ioanna
2011-01-01
, and for observation of the morphological changes. The two experimental conditions were maintained as similar as possible. The experiments showed that the complete sequence of the plunging solitary wave involves the following processes: Shoaling and wave breaking; Runup; Rundown and hydraulic jump; and Trailing wave...... affected, by as much as a factor of 2, in the runup and hydraulic jump stages. The pore-water pressure measurements showed that the sediment at (or near) the surface of the bed experiences upward-directed pressure gradient forces during the downrush phase. The magnitude of this force can reach values...
Electron acoustic solitary waves with kappa-distributed electrons
Devanandhan, S; Singh, S V; Lakhina, G S, E-mail: satyavir@iigs.iigm.res.in [Indian Institute of Geomagnetism, New Panvel (West), Navi Mumbai (India)
2011-08-01
Electron acoustic solitary waves are studied in a three-component, unmagnetized plasma composed of hot electrons, fluid cold electrons and ions having finite temperatures. Hot electrons are assumed to have kappa distribution. The Sagdeev pseudo-potential technique is used to study the arbitrary amplitude electron-acoustic solitary waves. It is found that inclusion of cold electron temperature shrinks the existence regime of the solitons, and soliton electric field amplitude decreases with an increase in cold electron temperature. A decrease in spectral index, {kappa}, i.e. an increase in the superthermal component of hot electrons, leads to a decrease in soliton electric field amplitude as well as the soliton velocity range. The soliton solutions do not exist beyond T{sub c}/T{sub h}>0.13 for {kappa}=3.0 and Mach number M=0.9 for the dayside auroral region parameters.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Relativistic wave equations: an operational approach
Dattoli, G.; Sabia, E.; Górska, K.; Horzela, A.; Penson, K. A.
2015-03-01
The use of operator methods of an algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential equations, such as relativistic Schrödinger, Klein-Gordon, and Dirac. We discuss the free-particle hypotheses and those relevant to particles subject to non-trivial potentials. In the latter case we will show how the proposed method leads to easily implementable numerical algorithms.
Weakly nonlinear models for internal waves: inverse scattering transform and solitary wave contents
Chen, Shengqian
2016-01-01
The time evolution emanating from ``internal dam-break'' initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical simulations and experiments in wave tanks show that such initial conditions eventually give rise to coherent structures that are close to solitary-wave solutions moving ahead of a region of dispersive wave motion and turbulent mixing close to the location of the initial dam step. A priori theoretical predictions of the main features of these solitary waves, such as their amplitudes and speeds, appear to be unavailable, even for simplified models of wave evolution in stratified fluids. With the aim of providing estimates of the existence, amplitude and speed of such solitary waves, an approach based on Inverse Scattering Transform (IST) for completely integrable models is developed here and tested against direct numerical simulations of Euler fluids and some of their mode...
Calculation and analysis of solitary waves and kinks in elastic tubes
2013-01-01
The paper is devoted to analysis of different models that describe waves in fluid-filled and gas-filled elastic tubes and development of methods of calculation and numerical analysis of solutions with solitary waves and kinks for these models. Membrane model and plate model are used for tube. Two types of solitary waves are found. One-parametric families are stable and may be used as shock structures. Null-parametric solitary waves are unstable. The process of split of such solitary waves is ...
Rotating solitary wave at the wall of a cylindrical container
Amaouche, Mustapha
2013-04-30
This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg–de Vries equation for the wall wave profile, which did not account for the rotational character of the base flow. The present formulation is based on a less restricting condition and consequently corrects the last shortcoming. Now the influence of the background flow appears in the wave characteristics. The theory provides a better physical depiction of the unique experiment by predicting fairly well the wave profile at least in the first half of its lifetime and estimating the speed of the observed wave with good accuracy.
Loss of stability of a solitary wave through exciting a cnoidal wave on a Fermi-Pasta-Ulam ring
Yuan, Zongqiang; Chu, Min; Xia, Guodong; Zheng, Zhigang
2013-01-01
The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long time associated with the periodic exchange of energy between these two nonlinear waves. The module of the cnoidal wave, which is considered as an indicator of the nonlinearity, is found to oscillate with the same period of the energy exchange. After the stage of coexistence, the interaction between these two nonlinear waves leads to the destruction of the cnoidal wave by the radiation of phonons. Finally, the interaction of the solitary wave with phonons leads to the loss of stability of the solitary wave.
CHENYong; YANZhen－Ya; 等
2002-01-01
In this paper,we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method.As a result,many explicit exact solutions,which contain new solitary wave solutions,periodic wave solutions,and the combined formal solitary wave solutions,and periodic wave solutions ,are obtained.
Eady Solitary Waves: A Theory of Type B Cyclogenesis.
Mitsudera, Humio
1994-11-01
Localized baroclinic instability in a weakly nonlinear, long-wave limit using an Eady model is studied. The resulting evolution equations have a form of the KdV type, including extra terms representing linear coupling. Baroclinic instability is triggered locally by the collision between two neutral solitary waves (one trapped at the upper boundary and the other at the lower boundary) if their incident amplitudes are sufficiently large. This characteristic is explained from the viewpoint of resonance when the relative phase speed, which depends on the amplitudes, is less than a critical value. The upper and lower disturbances grow in a coupled manner (resembling a normal-mode structure) initially, but they reverse direction slowly as the amplitudes increase, and eventually separate from each other.The motivation of this study is to investigate a type of extratropical cyclogenesis that involves a preexisting upper trough (termed as Type B development) from the viewpoint of resonant solitary waves. Two cases are of particular interest. First, the author examines a case where an upper disturbance preexists over an undisturbed low-level waveguide. The solitary waves exhibit behavior similar to that conceived by Hoskins et al. for Type B development; the lower disturbance is forced one sidedly by a preexisting upper disturbance initially, but in turn forces the latter once the former attains a sufficient amplitude, thus resulting in mutual reinforcement. Second, if a weak perturbation exists at the surface ahead of the preexisting strong upper disturbance, baroclinic instability is triggered when the two waves interact. Even though the amplitude of the lower disturbance is initially much weaker, it is intensified quickly and catches up with the amplitude of the upper disturbance, so that the coupled vertical structure resembles that of an unstable normal mode eventually. These results describe the observed behavior in Type B atmospheric cyclogenesis quite well.
An experimental study on runup of two solitary waves on plane beaches
XUAN Rui-tao; WU Wei; LIU Hua
2013-01-01
Experiments of the runup of two solitary waves on a plane beach are carried out in a wave flume.The two solitary waves with the same amplitude and the crest separating distances are generated by using an improved wave generation method.It is found that,with regard to the two solitary waves with same wave amplitude,the runup amplification of the second wave is less than that of the first wave if the relative crest separating distance is reduced to a certain threshold value.The rundown of the first solitary wave depresses the maximum runup of the second wave.If the leading solitary wave is of relatively smaller amplitude for the two solitary waves,the runup amplification is affected by the overtaking process of two solitary waves.It turns out that the runup amplification of the second wave is larger than that of the first wave if the similarity factor is approximately larger than 15,which means the larger wave overtakes the smaller one before the waves runup on a beach.
The light filament as vector solitary wave
Kovachev, Lubomir M
2015-01-01
We present an analytical approach to the theory of nonlinear propagation of femtosecond optical pulses with broad-band spectrum in gases. The vector character of the nonlinear third-order polarization is investigated in details, taking into account the carrier to envelope phase. The corresponding system of vector amplitude equations is written by using left-hand and right-hand circular components of the electrical field. We found that this system nonlinear equations admits $3D+1$ vector soliton solution with Lorentz shape. The solution presents relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in plane, orthogonal to the direction of propagation. The evolution of the intensity profile demonstrate weak self-compression and week spherical wave in the first milliseconds of propagation.
Laboratory Generation of Solitary Waves:An Inversion Technique to Improve Available Methods
A.Romano; M.Guerrini; G.Bellotti; 琚烈红
2014-01-01
Solitary waves are often used in laboratory experiments to study tsunamis propagation and interaction with coasts. However, the experimental shape of the waves may differ from the theoretical one. In this paper, a correction technique aiming at minimizing the discrepancies between the two profiles is presented. Laboratory experiments reveal their effectiveness in correcting the experimental shape of solitary waves, mainly for low nonlinearities.
A double optical solitary wave in a nonlinear Schr(o)dinger-type equation
Yin Jiu-Li; Ding Shan-Yu
2013-01-01
A qualitative analysis method to efficiently solve the shallow wave equations is improved,so that a more complicated nonlinear Schr(o)dinger equation can be considered.By using the detailed study,some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.
Transition from Solitons to Solitary Waves in the Fermi-Pasta-Ulam Lattice
Wen, Zhenying; Wei, Nian
2016-01-01
In this paper, we study the smooth transition from solitons to solitary waves in localization, relation between energy and velocity, propagation and scattering property in the Fermi-Pasta-Ulam lattice analytically and numerically. A soliton is a very stable solitary wave that retains its permanent structure after interacting with other solitary waves. A soliton exists when the energy is small, and it becomes a solitary wave when the energy increases to the threshold. The transition could help to understand the distinctly different heat conduction behaviors of the Fermi-Pasta-Ulam lattice at low and high temperature.
Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma
Bandyopadhyay, P; Sen, A; Kaw, P K
2008-01-01
The excitation and propagation of finite amplitude low frequency solitary waves are investigated in an Argon plasma impregnated with kaolin dust particles. A nonlinear longitudinal dust acoustic solitary wave is excited by pulse modulating the discharge voltage with a negative potential. It is found that the velocity of the solitary wave increases and the width decreases with the increase of the modulating voltage, but the product of the solitary wave amplitude and the square of the width remains nearly constant. The experimental findings are compared with analytic soliton solutions of a model Kortweg-de Vries equation.
Interaction of Submerged Breakwater by a Solitary Wave Using WC-SPH Method
Afshin Mansouri
2014-01-01
Full Text Available Interaction of a solitary wave and submerged breakwater is studied in a meshless, Lagrangian approach. For this purpose, a two-dimensional smoothed particle hydrodynamics (SPH code is developed. Furthermore, an extensive set of simulations is conducted. In the first step, the generated solitary wave is validated. Subsequently, the interaction of solitary wave and submerged breakwater is investigated thoroughly. Results of the interaction of solitary wave and a submerged breakwater are also shown to be in good agreement with published experimental studies. Afterwards, the effects of the inclination and length of breakwater as well as distance between two breakwaters are evaluated on damping ratio of breakwater.
Generation of internal solitary waves by frontally forced intrusions in geophysical flows.
Bourgault, Daniel; Galbraith, Peter S; Chavanne, Cédric
2016-12-06
Internal solitary waves are hump-shaped, large-amplitude waves that are physically analogous to surface waves except that they propagate within the fluid, along density steps that typically characterize the layered vertical structure of lakes, oceans and the atmosphere. As do surface waves, internal solitary waves may overturn and break, and the process is thought to provide a globally significant source of turbulent mixing and energy dissipation. Although commonly observed in geophysical fluids, the origins of internal solitary waves remain unclear. Here we report a rarely observed natural case of the birth of internal solitary waves from a frontally forced interfacial gravity current intruding into a two-layer and vertically sheared background environment. The results of the analysis carried out suggest that fronts may represent additional and unexpected sources of internal solitary waves in regions of lakes, oceans and atmospheres that are dynamically similar to the situation examined here in the Saguenay Fjord, Canada.
Generation of internal solitary waves by frontally forced intrusions in geophysical flows
Bourgault, Daniel; Galbraith, Peter S.; Chavanne, Cédric
2016-12-01
Internal solitary waves are hump-shaped, large-amplitude waves that are physically analogous to surface waves except that they propagate within the fluid, along density steps that typically characterize the layered vertical structure of lakes, oceans and the atmosphere. As do surface waves, internal solitary waves may overturn and break, and the process is thought to provide a globally significant source of turbulent mixing and energy dissipation. Although commonly observed in geophysical fluids, the origins of internal solitary waves remain unclear. Here we report a rarely observed natural case of the birth of internal solitary waves from a frontally forced interfacial gravity current intruding into a two-layer and vertically sheared background environment. The results of the analysis carried out suggest that fronts may represent additional and unexpected sources of internal solitary waves in regions of lakes, oceans and atmospheres that are dynamically similar to the situation examined here in the Saguenay Fjord, Canada.
Relativistic NN scattering without partial wave decomposition
Ramalho, G; Peña, M T
2004-01-01
We consider the covariant Spectator equation with an appropriate OBE kernel, and apply it to the NN system. We develop a method, based on the Pad\\'e method,to solve the Spectator equation without partial wave decomposition, which is essential for high energies. Relativistic effects such as retardation and negative energy state components are considered. The on- and off-mass-shell amplitudes are calculated. The differential cross section obtained agrees fairly well with data at low energies.
Investigation on shock waves stability in relativistic gas dynamics
Alexander Blokhin
1993-05-01
Full Text Available This paper is devoted to investigation of the linearized mixed problem of shock waves stability in relativistic gas dynamics. The problem of symmetrization of relativistic gas dynamics equations is also discussed.
AKNS eigenvalue spectrum for densely spaced envelope solitary waves
Slunyaev, Alexey; Starobor, Alexey
2010-05-01
The problem of the influence of one envelope soliton to the discrete eigenvalues of the associated scattering problem for the other envelope soliton, which is situated close to the first one, is discussed. Envelope solitons are exact solutions of the integrable nonlinear Schrödinger equation (NLS). Their generalizations (taking into account the background nonlinear waves [1-4] or strongly nonlinear effects [5, 6]) are possible candidates to rogue waves in the ocean. The envelope solitary waves could be in principle detected in the stochastic wave field by approaches based on the Inverse Scattering Technique in terms of ‘unstable modes' (see [1-3]), or envelope solitons [7-8]. However, densely spaced intense groups influence the spectrum of the associated scattering problem, so that the solitary trains cannot be considered alone. Here we solve the initial-value problem exactly for some simplified configurations of the wave field, representing two closely placed intense wave groups, within the frameworks of the NLS equation by virtue of the solution of the AKNS system [9]. We show that the analogues of the level splitting and the tunneling effects, known in quantum physics, exist in the context of the NLS equation, and thus may be observed in application to sea waves [10]. These effects make the detecting of single solitary wave groups surrounded by other nonlinear wave groups difficult. [1]. A.L. Islas, C.M. Schober (2005) Predicting rogue waves in random oceanic sea states. Phys. Fluids 17, 031701-1-4. [2]. A.R. Osborne, M. Onorato, M. Serio (2005) Nonlinear Fourier analysis of deep-water random surface waves: Theoretical formulation and and experimental observations of rogue waves. 14th Aha Huliko's Winter Workshop, Honolulu, Hawaii. [3]. C.M. Schober, A. Calini (2008) Rogue waves in higher order nonlinear Schrödinger models. In: Extreme Waves (Eds.: E. Pelinovsky & C. Kharif), Springer. [4]. N. Akhmediev, A. Ankiewicz, M. Taki (2009) Waves that appear from
Polarized seismic and solitary waves run-up at the sea bed
Dennis, L. C.C.; Zainal, A. A.; Faisal, S. Y. [Universiti Teknologi PETRONAS, 31750 Tronoh, Perak (Malaysia); Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)
2012-09-26
The polarization effects in hydrodynamics are studied. Hydrodynamic equation for the nonlinear wave is used along with the polarized solitary waves and seismic waves act as initial waves. The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. The output demonstrates the inundation behaviors. Consequently, the polarized seismic waves along with the polarized solitary waves tend to generate dissimilar inundation which is more disastrous.
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
BGK electron solitary waves: 1D and 3D
L.-J. Chen
2002-01-01
Full Text Available This paper presents new results for 1D BGK electron solitary wave (phase-space electron hole solutions and, based on the new results, extends the solutions to include the 3D electrical interaction (E ~ 1/r 2 of charged particles. Our approach for extending to 3D is to solve the nonlinear 3D Poisson and 1D Vlasov equations based on a key feature of 1D electron hole (EH solutions; the positive core of an EH is screened by electrons trapped inside the potential energy trough. This feature has not been considered in previous studies. We illustrate this key feature using an analytical model and argue that the feature is independent of any specific model. We then construct azimuthally symmetric EH solutions under conditions where electrons are highly field-aligned and ions form a uniform background along the magnetic field. Our results indicate that, for a single humped electric potential, the parallel cut of the perpendicular component of the electric field (E⊥ is unipolar and that of the parallel component (E|| bipolar, reproducing the multi-dimensional features of the solitary waves observed by the FAST satellite. Our analytical solutions presented in this article capture the 3D electric interaction and the observed features of (E|| and E⊥. The solutions predict a dependence of the parallel width-amplitude relation on the perpendicular size of EHs. This dependence can be used in conjunction with experimental data to yield an estimate of the typical perpendicular size of observed EHs; this provides important information on the perpendicular span of the source region as well as on how much electrostatic energy is transported by the solitary waves.
Experiments and computation of onshore breaking solitary waves
Jensen, A.; Mayer, Stefan; Pedersen, G.K.
2005-01-01
This is a combined experimental and computational study of solitary waves that break on-shore. Velocities and accelerations are measured by a two-camera PIV technique and compared to theoretical values from an Euler model with a VOF method for the free surface. In particular, the dynamics of a so......-called collapsing breaker is scrutinized and the closure between the breaker and the beach is found to be akin to slamming. To the knowledge of the authors, no velocity measurements for this kind of breaker have been previously reported....
Deep-water bedforms induced by refracting Internal Solitary Waves
Falcini, Federico; Droghei, Riccardo; Casalbore, Daniele; Martorelli, Eleonora; Mosetti, Renzo; Sannino, Gianmaria; Santoleri, Rosalia; Latino Chiocci, Francesco
2017-04-01
Subaqueous bedforms (or sand waves) are typically observed in those environments that are exposed to strong currents, characterized by a dominant unidirectional flow. However, sand-wave fields may be also observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs), induced by tides, can produce an effective, unidirectional boundary flow filed that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.
A unified intrinsic functional expansion theory for solitary waves
Theodore Yaotsu Wu; John Kao; Jin E. Zhang
2005-01-01
A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120° down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokes's formula, F2μπ = tanμπ, relating the wave speed (the Froude number F) and the logarithmic decrement μ of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokes's basic term (singular inμ), such that 2Mμ is just somewhat beyond unity, i.e. 2Mμ (~-) 1. This fundamental criterion is fully validated by solutions for waves Dedicated to Zhemin Zheng for celebration of his Eightieth Anniversary It gives us a great pleasure to dedicate this study to Prof. Zhemin Zheng and join our distinguished colleagues and friends for the jubilant celebration of his Eightieth Anniversary. Warmest tribute is due from us, as from many others unlimited by borders and boundaries, for his contributions of great significance to science, engineering science and engineering, his tremendous influence as a source of inspiration and unerring guide to countless workers in the field, his admirable leadership in fostering the Institute of Mechanics of world renown, as well as for his untiring endeavor in promoting international interaction and cooperation between academies of various nations
Kazantseva, E. V.; Maimistov, A. I.
2016-08-01
In a model which describes asymmetric oppositely directed nonlinear waveguide coupler it was observed in the numerical simulation a phenomenon of solitary wave formation from the input constant continuous wave set at the entrance of a waveguide with negative index of refraction. Threshold value of the amplitude of the constant continuous wave, which defines the condition of appearance of the first solitary wave, decreases with increasing of the parameter of nonlinearity. The period of solitary wave formation decreases with increasing of the continuum wave amplitude.
Internal solitary waves in the East China Sea
LI Xiaofeng; ZHAO Zhongxiang; HAN Zhen; XU Liuxiong
2008-01-01
A European Space Agency's ENVISAT advanced synthetic aperture radar (ASAR) image covering Zhejiang coastal water in the East China Sea (ECS) was acquired on 1 August 2007. This image shows that there are about 20 coherent internal solitary wave (ISW) packets propagating southwestward toward Zhejiang coast. These ISW packets are separated by about 10 kin, suggesting that these ISWs are tide-generated waves. Each ISW packet contains 5--15 wave crests. The wavelengths of the wave crests with-in the ISW packets are about 300 m. The lengths of the leading wave crests are about 50 km. The ISW amplitude is estimated from solving KdV equation in an ideal two-layer ocean model. It is found that the ISW amplitudes is about 8 m. Further analysis of the ASAR image and ocean stratification profiles show that the observed ISWs are depression waves. Analyzing the tidal current finds that these waves are locally generated. The wavelength and amplitude of the ECS ISW are much smaller than their counter-parts in the South China Sea (SCS). The propagation speed of the ECS ISW is also an order of magnitude smaller than that of the SCS ISW. The observed ISWs in the ECS happened during a spring tide period.
Numerical simulations of shoaling internal solitary waves of elevation
Xu, Chengzhu; Subich, Christopher; Stastna, Marek
2016-07-01
We present high-resolution, two- and three-dimensional direct numerical simulations of large amplitude internal solitary waves of elevation on the laboratory scale, shoaling onto and over a small-amplitude shelf. The three-dimensional, mapped coordinate, spectral collocation method used for the simulations allows for accurate modelling of both the shoaling waves and the bottom boundary layer. The shoaling of the waves is characterized by the formation of a quasi-trapped core which undergoes a spatially growing stratified shear instability at its edge and a lobe-cleft instability in its nose. Both of these instabilities develop and three-dimensionalize concurrently, leading to strong bottom shear stress. We explore significant regions of Schmidt and Reynolds number space and demonstrate that the formation of shear instabilities during shoaling is robust and should be readily observable in a number of standard laboratory setups. In the experiments with a corrugated bottom boundary, boundary layer separation is found inside each of the corrugations during shoaling. This more complex boundary layer phenomenology precludes the formation of the lobe-cleft instability almost completely and hence provides a different mechanism for fluid and material exchange across the bottom boundary layer. Our analyses suggest that all of these wave-induced instabilities can lead to enhanced turbulence in the water column and increased shear stress on the bottom boundary. Through the generation and evolution of these instabilities, the shoaling of internal solitary waves of elevation is likely to provide systematic mechanisms for material mixing, cross-boundary layer transport, and sediment resuspension.
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
Large Amplitude Solitary Waves in a Fluid－Filled Elastic Tube
DUANWen-Shah
2003-01-01
By usign the potential method to a fluid filled elastic tube, we obtained a solitary wave solution.Compared with recluetive perturbation method, this method can be used for larger amplitude solitary waves. The result is in agreement with that of small amplitude approximation from reduetive perturbation method when the amplitude is small enough.
Large Amplitude Solitary Waves in a Fluid-Filled Elastic Tube
DUAN Wen-Shan
2003-01-01
By using the potential method to a fluid filled elastic tube, we obtained a solitary wave solution. Comparedwith reductive perturbation method, this method can be used for larger amplitude solitary waves. The result is inagreement with that of small amplitude approximation from reductive perturbation method when the amplitude is smallenough.
Solitary-like waves in a liquid foam microchannel
Bouret, Yann; Cohen, Alexandre; Fraysse, Nathalie; Argentina, Médéric; Raufaste, Christophe
2016-08-01
Plateau borders (PBs) are liquid microchannels located at the contact between three bubbles in liquid foams. They are stable, deformable, and can be thought of as quasi-one-dimensional model systems to study surface waves in fluid dynamics. We show that the burst of a bubble trapped in a PB produces local constrictions which travel along the liquid channel at constant velocity, without significant change in shape. These patterns are reminiscent of the depression solitary waves encountered in nonlinear systems. By coupling flow inertia to capillary stresses, we derive a simple model that admits solitonic solutions, which we characterized numerically and analytically in the limit of small deformation. These solutions capture most of the features observed experimentally.
Duan Wen-Shan
2004-01-01
The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov-Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.
Bifurcation and Solitary Waves of the Combined KdV and KdV Equation
HUA Cun-Cai; LIU Yan-Zhu
2002-01-01
Bifurcation, bistability and solitary waves of the combined KdV and mKdV equation are investigatedsystematically. At first, bifurcation and bistability are analyzed by selecting an integral constant as the bifurcationparameter. Then, different conditions expressed in terms of the bifurcation parameter are obtained for the existence ofbreather-like, algebraic, pulse-like solitary waves, and shock waves. All types of the solitary wave and shock wave solutionsare given by direct integration. Finally, an approximate analytic method by employing the interpolation polynomials iscomplete and the theoretical methods are the simplest hitherto.
Solitary SH waves in two-layered traction-free plates
Djeran-Maigre, Irini; Kuznetsov, Sergey
2008-01-01
A solitary wave, resembling a soliton wave, is observed when analyzing the linear problem of polarized shear (SH) surface acoustic waves propagating in elastic orthotropic two-layered traction-free plates. The analysis is performed by applying a special complex formalism and the Modified Transfer Matrix (MTM) method. Conditions for the existence of solitary SH waves are obtained. Analytical expressions for the phase speed of the solitary wave are derived. To cite this article: I. Djeran-Maigre, S. Kuznetsov, C. R. Mecanique 336 (2008).
Linear wave propagation in relativistic magnetohydrodynamics
Keppens, R
2008-01-01
The properties of linear Alfv\\'en, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions co...
Oceanic pycnocline depth retrieval from SAR imagery in the existence of solitary internal waves
无
2005-01-01
Oceanic pycnocline depth is usually inferred from in situ measurements. It is attempted to estimate the depth remotely. As solitary internal waves occur on oceanic pycnocline and propagate along it, it is possible to retrieve the depth indirectly in virtue of the solitary internal waves. A numerical model is presented for retrieving the pycnocline depth from synthetic aperture radar (SAR) images where the solitary internal waves are visible and when ocean waters are fully stratified. This numerical model is constructed by combining the solitary internal wave model and a two-layer ocean model. It is also assumed that the observed groups of solitary internal wave packets on the SAR imagery are generated by local semidiurnal tides. A case study in the East China Sea shows a good agreement with in situ CTD (conductivity-temperature-depth) data.
Electrostatic Korteweg-deVries solitary waves in a plasma with Kappa-distributed electrons
Choi, C.-R.; Min, K.-W. [Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-701 (Korea, Republic of); Rhee, T.-N. [National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of)
2011-09-15
The Korteweg-deVries (KdV) equation that describes the evolution of nonlinear ion-acoustic solitary waves in plasmas with Kappa-distributed electrons is derived by using a reductive perturbation method in the small amplitude limit. We identified a dip-type (negative) electrostatic KdV solitary wave, in addition to the hump-type solution reported previously. The two types of solitary waves occupy different domains on the {kappa} (Kappa index)-V (propagation velocity) plane, separated by a curve corresponding to singular solutions with infinite amplitudes. For a given Kappa value, the dip-type solitary wave propagates faster than the hump-type. It was also found that the hump-type solitary waves cannot propagate faster than V = 1.32.
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2004-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.
Electrostatic solitary waves in dusty pair-ion plasmas
Misra, A P
2013-01-01
The propagation of electrostatic waves in an unmagnetized collisionless pair-ion plasma with immobile positively charged dusts is studied for both large- and small-amplitude perturbations. Using a two-fluid model for pair-ions, it is shown that there appear two linear ion modes, namely the "fast" and "slow" waves in dusty pair-ion plasmas. The properties of these wave modes are studied with different mass $(m)$ and temperature $(T)$ ratios of negative to positive ions, as well as the effects of immobile charged dusts $(\\delta)$. For large-amplitude waves, the pseudopotential approach is performed, whereas the standard reductive perturbation technique (RPT) is used to study the small-amplitude Korteweg-de Vries (KdV) solitons. The profiles of the pseudopotential, the large amplitude solitons as well as the dynamical evolution of KdV solitons are numerically studied with the system parameters as above. It is found that the pair-ion plasmas with positively charged dusts support the propagation of solitary waves ...
Electrostatic solitary waves in dusty pair-ion plasmas
Misra, A. P. [Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan-731 235, West Bengal (India); Adhikary, N. C. [Physical Sciences Division, Institute of Advanced Study in Science and Technology, Vigyan Path, Paschim Boragaon, Garchuk, Guwahati-781035, Assam (India)
2013-10-15
The propagation of electrostatic waves in an unmagnetized collisionless pair-ion plasma with immobile positively charged dusts is studied for both large- and small-amplitude perturbations. Using a two-fluid model for pair-ions, it is shown that there appear two linear ion modes, namely the “fast” and “slow” waves in dusty pair-ion plasmas. The properties of these wave modes are studied with different mass (m) and temperature (T) ratios of negative to positive ions, as well as the effects of immobile charged dusts (δ). For large-amplitude waves, the pseudopotential approach is performed, whereas the standard reductive perturbation technique is used to study the small-amplitude Korteweg-de Vries (KdV) solitons. The profiles of the pseudopotential, the large amplitude solitons as well as the dynamical evolution of KdV solitons, are numerically studied with the system parameters as above. It is found that the pair-ion plasmas with positively charged dusts support the propagation of solitary waves (SWs) with only the negative potential. The results may be useful for the excitation of SWs in laboratory dusty pair-ion plasmas, electron-free industrial plasmas as well as for observation in space plasmas where electron density is negligibly small compared to that of negative ions.
Dust acoustic solitary and shock waves in strongly coupled dusty plasmas with nonthermal ions
Hamid Reza Pakzad; Kurosh Javidan
2009-11-01
The Korteweg–de Vries–Burgers (KdV–Burgers) equation and modified Korteweg–de Vries–Burgers equation are derived in strongly coupled dusty plasmas containing nonthermal ions and Boltzmann distributed electrons. It is found that solitary waves and shock waves can be produced in this medium. The effects of important parameters such as ion nonthermal parameter, temperature, density and velocity on the properties of shock waves and solitary waves are discussed.
2016-06-07
northern South China Sea in idealized settings, and 3) to provide information on wave characteristics to principal investigators in NLIWI (Nonlinear...Solitary Waves in the Northern South China Sea : a Nonhydrostatic Numerical Investigation.” The study of waves in a two-ridge system emphasizes the...Solitary Waves in the Northern South China Sea : a Nonhydrostatic Numerical Investigation.” IMPLICATION/APPLICATIONS See the report for
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma
El-Shamy, E. F.
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Numerical study of interfacial solitary waves propagating under an elastic sheet
Wang, Zhan; Părău, Emilian I.; Milewski, Paul A.; Vanden-Broeck, Jean-Marc
2014-01-01
Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field. PMID:25104909
Wei-guo Zhang; Shao-wei Li; Wei-zhong Tian; Lu Zhang
2008-01-01
By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Bonssinesq equation. We also discuss the boundedness of these solutions. More over,we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity's variation.
Dust Acoustic Solitary Waves in Saturn F-ring's Region
E.K. El-Shewy; M.I. Abo el Maaty; H.G. Abdelwahed; M.A.Elmessary
2011-01-01
Effect of hot and cold dust charge on the propagation of dust-acoustic waves (DAWs) in unmagnetized plasma having electrons, singly charged ions, hot and cold dust grains has been investigated.The reductive perturbation method is employed to reduce the basic set of fluid equations to the Kortewege-de Vries (KdV) equation.At the critical hot dusty plasma density NhO, the KdV equation is not appropriate for describing the system.Hence, a set of stretched coordinates is considered to derive the modified KdV equation.It is found that the presence of hot and cold dust charge grains not only significantly modifies the basic properties of solitary structure, but also changes the polarity of the solitary profiles.In the vicinity of the critical hot dusty plasma density NhO, neither KdV nor mKdV equation is appropriate for describing the DAWs.Therefore, a further modified KdV (fmKdV) equation is derived, which admits both soliton and double layer solutions.
Generation of internal solitary waves in a pycnocline by an internal wave beam: a numerical study
Grisouard, N.; Staquet, C.; Gerkema, T.
2011-01-01
Oceanic observations from western Europe and the south-western Indian ocean have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the pycnocline from below - a process referred to as 'local generation' (as opposed to the more direct generation
Direct bed stress measurements under solitary tsunami-type waves and breaking tsunami wave fronts
JayaKumar, S.; Baldock, T.E.
in the stability of submarine sediments. Laboratory experiments were performed to obtain total shear stresses under tsunami-type breaking and non-breaking solitary waves. The total stress comprises arises from a pressure gradient force and a skin friction shear...
Periodic Semifolded Solitary Waves for (2+1)-Dimensional Variable Coefficient Broer-Kaup System
JI Jie; HUANG Wen-Hua
2008-01-01
Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the (2+1)-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.
Equations of motion for a relativistic wave packet
L Kocis
2012-05-01
The time derivative of the position of a relativistic wave packet is evaluated. It is found that it is equal to the mean value of the momentum of the wave packet divided by the mass of the particle. The equation derived represents a relativistic version of the second Ehrenfest theorem.
Identification and determination of solitary wave structures in nonlinear wave propagation
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs.
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Solitary wave propagation through two-dimensional treelike structures.
Falls, William J; Sen, Surajit
2014-02-01
It is well known that a velocity perturbation can travel through a mass spring chain with strongly nonlinear interactions as a solitary and antisolitary wave pair. In recent years, nonlinear wave propagation in 2D structures have also been explored. Here we first consider the propagation of such a velocity perturbation for cases where the system has a 2D "Y"-shaped structure. Here each of the three pieces that make up the "Y" are made of a small mass spring chain. In addition, we consider a case where multiple "Y"-shaped structures are used to generate a "tree." We explore the early time dynamical behavior associated with the propagation of a velocity perturbation initiated at the trunk and at the extremities for both cases. We are looking for the energy transmission properties from one branch to another of these "Y"-shaped structures. Our dynamical simulations suggest the following broad observations: (i) for strongly nonlinear interactions, mechanical energy propagation resembles pulse propagation with the energy propagation being dispersive in the linear case; (ii) for strong nonlinear interactions, the tree-like structure acts as an energy gate showing preference for large perturbations in the system while the behavior of the linear case shows no such preference, thereby suggesting that such structures can possibly act as switches that activate at sufficiently high energies. The study aspires to develop insights into the nature of nonlinear wave propagation through a network of linear chains.
Coupling between whistler waves and slow-mode solitary waves
Tenerani, Anna; Pegoraro, Francesco; Contel, Olivier Le
2012-01-01
The interplay between electron-scale and ion-scale phenomena is of general interest for both laboratory and space plasma physics. In this paper we investigate the linear coupling between whistler waves and slow magnetosonic solitons through two-fluid numerical simulations. Whistler waves can be trapped in the presence of inhomogeneous external fields such as a density hump or hole where they can propagate for times much longer than their characteristic time scale, as shown by laboratory experiments and space measurements. Space measurements have detected whistler waves also in correspondence to magnetic holes, i.e., to density humps with magnetic field minima extending on ion-scales. This raises the interesting question of how ion-scale structures can couple to whistler waves. Slow magnetosonic solitons share some of the main features of a magnetic hole. Using the ducting properties of an inhomogeneous plasma as a guide, we present a numerical study of whistler waves that are trapped and transported inside pr...
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Basic properties of solitary waves in granular crystals
Hasan, M. Arif; Nemat-Nasser, Sia
We consider a chain of lightly contacting identical spherical elastic granules and provide explicit analytical expressions to fully characterize solitary waves (SWs) that may be generated in the chain by an impact or an applied shock force. These SWs consist of individual packages of linear momentum/energy transmitted across the granules through Hertzian contacts. They are nonlinear translational waves (involving no vibrations) that propagate through the granular chain without distortion, i.e., without any temporal evolution in shape or size. In particular, we focus on a fully-formed SW and provide analytical expressions for the associated peak value as well as the time variation of the granules' displacement, velocity, acceleration, and compressive contact force acting across any two contacting granules. In addition, by considering a SW as an "effective particle", we provide explicit analytical expressions for its linear momentum, total energy, equivalent (or effective) mass and effective velocity. All of the above mentioned results are shown to depend only on the peak value of the SW's contact force and the properties of the granules, i.e., their diameter, density, and elastic moduli. Then we provide a simple recipe to calculate the peak value of the SW's contact force in terms of a given shock force. Finally, we check by numerical simulations the accuracy of the analytical predictions.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
Different Types of Solitary Wave Scattering in the Fermi-Pasta-Ulam Model
WEN Zhen-Ying; ZHAO Hong
2005-01-01
@@ We show that the scattering between two solitary waves in the Fermi-Pasta-Ulam model with interaction potential V(x) = αx2/2 + x4/4 can be classified into four types according to the configurations of the solitary waves. For three of the four types, the large solitary wave can lose energy and the small one can gain in average by collision.For the other one type in a special parameter region we encounter an anomalous scattering, i.e. the large solitary wave gains energy and the small one loses energy. Numerical investigations are performed for the anharmonic limit case of α = 0 and the general case of α≠ 0 and comparisons between them are made.
Relativistic soliton-like collisionless ionization wave
Arefiev, Alexey; McCormick, Matthew; Quevedo, Hernan; Bengtson, Roger; Ditmire, Todd
2014-10-01
It has been observed in recent experiments with laser-irradiated gas jets that a plasma filament produced by the laser and containing energetic electrons can launch a relativistic ionization wave into ambient gas. Here we present a self-consistent theory that explains how a collisionless ionization wave can propagate in a self-sustaining regime. A population of hot electrons necessarily generates a sheath electric field at the plasma boundary. This field penetrates the ambient gas, ionizing the gas atoms and thus causing the plasma boundary to expand. We show that the motion of the newly generated electrons can form a potential well adjacent to the plasma boundary. The outwards motion of the well causes a bunch of energetic electrons to become trapped, while allowing the newly generated electrons to escape into the plasma without retaining much energy. The resulting soliton-like ionizing field structure propagates outwards with a bunch of hot electrons that maintain a strong sheath field despite significant plasma expansion. We also present 1D and 2D particle-in-cell simulations that illustrate the described mechanism. The simulations were performed using HPC resources provided by the Texas Advanced Computing Center. This work was supported by NNSA Contract No. DE-FC52-08NA28512 and U.S. DOE Contract No. DE-FG02-04ER54742.
A unified approach in seeking the solitary wave solutions to sine-Gordon type equations
Xie Yuan-Xi; Tang Jia-Shi
2005-01-01
By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine-Gordon type equations.As illustrative examples, the exact solitary wave solutions of some physically significant sine-Gordon type equations,including the sine-Gordon equation, double sine-Gordon equation and mKdV-sine-Gordon equation, are investigated by means of this method.
The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation
Yuanxi Xie; Jilashi Tang
2006-03-01
In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.
Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures.
Kominis, Y
2006-06-01
A phase space method is employed for the construction of analytical solitary wave solutions of the nonlinear Kronig-Penney model in a photonic structure. This class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems. The location of the solutions on the spectral band gap structure as well as on the low dimensional space of system's conserved quantities is studied, and robust solitary wave propagation is shown.
Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.
Feng, Peihua; Zhang, Jiazhong; Wang, Wei
2016-06-01
Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.
S. S. Ghosh
2004-01-01
Full Text Available The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.
Rogue wave variational modelling through the interaction of two solitary waves
Gidel, Floriane; Bokhove, Onno
2016-04-01
The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a
Solitary waves observed in the auroral zone: the Cluster multi-spacecraft perspective
J. S. Pickett
2004-01-01
Full Text Available We report on recent measurements of solitary waves made by the Wideband Plasma Wave Receiver located on each of the four Cluster spacecraft at 4.5-6.5RE (well above the auroral acceleration region as they cross field lines that map to the auroral zones. These solitary waves are observed in the Wideband data as isolated bipolar and tripolar waveforms. Examples of the two types of pulses are provided. The time durations of the majority of both types of solitary waves observed in this region range from about 0.3 up to 5ms. Their peak-to-peak amplitudes range from about 0.05 up to 20mV/m, with a few reaching up to almost 70mV/m. There is essentially no potential change across the bipolar pulses. There appears to be a small, measurable potential change, up to 0.5V, across the tripolar pulses, which is consistent with weak or hybrid double layers. A limited cross-spacecraft correlation study was carried out in order to identify the same solitary wave on more than one spacecraft. We found no convincing correlations of the bipolar solitary waves. In the two cases of possible correlation of the tripolar pulses, we found that the solitary waves are propagating at several hundred to a few thousand km/s and that they are possibly evolving (growing, decaying as they propagate from one spacecraft to the next. Further, they have a perpendicular (to the magnetic field width of 50km or greater and a parallel width of about 2-5km. We conclude, in general, however, that the Cluster spacecraft at separations along and perpendicular to the local magnetic field direction of tens of km and greater are too large to obtain positive correlations in this region. Looking at the macroscale of the auroral zone at 4.5-6.5RE, we find that the onsets of the broadband electrostatic noise associated with the solitary waves observed in the spectrograms of the WBD data are generally consistent with propagation of the solitary waves up the field lines (away from Earth, or with
Integrability: mathematical methods for studying solitary waves theory
Wazwaz, Abdul-Majid
2014-03-01
In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the
Viscous damping of solitary waves in the mud banks of Kerala, West coast of India
Shenoi, S.S.C.; Murty, C.S.
Analysis of wave damping in mud bank region following the process of transfer of wave energy to the interior of fluid column through the boundary layer and the energy loss computations owing to viscous shear beneath the solitary wave over a smooth...
Relativistic wave equation for hypothetic composite quarks
Krolikowski, W. [Institute of Theoretical Physics, Warsaw University, Warsaw (Poland)
1997-05-01
A two-body wave equation is derived, corresponding to the hypothesis (discussed already in the past) that u and d current quarks are relativistic bound states of a spin-1/2 preon existing in two weak flavors and three colors, and a spin-0 preon with no weak flavor nor color, held together by a new strong but Abelian, vectorlike gauge force. Some non-conventional (though somewhat nostalgic) consequences of this strong Abelian binding within composite quarks are pointed out. Among them are: new tiny magnetic-type moments of quarks (and nucleons) and new isomeric nucleon states possibly excitable at some high energies. The letter may arise through a rearrangement mechanism for quark preons inside nucleons. In the interaction q (anti)q{yields}q (anti)q of preon-composite quarks, beside the color forces, there act additional exchange forces corresponding to diagrams analogical to the so called dual diagrams for the interaction {pi}{pi}{yields}{pi}{pi} of quark-composite pions. (author)
Dust-acoustic solitary waves in a dusty plasma with two-temperature nonthermal ions
Zhi-Jian Zhou; Hong-Yan Wang; Kai-Biao Zhang
2012-01-01
By using reductive perturbation method, the nonlinear propagation of dust-acoustic waves in a dusty plasma (containing a negatively charged dust ﬂuid, Boltzmann distributed electrons and two-temperature nonthermal ions) is investigated. The effects of two-temperature nonthermal ions on the basic properties of small but ﬁnite amplitude nonlinear dust-acoustic waves are examined. It is found that two-temperature nonthermal ions affect the basic properties of the dust-acoustic solitary waves. It is also observed that only compressive solitary waves exist in this system.
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
New Relativistic Effects in the Dynamics of Nonlinear Hydrodynamical Waves
Rezzolla, L
2002-01-01
In Newtonian and relativistic hydrodynamics the Riemann problem consists of calculating the evolution of a fluid which is initially characterized by two states having different values of uniform rest-mass density, pressure and velocity. When the fluid is allowed to relax, one of three possible wave-patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a special relativistic Riemann problem when velocities tangential to the initial discontinuity surface are present. We show that a smooth transition from one wave-pattern to another can be produced by varying the initial tangential velocities while otherwise maintaining the initial states unmodified. These special relativistic effects are produced by the coupling through the relativistic Lorentz factors and do not have a Newtonian counterpart.
CHEN Yong; YAN Zhen-Ya; LI Biao; ZHANG Hong-Qing
2002-01-01
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath
J. S. Pickett
2005-01-01
Full Text Available Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any distance from the bow shock and that this distance has no dependence on the time durations and amplitudes of the solitary waves. In addition we have found that these same two quantities show no dependence on either the ion velocity or the angle between the ion velocity and the local magnetic field direction. These results point to the conclusion that the solitary waves are probably created locally in the magnetosheath at multiple locations, and that the generation mechanism is most likely not solely related to ion dynamics, if at all. To gain insight into a possible local generation mechanism, we have examined the electron differential energy flux characteristics parallel and perpendicular to the magnetic field, as well as the local electron plasma and cyclotron frequencies and the type of bow shock that Cluster is behind, for several time intervals where solitary waves were observed in the magnetosheath. We have found that solitary waves are most likely to be observed when there are counterstreaming (~parallel and anti-parallel to the magnetic field electrons at or below about 100eV. However, there are times when these counterstreaming electrons are present when solitary waves are not. During these times the background magnetic field strength is usually very low (<10nT, implying that the amplitudes of the solitary waves, if present, would be near or below those of
RANS-VOF Solver for Solitary Wave Run-up on A Circular Cylinder
曹洪建; 万德成
2015-01-01
Simulation of solitary wave run-up on a vertical circular cylinder is carried out in a viscous numerical wave tank developed based on the open source codes OpenFOAM. An incompressible two-phase flow solver naoe-FOAM-SJTU is used to solve the Reynolds-Averaged Navier–Stokes (RANS) equations with the SST k-wturbulence model. The PISO algorithm is utilized for the pressure-velocity coupling. The air-water interface is captured via Volume of Fluid (VOF) technique. The present numerical model is validated by simulating the solitary wave run-up and reflected against a vertical wall, and solitary wave run-up on a vertical circular cylinder. Comparisons between numerical results and available experimental data show satisfactory agreement. Furthermore, simulations are carried out to study the solitary wave run-up on the cylinder with different incident wave height H and different cylinder radius a. The relationships of the wave run-up height with the incident wave height H, cylinder radius a are analyzed. The evolutions of the scattering free surface and vortex shedding are also presented to give a better understanding of the process of nonlinear wave-cylinder interaction.
Waves in relativistic electron beam in low-density plasma
Sheinman, I.; Sheinman (Chernenco, J.
2016-11-01
Waves in electron beam in low-density plasma are analyzed. The analysis is based on complete electrodynamics consideration. Dependencies of dispersion laws from system parameters are investigated. It is shown that when relativistic electron beam is passed through low-density plasma surface waves of two types may exist. The first type is a high frequency wave on a boundary between the beam and neutralization area and the second type wave is on the boundary between neutralization area and stationary plasma.
Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas
Ata-ur-Rahman [Institute of Physics and Electronics, University of Peshawar, Peshawar 25000 (Pakistan); National Centre for Physics at QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Centre for Physics at QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Moslem, W. M. [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Mushtaq, A. [National Centre for Physics at QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan)
2013-07-15
The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are strongly influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.
Ion acceleration in a solitary wave by an intense picosecond laser pulse.
Zhidkov, A; Uesaka, M; Sasaki, A; Daido, H
2002-11-18
Acceleration of ions in a solitary wave produced by shock-wave decay in a plasma slab irradiated by an intense picosecond laser pulse is studied via particle-in-cell simulation. Instead of exponential distribution as in known mechanisms of ion acceleration from the target surface, these ions accelerated forwardly form a bunch with relatively low energy spread. The bunch is shown to be a solitary wave moving over expanding plasma; its velocity can exceed the maximal velocity of ions accelerated forward from the rear side of the target.
An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials
Rushchitsky, J. J.; Yurchuk, V. N.
2016-05-01
Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically
Autonomous generation of a thermoacoustic solitary wave in an air-filled tube
Shimizu, Dai; Sugimoto, Nobumasa
2016-10-01
Experiments are performed to demonstrate the autonomous generation of an acoustic solitary wave in an air-filled, looped tube with an array of Helmholtz resonators. The solitary wave is generated spontaneously due to thermoacoustic instability by a pair of stacks installed in the tube and subject to a temperature gradient axially. No external drivers are used to create initial disturbances. Once the solitary wave is generated, it keeps on propagating to circulate along the loop endlessly. The stacks, which are made of ceramics and of many pores of square cross section, are placed in the tube diametrically on exactly the opposite side of the loop, and they are sandwiched by hot and cold (ambient) heat exchangers. When the temperature gradient along both stacks is appropriate, pulses of smooth profiles are generated and propagated in both directions of the tube. From good agreements of not only the pressure profile measured but also the propagation speed with the theory, the pulse is identified as the acoustic solitary wave, and it can be called thermoacoustic solitary wave or thermoacoustic soliton corresponding to the soliton solution of the K-dV equation in one limit.
Muñoz Mateo, A.; Brand, J.
2015-12-01
We analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose-Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring and more complex structures of intersecting vortex lines known collectively as Chladni solitons. The particle-like dynamics of these guided solitary waves provides potentially profitable features for their implementation in atomtronic circuits, and play a key role in the generation of metastable loop currents. Based on the time-dependent Gross-Pitaevskii equation we calculate the dispersion relations of moving solitary waves and their modes of dynamical instability. The dispersion relations reveal a complex crossing and bifurcation scenario. For stationary structures we find that for μ /{\\hslash }{ω }\\perp \\gt 2.65 the solitonic vortex is the only stable solitary wave. More complex Chladni solitons still have weaker instabilities than planar dark solitons and may be seen as transient structures in experiments. Fully time-dependent simulations illustrate typical decay scenarios, which may result in the generation of multiple separated solitonic vortices.
Investigating EMIC Waves as a Precipitation Mechanism for Relativistic Electrons
Li, Z.; Millan, R. M.; Woodger, L. A.
2012-12-01
Evidence has indicated that EMIC waves may be one of the major causes of relativistic electron precipitation (REP). We solved the pitch-angle diffusion equation for the scattering of relativistic electrons by EMIC waves, and generated flux-energy spectra of the precipitating electrons. After being converted into Bremsstrahlung X-ray counts, these spectra can be directly compared with previous (e.g. MAXIS, MINIS, BARREL test campaigns) and future (e.g. BARREL) balloon spectra measurements to determine if EMIC waves are the causes of the REP events. Parameter studies have also been conducted to investigate the influence of various geomagnetic parameters and environmental conditions on the REP spectra.
On asymmetric generalized solitary gravity-capillary waves in finite depth.
Gao, T; Wang, Z; Vanden-Broeck, J-M
2016-10-01
Generalized solitary waves propagating at the surface of a fluid of finite depth are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. Both the effects of gravity and surface tension are included. It is shown that in addition to the classical symmetric waves, there are new asymmetric solutions. These new branches of solutions bifurcate from the branches of symmetric waves. The detailed bifurcation diagrams as well as typical wave profiles are presented.
RELATIVISTIC ELECTRON LOSSES RELATED TO PROTON PRECIPITATION AND EMIC WAVES
Soraas, F.; Sandanger, M. I.; Aarsnes, K.; Oksavik, K.; Evans, D. S.
2009-12-01
Observations of loss of relativistic electrons to the atmosphere is presented and related to SW parameters. It is shown that the L-region of relativistic electron loss matched the anisotropic proton zone. In this zone the pitch angle distribution of the protons are unstable and can generate/amplify EMIC waves which in turn scatter the electrons into the atmosphere. In spatial limited regions, located close to the plasma pause, there can be enhanced losses of protons (sometime completely filling the loss cone). These regions of proton losses (spikes) are shown to give rise to EMIC waves leading to enhance scattering of the relativistic electrons. In the main phase of the storm the proton spikes are located in the midnight/evening sector, but in the storm recovery phase they are located at all MLTs. The anisotropic proton zone and proton spikes are observed in all storms, but not all storms contain an elevated flux of relativistic electrons.
Propagation of linear waves in relativistic anisotropic magnetohydrodynamics.
Gebretsadkan, W B; Kalra, G L
2002-11-01
Gedalin [Phys. Rev. E 47, 4354 (1993)] derived a dispersion relation for linear waves in relativistic anisotropic Magnetohydrodynamics (MHD). This dispersion relation is used to point out the regions where the relativistic anisotropic MHD leads to new results that cannot be obtained using usual collisional relativistic MHD. This is highlighted by plotting a Fresnal ray surface. Conditions for the onset of firehose and mirror instabilities are also indicated. Such a study can be applied to astrophysical features such as pulsar winds, propagation of cosmic rays, etc.
NUMERICAL SIMULATION OF SOLITARY WAVE RUN-UP AND OVERTOPPING USING BOUSSINESQ-TYPE MODEL
TSUNG Wen-Shuo; HSIAO Shih-Chun; LIN Ting-Chieh
2012-01-01
In this article,the use of a high-order Boussinesq-type model and sets of laboratory experiments in a large scale flume of breaking solitary waves climbing up slopes with two inclinations are presented to study the shoreline behavior of breaking and non-breaking solitary waves on plane slopes.The scale effect on run-up height is briefly discussed.The model simulation capability is well validated against the available laboratory data and present experiments.Then,serial numerical tests are conducted to study the shoreline motion correlated with the effects of beach slope and wave nonlinearity for breaking and non-breaking waves.The empirical formula proposed by Hsiao et al.for predicting the maximum run-up height of a breaking solitary wave on plane slopes with a wide range of slope inclinations is confirmed to be cautious.Furthermore,solitary waves impacting and overtopping an impermeable sloping seawall at various water depths are investigated.Laboratory data of run-up height,shoreline motion,free surface elevation and overtopping discharge are presented.Comparisons of run-up,run-down,shoreline trajectory and wave overtopping discharge are made.A fairly good agreement is seen between numerical results and experimental data.It elucidates that the present depth-integrated model can be used as an efficient tool for predicting a wide spectrum of coastal problems.
Artemyev, A. V., E-mail: ante0226@gmail.com [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS - University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2015-06-15
In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail.
Kodaira, Tsubasa; Waseda, Takuji
2013-04-01
We have conducted ADCP and CTD measurements from 31/8/2010 to 2/9/2010 at the Miyake Island, located approximately 180 km south of Tokyo. The Kuroshio Current approached the island in this period, and the PALSAR image showed parabolic bright line upstream of the island. This bright line may be a surface signature of large amplitude internal solitary wave. Although our measurements did not explicitly show evidence of the internal solitary wave, critical condition might have been satisfied because of the Kuroshio Current and strong seasonal thermocline. To discover the generation mechanism of the large amplitude internal solitary wave at the Miyake Island, we have conducted non-hydrostatic numerical simulation with the MITgcm. A simple box domain, with open boundaries at all sides, is used. The island is simplified to circular cylinder or Gaussian Bell whose radius is 3km at ocean surface level. The size of the domain is 40kmx40kmx500m for circular cylinder cases and 80kmx80kmx500m for Gaussian bell cases. By looking at our CTD data, we have chosen for initial and boundary conditions a tanh function for vertical temperature profile. Salinity was kept constant for simplicity. Vertical density profile is also described by tanh function because we adopt linear type of equation of state. Vertical velocity profile is constant or linearly changed with depth; the vertical mean speed corresponds to the linear phase speed of the first baroclinic mode obtained by solving the eigen-value problem. With these configurations, we have conducted two series of simulations: shear flow through cylinder and uniform flow going through Gaussian Bell topography. Internal solitary waves were generated in front of the cylinder for the first series of simulations with shear flow. The generated internal waves almost purely consisted of 1st baroclinic component. Their intensities were linearly related with upstream vertical shear strength. As the internal solitary wave became larger, its width
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation
Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang
2017-02-01
Three (2+1)-dimensional equations-KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001
A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment
Goodman, Roy H.; Rahman, Aminur; Bellanich, Michael J.; Morrison, Catherine N.
2015-04-01
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to exhibit the two-bounce resonance.
Damping solitary wave under the second and third boundary condition of a viscous plasma
Li, G.; Ren, Y.-Q.
2016-08-01
In this paper, the solitary waves of a viscous plasma confined in a cylindrical pipe is investigated under two types of boundary condition. By using the reductive perturbation theory, a quasi-KdV equation is derived and a damping solitary wave is obtained. It is found that the damping rate increases with the viscosity coefficient of the plasma ν ' increasing and the radius of the cylindrical pipe R decreasing for second and third boundary condition. The magnitude of the damping rate is also dominated by boundary condition type. From the fact that the amplitude reduces rapidly when R approaches zero or ν ' approaches infinite, we confirm the existence of a damping solitary wave.
Solitary waves and their stability in colloidal media: semi-analytical solutions
Marchant, T R
2012-01-01
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas compressibility. Semi-analytical solutions, for both one and two spatial dimensions, are derived using an averaged Lagrangian and suitable trial functions for the solitary waves. Power versus propagation constant curves and neutral stability curves are obtained for both cases, which illustrate that multiple solution branches occur for both the one and two dimensional geometries. For the one-dimensional case it is found that three solution branches (with a bistable regime) occur, while for the two-dimensional case two solution branches (with a single stable branch) occur in the limit of low background packing fractions. For high background packing fractions the power versus propagation constant curves are monotonic and the solitary waves stable for all parameter values. Comparisons are mad...
(2+1-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves
Chunlei Wang
2015-01-01
Full Text Available By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1-dimensional mKdV hierarchy is derived which popularizes the results of (1+1-dimensional integrable system. Furthermore, the (2+1-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.
Application of artificial neural network to calculation of solitary wave run-up
You-xing WEI
2010-09-01
Full Text Available The prediction of solitary wave run-ups has important practical significance in coastal and ocean engineering. But the precision of calculating is limited from the existing models. Artificial neural network technology has rapidly developed and been widely used in many fields. In this paper, a solitary wave run-up calculation model is established based on artificial neural networks. A BP network with one hidden layer is modified by an additional momentum method and an auto-adjusting learning rate. The correlation coefficients between the model results and the experimental values are 0.9635 and 0.9965, respectively. It is concluded that the neural network model is an appropriate methodology to be applied to solitary wave run-up scenario calculation and analysis.
Relativistic electromagnetic waves in an electron-ion plasma
Chian, Abraham C.-L.; Kennel, Charles F.
1987-01-01
High power laser beams can drive plasma particles to relativistic energies. An accurate description of strong waves requires the inclusion of ion dynamics in the analysis. The equations governing the propagation of relativistic electromagnetic waves in a cold electron-ion plasma can be reduced to two equations expressing conservation of energy-momentum of the system. The two conservation constants are functions of the plasma stream velocity, the wave velocity, the wave amplitude, and the electron-ion mass ratio. The dynamic parameter, expressing electron-ion momentum conversation in the laboratory frame, can be regarded as an adjustable quantity, a suitable choice of which will yield self-consistent solutions when other plasma parameters were specified. Circularly polarized electromagnetic waves and electrostatic plasma waves are used as illustrations.
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.
Stable Propagating Waves and Wake Fields in Relativistic Electromagnetic Plasma
DUAN Yi-Shi; XIE Bai-Song; TIAN Miao; YIN Xin-Tao; ZHANG Xin-Hui
2008-01-01
Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of electrons is taken into account in the problem. It is found that in the moving frame with transverse wave group velocity the stable propagating transverse electromagnetic waves and longitudinal plasma wake fields can exist in the appropriate regime of plasma.
Investigation of Relativistic Electron Resonance with EMIC Waves
Woodger, L. A.; Millan, R. M.; Denton, R. E.
2008-12-01
Wave-particle interaction of relativistic electrons with EMIC waves has been proposed as an important loss mechanism for radiation belt electrons (e.g. Thorne and Andreoli, 1980). Lorentzen et al (2000) and Millan et al (2002) suggested this mechanism to be responsible for dusk side relativistic electron precipitation (REP) detected by balloon borne instrumentation. This study will use the linear electromagnetic dispersion code WHAMP to investigate the effects of density, magnetic field, anisotropy, and heavy ions on the minimum resonance energy for relativistic electrons with EMIC waves. Results will be compared with observations of REP during the MAXIS balloon campaign on Jan. 19, 2000 and the MINIS balloon campaign on Jan. 21, 2005.
Experimental observation of gravity-capillary solitary waves generated by a moving air-suction
Park, Beomchan; Cho, Yeunwoo
2016-11-01
Gravity-capillary solitary waves are generated by a moving "air-suction" forcing instead of a moving "air-blowing" forcing. The air-suction forcing moves horizontally over the surface of deep water with speeds close to the minimum linear phase speed cmin = 23 cm/s. Three different states are observed according to forcing speed below cmin. At relatively low speeds below cmin, small-amplitude linear circular depressions are observed, and they move steadily ahead of and along with the moving forcing. As the forcing speed increases close to cmin, however, nonlinear 3-D gravity-capillary solitary waves are observed, and they move steadily ahead of and along with the moving forcing. Finally, when the forcing speed is very close to cmin, oblique shedding phenomena of 3-D gravity-capillary solitary waves are observed ahead of the moving forcing. We found that all the linear and nonlinear wave patterns generated by the air-suction forcing correspond to those generated by the air-blowing forcing. The main difference is that 3-D gravity-capillary solitary waves are observed "ahead of" the air-suction forcing, whereas the same waves are observed "behind" the air-blowing forcing. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1002441).
Interaction of solitary waves in magnetized warm dusty plasmas with dust charging effects
Xue Ju-Kui
2006-01-01
In consideration of adiabatic dust charge variation, the combined effect of the external magnetized field and the dust temperature on head-on collision of the three-dimensional dust acoustic solitary waves is investigated. By using the extended Poincaré-Lighthill-Kuo method, the phase shifts and the trajectories of two solitons after the collision are obtained. The effects of the magnitude and the obliqueness of the external magnetic field and the dust temperature on the solitary wave collisions are discussed in detail.
Solitary Density Waves for Improved Traffic Flow Model with Variable Brake Distances
朱文兴; 丁瑞玲
2012-01-01
Traffic flow model is improved by introducing variable brake distances with varying slopes. Stability of the traffic flow on a gradient is analyzed and the neutral stability condition is obtained. The KdV （Korteweg-de Vries） equation is derived the use of nonlinear analysis and soliton solution is obtained in the meta-stable region. Solitary density waves are reproduced in the numerical simulations. It is found that as uniform headway is less than the safety distance solitary wave exhibits upward form, otherwise it exhibits downward form. In general the numerical results are in good agreement with the analytical results.
Numerical Simulation of Solitary Wave Induced Flow Motion around a Permeable Submerged Breakwater
Jisheng Zhang
2012-01-01
Full Text Available This paper presents a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave-structure interaction is obtained by solving the Volume-Averaged Reynolds-Averaged Navier-Stokes governing equations (VARANS and volume of fluid (VOF theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media, structure height, and structure width on the propagation of a solitary wave in the vicinity of a permeable submerged structure. The results show that solitary wave propagation around a permeable breakwater is essentially different from that around impermeable one. It is also found that the structure porosity has more impact than equivalent mean diameter on the wave transformation and flow structure. After interacting with the higher structure, the wave has smaller wave height behind the structure with a lower travelling speed. When the wave propagates over the breakwater with longer width, the wave travelling speed is obviously reduced with more wave energy dissipated inside porous structure.
YANG Qiu-Ying; MA Song-Hua; ZHANG Ying-Yue; FANG Jian-Ping; CHEN Tian-Lun; HONG Bi-Hai; ZHENG Chun-Long
2008-01-01
By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system.
Gidel, Floriane; Bokhove, Onno; Kalogirou, Anna
2017-01-01
In this work, we model extreme waves that occur due to Mach reflection through the intersection of two obliquely incident solitary waves. For a given range of incident angles and amplitudes, the Mach stem wave grows linearly in length and amplitude, reaching up to 4 times the amplitude of the incident waves. A variational approach is used to derive the bidirectional Benney-Luke equations, an asymptotic equivalent of the three-dimensional potential-flow equations modelling water waves. This nonlinear and weakly dispersive model has the advantage of allowing wave propagation in two horizontal directions, which is not the case with the unidirectional Kadomtsev-Petviashvili (KP) equation used in most previous studies. A variational Galerkin finite-element method is applied to solve the system numerically in Firedrake with a second-order Störmer-Verlet temporal integration scheme, in order to obtain stable simulations that conserve the overall mass and energy of the system. Using this approach, we are able to get close to the 4-fold amplitude amplification predicted by Miles.
S. A. El-Wakil
2012-01-01
Full Text Available The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV equation for small- but finite-amplitude electrostatic ion-acoustic waves in weakly relativistic plasma consisting of warm ions and isothermal electrons. An algebraic method with computerized symbolic computation is applied in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters which reveal different solutions, that is, bell-shaped solitary pulses, rational pulses, and solutions with singularity at finite points, which called “blowup” solutions in addition to the propagation of an explosive pulses. The weakly relativistic effect is found to significantly change the basic properties (namely, the amplitude and the width of the ion-acoustic waves. The result of the present investigation may be applicable to some plasma environments, such as ionosphere region.
Saha, Asit; Chatterjee, Prasanta; Chatterjee
2014-08-01
Ion acoustic solitary waves and periodic waves in an unmagnetized plasma with superthermal (kappa-distributed) electrons and positrons are investigated through a non-perturbative approach. Model equations are transformed to a planar dynamical system. Then by using the bifurcations of phase portraits of this planar dynamical system, we have established that our model has solitary wave and periodic wave solutions. We have obtained two analytical solutions for these solitary and periodic waves depending on the parameters. From these solitary wave and periodic wave solutions, we have shown the combined effects of temperature ratio (σ) of electrons and positrons, spectral index (κ), speed of the traveling wave (v), and density ratio (p) of positrons and electrons on the characteristics of ion acoustic solitary and periodic waves. The spectral index, density ratio, speed of the traveling wave, and temperature ratio significantly affect the characteristics of ion acoustic solitary and periodic structures. The present study might be helpful to understand the salient features of nonlinear ion acoustic solitary and periodic structures in the interstellar medium.
Bulanov, Stepan; Maksimchuk, Anatoly; Zhidkov, Alexei
2009-11-01
We report on the analytic and computer simulation study of a relativistic spherical wake wave. Such a wave in the breaking regime, traveling towards the center is able to reflect and focus the incoming radiation and up-shifting its frequency. The reflected and focused electromagnetic pulse can have such high intensity, that it is able to create e^+e^- pairs via Schwinger process.
Electron-acoustic solitary waves in a beam plasma with electron trapping and nonextensivity effects
Ali Shan, S.; Aman-ur-Rehman, Mushtaq, A.
2016-09-01
A theoretical investigation is carried out for understanding the properties of electron-acoustic solitary waves (EASWs) in a beam plasma whose constituents are a cold beam electron fluid, hot nonextensive electrons obeying a vortex-like distribution with nonextensive factor q, and stationary ions. An energy integral (Schamel KdV) equation is derived by employing pseudo-potential (reductive perturbation) approach. The presence of nonextensive q-distributed hot trapped electrons and cold electron beam has been shown to influence the soliton structure quite significantly. The nonlinear dispersion relation is derived to analyze the dependency of the electron acoustic solitary wave quantities. From the analysis of our results, it is shown that the present plasma model supports the compressive EASWs. As the real plasma situations are observed with plasma species having a relative flow, so our present analysis should be useful for understanding the electrostatic solitary structures observed in the dayside auroral zone and other regions of the magnetosphere.
Advection of pollutants by internal solitary waves in oceanic and atmospheric stable stratifications
G. W. Haarlemmer
1998-01-01
Full Text Available When a pollutant is released into the ocean or atmosphere under turbulent conditions, even a steady release is captured by large eddies resulting in localized patches of high concentration of the pollutant. If such a cloud of pollutant subsequently enters a stable stratification-either a pycnocline or thermocline-then internal waves are excited. Since large solitary internal waves have a recirculating core, pollutants may be trapped in the sclitary wave, and advected large distances through the waveguide provided by the stratification. This paper addresses the mechanisms, through computer and physical simulation, by which a localized release of a dense pollutant results in solitary waves that trap the pollutant or disperse the pollutant faster than in the absence of the waves.
Shoaling of internal solitary waves at the ASIAEX site in the South China Sea
K. G. Lamb
2014-07-01
Full Text Available The interaction of barotropic tides with Luzon Strait topography generates westward propagating internal bores and solitary waves trains which eventually shoal and dissipate on the western side of the South China Sea. Two-dimensional numerical simulations of this shoaling process at the site of the Asian Seas International Acoustic Experiment (ASIAEX have been undertaken in order to investigate the sensitivity of the shoaling process to the stratification and the underlying bathymetry, and to explore the influence of rotation. A range of wave amplitudes are considered. Comparisons with adiabatic shoaling waves are also made and the potential impact of a non-slip boundary condition are briefly explored. On the slope secondary solitary waves and mode-two wave packets are generated which propagate towards the shelf. Comparisons with observations made during the ASIAEX experiment are made.
Quasi-periodic behavior of ion acoustic solitary waves in electron-ion quantum plasma
Sahu, Biswajit [Department of Mathematics, West Bengal State University Barasat, Kolkata-700126 (India); Poria, Swarup [Department of Applied Mathematics, University of Calcutta Kolkata-700009 (India); Narayan Ghosh, Uday [Department of Mathematics, Siksha Bhavana, Visva Bharati University Santiniketan (India); Roychoudhury, Rajkumar [Physics and Applied Mathematics Unit, Indian Statistical Institute Kolkata-700108 (India)
2012-05-15
The ion acoustic solitary waves are investigated in an unmagnetized electron-ion quantum plasmas. The one dimensional quantum hydrodynamic model is used to study small as well as arbitrary amplitude ion acoustic waves in quantum plasmas. It is shown that ion temperature plays a critical role in the dynamics of quantum electron ion plasma, especially for arbitrary amplitude nonlinear waves. In the small amplitude region Korteweg-de Vries equation describes the solitonic nature of the waves. However, for arbitrary amplitude waves, in the fully nonlinear regime, the system exhibits possible existence of quasi-periodic behavior for small values of ion temperature.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
The adiabatic approximation solutions of cylindrical and spherical dust ion-acoustic solitary waves
吕克璞; 豆福全; 孙建安; 段文山; 石玉仁
2005-01-01
By using the equivalent particle theory, the adiabatic approximation solutions of the Korteweg-de Vries type equation (including KdV equation, cylindrical KdV equation and spherical KdV equation) in dust ion-acoustic solitary waves were obtained. The method can be extended to other nonlinear evolution equations.
Oblique propagation of ion-acoustic solitary waves in a magnetized electron-positron-ion plasma
Ferdousi, M.; Sultana, S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-03-15
The properties of obliquely propagating ion-acoustic solitary waves in the presence of ambient magnetic field have been investigated theoretically in an electron-positron-ion nonthermal plasma. The plasma nonthermality is introduced via the q-nonextensive distribution of electrons and positrons. The Korteweg-de Vries (K-dV) and modified K-dV (mK-dV) equations are derived by adopting reductive perturbation method. The solution of K-dV and modified K-dV equation, which describes the solitary wave characteristics in the long wavelength limit, is obtained by steady state approach. It is seen that the electron and positron nonextensivity and external magnetic field (obliqueness) have significant effects on the characteristics of solitary waves. A critical value of nonextensivity is found for which solitary structures transit from positive to negative potential. The findings of this investigation may be used in understanding the wave propagation in laboratory and space plasmas where static external magnetic field is present.
STABILITY AND INSTABILITY OF SOLITARY WAVES FOR ABSTRACT COMPLEX HAMILTONIAN SYSTEM
Zhao Ye
2005-01-01
This paper is concerned with the orbital stability and orbital instability of solitary waves for some complex Hamiltonian systems in abstract form. Under some assumptions on the spectra of the related operator and the decaying estimates of the semigroup, the sufficient conditions on orbital stability and instability are obtained.
Solitary waves in Galilean covariant Fermi field theories with self-interaction
Saradzhev, Fuad M
2014-01-01
The generalized Levy-Leblond equation for a $(3+1)$-dimensional self-interacting Fermi field is considered. Spin up solitary wave solutions with space oscillations in the $x^3$-coordinate are constructed. The solutions are shown to accumulate non-equal amounts of inertial and rest masses.
Modified KdV equation for solitary Rossby waves with β effect in barotropic fluids
Song Jian; Yang Lian-Gui
2009-01-01
This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation, and the modified Korteweg-de Vries(mKdV) equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β(y) with latitude y is obtained.
Is DNA a nonlinear dynamical system where solitary conformational waves are possible?
Ludmila V Yakushevich
2001-09-01
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The history of the approach, the main results, and arguments in favour and against are presented. Perspectives are discussed pertaining to studies of DNA’s nonlinear properties.
A Comparative Study on Three Different Transducers for the Measurement of Nonlinear Solitary Waves
Piervincenzo Rizzo
2013-01-01
Full Text Available In the last decade there has been an increasing interest in the use of highly- and weakly- nonlinear solitary waves in engineering and physics. Nonlinear solitary waves can form and travel in nonlinear systems such as one-dimensional chains of particles, where they are conventionally generated by the mechanical impact of a striker and are measured either by using thin transducers embedded in between two half-particles or by a force sensor placed at the chain’s base. These waves have a constant spatial wavelength and their speed, amplitude, and duration can be tuned by modifying the particles’ material or size, or the velocity of the striker. In this paper we propose two alternative sensing configurations for the measurements of solitary waves propagating in a chain of spherical particles. One configuration uses piezo rods placed in the chain while the other exploits the magnetostrictive property of ferromagnetic materials. The accuracy of these two sensing systems on the measurement of the solitary wave’s characteristics is assessed by comparing experimental data to the numerical prediction of a discrete particle model and to the experimental measurements obtained by means of a conventional transducer. The results show very good agreement and the advantages and limitations of the new sensors are discussed.
Derivation of relativistic wave equation from the Poisson process
Tomoshige Kudo; Ichiro Ohba
2002-08-01
A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.
On solitary waves. Part 2 A unified perturbation theory for higher-order waves
Theodore Yaotsu Wu; Xinlong Wang; Wendong Qu
2005-01-01
A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on (i) the accuracy of the theoretically predicted wave properties and (ii) the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property (e.g.the wave amplitude, speed, its profile, excess mass, momentum, and energy), on what range in value of the base, and on the rank of the order n in the expansion being addressed.Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ (n) (the relative mean-square difference between successive orders n of wave elevations) reaching a minimum,δm, at a specific order, n = nm, both depending on the base adopted, e.g. n = 11-12 based on parameter α (wave amplitude), nm,β = 15 onβ (amplitude-speed square ratio),and nm.∈ = 17 on ∈ ( wave number squared). The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.
Coherent structures in wave boundary layers. Part 2. Solitary motion
Sumer, B. Mutlu; Jensen, Palle Martin; Sørensen, Lone B.;
2010-01-01
in an oscillating water tunnel. Two kinds of measurements were made: bed shear stress measurements and velocity measurements. The experiments show that the solitary-motion boundary layer experiences three kinds of flow regimes as the Reynolds number is increased: (i) laminar regime; (ii) laminar regime where...... the boundary-layer flow experiences a regular array of vortex tubes near the bed over a short period of time during the deceleration stage; and (iii) transitional regime characterized with turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress traces...
The effect of stochastic perturbations on plankton transport by internal solitary waves
M. Stastna
2011-12-01
Full Text Available Internal solitary and solitary-like waves are a commonly observed feature of density stratified natural waters, including lakes and the coastal ocean. Since such waves induce significant currents throughout the water column they can be responsible for significant transport of both passive and swimming biota. We consider simple models of moving zooplankton based on the Langevin equation. The small amplitude randomness significantly alters the nature of particle motion. In particular, passage through the wave leads to strongly non Gaussian particle distributions. When the plankton swims to return to its equilibrium photic level, a steady state that balances randomness, swimming and wave-induced motions is possible. We discuss possible implications of this steady state for organisms that feed on plankton.
Single and multi-solitary wave solutions to a class of nonlinear evolution equations
Wang, Deng-Shan; Li, Hongbo
2008-07-01
In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
Singh, S. V.; Devanandhan, S.; Lakhina, G. S.; Bharuthram, R.
2016-08-01
A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increases by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of "burst a" event by Viking satellite on the auroral field lines.
Solitary and cnoidal wave scattering by a submerged horizontal plate in shallow water
Hayatdavoodi, Masoud; Ertekin, R. Cengiz; Valentine, Benjamin D.
2017-06-01
Solitary and cnoidal wave transformation over a submerged, fixed, horizontal rigid plate is studied by use of the nonlinear, shallow-water Level I Green-Naghdi (GN) equations. Reflection and transmission coefficients are defined for cnoidal and solitary waves to quantify the nonlinear wave scattering. Results of the GN equations are compared with the laboratory experiments and other theoretical solutions for linear and nonlinear waves in intermediate and deep waters. The GN equations are then used to study the nonlinear wave scattering by a plate in shallow water. It is shown that in deep and intermediate depths, the wave-scattering varies nonlinearly by both the wavelength over the plate length ratio, and the submergence depth. In shallow water, however, and for long-waves, only the submergence depth appear to play a significant role on wave scattering. It is possible to define the plate submergence depth and length such that certain wave conditions are optimized above, below, or downwave of the plate for different applications. A submerged plate in shallow water can be used as a means to attenuate energy, such as in wave breakers, or used for energy focusing, and in wave energy devices.
Small amplitude electron acoustic solitary waves in a magnetized superthermal plasma
Devanandhan, S.; Singh, S. V.; Lakhina, G. S.; Bharuthram, R.
2015-05-01
The propagation of electron acoustic solitary waves in a magnetized plasma consisting of fluid cold electrons, electron beam and superthermal hot electrons (obeying kappa velocity distribution function) and ion is investigated in a small amplitude limit using reductive perturbation theory. The Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation governing the dynamics of electron acoustic solitary waves is derived. The solution of the KdV-ZK equation predicts the existence of negative potential solitary structures. The new results are: (1) increase of either the beam speed or temperature of beam electrons tends to reduce both the amplitude and width of the electron acoustic solitons, (2) the inclusion of beam speed and temperature pushes the allowed Mach number regime upwards and (3) the soliton width maximizes at certain angle of propagation (αm) and then decreases for α >αm . In addition, increasing the superthermality of the hot electrons also results in reduction of soliton amplitude and width. For auroral plasma parameters observed by Viking, the obliquely propagating electron-acoustic solitary waves have electric field amplitudes in the range (7.8-45) mV/m and pulse widths (0.29-0.44) ms. The Fourier transform of these electron acoustic solitons would result in a broadband frequency spectra with peaks near 2.3-3.5 kHz, thus providing a possible explanation of the broadband electrostatic noise observed during the Burst a.
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian
2016-07-01
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.
Wave-Induced Pressure Under an Internal Solitary Wave and Its Impact at the Bed
Rivera, Gustavo; Diamesis, Peter; Jenkins, James; Berzi, Diego
2015-11-01
The bottom boundary layer (BBL) under a mode-1 internal solitary wave (ISW) of depression propagating against an oncoming model barotropic current is examined using 2-D direct numerical simulation based on a spectral multidomain penalty method model. Particular emphasis is placed on the diffusion into the bed of the pressure field driven by the wake and any near-bed instabilities produced under specific conditions. To this end, a spectral nodal Galerkin approach is used for solving the diffusion equation for the wave-induced pressure. At sufficiently high ISW amplitude, the BBL undergoes a global instability which produces intermittent vortex shedding from within the separation bubble in the lee of the wave. The interplay between the bottom shear stress field and pressure perturbations during vortex ejection events and the subsequent evolution of the vortices is examined. The potential for bed failure upon the passage of the ISW trough and implications for resuspension of bottom particulate matter are both discussed in the context of specific sediment transport models.
On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current
Dali Guo
2014-01-01
Full Text Available The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.
BAI Yefei; SONG Jinbao
2006-01-01
A two-dimensional, depth-integrated model proposed by Lynett and Liu (2002) was checked carefully, and several misprints in the model were corrected after detailed examination on both the theory and the numerical program. Several comparisons were made on wave profile, system energy and maximum wave amplitude. It is noted that the modified model can simulate the propagation of the internal solitary waves over variable bathymetry more reasonably to a certain degree, and the wave profiles obtained based on the modified model can better fit the experiment data reported by Helfrich (1992)than those from original model.
Structure of internal solitary waves in two-layer fluid at near-critical situation
Kurkina, O.; Singh, N.; Stepanyants, Y.
2015-05-01
A new model equation describing weakly nonlinear long internal waves at the interface between two thin layers of different density is derived for the specific relationships between the densities, layer thicknesses and surface tension between the layers. The equation derived and dubbed here the Gardner-Kawahara equation represents a natural generalisation of the well-known Korteweg-de Vries (KdV) equation containing the cubic nonlinear term as well as fifth-order dispersion term. Solitary wave solutions are investigated numerically and categorised in terms of two dimensionless parameters, the wave speed and fifth-order dispersion. The equation derived may be applicable to wave description in other media.
Measurement and modeling of bed shear stress under solitary waves
Jayakumar, S.; Guard, P.A.; Baldock, T.E.
convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total...
Rarefaction wave in relativistic steady magnetohydrodynamic flows
Sapountzis, Konstantinos, E-mail: ksapountzis@phys.uoa.gr; Vlahakis, Nektarios, E-mail: vlahakis@phys.uoa.gr [Faculty of Physics, University of Athens, 15784 Zografos, Athens (Greece)
2014-07-15
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity, we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow, we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.
Yang, Jianke
2012-03-01
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that stability of solitary waves does not switch at saddle-node bifurcations. This analytical result is confirmed by numerical examples where both soliton branches are stable at saddle-node bifurcations.
Deka, Manoj Kr.
2016-12-01
In this report, a detailed investigation on the study of dust acoustics solitary waves solution with negatively dust charge fluctuation in dusty plasma corresponding to lower and higher temperature nonthermal ions with trapped electrons is presented. We consider temporal variation of dust charge as a source of dissipation term to derive the lower order modified Kadomtsev-Petviashvili equation by using the reductive perturbation technique. Solitary wave solution is obtained with the help of sech method in presence of trapped electrons and low (and high) temperature nonthermal ions. Both nonthermality of ions and trapped state of the electrons are found to have an imperative control on the nonlinear coefficient, dissipative coefficient as well as height of the wave potential.
PIC simulation of compressive and rarefactive dust ion-acoustic solitary waves
Li, Zhong-Zheng; Zhang, Heng; Hong, Xue-Ren; Gao, Dong-Ning; Zhang, Jie; Duan, Wen-Shan; Yang, Lei
2016-08-01
The nonlinear propagations of dust ion-acoustic solitary waves in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated by the particle-in-cell method. By comparing the simulation results with those obtained from the traditional reductive perturbation method, it is observed that the rarefactive KdV solitons propagate stably at a low amplitude, and when the amplitude is increased, the prime wave form evolves and then gradually breaks into several small amplitude solitary waves near the tail of soliton structure. The compressive KdV solitons propagate unstably and oscillation arises near the tail of soliton structure. The finite amplitude rarefactive and compressive Gardner solitons seem to propagate stably.
El-Wakil, S A; Abd-El-Hamid, H M; Abulwafa, E M
2010-01-01
A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called blowup solutions in addition to the propagation of an explosive pu...
Algebraic method for constructing singular steady solitary waves: A case study
Clamond, Didier; Galligo, André
2016-01-01
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equations with surface tension, because it provides a tractable model that, in the same time, is not too simple so the interest of the method can be emphasised. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of Physics. In capillary-gravity regime, there are two kinds of localised infinitely smooth travelling wave solutions -- solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, the "zoology" of solutions becomes much richer and the main goal of this study is to provide a complete classification of such singular localised solutions using the methods of the effective Algebraic Geometry.
Algebraic method for constructing singular steady solitary waves: a case study
Clamond, Didier; Dutykh, Denys; Galligo, André
2016-07-01
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.
Gaussian solitary waves and compactons in Fermi–Pasta–Ulam lattices with Hertzian potentials
James, Guillaume; Pelinovsky, Dmitry
2014-01-01
We consider a class of fully nonlinear Fermi–Pasta–Ulam (FPU) lattices, consisting of a chain of particles coupled by fractional power nonlinearities of order α>1. This class of systems incorporates a classical Hertzian model describing acoustic wave propagation in chains of touching beads in the absence of precompression. We analyse the propagation of localized waves when α is close to unity. Solutions varying slowly in space and time are searched with an appropriate scaling, and two asymptotic models of the chain of particles are derived consistently. The first one is a logarithmic Korteweg–de Vries (KdV) equation and possesses linearly orbitally stable Gaussian solitary wave solutions. The second model consists of a generalized KdV equation with Hölder-continuous fractional power nonlinearity and admits compacton solutions, i.e. solitary waves with compact support. When , we numerically establish the asymptotically Gaussian shape of exact FPU solitary waves with near-sonic speed and analytically check the pointwise convergence of compactons towards the limiting Gaussian profile. PMID:24808748
Yang, Yang Yang; Liu, Shi Wei; Yang, Qiong; Zhang, Zhen Bin; Duan, Wen Shan; Yang, Lei
2016-07-01
The paper work relates to Nesterenko's problem to further study the solitary wave when the strong external force acts on the granular chain. We also study the problem under the long-wavelength approximation and find that such kind of solitary wave in system with the initial prestress can be described by the Korteweg-de Vries (KdV) equation. It is found that the results of analytical and numerical are in an excellent agreement. Furthermore, we study the scattering of the KdV solitary wave in different granular materials both in theoretical and numerical methods. It is found that the numbers and the amplitudes of both the reflected and the transmitted waves depend not only on the amplitude of the incident solitary wave but also on the variations of both sides of the discontinuity such as the mass, Young's modulus or radius of the grains.
Ship-induced solitary Riemann waves of depression in Venice Lagoon
Parnell, Kevin E. [College of Marine and Environmental Sciences and Centre for Tropical Environmental and Sustainability Sciences, James Cook University, Queensland 4811 (Australia); Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Soomere, Tarmo, E-mail: soomere@cs.ioc.ee [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn (Estonia); Zaggia, Luca [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rodin, Artem [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Lorenzetti, Giuliano [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rapaglia, John [Sacred Heart University Department of Biology, 5151 Park Avenue, Fairfield, CT 06825 (United States); Scarpa, Gian Marco [Università Ca' Foscari, Dorsoduro 3246, 30123 Venice (Italy)
2015-03-06
We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope.
Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation
Zhang, Ben-gong; Li, Weibo; Li, Xiangpeng
2017-06-01
In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan
2015-04-01
Satellite observations recently revealed the existence of trains of internal solitary waves in the southern Red Sea between 16.0°N and 16.5°N, propagating from the centre of the domain toward the continental shelf [Da silva et al., 2012]. Given the relatively weak tidal velocity in this area and their generation in the central of the domain, Da Silva suggested three possible mechanisms behind the generation of the waves, namely Resonance and disintegration of interfacial tides, Generation of interfacial tides by impinging, remotely generated internal tidal beams and for geometrically focused and amplified internal tidal beams. Tide analysis based on tide stations data and barotropic tide model in the Red Sea shows that tide is indeed very weak in the centre part of the Red Sea, but it is relatively strong in the northern and southern parts (reaching up to 66 cm/s). Together with extreme steep slopes along the deep trench, it provides favourable conditions for the generation of internal solitary in the southern Red Sea. To investigate the generation mechanisms and study the evolution of the internal waves in the off-shelf region of the southern Red Sea we have implemented a 2-D, high-resolution and non-hydrostatic configuration of the MIT general circulation model (MITgcm). Our simulations reproduce well that the generation process of the internal solitary waves. Analysis of the model\\'s output suggests that the interaction between the topography and tidal flow with the nonlinear effect is the main mechanism behind the generation of the internal solitary waves. Sensitivity experiments suggest that neither tidal beam nor the resonance effect of the topography is important factor in this process.
Development of a 2 MW relativistic backward wave oscillator
Yaduvendra Choyal; Lalit Gupta; Prasad Deshpande; Krishna Prasad Maheshwari; Kailash Chander Mittal; Suresh Chand Bapna
2008-12-01
In this paper, a high power relativistic backward wave oscillator (BWO) experiment is reported. A 230 keV, 2 kA, 150 ns relativistic electron beam is generated using a Marx generator. The beam is then injected into a hollow rippled wall metallic cylindrical tube that forms a slow wave structure. The beam is guided using an axial pulsed magnetic field having a peak value 1 T and duration 1 ms. The field is generated by the discharge of a capacitor bank into a solenoidal coil. A synchronization circuit ensures the generation of the electron beam at the instant when the axial magnetic field attains its peak value. The beam interacts with the SWS modes and generates microwaves due to Cherenkov interaction. Estimated power of 2 MW in TM 01 mode is observed.
Numerical modeling on the interaction of internal solitary wave with slope-shelf and modal analysis
无
2007-01-01
On the basis of a nonhydrostatic numerical model, the interaction of internal solitary wave with slope-shelf was studied. The breaking and polarity transformation were analyzed. A "kink" structure, due to shoaling topography and higher nonlinear effect, was found to be generated by the leading wave before breaking. Coherent vortex shedding behind the leading wave was presented. The evolution characteristics of the modal structure were analyzed based on the empirical orthogonal function method. The modal structure was complicated due to the effect of the variable topography, especially when breaking occurred. In the performed experiments, the contributions to the total variance from higher mode jumped from no more than 20% to over 40%.
Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata-700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009 (India); Roychoudhury, Rajkumar [Indian Statistical Institute, Kolkata-700 108 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar Kolkata-700 064 (India)
2013-01-15
Nonlinear propagation of electron acoustic waves in homogeneous, dispersive plasma medium with two temperature electron species is studied in presence of externally applied magnetic field. The linear dispersion relation is found to be modified by the externally applied magnetic field. Lagrangian transformation technique is applied to carry out nonlinear analysis. For small amplitude limit, a modified KdV equation is obtained, the modification arising due to presence of magnetic field. For weakly magnetized plasma, the modified KdV equation possesses stable solitary solutions with speed and amplitude increasing temporally. The solutions are valid upto some finite time period beyond which the nonlinear wave tends to wave breaking.
Solitary Shock Waves near Phase Transition in Lipid Interfaces and Nerves
Shrivastava, Shamit; Schneider, Matthias
2014-01-01
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase boundary requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave amplitude and the splitting of the wave at the phase boundaries. The observed phenomenon has far reaching consequences for dynamic biological processes and is hypothesized to be closely tied to the existence of both, the threshold and thermodynamic blockage of nerve pulse propagation.
Solitary shock waves and adiabatic phase transition in lipid interfaces and nerves.
Shrivastava, Shamit; Kang, Kevin Heeyong; Schneider, Matthias F
2015-01-01
This study shows that the stability of solitary waves excited in a lipid monolayer near a phase transition requires positive curvature of the adiabats, a known necessary condition in shock compression science. It is further shown that the condition results in a threshold for excitation, saturation of the wave's amplitude, and the splitting of the wave at the phase boundaries. Splitting in particular confirms that a hydrated lipid interface can undergo condensation on adiabatic heating, thus showing retrograde behavior. Finally, using the theoretical insights and state dependence of conduction velocity in nerves, the curvature of the adiabatic state diagram is shown to be closely tied to the thermodynamic blockage of nerve pulse propagation.
Ghosh, Uday Narayan, E-mail: unghosh1@rediffmail.com; Chatterjee, Prasanta; Roychoudhury, Rajkumar [Department of Mathematics, Siksha Bhavana, Visva Bharati, Santiniketan 731235 (India)
2015-07-15
Recently Gun Li et al. discussed “Effects of damping solitary wave in a viscosity bounded plasma” [Phys. Plasmas 21, 022118 (2014)]. The paper contains some serious errors which have been pointed out in this Comment.
Hongwei Yang
2013-01-01
solitary waves generated by topography, especially in the resonant case; a large amplitude nonstationary disturbance is generated in the forcing region. This condition may explain the blocking phenomenon which exists in the atmosphere and ocean and generated by topographic forcing.
Equatorial Rossby Solitary Wave Under the External Forcing
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2005-01-01
A simple shallow-water model with influence of external forcing on a β-plane is applied to investigate the nonlinear equatorial Rossby waves in a shear flow. By the perturbation method, the extended variable-coefficient KdV equation under an external forcing is derived for large amplitude equatorial Rossby wave in a shear flow. And then various periodic-like structures for these equatorial Rossby waves are obtained with the help of Jacobi elliptic functions.It is shown that the external forcing plays an important role in various periodic-like structures.
Development of internal solitary waves in various thermocline regimes - a multi-modal approach
T. Gerkema
2003-01-01
Full Text Available A numerical analysis is made on the appearance of oceanic internal solitary waves in a multi-modal setting. This is done for observed profiles of stratification from the Sulu Sea and the Bay of Biscay, in which thermocline motion is dominated by the first and third mode, respectively. The results show that persistent solitary waves occur only in the former case, in accordance with the observations. In the Bay of Biscay much energy is transferred from the third mode to lower modes, implying that a uni-modal approach would not have been appropriate. To elaborate on these results in a systematic way, a simple model for the stratification is used; an interpretation is given in terms of regimes of thermocline strength.
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
Propagation of optical spatial solitary waves in bias-free nematic-liquid-crystal cells
Minzoni, Antonmaria A. [Fenomenos Nonlineales y Mecanica (FENOMEC), Department of Mathematics and Mechanics, Instituto de Investigacion en Matematicas Aplicadas y Sistemas, Universidad Nacional Autonoma de Mexico, 01000 Mexico D.F. (Mexico); Sciberras, Luke W.; Worthy, Annette L. [School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, New South Wales 2522 (Australia); Smyth, Noel F. [School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom)
2011-10-15
The propagation of a bulk optical solitary wave in a rectangular cell filled with a nematic liquid crystal--a nematicon--is mathematically modelled. In order to overcome the Freedricksz threshold the cell walls are rubbed to pretilt the nematic. A modulation theory, based on a Lagrangian formulation, is developed for the (2+1)-dimensional propagation of the solitary wave beam down the cell. This modulation theory is based on two different formulations of the director distribution. The relative advantages and disadvantages of these two methods are discussed. A previously unexplored method based on images is found to possess significant advantages. Excellent agreement with full numerical solutions of the nematicon equations is found for both methods. Finally, the implications of the results obtained for some widely used approximations to the nematicon equations are discussed, particularly their use in comparisons with experimental results.
Evidence for 2D Solitary Sound Waves in a Lipid Controlled Interface and its Biological Implications
Shrivastava, Shamit
2014-01-01
Biological membranes by virtue of their elastic properties should be capable of propagating localized perturbations analogous to sound waves. However, the existence and the possible role of such waves in communication in biology remains unexplored. Here we report the first observations of 2D solitary elastic pulses in lipid interfaces, excited mechanically and detected by FRET. We demonstrate that the nonlinearity near a maximum in the susceptibility of the lipid monolayer results in solitary pulses that also have a threshold for excitation. These experiments clearly demonstrate that the state of the interface regulates the propagation of pulses both qualitatively and quantitatively. We elaborate on the striking similarity of the observed phenomenon to nerve pulse propagation and a thermodynamic basis of cell signaling in general.
Heavy-ion-acoustic solitary and shock waves in an adiabatic multi-ion plasma
Hossen, M.A.; Rahman, M.M.; Mamun, A.A., E-mail: armanplasma@gmail.com [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh); Hossen, M.R. [Department of Natural Sciences, Daffodil International University, Dhanmondi, Dhaka (Bangladesh)
2015-08-15
The standard reductive perturbation method has been employed to derive the Korteweg-deVries (K-dV) and Burgers (BG) equations to investigate the basic properties of heavy-ion-acoustic (HIA) waves in a plasma system which is supposed to be composed of nonthermal electrons, Boltzmann distributed light ions, and adiabatic positively charged inertial heavy ions. The HIA solitary and shock structures are found to exist with either positive or negative potential. It is found that the effects of adiabaticity of inertial heavy ions, nonthermality of electrons, and number densities of plasma components significantly modify the basic properties of the HIA solitary and shock waves. The implications of our results may be helpful in understanding the electrostatic perturbations in various laboratory and astrophysical plasma environments. (author)
Solitary waves of α-helix propagation in media with arbitrary inhomogeneities
Mvogo, Alain; Ben-Bolie, Germain Hubert; Kofané, Timoléon Crépin
2013-05-01
We study the dynamics of solitary waves in α-helical proteins going beyond the standard nearest-neighbour interaction by taking into account influence long-range dipole-dipole interactions of the Kac-Baker type. By means of the coherent state representation of operators, the model Hamiltonian is transformed into a pair of classical lattice equations, which is further reduced to a sole nonlinear Schrödinger (NLS) equation using the continuum approximation of which the dispersive coefficient depends on the long-range interactions (LRI) parameter. It comes out from our results that the bright-like solitons, solitary waves which govern the energy transfer in α-helix, are deeply influenced by the LRI. At the end, we transform the NLS equation for more currently-important inhomogeneous NLS models in media with inhomogeneities. Application of this transformation to two example models is illustrated and soliton-like solutions are also graphically discussed.
Mayout, Saliha; Tribeche, Mouloud, E-mail: mouloudtribeche@yahoo.fr [Plasma Physics Group (PPG), Theoretical Physics Laboratory (TPL), Faculty of Sciences- Physics, University of Bab-Ezzouar, U.S.T.H.B, B.P. 32, El Alia, Algiers 16111 (Algeria); Sahu, Biswajit [Department of Mathematics, West Bengal State University, Barasat, Kolkata-700126 (India)
2015-12-15
A theoretical study on the nonlinear propagation of nonplanar (cylindrical and spherical) dust ion-acoustic solitary waves (DIASW) is carried out in a dusty plasma, whose constituents are inertial ions, superthermal electrons, and charge fluctuating stationary dust particles. Using the reductive perturbation theory, a modified Korteweg-de Vries equation is derived. It is shown that the propagation characteristics of the cylindrical and spherical DIA solitary waves significantly differ from those of their one-dimensional counterpart.
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
Measurement and modelling of bed shear induced by solitary waves
JayaKumar, S.
to combined waves and current. Ocean Engineering, 29(7): 753-768. Coussot, P., 1997. Mudflow rheology and dynamics, xvi, Balkema, Rotterdam, 255 pp. DHI, 2009. Mike21 flow model - hydrodynamic module - scientific documentation. DHI, Denmark, 60 pp...
XueJu-Kui; LangHe
2003-01-01
The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may exite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).
薛具奎; 郎和
2003-01-01
The effect of dust charge variation on the dust-acoustic solitary structures is investigated in a warm magnetized two-ion-temperature dusty plasma consisting of a negatively and variably charged extremely massive dust fluid and ions of two different temperatures. It is shown that the dust charge variation as well as the presence of a second component of ions would modify the properties of the dust-acoustic solitary structures and may excite both dust-acoustic solitary holes (soliton waves with a density dip) and positive solitons (soliton waves with a density hump).
On Global attraction to solitary waves for Klein-Gordon equation with concentrated nonlinearity
Kopylova, Elena
2016-01-01
The global attraction is proved for the nonlinear 3D Klein-Gordon equation with a nonlinearity concentrated at one point. Our main result is the convergence of each "finite energy solution" to the manifold of all solitary waves as $t\\to\\pm\\infty$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersion radiation. We justify this mechanism by the following strategy based on inflation of spectrum by the nonlinea...
Formation of Vector Solitary waves with Mixed Dispersion in Bose-Einstein Condensates
Plaja, L.; Roman, J. San
2005-01-01
We demonstrate the existence of a new class of two-component vector solitary waves in which dispersion coefficients have of opposite signs. Stability is achieved by inclusion of an additional linear coupling between the vector components that counterbalances the instability produced by the mixed dispersion and the non-linearity. In addition, we demonstrate that these solutions are experimentally observable as gap vector solitons in Bose-Einstein condensates located in oscillating optical latt...
Vaporization front in the interaction of a high-energy laser with aerosols - A solitary wave
Lee, C. T.; Miller, T. G.
1982-06-01
If a high-energy laser beam were to propagate through highly absorbent aerosols, the aerosols might be subject to extinction by evaporation. This could occur, for instance, if a high-energy CO2 laser beam were to propagate through a medium containing a mist of water droplets. The incident energy would evaporate the droplets, thus increasing the transmission with time. In this paper, solitary waves are obtained as the asymptotic solution to the coupled nonlinear equations describing such an interaction.
X band bifrequency coaxial relativistic backward wave oscillator
Dong Wang
2011-12-01
Full Text Available An idea of azimuthally dividing the slow wave structure (SWS of a relativistic backward wave oscillator (RBWO into two parts is introduced to realize a bifrequency oscillation. To enhance the stability of this device, two sectorial waveguides are inserted into the SWS specially. The synchronization condition that is necessary to get a sustainable microwave output is derived. In Particle in cell simulation, bifrequency microwave at frequencies of 9.7 GHz and 9.87 GHz is generated with average power of 0.66 GW, conversion efficiency is 15.8% when beam voltage is 520 kV and current 8 kA.
Chaotic Motion of Relativistic Electrons Driven by Whistler Waves
Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.
2007-01-01
Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.
Generalized relativistic wave equations with intrinsic maximum momentum
Ching, Chee Leong; Ng, Wei Khim
2014-05-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wave functions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential is stronger than vector potential. The energy spectrum of the systems studied is bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Interaction of a mode-2 internal solitary wave with narrow isolated topography
Deepwell, David; Stastna, Marek; Carr, Magda; Davies, Peter A.
2017-07-01
Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a /ℓ . A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a /ℓ .
Laboratory Observations on Internal Solitary Wave Evolution over A Submarine Ridge
无
2006-01-01
Laboratory experiments were conducted in a wave flume on internal solitary wave (ISW) of depression and elevation types propagating over a submarine ridge in semicircular/triangular shape. Tests were arranged in series for combinations of submarine ridges of different heights and ISW of different amplitudes. The resultant wave motions were found differing from those of surface gravity waves. In deeper water, where an ISW of depression-type prevailed, the process of wave breaking displayed downward motion with continuous eddy on the front face of the ridge followed by upward motion towards the apex of the obstacle. Experimental results also suggested that blockage parameter ζ could be applied to classify various degrees of ISW-ridge interaction, i.e., ζ＜0.5 for weak interaction, 0.5＜ζ＜0.7 for moderate interaction, and 0.7＜ζ for wave breaking.
On the orbital stability of Gaussian solitary waves in the log-KdV equation
Carles, Rémi; Pelinovsky, Dmitry
2014-12-01
We consider the logarithmic Korteweg-de Vries (log-KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV equation in H^1({R}) with conserved L2 norm and energy, we construct a weak global solution of the log-KdV equation in a subset of H^1({R}) . This construction yields conditional orbital stability of Gaussian solitary waves of the log-KdV equation, provided that uniqueness and continuous dependence of the constructed solution holds. Furthermore, we study the linearized log-KdV equation at the Gaussian solitary wave and prove that the associated linearized operator has a purely discrete spectrum consisting of simple purely imaginary eigenvalues in addition to the double zero eigenvalue. The eigenfunctions, however, do not decay like Gaussian functions but have algebraic decay. Using numerical approximations, we show that the Gaussian initial data do not spread out but produce visible radiation at the left slope of the Gaussian-like pulse in the time evolution of the linearized log-KdV equation.
Internal solitary waves propagating through variable background hydrology and currents
Liu, Z.; Grimshaw, R.; Johnson, E.
2017-08-01
Large-amplitude, horizontally-propagating internal wave trains are commonly observed in the coastal ocean, fjords and straits. They are long nonlinear waves and hence can be modelled by equations of the Korteweg-de Vries type. However, typically they propagate through regions of variable background hydrology and currents, and over variable bottom topography. Hence a variable-coefficient Korteweg-de Vries equation is needed to model these waves. Although this equation is now well-known and heavily used, a term representing non-conservative effects, arising from dissipative or forcing terms in the underlying basic state, has usually been omitted. In particular this term arises when the hydrology varies in the horizontal direction. Our purpose in this paper is to examine the possible significance of this term. This is achieved through analysis and numerical simulations, using both a two-layer fluid model and a re-examination of previous studies of some specific ocean cases.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina
2014-01-01
Particle-in-cell code, EPOCH, is used for studying features of the wave component evident to propagate backwards from the front of the non-gyrotropic, relativistic beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile. According to recent findings presented in Tsiklauri (2011), Schmitz & Tsiklauri (2013) and Pechhacker & Tsiklauri (2012), in a 1.5-dimensional magnetised plasma system, the non-gyrotropic beam generates freely escaping electromagnetic radiation with properties similar to the Type-III solar radio bursts. In this study the backwards propagating wave component evident in the perpendicular components of the elecromagnetic field in such a system is presented for the first time. Background magnetic field strength in the system is varied in order to prove that the backwards propagating wave's frequency, prescribed by the whistler wave dispersion relation, is proportional to the specified magnetic field. Moreover, the identified whistlers are...
Numerical Computation of Large Amplitude Internal Solitary Waves,
1981-03-20
provide adequate resolution. All computations were performed on a CDC Cyber 176 computer, and it takes slightly less than one CPU second to obtain a...H. Segur , Lgn Internal Waves in Fluids of Great Depth, Studies in Applied Math., 62 (1980), pp. 249-262. [3] E. Allgower and K. Georg, Simlicial -and
Energy dissipation in breaking solitary and periodic waves
Battjes, J.A.
1986-01-01
It is well known (see Divoky et al., 1970, for a review) that on gentle slopes (slope S < 1:30, say) the wave height after breaking does not decay in proportion to the mean depth. The curve H/Hb vs h/hb is concave upwards (for plane bottom). The concavity increases with decreasing S and with inc
Self-similar ultra-relativistic jetted blast wave
Keshet, Uri
2015-01-01
Following a suggestion that a directed relativistic explosion may have a universal intermediate asymptotic, we derive a self-similar solution for an ultra-relativistic jetted blast wave. The solution involves three distinct regions: an approximately paraboloid head where the Lorentz factor $\\gamma$ exceeds $\\sim1/2$ of its maximal, nose value; a geometrically self-similar, expanding envelope slightly narrower than a paraboloid; and an axial core in which the radial flow $U$ converges inward towards the axis. Most ($\\sim 80\\%$) of the energy lies well beyond the head. Here, a radial cross section shows a maximal $\\gamma$ (separating the core and the envelope), a sign reversal in $U$, and a minimal $\\gamma$, at respectively $\\sim 1/6$, $\\sim1/4$, and $\\sim3/4$ of the shock radius. The solution is apparently unique, and approximately agrees with previous simulations, of different initial conditions, that resolved the head. This suggests that unlike a spherical relativistic blast wave, our solution is an attracto...
WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing
2005-01-01
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma
Awawdeh, Fadi; Jaradat, H. M.; Al-Shara', S.
2012-02-01
In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
Esfandyari-Kalejahi, Abdolrasoul; Saberian, Ehsan; 10.1585/pfr.5.045
2011-01-01
Arbitrary amplitude ion-acoustic solitary waves (IASWs) are studied using Sagdeev-Potential approach in electron-positron-ion plasma with ultra-relativistic or non-relativistic degenerate electrons and positrons and the matching criteria of existence of such solitary waves are numerically investigated. It has been shown that the relativistic degeneracy of electrons and positrons has significant effects on the amplitude and the Mach-number range of IASWs. Also it is remarked that only compressive IASWs can propagate in both non-relativistic and ultra-relativistic degenerate plasmas.
EFFECT OF INTERACTING RAREFACTION WAVES ON RELATIVISTICALLY HOT JETS
Matsumoto, Jin; Shibata, Kazunari [Kwasan and Hida Observatories, Kyoto University, Kyoto (Japan); Masada, Youhei, E-mail: jin@kusastro.kyoto-u.ac.jp [Graduate School of System Informatics, Department of Computational Science, Kobe University, Kobe (Japan)
2012-06-01
The effect of rarefaction acceleration on the propagation dynamics and structure of relativistically hot jets is studied through relativistic hydrodynamic simulations. We emphasize the nonlinear interaction of rarefaction waves excited at the interface between a cylindrical jet and the surrounding medium. From simplified one-dimensional (1D) models with radial jet structure, we find that a decrease in the relativistic pressure due to the interacting rarefaction waves in the central zone of the jet transiently yields a more powerful boost of the bulk jet than that expected from single rarefaction acceleration. This leads to a cyclic in situ energy conversion between thermal and bulk kinetic energies, which induces radial oscillating motion of the jet. The oscillation timescale is characterized by the initial pressure ratio of the jet to the ambient medium and follows a simple scaling relation, {tau}{sub oscillation}{proportional_to}(P{sub jet,0}/P{sub amb,0}){sup 1/2}. Extended two-dimensional simulations confirm that this radial oscillating motion in the 1D system manifests as modulation of the structure of the jet in a more realistic situation where a relativistically hot jet propagates through an ambient medium. We find that when the ambient medium has a power-law pressure distribution, the size of the reconfinement region along the propagation direction of the jet in the modulation structure {lambda} evolves according to a self-similar relation {lambda}{proportional_to}t{sup {alpha}/2}, where {alpha} is the power-law index of the pressure distribution.
Dust-acoustic solitary waves in a magnetized dusty plasma with nonthermal electrons and trapped ions
Misra, A. P.; Wang, Yunliang
2015-05-01
The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is studied. Using the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value (βc) of the nonthermal parameter β (>1), denoting the percentage of energetic electrons, below which the DA solitary waves cease to propagate. The soliton solution (traveling wave) of the KdV-like equation is obtained, and is shown to be only of the rarefactive type. The properties of the solitons are analyzed numerically with the system parameters. It is also seen that the effect of the static magnetic field (which only modifies the soliton width) becomes significant when the dust gyrofrequency is smaller than one-tenth of the dust plasma frequency. Furthermore, the amplitude of the soliton is found to increase (decrease) when the ratio of the free to trapped ion temperatures (σ) is positive (negative). The effects of the system parameters including the obliqueness of propagation (lz) and σ on the dynamics of the DA solitons are also discussed numerically, and it is found that the soliton structures can withstand perturbations and turbulence during a considerable time. The results should be useful for understanding the nonlinear propagation of DA solitary waves in laboratory and space plasmas (e.g., Earth's magnetosphere, auroral region, heliospheric environments, etc.).
Electron Bernstein-Greene-Kruskal hole for obliquely propagating solitary kinetic Alfvén waves
Woo, M.-H.; Dokgo, K.; Yoon, Peter H.; Lee, D.-Y.; Choi, Cheong R.
2017-04-01
A possible formation of an electron hole structure associated with an obliquely propagating solitary kinetic Alfvén wave (SKAW) in a strongly magnetized plasma is discussed. It is found that transverse electric field along the magnetic field plays a key role in the electron phase space hole formation. Owing to the presence of trapped electrons, SKAW can propagate in both super-Alfvénic and sub-Alfvénic regimes with different spatial structures. In particular, in the sub-Alfvénic case, the density perturbation possesses a dip at the center accompanied by a pair of humps at the edges. Such a feature may be relevant to satellite observation of solitary structures in the Earth's geomagnetic tail region.
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
J. C. Sánchez-Garrido
2009-09-01
Full Text Available The evolution of internal solitary waves (ISWs propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet.
Relativistic effects on the modulational instability of electron plasma waves in quantum plasma
Basudev Ghosh; Swarniv Chandra; Sailendra Nath Paul
2012-05-01
Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a twocomponent electron–ion dense quantum plasma. Using standard perturbation technique, a nonlinear Schrödinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects signiﬁcantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.
A model for large-amplitude internal solitary waves with trapped cores
K. R. Helfrich
2010-07-01
Full Text Available Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL equation. For finite ambient density gradients at the surface (bottom for waves of depression (elevation these solutions may develop recirculating cores for wave speeds above a critical value. As typically modeled, these recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticity-streamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of time-dependent non-hydrostatic equations initiated with the new stagnant-core DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.
Confirmation of EMIC wave-driven relativistic electron precipitation
Hendry, Aaron T.; Rodger, Craig J.; Clilverd, Mark A.; Engebretson, Mark J.; Mann, Ian R.; Lessard, Marc R.; Raita, Tero; Milling, David K.
2016-06-01
Electromagnetic ion cyclotron (EMIC) waves are believed to be an important source of pitch angle scattering driven relativistic electron loss from the radiation belts. To date, investigations of this precipitation have been largely theoretical in nature, limited to calculations of precipitation characteristics based on wave observations and small-scale studies. Large-scale investigation of EMIC wave-driven electron precipitation has been hindered by a lack of combined wave and precipitation measurements. Analysis of electron flux data from the POES (Polar Orbiting Environmental Satellites) spacecraft has been suggested as a means of investigating EMIC wave-driven electron precipitation characteristics, using a precipitation signature particular to EMIC waves. Until now the lack of supporting wave measurements for these POES-detected precipitation events has resulted in uncertainty regarding the driver of the precipitation. In this paper we complete a statistical study comparing POES precipitation measurements with wave data from several ground-based search coil magnetometers; we further present a case study examining the global nature of this precipitation. We show that a significant proportion of the precipitation events correspond with EMIC wave detections on the ground; for precipitation events that occur directly over the magnetometers, this detection rate can be as high as 90%. Our results demonstrate that the precipitation region is often stationary in magnetic local time, narrow in L, and close to the expected plasmapause position. Predominantly, the precipitation is associated with helium band rising tone Pc1 waves on the ground. The success of this study proves the viability of POES precipitation data for investigating EMIC wave-driven electron precipitation.
Classification of regimes of internal solitary waves transformation over a shelf-slope topography
Terletska, Kateryna; Maderich, Vladimir; Talipova, Tatiana; Brovchenko, Igor; Jung, Kyung Tae
2015-04-01
The internal waves shoal and dissipate as they cross abrupt changes of the topography in the coastal ocean, estuaries and in the enclosed water bodies. They can form near the coast internal bores propagating into the shallows and re-suspend seabed pollutants that may have serious ecological consequences. Internal solitary waves (ISW) with trapped core can transport masses of water and marine organisms for some distance. The transport of cold, low-oxygen waters results in nutrient pumping. These facts require development of classification of regimes of the ISWs transformation over a shelf-slope topography to recognize 'hot spots' of wave energy dissipation on the continental shelf. A new classification of regimes of internal solitary wave interaction with the shelf-slope topography in the framework of two-layer fluid is proposed. We introduce a new three-dimensional diagram based on parameters α ,β , γ. Here α is the nondimensional wave amplitude normalized on the thermocline thickness α = ain/h1 (α > 0), β is the blocking parameter introduced in (Talipova et al., 2013) that is the ratio of the height of the bottom layer on the the shelf step h2+ to the incident wave amplitude ain, β = h2+/ain (β > -3), and γ is the parameter inverse to the slope inclination (γ > 0.01). Two mechanisms are important during wave shoaling: (i) wave breaking resulting in mixing and (ii) changing of the polarity of the initial wave of depression on the slope. Range of the parameters at which wave breaking occurs can be defined using the criteria, obtained empirically (Vlasenko and Hutter, 2002). In the three-dimensional diagram this criteria is represented by the surface f1(β,γ) = 0 that separates the region of parameters where breaking takes place from the region without breaking. The polarity change surface f2(α,β) = 0 is obtained from the condition of equality of the depth of upper layer h1 to the depth of the lower layer h2. In the two-layer stratification waves of
AN EXPERIMENTAL OBSERVATION OF A SOLITARY WAVE IMPINGEMENT, RUN-UP AND OVERTOPPING ON A SEAWALL
LIN Ting-Chieh; HWANG Kao-Shu; HSIAO Shih-Chun; YANG Ray-Yeng
2012-01-01
A sequence of laboratory experiments using solitary waves was performed to model the effect of leading form of three types of tsunamis (a bore,an impinging wave and an overtopping wave) on a seawall on a sloping beach.The wave evolution process,impinging pressure along the seawall surface,total overtopping discharge behind the seawall and the maximum run-up height on the rear slope were measured and compared.Laboratory data were employed to re-examine relevant empirical formulae in the literature.The effect of the presence of the seawall in reducing maximum run-up height using the present setup was briefly discussed.The present data can be used for calibrating numerical and mathematical models.
Hongwei Yang
2012-01-01
Full Text Available The paper presents an investigation of the generation, evolution of Rossby solitary waves generated by topography in finite depth fluids. The forced ILW- (Intermediate Long Waves- Burgers equation as a model governing the amplitude of solitary waves is first derived and shown to reduce to the KdV- (Korteweg-de Vries- Burgers equation in shallow fluids and BO- (Benjamin-Ono- Burgers equation in deep fluids. By analysis and calculation, the perturbation solution and some conservation relations of the ILW-Burgers equation are obtained. Finally, with the help of pseudospectral method, the numerical solutions of the forced ILW-Burgers equation are given. The results demonstrate that the detuning parameter α holds important implications for the generation of the solitary waves. By comparing with the solitary waves governed by ILW-Burgers equation and BO-Burgers equation, we can conclude that the solitary waves generated by topography in finite depth fluids are different from that in deep fluids.
Baryon Wave Functions in Covariant Relativistic Quark Models
Dillig, M
2002-01-01
We derive covariant baryon wave functions for arbitrary Lorentz boosts. Modeling baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to a covariant 3-dimensional form by projecting on the relative quark-diquark energy. Guided by a phenomenological multigluon exchange representation of a covariant confining kernel, we derive for practical applications explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly comment on the interplay of boosts and center-of-mass corrections in relativistic quark models.
Synchrotron signature of a relativistic blast wave with decaying microturbulence
Lemoine, M
2012-01-01
Microphysics of weakly magnetized relativistic collisionless shock waves, corroborated by recent high performance numerical simulations, indicate the presence of a microturbulent layer of large magnetic field strength behind the shock front, which must decay beyond some hundreds of skin depths. The present paper discusses the dynamics of such microturbulence, borrowing from these same numerical simulations, and calculates the synchrotron signature of a powerlaw of shock accelerated particles. The decaying microturbulent layer is found to leave distinct signatures in the spectro-temporal evolution of the spectrum $F_\
Generalized Relativistic Wave Equations with Intrinsic Maximum Momentum
Ching, Chee Leong
2013-01-01
We examine the nonperturbative effect of maximum momentum on the relativistic wave equations. In momentum representation, we obtain the exact eigen-energies and wavefunctions of one-dimensional Klein-Gordon and Dirac equation with linear confining potentials, and the Dirac oscillator. Bound state solutions are only possible when the strength of scalar potential are stronger than vector potential. The energy spectrum of the systems studied are bounded from above, whereby classical characteristics are observed in the uncertainties of position and momentum operators. Also, there is a truncation in the maximum number of bound states that is allowed. Some of these quantum-gravitational features may have future applications.
Kinetic Alfv\\'{e}n solitary and rogue waves in superthermal plasmas
Bains, A; Xia, L -D
2014-01-01
We investigate the small but finite amplitude solitary Kinetic Alfv\\'{e}n waves (KAWs) in low $\\beta$ plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter $\\kappa$, plasma $\\beta$ and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfv\\'enic, compressive solitons are supported. We then extend the study to examine kinetic Alfv\\'en rogue waves by deriving a nonlinear Schr\\"{o}dinger equation from {the KdV} equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermal...
Compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas
Panwar, Anuraj; Rizvi, H.; Ryu, C. M. [Department of Physics, POSTECH, Hyoja-Dong San 31, KyungBuk, Pohang 790-784 (Korea, Republic of)
2013-08-15
Generation of compressional Alfvénic rogue and solitary waves in magnetohydrodynamic plasmas is investigated. Dispersive effect caused by non-ideal electron inertia currents perpendicular to the ambient magnetic field can balance the nonlinear steepening of waves leading to the formation of a soliton. The reductive perturbation method is used to obtain a Korteweg–de Vries (KdV) equation describing the evolution of the solitary wave. The height of a soliton is proportional to the soliton speed “U” and inversely proportional to plasma “β” (ratio of plasma thermal pressure to pressure of the confining magnetic field) and the width of soliton is proportional to the electron inertial length. KdV equation is used to study the nonlinear evolution of modulationally unstable compressional Alfvénic wavepackets via the nonlinear Schrödinger equation. The characteristics of rogue wave influenced by plasma “β” and the electron inertial length are described.
Kinetic Alfvén solitary and rogue waves in superthermal plasmas
Bains, A. S.; Li, Bo, E-mail: bbl@sdu.edu.cn; Xia, Li-Dong [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, 264209 Weihai (China)
2014-03-15
We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.
Dust-acoustic solitary waves in a magnetized dusty plasma with nonthermal electrons and trapped ions
Misra, A P
2014-01-01
The nonlinear theory of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is revisited. Previous theory in the literature [Phys. Plasmas {\\bf 20}, 104505 (2013)] is rectified and put forward to include the effects of the external magnetic field, the adiabatic pressure of charged dusts as well as the obliqueness of propagation to the magnetic field. Using the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value $(\\beta_c)$ of the nothermal parameter $\\beta (>1)$, denoting the percentage of energetic electrons, below which the DA solitary waves cease to propagate. The soliton solution (travelling wave) of the KdV-like equation is obtained, and is shown to be on...
Dust-acoustic solitary waves and shocks in strongly coupled quantum plasmas
Wang, Y
2014-01-01
We investigate the propagation characteristics of electrostatic dust-acoustic (DA) solitary waves and shocks in a strongly coupled dusty plasma consisting of intertialess electrons and ions, and strongly coupled inertial charged dust particles. A generalized viscoelastic hydrodynamic model with the effects of electrostatic dust pressure associated with the strong coupling of dust particles, and a quantum hydrodynamic model with the effects of quantum forces associated with the Bohm potential and the exchange-correlation potential for electrons and ions are considered. Both the linear and weakly nonlinear theory of DA waves are studied by the derivation and analysis of dispersion relations as well as Korteweg-de Vries (KdV) and KdV-Burgers (KdVB)-like equations. It is shown that in the kinetic regime ($\\omega\\tau_m\\gg1$, where $\\omega$ is the wave frequency and $\\tau_m$ is the viscoelastic relaxtation time), the amplitude of the DA solitary waves decays slowly with time with the effect of a small amount of dus...
Head-on collision of the second mode internal solitary waves
Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae
2017-04-01
Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the
Pseudolocalized Three-dimensional Solitary Waves as Quasi-Particles
Christov, C I
2012-01-01
A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of the integrability of the square of the profile over an infinite domain. For the new type of solutions, the gradient and/or the Hessian/Laplacian are square integrable. In the linear limiting case, analytical expression for the pseudolocalized solution is found and the method of variational approximation is applied to find the dynamics of the centers of the quasi-particles (QPs) corresponding to these solutions. A discrete Lagrangian can be derived due to the localization of the gradient and the Laplacian of the profile. The equations of motion of the QPs are derived from the discrete Lagrangian. The pseudomass ("wave mass") of a QP is defined as well as the potential of interaction. The most important trait of the new QPs is that at large distances, the force of attraction...
Ma, X.; Yan, J.; Hou, Y.; Lin, F.; Zheng, X.
2016-12-01
The northern South China Sea provides prominent examples of internal waves, however, rare studies have been done on the associated bedforms and sediment transport near the shelf break. Here, we report the unique data of bedform details which probably caused by the internal solitary waves and internal tides near the shelf break in the areas west of Dongsha Atoll. In the study area, most internal solitary waves (ISWs) are found to propagate onto the shelf obliquely in an approximately 290° through the MODIS image. Several typical events of ISWs were also captured during our observation by an mooring system on the continental slope. Bottom current data near the shelf break showed that extremely strong speed (exceeding 80 cm/s) occurred when the obliquely incident ISWs propagated. The strong currents have the capability to move coarse grains or suspend and transport fine grains but, cannot change the long-term trend of sediment transport on the slope (γ/c>1). Two types of sand waves were also found on the seabed. The upslope-dipping sand waves (type 1) are only found at depths of 120-150 m with flat crests and intersecting the depth contours, being ascribed to the obliquely incident ISWs. In contrast, the downslope-dipping sand waves (type 2) are parallel to the depth contours and obviously migrated over eight months, which were probably caused by internal tides. The ISWs could also produce along-slope currents to form and maintain channels on seabed with a larger gradient (γ>0.8°). The bedforms are likely widespread near the shelf break in the northern South China Sea and other seas but are limited on mild slopes where ISWs do not break. Additional detailed research needs to be deployed on wave behaviors, sediment transport, and the bedforms associated with obliquely incident ISWs.
Thermodynamics of relativistic quantum fields: extracting energy from gravitational waves
Bruschi, David Edward
2016-01-01
We investigate the quantum thermodynamical properties of localised relativistic quantum fields that can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical degrees of freedom, such as the energy input due to motion or to an impinging gravitational wave, and the excitations of the confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability to extract the energy and to store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein Condensates. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein Condensate. We find that, in this case, the amount of energy transfer to the phonons increases with time and quickly approaches unity. These results suggest that, in the future, it might be possible to...
Elastic wavelets and their application to problems of solitary wave propagation
Cattani, Carlo
2008-03-01
Full Text Available The paper can be referred to that direction in the wavelet theory, which was called by Kaiser "the physical wavelets". He developed the analysis of first two kinds of physical wavelets - electromagnetic (optic and acoustic wavelets. Newland developed the technique of application of harmonic wavelets especially for studying the harmonic vibrations. Recently Cattani and Rushchitsky proposed the 4th kind of physical wavelets - elastic wavelets. This proposal was based on three main elements: 1. Kaiser's idea of constructing the physical wavelets on the base of specially chosen (admissible solutions of wave equations. 2. Developed by one of authors theory of solitary waves (with profiles in the form of Chebyshov-Hermite functions propagated in elastic dispersive media. 3. The theory and practice of using the wavelet "Mexican Hat" system, the mother and farther wavelets (and their Fourier transforms of which are analytically represented as the Chebyshov-Hermite functions of different indexes. An application of elastic wavelets to studying the evolution of solitary waves of different shape during their propagation through composite materials is shown on many examples.
Excitation spectra of solitary waves in scalar field models with polynomial self-interaction
Gani, Vakhid A; Lizunova, Mariya A; Mrozovskaya, Elizaveta V
2016-01-01
We study excitations of solitary waves -- the kinks -- in scalar models with degree eight polynomial self-interaction in (1+1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other and analyse the occurring resonance phenomena. We connect these phenomena to the energy exchange between the translational and the vibrational modes of the colliding kinks. We also point out that the interaction of two kinks with power-law asymptotic can lead to a long-range interaction between the two kinks.
Experiments on the interactions between impurities and solitary waves in lattice model
ZHU; Yifei(朱逸斐); CHEN; Weizhong; (陈伟中); Lü; Lei; (吕镭)
2003-01-01
The interactions between solitary waves and impurities have been studied experimentally in a 1D nonlinear coupled pendulum chain under vertical excitation. The mass and the coupling are unique, except a single pendulum with length impurity in the chain. The experiment reveals: the long impurity repels breather and attracts kink while the short one attracts breather and repels kink under higher frequency driving, and the long impurity attracts breather and repels kink while the short one repels breather and attracts kink under the lower frequency driving. These results prove the current theoretical prediction based on continuum-limit approximation.
Nonlinear ion-acoustic solitary waves in ion-beam plasma
Das, G.C.; Karmakar, B. (Manipur Univ., Imphal (India). Dept. of Mathematics); Singh, K.I. (Modern Coll., Imphal, Manipur (India))
1989-01-01
The dynamics of solitary waves in an ion-beam plasma having multiple electron temperatures are investigated. The investigation is based on the derivation of the Korteweg-de Vries (Kd V) equation by applying the reductive perturbation technique to the basic equations governing the plasma dynamics. Fascinating results are derived first for a plasma with a small percentage of non-isothermality, then the soliton's behaviour is obtained for an isothermal as well as for a non-isothermal plasma, and finally a general comparison is made and conclusions given. (author).
Malaspina, David M.; Newman, David L.; Wilson, Lynn Bruce; Goetz, Keith; Kellogg, Paul J.; Kerstin, Kris
2013-01-01
A strong spatial association between bipolar electrostatic solitary waves (ESWs) and magnetic current sheets (CSs) in the solar wind is reported here for the first time. This association requires that the plasma instabilities (e.g., Buneman, electron two stream) which generate ESWs are preferentially localized to solar wind CSs. Distributions of CS properties (including shear angle, thickness, solar wind speed, and vector magnetic field change) are examined for differences between CSs associated with ESWs and randomly chosen CSs. Possible mechanisms for producing ESW-generating instabilities at solar wind CSs are considered, including magnetic reconnection.
Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation
Belobo, Didier Belobo; Das, Tapas
2017-07-01
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel [Plasma Physics Group, Faculty of Sciences-Physics, Theoretical Physics Laboratory, University of Bab-Ezzouar, USTHB BP 32, El Alia, Algiers 16111 (Algeria)], E-mail: mtribeche@usthb.dz
2009-09-15
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Flat Solitary Waves due to a Submerged Body Moving in a Stratified Fluid
WEI Gang; SU Xiao-Bing; LU Dong-Qiang; YOU Yun-Xiang; DAI Shi-Qiang
2008-01-01
A theoretical model for interaction of a submerged moving body with the conjugate flow in a three-layer fluid is proposed to depict the internal flat solitary wave, which is observed in experiments conducted by the present authors. A set of coupled nonlinear algebraic equations is derived for the interracial displacements. The numerical results indicate that (a) the conjugate flow due to a two-dimensional body moving at the bottom possesses an apparent behaviour with two convex interfaces; (b) the solution satisfying the existence criterion is always unique near the relatively stable state of system. Theoretical analysis is qualitatively consistent with the experimental results obtained.
Two- and three-dimensional computation of solitary wave runup on non-plane beach
B. H. Choi
2008-06-01
Full Text Available Solitary wave runup on a non-plane beach is studied analytically and numerically. For the theoretical approach, nonlinear shallow-water theory is applied to obtain the analytical solution for the simplified bottom geometry, such as an inclined channel whose cross-slope shape is parabolic. It generalizes Carrier-Greenspan approach for long wave runup on the inclined plane beach that is currently used now. For the numerical study, the Reynolds Averaged Navier-Stokes (RANS system is applied to study soliton runup on an inclined beach and the detailed characteristics of the wave processes (water displacement, velocity field, turbulent kinetic energy, energy dissipation are analyzed. In this study, it is theoretically and numerically proved that the existence of a parabolic cross-slope channel on the plane beach causes runup intensification, which is often observed in post-tsunami field surveys.
Transformation of mode-2 internal solitary wave over a pseudo slope-shelf
Cheng, Ming-Hung; Hsieh, Chih-Min; Hsu, John R.-C.; Hwang, Robert R.
2017-09-01
Numerical simulations are performed to investigate the effect of wave amplitude in a numerical wave tank on the evolution of a convex mode-2 internal solitary wave (ISW) propagating over a pseudo slope-shelf. A finite volume method based on a Cartesian grid system is adopted to solve the Navier-Stokes equations using Improved Delayed Detached Eddy Simulation model for the turbulent closure. Numerical results reveal three types of waveform during wave generation on the flat bottom: (1) pseudo vortex shedding in the case of very large initial amplitude; (2) PacMan phenomenon in large amplitude; and (3) smooth mode-2 ISW for small amplitude. During wave propagation on the plateau, the first type of waveform induces a quasi-elevated mode-1 ISW; the second generates chaotic internal waves with significant reduction in amplitude; while the third renders a slightly deformed mode-2 ISW across the plateau. Moreover, the decrease in the magnitude of leading trough is more intense than that in the leading crest due to strong wave-obstacle interaction in the case of very large initial wave amplitude.
Massless and Massive Gauge-Invariant Fields in the Theory of Relativistic Wave Equations
Pletyukhov, V A
2010-01-01
In this work consideration is given to massless and massive gauge-invariant spin 0 and spin 1 fields (particles) within the scope of a theory of the generalized relativistic wave equations with an extended set of the Lorentz group representations. The results obtained may be useful as regards the application of a relativistic wave-equation theory in modern field models.
NUMERICAL STUDIES OF INTERNAL SOLITARY WAVE GENERATION AND EVOLUTION BY GRAVITY COLLAPSE
LIN Zhen-hua; SONG Jin-bao
2012-01-01
In this study,an analysis on the internal wave generation via the gravity collapse mechanism is carried out based on the theoretical formulation and the numerical simulation.With the linear theoretical model,a rectangle shape wave is generated and propagates back and forth in the domain,while a two-dimensional non-hydrostatic numerical model could reproduce all the observed phenomena in the laboratory experiments conducted by Chen et al.(2007),and the related process realistically.The model results further provide more quantitative information in the whole domain,thus allowing an in depth understanding of the corresponding internal solitary wave generation and propagation.It is shown that the initial type of the internal wave is determined by the relative height between the perturbation and the environmental density interface,while the final wave type is related to the relative height of the upper and lower layers of the environmental fluid.The shape of the internal wave generated is consistent with that predicted by the KdV and EKdV theories if its amplitude is small,as the amplitude becomes larger,the performance of the EKdV becomes better after the wave adjusts itself to the ambient stratification and reaches an equilibrium state between the nonlinear and dispersion effects.The evolution of the mechanical energy is also analyzed.
Generation of undular bores in the shelves of slowly-varying solitary waves.
El, G. A.; Grimshaw, R. H. J.
2002-12-01
We study the long-time evolution of the trailing shelves that form behind solitary waves moving through an inhomogeneous medium, within the framework of the variable-coefficient Korteweg-de Vries equation. We show that the nonlinear evolution of the shelf leads typically to the generation of an undular bore and an expansion fan, which form apart but start to overlap and nonlinearly interact after a certain time interval. The interaction zone expands with time and asymptotically as time goes to infinity occupies the whole perturbed region. Its oscillatory structure strongly depends on the sign of the inhomogeneity gradient of the variable background medium. We describe the nonlinear evolution of the shelves in terms of exact solutions to the KdV-Whitham equations with natural boundary conditions for the Riemann invariants. These analytic solutions, in particular, describe the generation of small "secondary" solitary waves in the trailing shelves, a process observed earlier in various numerical simulations. (c) 2002 American Institute of Physics.
Effects of Charge in Heavy Ions on Solitary Kinetic Alfvén Waves in Double-Ion Plasmas
YANG Lei; WU De-Jin
2006-01-01
@@ After the charge of heavy ions is considered, a Sagdeev equation is obtained for the solitary kinetic Alfvén waves (SKAWs) in a low-β(me/mp＜＜β＜＜1 or mp/me＞＞α＞＞1), three-component (electrons, protons, and highly charged heavy ions) plasma. Numerical results show that the charge number q of heavy ions can cause the width of the solitary structure to decrease, but increase for the maximum of electron density nem≤1.2 and the initial abundance of heavy ions Cb0 ≤ 0.1. The parallel phase speed of the waves increases with larger q.
The effect of q-distributed electrons on the head-on collision of ion acoustic solitary waves
Ghosh, Uday Narayan; Chatterjee, Prasanta [Department of Mathematics, Siksha Bhavana Visva Bharati University, Santiniketan 731235 (India); Roychoudhury, Rajkumar [Physics and Applied Mathematics, ISI, Kolkata 700009 (India)
2012-01-15
The head-on collision of ion acoustic solitary waves (IASWs) in two component plasma comprising nonextensive distributed electrons is investigated. Two opposite directional Kortewg-de-vries (KdV) equations are derived and the phase shift due to collision is obtained using the extended version of Poincare-Lighthill-Kuo method. Different ranges of nonextensive parameter q are considered and their effects on phase shifts are observed. It is found that the presence of nonextensive distributed electrons plays a significant role on the nature of collision of ion acoustic solitary waves.
Hafez, M. G.; Roy, N. C.; Talukder, M. R.; Hossain Ali, M.
2016-08-01
The characteristics of the nonlinear oblique propagation of ion acoustic solitary waves in unmagnetized plasmas consisting of Boltzmann positrons, trapped electrons and ions are investigated. The modified Kadomtsev-Petviashivili ( m K P ) equation is derived employing the reductive perturbation technique. The parametric effects on phase velocity, Sagdeev potential, amplitude and width of solitons, and electrostatic ion acoustic solitary structures are graphically presented with the relevant physical explanations. This study may be useful for the better understanding of physical phenomena concerned in plasmas in which the effects of trapped electrons control the dynamics of wave.
Ding, Min; Li, Yachun
2017-04-01
We study the 1-D piston problem for the relativistic Euler equations under the assumption that the total variations of both the initial data and the velocity of the piston are sufficiently small. By a modified wave front tracking method, we establish the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength. Meanwhile, we consider the convergence of the entropy solutions to the corresponding entropy solutions of the classical non-relativistic Euler equations as the light speed c→ +∞.
ZHANG Wei-Guo; DONG Chun-Yan; FAN En-Gui
2006-01-01
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travellingwave form satisfies some special conditions.
Application of the SPH method to solitary wave impact on an offshore platform
Pan, K.; IJzermans, R. H. A.; Jones, B. D.; Thyagarajan, A.; van Beest, B. W. H.; Williams, J. R.
2016-04-01
This paper investigates the interaction between large waves and floating offshore structures. Here, the fluid-structure interaction is considered using the weakly compressible smoothed particle hydrodynamics (SPH) method. To ensure the applicability of this method, we validate its prediction for fluid forces and rigid-body motion against two sets of experimental data. These are impact due to dam break, and wave induced motion of a floating cube. For the dam break problem, the SPH method is used to predict impact forces on a rectangular column located downstream. In the second case of a floating cube, the SPH method simulates the motion of a buoyant cube under the action of induced waves, where a wall placed upstream of the cube is displaced sinusoidally to induce waves. In both cases, the SPH framework implemented is able to accurately reproduce the experimental results. Following validation, we apply this framework to simulation of a toy model of a tension-leg platform upon impact of a large solitary wave. This analysis shows that the platform may be pulled into the water by stretched tension legs, where the extension of the tension legs also governs the rotational behavior of the platform. The result also indicates that a tension-leg platform is very unlikely to topple over during the arrival of an extreme wave.
Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form
Reza Abazari
2013-01-01
Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
Ion-acoustic solitary waves in ion-beam plasma with multiple-electron-temperatures
Karmakar, B.; Das, G.C.; Singh, Kh.I.
1988-08-01
The solitary wave solution has been studied in an ion-beam plasma with multiple-electron-temperatures stemmed through the derivation of a modified Korteweg-de Vries (KdV) equation. The evolution of solitons shows that the existence and the behaviour depend effectively on the ion-beam as well as on the multiple-electron-temperatures. It has been shown that the solitons might be large amplitude waves with the addition of a small percentage of ion-beam concentration or by the increase of electron-temperatures. The present investigators believe and conclude that the solitons should also show experimentally these fascinating properties but one has to be careful about the range of the physical parameters in ion-beam plasma.
Tarsem Singh Gill; Harvinder Kaur
2000-11-01
The effects of nonthermal ion distribution and ﬁnite dust temperature are incorporated in the investigation of nonlinear dust acoustic waves in an unmagnetized dusty plasma. Sagdeev pseudopotential method which takes into account the full nonlinearity of plasma equations, is used here to study solitary wave solutions. Possibility of co-existence of refractive and compressive solitons as a function of Mach number, dust temperature and concentration of nonthermal ions, is considered. For the ﬁxed value of nonthermal ions, it is found that the effect of increase in dust temperature is to reduce the range of co-existence of compressive and refractive solitons. Particular concentration of nonthermal ions results in disappearance of refractive solitons while the decrease in dust temperature, at this concentration restores the lost refractive solitons.
Complex solitary waves and soliton trains in KdV and mKdV equations
Modak, Subhrajit; Singh, Akhil Pratap; Panigrahi, Prasanta Kumar
2016-06-01
We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.
Seismic, satellite, and site observations of internal solitary waves in the NE South China Sea.
Tang, Qunshu; Wang, Caixia; Wang, Dongxiao; Pawlowicz, Rich
2014-06-20
Internal solitary waves (ISWs) in the NE South China Sea (SCS) are tidally generated at the Luzon Strait. Their propagation, evolution, and dissipation processes involve numerous issues still poorly understood. Here, a novel method of seismic oceanography capable of capturing oceanic finescale structures is used to study ISWs in the slope region of the NE SCS. Near-simultaneous observations of two ISWs were acquired using seismic and satellite imaging, and water column measurements. The vertical and horizontal length scales of the seismic observed ISWs are around 50 m and 1-2 km, respectively. Wave phase speeds calculated from seismic observations, satellite images, and water column data are consistent with each other. Observed waveforms and vertical velocities also correspond well with those estimated using KdV theory. These results suggest that the seismic method, a new option to oceanographers, can be further applied to resolve other important issues related to ISWs.
On electromagnetic instabilities at ultra-relativistic shock waves
Lemoine, Martin
2009-01-01
(Abridged) This paper addresses the issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. The level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant longitudinal and oblique modes; for a magnetized shock, in a generic oblique configuration, the Weibel instability and the resonant Cerenkov instabilities with Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particula...
Unified relativistic physics from a standing wave particle model
Vera, R A
1995-01-01
An extremely simple and unified base for physics comes out by starting all over from a single postulate on the common nature of matter and stationary forms of radiation quanta. Basic relativistic, gravitational (G) and quantum mechanical properties of a standing wave particle model have been derived. This has been done from just dual properties of radiation's and strictly homogeneous relationships for nonlocal cases in G fields. This way reduces the number of independent variables and puts into relief (and avoid) important inhomogeneity errors of some G theories. It unifies and accounts for basic principles and postulates physics. The results for gravity depend on linear radiation properties but not on arbitrary field relations. They agree with the conventional tests. However they have some fundamental differences with current G theories. The particle model, at a difference of the conventional theories, also fixes well-defined cosmological and astrophysical models that are different from the rather convention...
Vacuum-Structure and a Relativistic Pilot Wave
Salehi, H; Golshani, M; Salehi, Hadi; Motavali, Hossein; Golshani, Mehdi
2000-01-01
We study a model for analyzing the effect of a principal violation of the Lorentz-invariance on the structure of vacuum. The model is based on the divergence theory developed by Salehi (1997). It is shown that the divergence theory can be used to model an ensemble of particles. The ensemble is characterized by the condition that its members are basically at rest in the rest frame of a preferred inertial observer in vacuum. In this way we find a direct dynamical interplay between a particle and its associated ensemble. We show that this effect can be understood in terms of the interaction of a particle with a relativistic pilot wave through an associated quantum potential.
Relativistic orbits and Gravitational Waves from gravitomagnetic corrections
Capozziello, Salvatore; Forte, Luca; Garufi, Fabio; Milano, Leopoldo
2010-01-01
Corrections to the relativistic theory of orbits are discussed considering higher order approximations induced by gravitomagnetic effects. Beside the standard periastron effect of General Relativity (GR), a new nutation effect was found due to the ${\\displaystyle c^{-3}}$ orbital correction. According to the presence of that new nutation effect we studied the gravitational waveforms emitted through the capture in a gravitational field of a massive black hole (MBH) of a compact object (neutron star (NS) or BH) via the quadrupole approximation. We made a numerical study to obtain the emitted gravitational wave (GW) amplitudes. We conclude that the effects we studied could be of interest for the future space laser interferometric GW antenna LISA.
Bagheri, Abdollah
The in-situ measurement of thermal stress in civil and mechanical structures may prevent structural anomalies such as unexpected buckling. In the first half of the dissertation, we present a study where highly nonlinear solitary waves (HNSWs) were utilized to measure axial stress in slender beams. HNSWs are compact non-dispersive waves that can form and travel in nonlinear systems such as one-dimensional chains of particles. The effect of the axial stress acting in a beam on the propagation of HNSWs was studied. We found that certain features of the solitary waves enable the measurement of the stress. In general, most guided ultrasonic waves (GUWs)-based health monitoring approaches for structural waveguides are based on the comparison of testing data to baseline data. In the second half of the dissertation, we present a study where some baseline-free signal processing algorithms were presented and applied to numerical and experimental data for the structural health monitoring (SHM) of underwater or dry structures. The algorithms are based on one or more of the following: continuous wavelet transform, empirical mode decomposition, Hilbert transform, competitive optimization algorithm, probabilistic methods. Moreover, experimental data were also processed to extract some features from the time, frequency, and joint time-frequency domains. These features were then fed to a supervised learning algorithm based on artificial neural networks to classify the types of defect. The methods were validated using the numerical model of a plate and a pipe, and the experimental study of a plate in water. In experiment, the propagation of ultrasonic waves was induced by means of laser pulses or transducer and detected with an array of immersion transducers. The results demonstrated that the algorithms are effective, robust against noise, and able to localize and classify the damage.
Rivera, Gustavo; Diamessis, Peter
2016-11-01
The shoaling of an internal solitary wave (ISW) of depression over gentle slopes is explored through fully nonlinear and non-hydrostatic simulations based on a high-accuracy deformed spectral multidomain penalty method. As recently observed in the South China Sea, in high-amplitude shoaling ISWs, the along-wave current can exceed the wave celerity resulting in convective instabilities. If the slope is less than 3%, the wave does not disintegrate as in the case of steeper slope shoaling but, instead, maintains its symmetric shape; the above convective instability may drive the formation of a turbulent recirculating core. The sensitivity of convective instabilities in an ISW is examined as a function of the bathymetric slope and wave steepness. ISWs are simulated propagating over both idealized and realistic bathymetry. Emphasis is placed on the structure of the above instabilities, the persistence of trapped cores and their potential for particle entrainment and transport. Additionally, the role of the baroclinic background current on the development of convective instabilities is explored. A preliminary understanding is obtained of the transition to turbulence within a high-amplitude ISW shoaling over progressively varying bathymetry.
Whistler wave generation by non-gyrotropic, relativistic, electron beams
Skender, Marina; Tsiklauri, David
2014-05-01
]. In this study [5], for the first time, the backwards propagating wave component evident in the perpendicular components of the electromagnetic field in such a system is presented. Features of the wave component propagating backwards from the front of the non-gyrotropic, relativistic, beam of electrons injected in the Maxwellian, magnetised background plasma with decreasing density profile are studied by using the Particle-In-Cell code EPOCH. Magnetic field in the 1.5-dimensional system is varied in order to prove that the backwards propagating wave is harmonic of the electron cyclotron frequency. The analysis has lead to the identification of the backwards travelling waves as whistlers. Moreover, the whistlers are shown to be generated by the normal and anomalous Doppler resonance. Large fraction of the energy of the perpendicular electromagnetic field components is found to be carried away by the whistler waves. [1] D. Tsiklauri, Phys. Plasmas 18, 052903 (2011). [2] D. Tsiklauri, H. Schmitz, Geophys. Res. Abs. 15, EGU2013-5403 (2013). [3] H. Schmitz, D. Tsiklauri, Phys. Plasmas 20, 062903 (2013). [4] R. Pechhacker, D. Tsiklauri, Phys. Plasmas 19, 112903 (2012). [5] M. Skender, D. Tsiklauri, submitted to Phys. Plasmas (2013): http://astro.qmul.ac.uk/ tsiklauri/
Discrete Solitary Waves in Systems with Nonlocal Interactions and the Peierls-Nabarro Barrier
Jenkinson, M.; Weinstein, M. I.
2017-04-01
We study a class of discrete focusing nonlinear Schrödinger equations (DNLS) with general nonlocal interactions. We prove the existence of onsite and offsite discrete solitary waves, which bifurcate from the trivial solution at the endpoint frequency of the continuous spectrum of linear dispersive waves. We also prove exponential smallness, in the frequency-distance to the bifurcation point, of the Peierls-Nabarro energy barrier (PNB), as measured by the difference in Hamiltonian or mass functionals evaluated on the onsite and offsite states. These results extend those of the authors for the case of nearest neighbor interactions to a large class of nonlocal short-range and long-range interactions. The appearance of distinct onsite and offsite states is a consequence of the breaking of continuous spatial translation invariance. The PNB plays a role in the dynamics of energy transport in such nonlinear Hamiltonian lattice systems. Our class of nonlocal interactions is defined in terms of coupling coefficients, J m , where {min{Z}} is the lattice site index, with {J_m˜eq m^{-1-2s}, sin[1,∞)} and {J_m˜ e^{-γ|m|}, s=∞, γ > 0,} (Kac-Baker). For {s≥1}, the bifurcation is seeded by solutions of the (effective/homogenized) cubic focusing nonlinear Schrödinger equation (NLS). However, for {1/4 equation, FNLS, with {(-Δ)^s} replacing {-Δ}. The proof is based on a Lyapunov-Schmidt reduction strategy applied to a momentum space formulation. The PN barrier bounds require appropriate uniform decay estimates for the discrete Fourier transform of DNLS discrete solitary waves. A key role is also played by non-degeneracy of the ground state of FNLS, recently proved by Frank, Lenzmann and Silvestrie.
Verheest, Frank; Hellberg, Manfred A.
2017-02-01
Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter β, and the angle ϑ between the directions of propagation and the static magnetic field. Below a critical β, only positive compressive solitons are possible, and their amplitudes increase with increasing β, M, and ϑ. Above the critical β, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with β but are independent of ϑ. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity.
Searching for the (3+1)-Dimensional Painlevé Integrable Model and its Solitary Wave Solution
李画眉
2002-01-01
A (3+1)-dimensional integrable model constructed by conformal invariants is proven to be integrable. The solitary wave solution of the model is obtained by a simple algebraic transformation relation between the (3 + 1)-dimensional Harry-Dym equation and the cubic nonlinear Klein-Gordon equation.
Alves, Claudianor O.; Miyagaki, Olímpio H.
2017-08-01
In this paper, we establish some results concerning the existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation. Variational methods are used to get an existence result, as well as, to study the concentration phenomenon, while the regularity is more delicate because we are leading with functions in an anisotropic Sobolev space.
ZHANG Yu-Feng; ZHANG Hong-Qing
2001-01-01
We make use of an extended tanh-function method and symbolic computation to construct four kinds of travelling solitary wave solutions for the coupled Ito system and a generalized Hirota-Satsuma coupled KdV system.PACS numbers: 02.90.+p, 03.40.-t
A repetitive 0.14 THz relativistic surface wave oscillator
Wang Guangqiang; Tong Changjiang; Li Xiaoze; Wang Xuefeng; Li Shuang; Lu Xicheng [Northwest Institute of Nuclear Technology, P.O. Box 69-1, Xi' an 710024 (China); Wang Jianguo [Northwest Institute of Nuclear Technology, P.O. Box 69-1, Xi' an 710024 (China); School of Electronic and Information Engineering, Xi' an Jiaotong University, Xi' an 710049 (China)
2013-04-15
Preliminary experimental results of a repetitive 0.14 THz overmoded relativistic surface wave oscillator (RSWO) are presented in this paper. The repetitive RSWO is developed by using a rectangularly corrugated slow-wave structure with overmoded ratio of 3 and a foilless diode emitting annular electron beam with thickness of 0.5 mm. The high quality electron beams at the repetition rate of 10 are obtained over a wide range of diode voltage (180 kV < U < 240 kV) and current (700 A < I < 1.2 kA). The generation experiments of RSWO are conducted at an axial pulsed magnetic field whose maximum strength and duration can reach about 2.7 T and 1 s, respectively. The experimental results show that the RSWO successfully produces reasonable uniform terahertz pulses at repetition rate of 10, and the pulse duration, frequency, and power of a single pulse are about 1.5 ns, 0.154 THz, and 2.6 MW, respectively, whereas the dominated radiation mode of the RSWO is TM{sub 02}.
Response of internal solitary waves to tropical storm Washi in the northwestern South China Sea
Z. H. Xu
2011-11-01
Full Text Available Based on in-situ time series data from an array of temperature sensors and an acoustic Doppler current profiler on the continental shelf of the northwestern South China Sea, a sequence of internal solitary waves (ISWs were observed during the passage of tropical storm Washi in the summer of 2005, which provided a unique opportunity to investigate the ISW response to the tropical cyclone. The passing tropical storm is found to play an important role in affecting the stratification structure of the water column, and consequently leading to significant variability in the propagating features of the ISWs, such as the polarity reversal and amplitude variations of the waves. The response of the ISWs to Washi can be divided into two stages, direct forcing by the strong wind (during the arrival of Washi and remote forcing via the near-inertial internal waves induced by the tropical storm (after the passage of Washi. The field observations as well as a theoretical analysis suggest that the variations of the ISWs closely coincide with the changing stratification structure and shear currents in accompanied by the typhoon wind and near-inertial waves. This study presents the first observations and analysis of the ISW response to the tropical cyclone in the South China Sea.
A Solitary Wave-Based Sensor to Monitor the Setting of Fresh Concrete
Piervincenzo Rizzo
2014-07-01
Full Text Available We present a proof-of-principle study about the use of a sensor for the nondestructive monitoring of strength development in hydrating concrete. The nondestructive evaluation technique is based on the propagation of highly nonlinear solitary waves (HNSWs, which are non-dispersive mechanical waves that can form and travel in highly nonlinear systems, such as one-dimensional particle chains. A built-in transducer is adopted to excite and detect the HNSWs. The waves are partially reflected at the transducer/concrete interface and partially transmitted into the concrete. The time-of-flight and the amplitude of the waves reflected at the interface are measured and analyzed with respect to the hydration time, and correlated to the initial and final set times established by the penetration test (ASTM C 403. The results show that certain features of the HNSWs change as the concrete curing progresses indicating that it has the potential of being an efficient, cost-effective tool for monitoring strengths/stiffness development.
Electro-acoustic solitary waves and double layers in a quantum plasma
Dip, P. R.; Hossen, M. A.; Salahuddin, M.; Mamun, A. A.
2017-02-01
A meticulous theoretical investigation has carried out to study the properties related to the higher-order nonlinearity of the electro-acoustic waves, specifically ion-acoustic (IA) waves in an unmagnetized, collisionless, quantum electron-positron-ion (EPI) plasma. The plasma system is supposed to be formed of positively charged inertial heavy ions, inertialess electrons and positrons. The reductive perturbation technique is employed to derive the modified Korteweg-de Vries (mK-dV) equation to analyze the solitary waves (SWs), and the standard Gardner (SG) equation to analyze the higher-order SWs as well as double layers (DLs). The basic features (viz. amplitude, width, phase speed, etc.) of the IA SWs and DLs are examined. The comparison between the mK-dV SWs and SG SWs is also made. It is found that the amplitude, width, phase speed, etc. of the IA SWs and DLs are significantly modified by the effects of the both Fermi temperatures as well as pressures and Bohm potentials of electrons and positrons. Our findings may be useful in explaining the physics behind the formation of the IA waves in both astrophysical and laboratory EPI plasmas (viz. white dwarfs, laser-solid matter interaction experiments, etc.).
Observation of equatorial Kelvin solitary waves in a slowly varying thermocline
Q. Zheng
1998-01-01
Full Text Available TOPEX/POSEIDON (T/P sea level deviation (SLD time series from 3 October 1992 to 15 May 1997 combined with upper ocean thermal structures are used to observe the characteristics and analyze the dynamics of equatorial waves in the Pacific Ocean. The evolution of the Kelvin wave propagating along an eastward shoaling thermocline in the equatorial Pacific is investigated. The behaviour of this wave as it propagates eastward can be approximately described with the solutions of the perturbed Korteweg-de Vries (PKDV equation and modified Green's Law. Assuming that the nonlinear term and dispersive term of this equation are balanced, the amplitude increases as the thermocline decreases to the power -3/8. Approaching the eastern Pacific, the nonlinearity increases and the relation changes to the power -9/8. The dispersion relation, and mass and energy conservations are investigated. The results indicate that under a varying thermocline, the nonlinear Kelvin solitary waves indeed exist in the real ocean.
A propagation model for the internal solitary waves in the northern South China Sea
Cai, Shuqun; Xie, Jieshuo
2010-12-01
A two-dimensional, regularized long-wave equation model is developed to study the dynamic mechanisms of the propagation and evolution of the internal solitary waves (ISWs) in the northern South China Sea (SCS). It is shown that the bottom topography would cause the polarity reversal of ISWs, the change of the local wave crestline shape, and some diminution in wave amplitude; even if the ISWs are induced at the small sill channel along the Luzon Strait, they could propagate westward with their crestlines covering a large area in the latitudinal direction in the northern SCS. When there are two trains of ISWs propagating from the same source site with a time lag but different amplitudes of initial solitons, the latter train of ISWs with a larger amplitude may catch then swallow the former one with a smaller amplitude, and the wave amplitude of the merged ISW train decreases while the wave number increases. When there are two trains of ISWs propagating from the different source sites at the same time with the same amplitude of initial solitons, the crestlines of the two ISW trains may meet and a new leading soliton is induced at the connection point. Once the ISW trains collide with the island, before the island, a weak ISW train is reflected; behind the island, the former crestlines of the ISW train are torn by the island into two new trains, which may reconnect after passing around the island. The propagation direction, the wave amplitude, and the reconnection point of the new merged ISW train behind the island depend on the relative orientation of the original soliton source site to the island.
Site-specific Quantification of Bone Quality using Highly Nonlinear Solitary Waves
Yang, Jinkyu; Borkowski, Sean; Silvestro, Claudio; De Nardo, Luigi; Daraio, Chiara; Ebramzadeh, Edward
2010-01-01
Osteoporosis is a well recognized problem affecting millions of individuals worldwide. Consequently, the need to effectively, efficiently, and affordably diagnose and identify those at risk is essential; moreover, site-specific assessment of bone quality is necessary, not only in the process of risk assessment, but may also be desirable for other applications. The present study evaluated a new one-dimensional granular crystal sensor, composed of a tightly packed chain of beads under Hertzian contact interaction, representing the most suitable fundamental component for solitary wave generation and propagation. First, the sensitivity of the novel sensor was tested using densities of rigid polyurethane foam, representing clinical bone quality ranging from healthy, to severely osteoporotic. Once the relationship between the signal response and known densities was established, the sensor was used to measure several sites located in the proximal femur of ten human cadaveric specimens. The accuracy of the model was ...
Ghebache, Siham; Tribeche, Mouloud
2017-10-01
The problem of arbitrary amplitude ion-acoustic solitary waves (IASWs), which accompany electronegative plasmas having positive ions, negative ions, and nonextensive electrons is addressed. The energy integral equation with a new Sagdeev potential is analyzed to examine the existence regions of the IASWs. Different types of electronegative plasmas inspired from the experimental studies of Ichiki et al. (2001) are discussed. Our results show that in such plasmas IASWs, the amplitude and nature of which depend sensitively on the mass and density ratio of the positive and negative ions as well as the q-nonextensive parameter, can exist. Interestingly, one finds that our plasma model supports the coexistence of smooth rarefactive and spiky compressive IASWs. Our results complement and provide new insights on previously published findings on this problem.
Finite element analysis of solitary wave propagation by acoustic velocity method
Maruoka, Akira; Uchiyama, Ichiro; Kawahara, Mutsuto
2017-01-01
There is discontinuity between compressible and incompressible states in fluid flows. If we subtract the thermal effect from compressible fluid flows, we obtain adiabatic fluid flows, from which incompressible fluid flows are obtained if we let the acoustic velocity tend to infinity. Thus, we employ the idea of adiabatic fluid flows to solve incompressible flows. In the computation, the physical value of the acoustic velocity is employed. This idea corresponds to an extension of artificial compressibility under physical considerations. We present the new SUPG formulation of adiabatic fluid flows, by which not only the effect of SUPG but also those of PSPG and LSIC of incompressible fluid flows are derived. After the numerical verifications, three-dimensional solitary wave propagations are computed. Close agreement between computed and experimental values is obtained.
Dissipative kinetic Alfvén solitary waves resulting from viscosity
Choi, C.-R.; Kang, S.-B.; Min, K.-W. [Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701 (Korea, Republic of); Woo, M.-H. [National Fusion Research Institute, Daejeon 305-333 (Korea, Republic of); Hwang, J.; Park, Y.-D. [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of)
2013-11-15
Nonlinear small-amplitude kinetic Alfvén solitary waves (KASWs) are investigated with their “anomalous” kinetic viscosity effect on electrons. It is found that the structure of a hump-type KASW solution develops into a shock-type (or double layer) KASW solution for large amplitude KASWs when viscosity exists. For small amplitude KASWs, the Korteweg-de Vries (KdV) equation with an approximate pseudopotential was solved, and it is found that the hump-type KASWs develop into oscillating shock-type (kink-type) KASWs. It is also found that the oscillating scale of this structure is related to the propagation velocity and plasma beta, while the damping scale is inversely proportional to the viscosity.
GPU acceleration of a nonhydrostatic model for the internal solitary waves simulation
CHEN Tong-qing; ZHANG Qing-he
2013-01-01
The parallel computing algorithm for a nonhydrostatic model on one or multiple Graphic Processing Units (GPUs) for the simulation of internal solitary waves is presented and discussed.The computational efficiency of the GPU scheme is analyzed by a series of numerical experiments,including an ideal case and the field scale simulations,performed on the workstation and the supercomputer system.The calculated results show that the speedup of the developed GPU-based parallel computing scheme,compared to the implementation on a single CPU core,increases with the number of computational grid cells,and the speedup can increase quasilinearly with respect to the number of involved GPUs for the problem with relatively large number of grid cells within 32 GPUs.
Quantum reflection of bright solitary matter-waves from a narrow attractive potential
Marchant, A L; Yu, M M H; Rakonjac, A; Helm, J L; Polo, J; Weiss, C; Gardiner, S A; Cornish, S L
2015-01-01
We report the observation of quantum reflection from a narrow, attractive, potential using bright solitary matter-waves formed from a 85Rb Bose-Einstein condensate. We create narrow potentials using a tightly focused, red-detuned laser beam, and observe reflection of up to 25% of the atoms, along with the trapping of atoms at the position of the beam. We show that the observed reflected fraction is much larger than theoretical predictions for a narrow Gaussian potential well; a more detailed model of bright soliton propagation, accounting for the generic presence of small subsidiary intensity maxima in the red-detuned beam, suggests that these small intensity maxima are the cause of this enhanced reflection.
Fast accurate computation of the fully nonlinear solitary surface gravity waves
Clamond, Didier
2013-01-01
In this short note, we present an easy to implement and fast algorithm for the computation of the steady solitary gravity wave solution of the free surface Euler equations in irrotational motion. First, the problem is reformulated in a fixed domain using the conformal mapping technique. Second, the problem is reduced to a single equation for the free surface. Third, this equation is solved using Petviashvili's iterations together with pseudo-spectral discretisation. This method has a super-linear complexity, since the most demanding operations can be performed using a FFT algorithm. Moreover, when this algorithm is combined with the multi-precision arithmetics, the results can be obtained to any arbitrary accuracy.
Deng Xi-Jun; Yan Zi-Zong; Han Li-Bo
2009-01-01
In this paper,the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied.By using the first integral method,which is based on the divisor theorem,some exact explicit travelling solitary wave solutions for the above equation are obtained.As a result,some minor errors and some known results in the previousl literature are clarified and improved.
Ghosh, Samiran [College of Textile Technology, Berhampore 742101, Murshidabad, West Bengal (India)]. E-mail: sran_g@yahoo.com
2005-04-11
It has been found that the dust ion acoustic solitary wave (DIASW) is governed by a modified form of Korteweg-de Vries (KdV) equation modified by the effects of ionization, particle collisions and bounded nonplanar geometry. Approximate analytical time evolution solution and also the numerical solution of modified form of KdV equation reveal that the wave amplitude grows exponentially with time due to ionization, whereas the bounded nonplanar geometry and collision reduce the instability growth rate.
Whistler-Mode Waves Growth by a Generalized Relativistic Kappa-Type Distribution
ZHOU Qing-Hua; JIANG Bin; SHI Xiang-Hua; LI Jun-Qiu
2009-01-01
The instability of field-aligned Whistler-mode waves in space plasmas is studied by using a recently developed generalized relativistic kappa-type (KT) distribution. Numerical calculations are performed for a direct compar-ison between the new KT distribution and the current kappa distribution. We show that the wave growth for the KT distribution tends to occur in the lower wave frequency (e.g., ω 0.1Ωe) due to a larger fractional num-ber of the resonant electrons ηrel (which controls the wave growth), while primarily locating in the higher wave frequency for the kappa distribution. Moreover, the relativistic anisotropy Arel by the KT distribution is found to be smaller than that by the kappa distribution, leading to a smaller peak of wave growth. The results present a further understanding of plasma wave instability particularly in those plasmas where relativistic electrons are present.
Statistical study of electrostatic solitary waves associated with reconnection: Geotail observations
Li, S. Y.; Deng, X. H.; Zhou, M.; Tang, R. X.; Liu, K.; Kojima, H.; Matsumoto, H.
2009-02-01
The role of waves in the dynamics of the magnetotail has long been a topic of interest in magnetospheric physics. The characteristics of Electrostatic Solitary Waves (ESWs) associated with reconnection have been studied statistically in the magnetotail by surveying the large amounts data obtained from Waveform Capture (WFC) which is an important component of Plasma Wave Instrument (PWI) on the Geotail spacecraft. About 150 reconnection events with WFC data available are selected, and approximately 10 thousands of ESW waveforms are picked up by hands for statistical study. The ESWs are observed near diffusion region and near the plasma sheet boundary layer (PSBL). Two kinds of waveforms of ESWs are observed: bi-polar and tri-polar pulses. It is found that the pulse width of the ESWs is in the order of 1 5 ms and the peak-to-peak amplitude is in the order of 0.1 5 mV/m. The amplitudes of ESWs are larger in the near-earth tail region than that in deep tail region. ESWs have been observed with or without guide magnetic field . The characteristics of ESWs in different reconnection region and under different strength of guild magnetic field, their possible generation mechanism will be discussed.
Dust kinetic Alfvén solitary and rogue waves in a superthermal dusty plasma
Saini, N. S., E-mail: nssaini@yahoo.com; Singh, Manpreet, E-mail: singhmanpreet185@gmail.com [Department of Physics, Guru Nanak Dev University, Amritsar 143005 (India); Bains, A. S., E-mail: bainsphysics@yahoo.co.in [Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E2 (Canada)
2015-11-15
Dust kinetic Alfvén solitary waves (DKASWs) have been examined in a low-β dusty plasma comprising of negatively charged dust grains, superthermal electrons, and ions. A nonlinear Korteweg-de Vries (KdV) equation has been derived using the reductive perturbation method. The combined effects of superthermality of charged particles (via κ), plasma β, obliqueness of propagation (θ), and dust concentration (via f) on the shape and size of the DKASWs have been examined. Only negative potential (rarefactive) structures are observed. Further, characteristics of dust kinetic Alfvén rogue waves (DKARWs), by deriving the non-linear Schrödinger equation (NLSE) from the KdV equation, are studied. Rational solutions of NLSE show that rogue wave envelopes are supported by this plasma model. It is observed that the influence of various plasma parameters (superthermality, plasma β, obliqueness, and dust concentration) on the characteristics of the DKARWs is very significant. This fundamental study may be helpful in understanding the formation of coherent nonlinear structures in space and astrophysical plasma environments where superthermal particles are present.
Effects of Tidal Currents on Nonlinear Internal Solitary Waves in the South China Sea
FAN Zhisong; SHI Xingang; Antony K. Liu; LIU Hailong; LI Peiliang
2013-01-01
The propagation and fission process of intemal solitary waves (ISWs) with amplitudes of about 170m are simulated in the northeast of the South China Sea (NSCS) by using the generalized Korteweg-de Vries (KdV) equation under continuous stratification.More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs.This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current.It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however,there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons (defined as the distance between two neighboring peaks of ISWs).The difference in nonlinearity coefficient α between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.
Large amplitude solitary waves in ion-beam plasmas with charged dust impurities
Misra, A P
2011-01-01
The nonlinear propagation of large amplitude dust ion-acoustic (DIA) solitary waves (SWs) in an ion-beam plasma with stationary charged dusts is investigated. For typical plasma parameters relevant for experiments [J. Plasma Phys. \\textbf{60}, 69 (1998)], when the beam speed is larger than the DIA speed ($v_{b0}\\gtrsim1.7c_s$), three stable waves, namely the "fast" and "slow" ion-beam modes and the plasma DIA wave are shown to exist. These modes can propagate as SWs in the beam plasmas. However, in the other regime ($c_s0)$ is found to be limited by a critical value which typically depends on $M$, $v_{b0}$ as well as the ion/beam temperature. The conditions for the existence of DIA solitons are obtained and their properties are analyzed numerically in terms of the system parameters. While the system supports both the compressive and rarefactive large amplitude SWs, the small amplitude solitons exist only of the compressive type. The theoretical results may be useful for observation of soliton excitations in l...
Analyses of electrostatic solitary waves (ESWs) observed by Kaguya near the Moon
Hashimoto, K.; Hashitani, M.; Omura, Y.; Kasahara, Y.; Kojima, H.; Ono, T.; Tsunakawa, H.
2011-12-01
In KAGUYA (SELENE) LRS [1], WFC-L [2] observes waveforms of plasma waves in 100Hz-100kHz and a lot of electrostatic solitary waves (ESWs) have been observed. Some results were reported [3]. Although the orthogonal dipole antennas are generally used in the observations, sometimes a pair of monopole antennas were used. We analyze observations mainly by the latter antennas in the present study. Observed waveforms are fitted to ideal ESW waveforms. The waveforms observed by the monopole mode are susceptive to noises and generally they are not similar each other. Since the waveforms observed by the dipole mode are less affected by noises, we re-analyzed the data by fitting these waveforms to the ideal ESW waveforms. The observed ESWs have often components perpendicular to the background magnetic field. This means that the ESW potential structure has two dimensions and they are observed near the generation regions. The propagation velocity, the potential width, the potential depth, etc. of each ESW are also evaluated by comparing the waveforms observed by the monopole antennas. The data fitted to the dipole waveforms are used as references. Acknowledgments: The SELENE project has been organized by the Japan Aerospace Exploration Agency (JAXA). The authors express their thanks to all members of the SELENE project team. References [1] Takayuki Ono, Atsushi Kumamoto, Yasushi Yamaguchi, Atsushi Yamaji, Takao Kobayashi, Yoshiya Kasahara, and Hiroshi Oya, Instrumentation and observation target of the Lunar Radar Sounder (LRS) experiment on-board the SELENE spacecraft, Earth Planets Space, 60, 321-332, 2008. [2] Y. Kasahara, Y. Goto, K. Hashimoto, T. Imachi, A. Kumamoto, T. Ono, and H. Matsumoto, Plasma Wave Observation Using Waveform Capture in the Lunar Radar Sounder on board the SELENE Spacecraft, Earth, Planets and Space, 60, 341-351, 2008. [3] K. Hashimoto, M. Hashitani, Y. Kasahara, Y. Omura, M.N. Nishino, Y. Saito, S. Yokota, T. Ono, H. Tsunakawa, H. Shibuya, M
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts
Shprits, Yuri Y.; Drozdov, Alexander Y.; Spasojevic, Maria; Kellerman, Adam C.; Usanova, Maria E.; Engebretson, Mark J.; Agapitov, Oleksiy V.; Zhelavskaya, Irina S.; Raita, Tero J.; Spence, Harlan E.; Baker, Daniel N.; Zhu, Hui; Aseev, Nikita A.
2016-01-01
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes. PMID:27678050
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.
Shprits, Yuri Y; Drozdov, Alexander Y; Spasojevic, Maria; Kellerman, Adam C; Usanova, Maria E; Engebretson, Mark J; Agapitov, Oleksiy V; Zhelavskaya, Irina S; Raita, Tero J; Spence, Harlan E; Baker, Daniel N; Zhu, Hui; Aseev, Nikita A
2016-09-28
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.
Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts
Shprits, Yuri Y.; Drozdov, Alexander Y.; Spasojevic, Maria; Kellerman, Adam C.; Usanova, Maria E.; Engebretson, Mark J.; Agapitov, Oleksiy V.; Zhelavskaya, Irina S.; Raita, Tero J.; Spence, Harlan E.; Baker, Daniel N.; Zhu, Hui; Aseev, Nikita A.
2016-09-01
The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes.
O Rahman; A A Mamun
2013-06-01
A theoretical investigation of dust-acoustic solitary waves in three-component unmagnetized dusty plasma consisting of trapped electrons, Maxwellian ions, and arbitrarily charged cold mobile dust was done. It has been found that, owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of small but finite amplitude dust-acoustic (DA) waves is governed by a nonlinear equation of modified Korteweg–de Vries (mKdV) type (instead of KdV). The reductive perturbation method was employed to study the basic features (amplitude, width, speed, etc.) of DA solitary waves which are significantly modified by the presence of trapped electrons. The implications of our results in space and laboratory plasmas are briefly discussed.
ALY R SEADAWY
2017-09-01
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
El-Wakil, S A; El-Shewy, E K; Abd-El-Hamid, H M
2010-01-01
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type distributions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of Solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation, is used here. Numerical studies have been made using plasma parameters close to those values corresponding to Earth's plasma sheet boundary layer region reveals different solutions i.e., bell-shaped solitary pulses and singularity solutions at a finite point which called "blowup" solutions, Jaco...
Waves in General Relativistic Two-fluid Plasma around a Schwarzschild Black Hole
Rahman, M Atiqur
2010-01-01
Waves propagating in the relativistic electron-positron or ions plasma are investigated in a frame of two-fluid equations using the 3+1 formalism of general relativity developed by Thorne, Price and Macdonald (TPM). The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The local dispersion relations for transverse and longitudinal waves have been derived, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon using WKB approximation
Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering
Gamayunov, K. V.; Khazanov, G. V.
2006-01-01
The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we
Shahmansouri, M.; Misra, A. P.
2016-12-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived, which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k - θ plane, where k is the wave number and θ ( 0 ≤ θ ≤ π ) the angle of modulation. It is also found that as the electron thermal velocity or θ increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effect of the thermal pressure or the relativistic flow is slightly relaxed. The present results may be useful to the MI and the formation of localized LW envelopes in cosmic plasmas with a relativistic flow of electrons.
Towards Relativistic Atomic Physics and Post-Minkowskian Gravitational Waves
Lusanna, Luca
2009-01-01
A review is given of the formulation of relativistic atomic theory, in which there is an explicit realization of the Poincare' generators, both in the inertial and in the non-inertial rest-frame instant form of dynamics in Minkowski space-time. This implies the need to solve the problem of the relativistic center of mass of an isolated system and to describe the transitions from different conventions for clock synchronization, namely for the identifications of instantaneous 3-spaces, as gauge transformations. These problems, stemming from the Lorentz signature of space-time, are a source of non-locality, which induces a spatial non-separability in relativistic quantum mechanics, with implications for relativistic entanglement. Then the classical system of charged particles plus the electro-magnetic field is studied in the framework of ADM canonical tetrad gravity in asymptotically Minkowskian space-times admitting the ADM Poincare' group at spatial infinity, which allows to get the general relativistic extens...
An extreme internal solitary wave event observed in the northern South China Sea
Huang, Xiaodong; Chen, Zhaohui; Zhao, Wei; Zhang, Zhiwei; Zhou, Chun; Yang, Qingxuan; Tian, Jiwei
2016-07-01
With characteristics of large amplitude and strong current, internal solitary wave (ISW) is a major hazard to marine engineering and submarine navigation; it also has significant impacts on marine ecosystems and fishery activity. Among the world oceans, ISWs are particular active in the northern South China Sea (SCS). In this spirit, the SCS Internal Wave Experiment has been conducted since March 2010 using subsurface mooring array. Here, we report an extreme ISW captured on 4 December 2013 with a maximum amplitude of 240 m and a peak westward current velocity of 2.55 m/s. To the authors’ best knowledge, this is the strongest ISW of the world oceans on record. Full-depth measurements also revealed notable impacts of the extreme ISW on deep-ocean currents and thermal structures. Concurrent mooring measurements near Batan Island showed that the powerful semidiurnal internal tide generation in the Luzon Strait was likely responsible for the occurrence of the extreme ISW event. Based on the HYCOM data-assimilation product, we speculate that the strong stratification around Batan Island related to the strengthening Kuroshio may have contributed to the formation of the extreme ISW.
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
Barman, A
2014-01-01
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg de-Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids {\\bf 12}, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive io...
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
Barman, Arnab; Misra, A. P., E-mail: apmisra@visva-bharati.ac.in, E-mail: apmisra@gmail.com [Department of Mathematics, Siksha Bhavana, Visva-Bharati University, Santiniketan 731 235, West Bengal (India)
2014-07-15
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μ{sub pd}) as well as the ratios of positive to negative ion temperatures (σ) and masses (m)
L Haibin; XIE Jieshuo; YAO Yuan; XU Jiexin; CHEN Zhiwu; HE Yinghui; CAI Shuqun
2016-01-01
Based on modifications of the observed background parabolic current in upper layer of the northeastern South China Sea (SCS), the effects of eight kinds of background currents on the characteristics and energy conversion of internal solitary waves (ISWs) are investigated by an Internal Gravity Wave (IGW) model. It is found that, although the background current has little effect on the number of the generated ISWs, it reduces the resulted phase speed of ISW. When the background parabolic current appears with its lower boundary near or above the main thermocline, the ISW amplitude and the depth of the isopycnal undergoing maximum displacement increase;when the background parabolic current curvature is reduced, the ISW amplitude and the ratio of baroclinic to barotropic energy reduce, whilst the phase speed of ISW, the baroclinic energy, and the ratio of baroclinic kinetic energy (KE) to available potential energy (APE) increase; when the lower boundary of background parabolic current extends down to the seabed and the background current curvature is reduced, the ISW amplitude and phase speed decrease, whilst the barotropic kinetic energy, the baroclinic energy and the ratio of KE to APE increase. At a whole depth, when the lower background current curvature is reduced and the upper current curvature is increased, the ISW amplitude, and phase speed, the ratio of baroclinic to barotropic energy, the baroclinic energy, and the ratio of KE to APE all increase.
Arbitrary amplitude kinetic Alfven solitary waves in two temperature electron superthermal plasma
Singh, Manpreet; Singh Saini, Nareshpal; Ghai, Yashika
2016-07-01
Through various satellite missions it is observed that superthermal velocity distribution for particles is more appropriate for describing space and astrophysical plasmas. So it is appropriate to use superthermal distribution, which in the limiting case when spectral index κ is very large ( i.e. κ→∞), shifts to Maxwellian distribution. Two temperature electron plasmas have been observed in auroral regions by FAST satellite mission, and also by GEOTAIL and POLAR satellite in the magnetosphere. Kinetic Alfven waves arise when finite Larmor radius effect modifies the dispersion relation or characteristic perpendicular wavelength is comparable to electron inertial length. We have studied the kinetic Alfven waves (KAWs) in a plasma comprising of positively charged ions, superthermal hot electrons and Maxwellian distributed cold electrons. Sagdeev pseudo-potential has been employed to derive an energy balance equation. The critical Mach number has been determined from the expression of Sagdeev pseudo-potential to see the existence of solitary structures. It is observed that sub-Alfvenic compressive solitons and super-Alfvenic rarefactive solitons exist in this plasma model. It is also observed that various parameters such as superthermality of hot electrons, relative concentration of cold and hot electron species, Mach number, plasma beta, ion to cold electron temperature ratio and ion to hot electron temperature ratio have significant effect on the amplitude and width of the KAWs. Findings of this investigation may be useful to understand the dynamics of coherent non-linear structures (i.e. KAWs) in space and astrophysical plasmas.
Hafez, M. G.; Talukder, M. R.; Hossain Ali, M.
2017-04-01
The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the ( G'/ G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.
Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons.
Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang; Zong, Q-G; Zhou, X-Z; Zheng, Huinan; Wang, Yuming; Wang, Shui; Hao, Y-X; Gao, Zhonglei; He, Zhaoguo; Baker, D N; Spence, H E; Reeves, G D; Blake, J B; Wygant, J R
2015-12-22
Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. Our results demonstrate that the ULF waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.
Kersten, K.; Cattell, C. A.; Breneman, A.; Goetz, K.; Kellogg, P. J.; Wygant, J. R.; Wilson, L. B., III; Blake, J. B.; Looper, M. D.; Roth, I.
2011-01-01
We present multi-satellite observations of large amplitude radiation belt whistler-mode waves and relativistic electron precipitation. On separate occasions during the Wind petal orbits and STEREO phasing orbits, Wind and STEREO recorded intense whistler-mode waves in the outer nightside equatorial radiation belt with peak-to-peak amplitudes exceeding 300 mV/m. During these intervals of intense wave activity, SAMPEX recorded relativistic electron microbursts in near magnetic conjunction with Wind and STEREO. This evidence of microburst precipitation occurring at the same time and at nearly the same magnetic local time and L-shell with a bursty temporal structure similar to that of the observed large amplitude wave packets suggests a causal connection between the two phenomena. Simulation studies corroborate this idea, showing that nonlinear wave.particle interactions may result in rapid energization and scattering on timescales comparable to those of the impulsive relativistic electron precipitation.
Hongwei Yang
2014-01-01
Full Text Available In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.
Zha Qi-Lao; Sirendaoreji
2006-01-01
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach.This approach can also be applied to other nonlinear differential-difference equations.
Louis, Hélène; Odent, Vincent; Louvergneaux, Eric
2016-04-01
Shock waves are well-known nonlinear waves, displaying an abrupt discontinuity. Observation can be made in a lot of physical fields, as in water wave, plasma and nonlinear optics. Shock waves can either break or relax through either catastrophic or regularization phenomena. In this work, we restrain our study to dispersive shock waves. This regularization phenomenon implies the emission of dispersive waves. We demonstrate experimentally and numerically the generation of spatial dispersive shock waves in a nonlocal focusing media. The generation of dispersive shock wave in a focusing media is more problematic than in a defocusing one. Indeed, the modulational instability has to be frustrated to observe this phenomenon. In 2010, the dispersive shock wave was demonstrated experimentally in a focusing media with a partially coherent beam [1]. Another way is to use a nonlocal media [2]. The impact of nonlocality is more important than the modulational instability frustration. Here, we use nematic liquid crystals (NLC) as Kerr-like nonlocal medium. To achieve shock formation, we use the Riemann condition as initial spatial condition (edge at the beam entrance of the NLC cell). In these experimental conditions, we generate, experimentally and numerically, shock waves that relax through the emission of dispersive waves. Associated with this phenomenon, we evidence the emergence of a localized wave that travels through the transverse beam profile. The beam steepness, which is a good indicator of the shock formation, is maximal at the shock point position. This latter follows a power law versus the injected power as in [3]. Increasing the injected power, we found multiple shock points. We have good agreements between the numerical simulations and the experimental results. [1] W. Wan, D. V Dylov, C. Barsi, and J. W. Fleischer, Opt. Lett. 35, 2819 (2010). [2] G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A - At. Mol. Opt. Phys. 78, 1 (2008). [3] N. Ghofraniha, L. S
Compression-amplified EMIC waves and their effects on relativistic electrons
Li, L. Y., E-mail: lyli-ssri@buaa.edu.cn; Yu, J.; Cao, J. B. [School of Space and Environment, Beihang University, Beijing (China); Yuan, Z. G. [School of Electronic Information, Wuhan University, Wuhan (China)
2016-06-15
During enhancement of solar wind dynamic pressure, we observe the periodic emissions of electromagnetic ion cyclotron (EMIC) waves near the nightside geosynchronous orbit (6.6R{sub E}). In the hydrogen and helium bands, the different polarized EMIC waves have different influences on relativistic electrons (>0.8 MeV). The flux of relativistic electrons is relatively stable if there are only the linearly polarized EMIC waves, but their flux decreases if the left-hand polarized (L-mode) EMIC waves are sufficiently amplified (power spectral density (PSD) ≥ 1 nT{sup 2}/Hz). The larger-amplitude L-mode waves can cause more electron losses. In contrast, the R-mode EMIC waves are very weak (PSD < 1 nT{sup 2}/Hz) during the electron flux dropouts; thus, their influence may be ignored here. During the electron flux dropouts, the relativistic electron precipitation is observed by POES satellite near the foot point (∼850 km) of the wave emission region. The quasi-linear simulation of wave-particle interactions indicates that the L-mode EMIC waves can cause the rapid precipitation loss of relativistic electrons, especially when the initial resonant electrons have a butterfly-like pitch angle distribution.
Relativistic and non-relativistic solitons in plasmas
Barman, Satyendra Nath
This thesis entitled as "Relativistic and Non-relativistic Solitons in Plasmas" is the embodiment of a number of investigations related to the formation of ion-acoustic solitary waves in plasmas under various physical situations. The whole work of the thesis is devoted to the studies of solitary waves in cold and warm collisionless magnetized or unmagnetized plasmas with or without relativistic effect. To analyze the formation of solitary waves in all our models of plasmas, we have employed two established methods namely - reductive perturbation method to deduce the Korteweg-de Vries (KdV) equation, the solutions of which represent the important but near exact characteristic concepts of soliton-physics. Next, the pseudopotential method to deduce the energy integral with total nonlinearity in the coupling process for exact characteristic results of solitons has been incorporated. In Chapter 1, a brief description of plasma in nature and laboratory and its generation are outlined elegantly. The nonlinear differential equations to characterize solitary waves and the relevant but important methods of solutions have been mentioned in this chapter. The formation of solitary waves in unmagnetized and magnetized plasmas, and in relativistic plasmas has been described through mathematical entity. Applications of plasmas in different fields are also put forwarded briefly showing its importance. The study of plasmas as they naturally occur in the universe encompasses number of topics including sun's corona, solar wind, planetary magnetospheres, ionospheres, auroras, cosmic rays and radiation. The study of space weather to understand the universe, communications and the activities of weather satellites are some useful areas of space plasma physics. The surface cleaning, sterilization of food and medical appliances, killing of bacteria on various surfaces, destroying of viruses, fungi, spores and plasma coating in industrial instruments ( like computers) are some of the fields
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan
2016-11-28
Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off-shelf region between 16.0 degrees N and 16.5 degrees N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though, as the observed generation sites are far away (50 km) from the shelf break and tidal currents are considered relatively weak in the Red Sea. Upon closer examination of the tide properties in the Red Sea and the unique geometry of the basin, it is argued that the steep bathymetry and a relatively strong tidal current in the southern Red Sea provide favorable conditions for the generation of ISWs. To test this hypothesis and further explore the evolution of ISWs in the basin, 2-D numerical simulations with the nonhydrostatic MIT general circulation model (MITgcm) were conducted. The results are consistent with the satellite observations in regard to the generation sites, peak amplitudes and the speeds of first-mode ISWs. Moreover, our simulations suggest that the generation process of ISWs in the southern Red Sea is similar to the tide-topography interaction mechanism seen in the South China Sea. Specifically, instead of ISWs arising in the immediate vicinity of the shelf break via a hydraulic lee wave mechanism, a broad, energetic internal tide is first generated, which subsequently travels away from the shelf break and eventually breaks down into ISWs. Sensitivity runs suggest that ISW generation may also be possible under summer stratification conditions, characterized by an intermediate water intrusion from the strait of Bab el Mandeb.
SU Zhen-Peng; ZHENG Hui-Nan
2009-01-01
The bounce-averaged Fokker-Planck equation is solved to study the relativistic electron phase space density(PSD)evolution in the outer radiation belt due to resonant interactions with plasmaspheric plume electromagnetic ion cyclotron(EMIC)waves.It is found that the PSDs of relativistic electrons can be depleted by 1-3 orders of magnitude in 5h,supporting the previous finding that resonant interactions with EMIC waves may account for the frequently observed relativistic electron flux dropouts in the outer radiation belt during the main phase of a storm.The significant precipitation Joss of ～Me V electrons is primarily induced by the EMIC waves in H~+ and He~+ bands.The rapid remove of highly relativistic electrons(＞5 MeV)is mainly driven by the EMIC waves in O~+ band at lower pitch-angles,as well as the EMIC waves in H~+ and He~+ bands at larger pitch-angles.Moreover,a stronger depletion of relativistic electrons is found to occur over a wider pitch angle range when EMIC waves are centering relatively higher in the band.
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
Wu Xiao-Fei; Zhu Jia-Min; Ma Zheng-Yi
2007-01-01
In this paper, the improved Jacobian elliptic function expansion approach is extended and applied to constructing discrete solutions of the semi-discrete coupled modified Korteweg de Vries (mKdV) equations with the aid of the symbolic computation system Maple. Some new discrete Jacobian doubly periodic solutions are obtained. When the modulus M → 1, these doubly periodic solutions degenerate into the corresponding solitary wave solutions, including kink-type, bell-type and other types of excitations.
Wei, Gang; Du, Hui; Xu, XiaoHui; Zhang, YuanMing; Qu, ZiYun; Hu, TianQun; You, YunXiang
2014-01-01
A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is proposed according to the `jalousie' control mode. A new wave-maker based on the principle was manufactured and the experiments on the generation and evolution of internal solitary wave were conducted. Both the validity of the new device and applicability range of the KdV-type internal soliton theory were tested. Furthermore, a measurement technique of hydrodynamic load of internal waves was developed. By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank, their interaction characteristics were determined. It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement results of internal wave forces are confirmed to be correct.
Jia Lin Wu
2013-06-01
Full Text Available In macromolecular self-avoiding random walk, movement of each chain-particle accompanies an instantaneous spin system with de Gennes n = 0 that provides extra energy, extra vacancy volume and relaxation time needed for chain-particles co-movement. Using these additional and instantaneous spin systems not only directly yields the same Brownian motion mode in glass transition (GT and reptation-tube model, but also proves that the entangled chain length corresponding to the Reynolds number in hydrodynamics and the inherent diffusion - delocalization mode of entangled chains, from frozen glass state to melt liquid state, is a chain-size solitary wave with transverse ripplon-like soft wave. Thus, the order parameter of GT is found. The various currently available GT theories, such as Static Replica, Random First-Order Transition, Potential Energy Landscape, Mode-Coupling and Nanoscale Heterogeneity, can be unified using the additional and instantaneous spin system. GT served as an inspiration and continues to serve as the paradigm in the universal random delocalization transitions from disorder to more disorder until turbulence.
Yunlong Shi
2014-01-01
Full Text Available We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, and β effect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.
Liu, Chuangye; Nguyen, Nghiem V.; Wang, Zhi-Qiang
2016-10-01
In this paper, we investigate the orbital stability of solitary-wave solutions for an m-coupled nonlinear Schrödinger system i /∂ ∂ t u j + /∂ 2 ∂ x 2 u j + ∑ i = 1 m b i j |" separators=" u i | 2 u j = 0 , j = 1 , … , m , where m ≥ 2, uj are complex-valued functions of (x, t) ∈ ℝ2, bjj ∈ ℝ, j = 1, 2, …, m, and bij, i ≠ j are positive coupling constants satisfying bij = bji. It will be shown that spatially synchronized solitary-wave solutions of the m-coupled nonlinear Schrödinger system exist and are orbitally stable. Here, by synchronized solutions we mean solutions in which the components are proportional to one another. Our results completely settle the question on the existence and stability of synchronized solitary waves for the m-coupled system while only partial results were known in the literature for the cases of m ≥ 3 heretofore. Furthermore, the conditions imposed on the symmetric matrix B = (bij) satisfied here are both sufficient and necessary for the m-coupled nonlinear Schrödinger system to admit synchronized ground-state solutions.
Investigation of EMIC Waves During Balloon Detected Relativistic Electron Precipitation Events
Woodger, L. A.; Millan, R. M.
2009-12-01
Multiple relativistic electron precipitation (REP) events were detected by balloon-borne instrumentation during the MAXIS 2000 and MINIS 2005 campaigns. It has been suggested that resonance with EMIC waves caused these precipitation events (Lorentzen et al, 2000 and Millan et al, 2002) due to their location in the dusk sector. We present observations of dusk-side relativistic electron precipitation events, and use supporting satellite and theoretical data to investigate the relationship between EMIC waves and the detected REP. Satellite data can provide direct measurements of not only the waves themselves but also important resonance condition parameters. The data will be presented collectively with each event to showcase similarities and differences between events and the challenges that arise in trying to understand the relationship between dusk-side relativistic electron precipitation and EMIC waves.
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Dynamics and stability of relativistic gamma-ray-bursts blast waves
Meliani, Z.; Keppens, R.
2010-01-01
Aims. In gamma-ray-bursts (GRBs), ultra-relativistic blast waves are ejected into the circumburst medium. We analyse in unprecedented detail the deceleration of a self-similar Blandford-McKee blast wave from a Lorentz factor 25 to the nonrelativistic Sedov phase. Our goal is to determine the stabili
Relativistic n-body wave equations in scalar quantum field theory
Emami-Razavi, Mohsen [Centre for Research in Earth and Space Science, York University, Toronto, Ontario, M3J 1P3 (Canada)]. E-mail: mohsen@yorku.ca
2006-09-21
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields.
Vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates
Danaila, I.; Khamehchi, M. A.; Gokhroo, V.; Engels, P.; Kevrekidis, P. G.
2016-11-01
Multicomponent Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work [C. Qu, L. P. Pitaevskii, and S. Stringari, Phys. Rev. Lett. 116, 160402 (2016), 10.1103/PhysRevLett.116.160402], the notion of magnetic solitons has been introduced. Here we examine a variant of this concept in the form of vector dark-antidark solitary waves in multicomponent Bose-Einstein condensates (BECs). We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and intercomponent repulsion. Armed with this more general conceptual framework, we expand the notion of such states to higher dimensions presenting the possibility of both vortex-antidark states and ring-antidark-ring (dark soliton) states. We perform numerical continuation studies, investigate the existence of these states, and examine their stability using the method of Bogoliubov-de Gennes analysis. Dark-antidark and vortex-antidark states are found to be stable for broad parametric regimes. In the case of ring dark solitons, where the single-component ring state is known to be unstable, the vector entity appears to bear a progressively more and more stabilizing role as the intercomponent coupling is increased.
A note on radar altimeter signatures of internal solitary waves in the ocean
da Silva, J. C. B.; Cerqueira, A. L. F.
2016-10-01
It is well known that Internal Waves of tidal frequency (i.e. Internal Tides) are successfully detected in seasurface height (SSH) by satellite altimetry [1]. Shorter period Internal Solitary Waves (ISWs), whose periods are an order of magnitude smaller than tidal internal waves, are however generally assumed too small to be detected with standard altimeters (at low sampling rates, i.e. 1 Hz). This is because the Radar Altimeter (RA) footprint is somewhat larger, or of similar size at best, than the ISWs typical wavelengths. Here it will be demonstrated that new generation high sampling rate satellite altimetry data (i.e. 20 Hz) hold a variety of short-period signatures that are consistent with surface manifestations of ISWs in the ocean. Our observational method is based on satellite synergy with imaging sensors such as Synthetic Aperture Radar (SAR) and other high-resolution optical sensors (e.g. 250m resolution MODIS images) with which ISWs are unambiguously recognized. A first order commonly accepted ISW radar imaging mechanism is based on hydrodynamic modulation models [2] [3] in which the straining of surface waves due to ISW orbital currents is known to cause modulation of decimeter-scale surface waves, which have group velocities close to the IW phase velocity. This effect can be readily demonstrated by measurements of wind wave slope variances associated with short-period ISWs, as accomplished in the pioneer work of Hughes and Grant [4]. Mean square slope can be estimated from nadir looking RAs using a geometric optics (specular) scattering model [5][6][7], and directly obtained from normalized backscatter (sigma0) along-track records. We use differential scattering from the dual-band (Ku- and C-bands) microwave pulses of the Jason- 2 high-rate RA to isolate the contribution of small-scale surface waves to mean square slope. The differenced altimeter mean square slope estimate, derived for the nominal wave number range 40-100 rad/m, is then used to detect
YAN ZhenYa; XIE FuDing; ZHANG HongQing
2001-01-01
Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.``
Simulation of laser-driven plasma beat-wave propagation in collisional weakly relativistic plasmas
Kaur, Maninder; Nandan Gupta, Devki
2016-11-01
The process of interaction of lasers beating in a plasma has been explored by virtue of particle-in-cell (PIC) simulations in the presence of electron-ion collisions. A plasma beat wave is resonantly excited by ponderomotive force by two relatively long laser pulses of different frequencies. The amplitude of the plasma wave become maximum, when the difference in the frequencies is equal to the plasma frequency. We propose to demonstrate the energy transfer between the laser beat wave and the plasma wave in the presence of electron-ion collision in nearly relativistic regime with 2D-PIC simulations. The relativistic effect and electron-ion collision both affect the energy transfer between the interacting waves. The finding of simulation results shows that there is a considerable decay in the plasma wave and the field energy over time in the presence of electron-ion collisions.
Noureen, S.; Abbas, G.; Farooq, H.
2017-09-01
Using Vlasov-Maxwell's equations, the spectra of the perpendicular propagating Bernstein wave and Extraordinary wave in ultra-relativistic fully degenerate electron plasma are studied. The equilibrium particle distribution function is assumed to be isotropic Fermian. The analysis of high frequency spectra of the waves is carried out in the weak propagation limit Ω≫k .v and in the weak magnetic field limit |ω-k .v | ≫Ω and graphically observed.
Kozyreva, O. V.; Pilipenko, V. A.; Engebretson, M. J.; Yumoto, K.
2004-05-01
A new ULF wave index, characterizing the turbulent level of the geomagnetic field, has been calculated and applied for the analysis of relativistic electron enhancements during Space Weather Month (10-30 September 1999). The wave index has been produced from the INTERMAGNET, MACCS and CPMN dense arrays of ULF magnetometers in the Northern hemisphere. During the analyzed period two magnetic storms occurred (on September 12 and 22), and several significant increases of relativistic electron flux at geostationary orbit (up to 2-3 orders of magnitude) were detected by geostationary monitors. However, these electron enhancements were not related to the magnetic storm intervals. Instead, and rather unexpectedly, they correlated well with intervals of elevated ULF wave index, caused by the occurrence of intense Pc5 pulsations in the magnetosphere. This comparison is an additional indication of the possible importance of magnetospheric turbulence in energizing relativistic electrons.
Shahmansouri, M
2016-01-01
The modulational instability (MI) and the evolution of weakly nonlinear two-dimensional (2D) Langmuir wave (LW) packets are studied in an unmagnetized collisionless plasma with weakly relativistic electron flow. By using a 2D self-consistent relativistic fluid model and employing the standard multiple-scale technique, a coupled set of Davey-Stewartson (DS)-like equations is derived which governs the slow modulation and the evolution of LW packets in relativistic plasmas. It is found that the relativistic effects favor the instability of LW envelopes in the k{\\theta} plane, where k is the wave number and {\\theta} the angle of modulation. It is also found that as the electron thermal velocity or {\\theta} increases, the growth rate of MI increases with cutoffs at higher wave numbers of modulation. Furthermore, in the nonlinear evolution of the DS-like equations, it is seen that with an effect of the relativistic flow, a Gaussian wave beam collapses in a finite time, and the collapse can be arrested when the effe...
Jalil Manafian; Mehrdad Lakestani
2015-07-01
An application of the (′/)-expansion method to search for exact solutions of nonlinear partial differential equations is analysed. This method is used for Burgers, Fisher, Huxley equations and combined forms of these equations. The (′/)-expansion method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the (′/)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.
Development of the relativistic backward wave oscillator with a permanent magnet
MA Qiao-Sheng; LIU Zhong; LI Zheng-Hong; JIN Xiao
2012-01-01
Firstly,an X-band relativistic backward wave oscillator with a low guiding magnetic field is simulated,whose output microwave power is 520 MW.Then,an experiment is carried out on an accelerator to investigate a relativistic backward wave oscillator with a permanent magnetic field whose strength is 0.46 T.When the energy of the electron is 630 keV and the current of the electron beam is 6.7 kA,a 15 ns width pulsed microwave with 510 MW output power at 8.0 GHz microwave frequency is achieved.
Reformed Solitary Kinetic Alfvén Waves due to Dissipations and Auroral Electron Acceleration
WU De-Jin; CHAO Jih-Kwin; LEE Luo-Chuan; FENG Xue-Shang
2001-01-01
The physical nature of the auroral electron acceleration has been an outstanding problem in space physics for decades.Some recent observations from the auroral orbit satellites,FREJA and FAST,showed that large amplitude solitary kinetic Alfvén waves (SKAWs) are a common electromagnetic active phenomenon in the auroral magnetosphere. In a Iow-ββ/2 (i.e.,β/2 < me/mi < 1) plasma,the drift velocity of electrons relative to ions within SKAWs is much larger than thermal velocities of both electrons and ions.This leads to instabilities and causes dissipations of SKAWs.In the present work,based on the analogy of classical particle motion in a potential well,it is shown that a shock-like structure can be formed from SKAWs if dissipation effects are included.The reformed SKAWs with a shock-like structure have a local density jump and a net field-aligned electric potential drop of order of mev2A/e over a characteristic width of several )e.As a consequence,the reformed SKAWs can efficiently accelerate electrons field-aligned to the order of the local Alfvén velocity.In particular,we argue that this electron acceleration mechanism by reformed SKAWs can play an important role in the auroral electron acceleration problem.The result shows that not only the location of acceleration regions predicted by this model is well consistent with the observed auroral electron acceleration region of I 2 RE above the auroral ionosphere,but also the accelerated electrons from this region can obtain an energy of several keV and carry a field-aligned current of several/A/m2 which are comparable to the observations of auroral electrons.
Saini, N. S.; Kaur, Barjinder; Singh, Manpreet; Bains, A. S.
2017-07-01
A theoretical investigation is carried out to study small amplitude dust kinetic Alfvén solitary waves (DKASWs) and rogue waves in a low-β, electron depleted plasma consisting of negatively charged dust grains and two temperature ions which are modelled by q-nonextensive distribution. A nonlinear Korteweg-de Vries equation, which governs the evolution of DKASWs, has been derived using the reductive perturbation method. Combined effects of the nonextensivity of ions, plasma beta, temperature ratio of low and high temperature ions, concentration of ions as well as dust, and angle of propagation (θ) have been studied in detail on the propagation properties of DKASWs. Only negative potential Alfvénic solitary waves are observed in the present study. Further, the study is extended for dust kinetic Alfvén rogue wave (DKARW) solutions. The properties of DKARWs, influenced by plasma parameters in question, are discussed in detail. The findings of this study may be useful to understand the formation of nonlinear coherent structures in Saturn's F-ring.
Ultrafast ignition with relativistic shock waves induced by high power lasers
Shalom; Eliezer; Noaz; Nissim; Shirly; Vinikman; Pinhasi; Erez; Raicher; José; Maria; Martinez; Val
2014-01-01
In this paper we consider laser intensities greater than 1016 W cm-2where the ablation pressure is negligible in comparison with the radiation pressure.The radiation pressure is caused by the ponderomotive force acting mainly on the electrons that are separated from the ions to create a double layer(DL).This DL is accelerated into the target,like a piston that pushes the matter in such a way that a shock wave is created.Here we discuss two novel ideas.Firstly,the transition domain between the relativistic and non-relativistic laser-induced shock waves.Our solution is based on relativistic hydrodynamics also for the above transition domain.The relativistic shock wave parameters,such as compression,pressure,shock wave and particle flow velocities,sound velocity and rarefaction wave velocity in the compressed target,and temperature are calculated.Secondly,we would like to use this transition domain for shockwave-induced ultrafast ignition of a pre-compressed target.The laser parameters for these purposes are calculated and the main advantages of this scheme are described.If this scheme is successful a new source of energy in large quantities may become feasible.
Uphill diffusion, zero-flux planes and transient chemical solitary waves in garnet
Vielzeuf, D.; Saúl, A.
2011-05-01
Diffusion profiles in minerals are increasingly used to determine the duration of geological events. For this purpose, the distinction between growth and diffusion zoning is critical; it requires the understanding of complex features associated with multicomponent diffusion. Seed-overgrowth interdiffusion experiments carried out in the range 1,050-1,250°C at 1.3 GPa have been designed to quantify and better understand Fe-Mg-Ca interdiffusion in garnet. Some of the diffusion profiles measured by analytical transmission electron microscope show characteristic features of multicomponent diffusion such as uphill diffusion, chemical solitary waves, zero-flux planes and complex diffusion paths. We implemented three different methods to calculate the interdiffusion coefficients of the D matrix from the experimental penetration curves and determined that with Ca as the dependent component, the crossed coefficients of the D matrix are negative. Experiments and numerical simulations indicate that: (1) uphill diffusion in garnet can be observed indifferently on the three components Fe, Mg and Ca, (2) it takes the form of complementary depletion/repletion waves and (3) chemical waves occur preferentially on initially flat concentration profiles. Derived D matrices are used to simulate the fate of chemical waves in time, in finite crystals. These examples show that the flow of atoms in multicomponent systems is not necessarily unidirectional for all components; it can change both in space along the diffusion profile and in time. Moving zero-flux planes in finite crystals are transitory features that allow flux reversals of atoms in the diffusion zone. Interdiffusion coefficients of the D matrices are also analyzed in terms of eigenvalues and eigenvectors. This analysis and the experimental results show that depending on the composition of the diffusion couple, (1) the shape of chemical waves and diffusion paths changes; (2) the width of the diffusion zone for each component
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
Interacting relativistic quantum dynamics for multi-time wave functions
Lienert, Matthias
2016-11-01
In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
无
2006-01-01
By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitarywave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.
2015-05-05
AND SUBTITLE LASER-DRIVEN ULTRA-RELATIVISTIC PLASMAS - NUCLEAR FUSION IN COULOMB SHOCK WAVES, ROUGE WAVES, AND BACKGROUND MATTER. 5a. CONTRACT...blackbody radiation on free electrons .........................9 2.vi. Proposal of ultimate test of laser nuclear fusion efficiency in clusters...domain of energies and temperatures, with applications in particular to controlled nuclear fusion . 2. Final technical report on the grant #F49620-11-1
Uzbekov, Bogdan; Shprits, Yuri Y.; Orlova, Ksenia
2016-10-01
Electromagnetic Ion Cyclotron (EMIC) waves are transverse plasma waves that are generated in the Earth magnetosphere by ring current protons with temperature anisotropy in three different bands: below the H+, He+ and O+ ion gyrofrequencies. EMIC events are enhanced during the main phase of a geomagnetic storm when intensifications in the electric field result in enhanced injections of ions and are usually confined to high-density regions just inside the plasmapause or within drainage plumes. EMIC waves are capable of scattering radiation belt electrons and thus provide an important link between the intensification of the electric field, ion populations, and radiation belt electrons. Bounce-averaged diffusion coefficients computed with the assumption of parallel wave propagation are compared to the results of the code that uses the full cold plasma dispersion relation taking into account oblique propagation of waves and higher-order resonances. We study the sensitivity of the scattering rates to a number of included higher-order resonances, wave spectral distribution parameters, wave normal angle distribution parameters, ambient plasma density, and ion composition. Inaccuracies associated with the neglect of higher-order resonances and oblique propagation of waves are compared to potential errors introduced by uncertainties in the model input parameters.
Solitary waves in a self-gravitating opposite polarity dust-plasma medium
Mamun, A. A.; Schlickeiser, R. [Institut für Theoretische Physik, Lehrstuhl IV, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum, D-44780 Bochum (Germany)
2015-10-15
A more general and realistic dusty plasma model, namely, self-gravitating opposite polarity dust-plasma system (containing inertial positive and negative dust, and inertialess ions and electrons following Maxwellian distribution) is considered. The possibility for the formation of solitary electrostatic and self-gravitational potential structures in such a dust-plasma system is thoroughly examined. The standard reductive perturbation method, which is valid for small but finite amplitude solitary structures, is employed. The parametric regimes for the existence of solitary electrostatic and self-gravitational potential structures, and their basic properties (viz., polarity, amplitude, width, and speed) are found to be significantly modified by the combined effects of positively charged dust component and self-gravitational field. The applications of the present investigation in different space dusty plasma environments and laboratory dusty plasma devices are briefly discussed.
Singh, S. V.; Devanandhan, S.; Lakhina, G. S. [Indian Institute of Geomagnetism, Navi Mumbai (India); Bharuthram, R. [University of the Western Cape, Bellville (South Africa)
2013-01-15
Obliquely propagating ion-acoustic soliatry waves are examined in a magnetized plasma composed of kappa distributed electrons and fluid ions with finite temperature. The Sagdeev potential approach is used to study the properties of finite amplitude solitary waves. Using a quasi-neutrality condition, it is possible to reduce the set of equations to a single equation (energy integral equation), which describes the evolution of ion-acoustic solitary waves in magnetized plasmas. The temperature of warm ions affects the speed, amplitude, width, and pulse duration of solitons. Both the critical and the upper Mach numbers are increased by an increase in the ion temperature. The ion-acoustic soliton amplitude increases with the increase in superthermality of electrons. For auroral plasma parameters, the model predicts the soliton speed, amplitude, width, and pulse duration, respectively, to be in the range of (28.7-31.8) km/s, (0.18-20.1) mV/m; (590-167) m, and (20.5-5.25) ms, which are in good agreement with Viking observations.
Uddin, M. J., E-mail: josim.phys2007@gmail.com; Alam, M. S.; Mamun, A. A. [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-02-15
Nonplanar (cylindrical and spherical) positron-acoustic (PA) Gardner solitary waves (SWs) in an unmagnetized plasma system consisting of immobile positive ions, mobile cold positrons, and superthermal (kappa distributed) hot positrons and electrons are investigated. The modified Gardner equation is derived by using the reductive perturbation technique. The effects of cylindrical and spherical geometries, superthermal parameter of hot positrons and electrons, relative temperature ratios, and relative number density ratios on the PA Gardner SWs are studied by using the numerical simulations. The implications of our results in various space and laboratory plasma environments are briefly discussed.
Frequency conversion of probe wave produced by 2D interaction with relativistic ionization front
Yan Li-Xin; Zhang Yong-Sheng; Liu Jing-Ru; Lü Min
2005-01-01
Frequency conversion of probe electromagnetic wave induced by relativistic ionization front is theoretically analysed based on ray-tracing equations in different regimes. Downshifting as well as upshifting in frequency produced by the front is predicted. The reflected and transmitted angles can be also dramatically changed in certain cases.
Zhang, Sun, E-mail: szhang@pmo.ac.cn [Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008 (China); Key Laboratory of Dark Matter and Space Astronomy, Chinese Academy of Sciences, Nanjing 210008 (China); Joint Center for Particle, Nuclear Physics and Cosmology (J-CPNPC), PMO-NJU, Nanjing 210008 (China)
2014-02-05
In this Letter, we have studied the shock wave and discontinuity propagation for relativistic superfluid with spontaneous U(1) symmetry breaking in the framework of hydrodynamics. General features of shock waves are provided, the propagation of discontinuity and the sound modes of shock waves are also presented. The first sound and the second sound are identified as the propagation of discontinuity, and the results are in agreement with earlier theoretical studies. Moreover, a differential equation, called the growth equation, is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and special cases of diverging waves are also discussed.
Clayton, C. E.; Marsh, K. A.; Dyson, A.; Everett, M.; Lal, A.; Leemans, W. P.; Williams, R.; Joshi, C.
1993-01-01
High-gradient acceleration of externally injected 2.1-MeV electrons by a laser beat wave driven relativistic plasma wave has been demonstrated for the first time. Electrons with energies up to the detection limit of 9.1 MeV were detected when such a plasma wave was resonantly excited using a two-frequency laser. This implies a gradient of 0.7 GeV/m, corresponding to a plasma-wave amplitude of more than 8%. The electron signal was below detection threshold without injection or when the laser was operated on a single frequency.
Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins
Niederle, J
2001-01-01
New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins $s$ interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $2n$ ($n=s-\\frac12$) antisymmetric w.r.t. $n$ pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles.
Particle acceleration in ultra-relativistic parallel shock waves
Meli, A
2003-01-01
Monte-Carlo computations for highly relativistic parallel shock particle acceleration are presented for upstream flow gamma factors, $\\Gamma=(1-V_{1}^{2}/c^{2})^{-0.5}$ with values between 5 and $10^{3}$. The results show that the spectral shape at the shock depends on whether or not the particle scattering is small angle with $\\delta \\theta 2r_{g} \\Gamma^{2}$ where $\\lambda$ is the scattering mean free path along the field line and $r_{g}$ the gyroradius, these quantities being measured in the plasma flow frame. The large angle scattering case exhibits distinctive structure superimposed on the basic power-law spectrum, largely absent in the pitch angle case. Also, both cases yield an acceleration rate faster than estimated by the conventional, non-relativistic expression, $t_{acc}=[c/(V_{1}-V_{2})] [\\lambda_{1}/V_{1}+\\lambda_{2}/V_{2}]$ where '1' and '2' refer to upstream and downstream and $\\lambda$ is the mean free path. A $\\Gamma^{2}$ energy enhancement factor in the first shock crossing cycle and a sign...
Li, Shiyou; Chen, Xiaoqian; Guo, Jianming
2016-07-01
The electrostatic solitary waves (ESWs) have been widely observed and studied for many years. In the magnetic reconnection process, ESWs are regarded as one kind of means for the fast energy release by outward propagating electrons along re-connecting magnetic field lines. In this report, we present observation evidences of two kinds of unusual structures of ESWs associated with magnetic reconnection in the near-Earth magnetotail, including the 2-D ESWs and the tri-polar ESWs. First of all, more than 300 of electrostatic solitary waves (ESWs) with large perpendicular component which is bi-polar waveform structure are observed in the boundary layer within magnetic reconnection diffusion region in the near-Earth magnetotail. Such kinds of ESWs are named as 2-D ESWs. Singe-Reconnection-Based-Statistical study of 2-D ESWs is performed. Secondly, more than 200 waveforms with clear tri-polar characteristics are differentiated along the plasma sheet boundary layer near the magnetic reconnection X-line in the near-Earth magnetotail. Within reconnection diffusion region, the tri-polar ESWs are ample and are continuously observed during one burst interval (8.75 seconds) of the Geotail/WFC in the neutral plasma sheet where and thus the tri-polar ESW is suggested to be one kind of steady-going solitary structure. Statistical analysis to the characteristics of tri-polar ESWs will also be carried out. The observation of 2-D ESWs and the tri-polar ESWs presents evidence of complex structure of electron holes within the reconnection diffusion region and is helpful to the understanding of the energy release process of reconnection.
Strong electromagnetic waves in a magnetized relativistic electron-positron plasma
Yu, M.Y.; Shukla, P.K.; Rao, N.N. (Bochum Univ. (Germany, F.R.). Inst. fuer Theoretische Physik)
1984-12-01
It is shown that in a strongly magnetized relativistic electron-positron plasma, strongly localized large amplitude circularly polarized electromagnetic wave pulses exist. The localization is due to relativistic mass variation as well as ponderomotive force effects. Three types of pulses are found analytically: the sharply spiked pulse in a strongly magnetized cold plasma, the smooth pulse in a weak magnetized warm plasma, and the moderately spiked pulse for a weakly magnetized cold plasma. The physical mechanisms giving rise to these pulses are distinct for each case. Possible implications of our investigation to pulsar radiation are discussed.
Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements
Hossen, M. A., E-mail: armanplasma@gmail.com; Mamun, A. A., E-mail: mamun-phys@yahoo.co.uk [Department of Physics, Jahangirnagar University, Savar, Dhaka-1342 (Bangladesh)
2015-10-15
The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.
Study of trapping effect on ion-acoustic solitary waves based on a fully kinetic simulation approach
Jenab, S M
2016-01-01
A fully kinetic simulation approach, treating each plasma component based on the Vlasov equation, is adopted to study the disintegration of an initial density perturbation (IDP) into a number of ion-acoustic solitary waves (IASWs) in the presence of the trapping effect of electrons. The non-linear fluid theory developed by Schamel has identified three separate regimes of ion-acoustic solitary waves based on the trapping parameter. Here, the disintegration process and the resulting self-consistent IASWs are studied in a wide range of trapping parameters covering all the three regimes continuously. The dependency of features such as the time of disintegration, the number, speed and size of IASWs on the trapping parameter are focused upon. It is shown that an increase in this parameter slows down the propagation of IASWs while decreases their sizes in the phase space. These features of IASWs tend to saturate for large value of trapping parameters. The disintegration time shows a more complicated behavior than wh...
Maroof, R. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Ali, S. [National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Mushtaq, A. [Department of Physics, Abdul Wali Khan University, Mardan 23200 (Pakistan); National Center for Physics (NCP) at QAU Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Qamar, A. [Department of Physics, University of Peshawar, Peshawar 25000 (Pakistan)
2015-11-15
Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.
A nonextensive statistics approach for Langmuir waves in relativistic plasmas
V. Muñoz
2006-01-01
Full Text Available The nonextensive statistics formalism proposed by Tsallis has found many applications in systems with memory effects, long range spatial correlations, and in general whenever the phase space has fractal or multi-fractal structure. These features may appear naturally in turbulent or non-neutral plasmas. In fact, the equilibrium distribution functions which maximize the nonextensive entropy strongly resemble the non-Maxwellian particle distribution functions observed in space and laboratory and turbulent pure electron plasmas. In this article we apply the Tsallis entropy formalism to the problem of longitudinal oscillations in a proton-electron plasma. In particular, we study the equilibrium distribution function and the dispersion relation of longitudinal oscillations in a relativistic plasma, finding interesting differences with the nonrelativistic treatment.
Strumik, Marek
2016-01-01
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of ...
Natale, G.
This work is a further development of the modern thermo-poro-elasticity theory which has recently been applied to understand how fluid-rock coupling dynamics related to unrest episodes in volcanic domains can both determine, and occur with, ground deformation and rock fracturing processes. In particular by reformulating the energy equation, one of the two nonlinear heat-like equations upon which the thermo-poroelasticity theory is based, it is shown here how fluid thermal expansivity may influence fluid migration during its movement through subsurface volcanic porous-per meable horizons. With these new considerations it is found that a recent theory in which fluid-rock coupling dynamics is interpreted in terms of thermal and mechanical solitary shock wave propagation remains valid. However, the natural time scale of the propagating wave is reduced and consequently Darcy's velocity is increased as a result of fluid thermal expansivity.
Ion waves driven by shear flow in a relativistic degenerate astrophysical plasma
KHAN SHABBIR A; BAKHTIAR-UD-DIN; ILYAS MUHAMMAD; WAZIR ZAFAR
2016-05-01
We investigate the existence and propagation of low-frequency (in comparison to ion cyclotron frequency) electrostatic ion waves in highly dense inhomogeneous astrophysical magnetoplasma comprising relativistic degenerate electrons and non-degenerate ions. The dispersion equation is obtained by Fourier analysis under mean-field quantum hydrodynamics approximationfor various limits of the ratio of rest mass energy to Fermi energy of electrons, relevant to ultrarelativistic, weakly-relativistic and non-relativistic regimes. It is found that the system admits an oscillatory instability under certain condition in the presence of velocity shear parallel to ambient magnetic field. The dispersive role of plasma density and magnetic field is also discussed parametrically in the scenario of dense and degenerate astrophysical plasmas.
The efficiency of fast wave current drive for a weakly relativistic plasma
Chiu, S. C.; Lin-Liu, Y. R.; Karney, C. F. F.
1994-10-01
Current drive by fast waves (FWCD) is an important candidate for steady-state operation of tokamaks. Major experiments using this scheme are being carried out on DIII-D. There has been considerable study of the theoretical efficiency of FWCD. In Refs. 4 and 5, the nonrelativistic efficiency of FWCD at arbitrary frequencies was studied. For DIII-D parameters, the results can be considerably different from the Landau and Alfvén limits. At the high temperatures of reactors and DIII-D upgrade, relativistic effects become important. In this paper, the relativistic FWCD efficiency for arbitrary frequencies is studied. Assuming that the plasma is weakly relativistic, i.e., Te/mc2 is small, an analytic expression for FWCD is obtained for high resonant energies (uph/uTe≫1). Comparisons with the results from a numerical code ADJ and the nonrelativistic results shall be made and analytical fits in the whole range of velocities shall be presented.
Gravitational Waves from Perturbed Black Holes and Relativistic Stars
Rezzolla, Luciano
2003-01-01
These lectures aim at providing an introduction to the properties of gravitational waves and in particular to those gravitational waves that are expected as a consequence of perturbations of black holes and neutron stars. Imprinted in the gravitational radiation emitted by these objects is, in fact, a wealth of physical information. In the case of black holes, a detailed knowledge of the gravitational radiation emitted as a response to perturbations will reveal us important details about thei...
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves.
Schroeder, C B; Esarey, E
2010-05-01
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
Disperson relation of finite amplitude Alfven wave in a relativistic electron- positron plasma
Hada, T; Muñoz, V; Hada, Tohru; Matsukiyo, Shuichi; Munoz, Victor
2004-01-01
The linear dispersion relation of a finite amplitude, parallel, circularly polarized Alfv\\'en wave in a relativistic electron-positron plasma is derived. In the nonrelativistic regime, the dispersion relation has two branches, one electromagnetic wave, with a low frequency cutoff at $\\sqrt{1+2\\omega_p^2/\\Omega_p^2}$ (where $\\omega_p=(4\\pi n e^2/m)^{1/2}$ is the electron/positron plasma frequency), and an Alfv\\'en wave, with high frequency cutoff at the positron gyrofrequency $\\Omega_p$. There is only one forward propagating mode for a given frequency. However, due to relativistic effects, there is no low frequency cutoff for the electromagnetic branch, and there appears a critical wave number above which the Alfv\\'en wave ceases to exist. This critical wave number is given by $ck_c/\\Omega_p=a/\\eta$, where $a=\\omega_p^2/\\Omega_p^2$ and $\\eta$ is the ratio between the Alfv\\'en wave magnetic field amplitude and the background magnetic field. In this case, for each frequency in the Alfv\\'en branch, two additional...
Interaction of Oblique Incident Electromagnetic Wave with Relativistic Ionization Front
无
2005-01-01
Interactions of oblique incident probe wave with oncoming ionization fronts have been investigated using moving boundary conditions. Field conversion coefficients of reflection,transmission and magnetic modes produced in the interactions are derived. Phase matching conditions at the front and frequency up-shifting formulas for the three modes are also presented.
Droghei, R.; Falcini, F.; Casalbore, D.; Martorelli, E.; Mosetti, R.; Sannino, G.; Santoleri, R.; Chiocci, F. L.
2016-11-01
Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.
Droghei, R; Falcini, F; Casalbore, D; Martorelli, E; Mosetti, R; Sannino, G; Santoleri, R; Chiocci, F L
2016-11-03
Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary "current" that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.
Non-linear collisionless damping of Weibel turbulence in relativistic blast waves
Lemoine, Martin
2014-01-01
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the first-order non-linear terms associated to the diffusive nature of the particle trajectories. These corrections are found to systematically increase the damping rate, assuming that the scattering length remains larger than the coherence length of the magnetic fluctuations. The relevance of such corrections is discussed in a broader astrophysical perspective, in particular regarding the physics of the external relativistic ...
Shanmugasundaram Rajaian
2010-01-01
Full Text Available Purpose : To evaluate the outcome of shock wave lithotripsy (SWL as monotherapy for solitary renal stones larger than 2 cm without ureteral stenting. Materials and Methods : Our retrospective study included patients with solitary renal radio opaque stones larger than 2 cm treated with SWL using electromagnetic Dornier Compact S lithotripter device (Wessling, Germany for a period of 3 years (September 2002-2005. Stone clearance was assessed at 1 week, 1 month, and 3 months with plain X-rays of kidney, ureter, and bladder region, ultrasonography, and tomograms. Stone-free status, morbidity of the procedure, and fate of clinically insignificant residual fragments (CIRF were studied. A stone-free state was defined as no radiologic evidence of stone. Success was defined as complete clearance + CIRF. Results : Fifty-five patients, aged 11-65 years (mean 49.8 underwent SWL. Of them, only two were children. Male-to-female ratio was 3:1. The stone size was 21-28 mm (average 24 mm. The mean number of shocks were 3732 (range 724-12,100 and average energy level was 14 kV (range 11-16 kV. The mean follow-up was 18 months (range 3-22 months. Over all, stone-free status was achieved in 50% and success in 81% at 3 months. Stone clearance was not affected by stone location. Stones 26 mm (P = -0.10. Of 54 patients, 39 developed steinstrasse with mean length of 3.2 cm (range 1.4-6.2 cm and only four required intervention. Effectiveness quotient (EQ for SWL monotherapy for solitary renal stones more than 2 cm was 25.3%. The EQ for stones <25 mm and those more than 25 mm were 28.4% and 10% (P = -0.12, respectively. There was a lesser trend of difference between stones with size <25 and more than 25 mm. During the last review, the overall stone-free rate was 67.2%. Conclusions : SWL monotherapy was safe but significantly less effective for solitary renal stones larger than 2 cm. It can only be suggested to those who refuse surgical intervention. Pretreatment DJ
Trapped electron acceleration by a laser-driven relativistic plasma wave
Everett, M.; Lal, A.; Gordon, D.; Clayton, C. E.; Marsh, K. A.; Joshi, C.
1994-04-01
THE aim of new approaches for high-energy particle acceleration1 is to push the acceleration rate beyond the limit (~100 MeV m-1) imposed by radio-frequency breakdown in conventional accelerators. Relativistic plasma waves, having phase velocities very close to the speed of light, have been proposed2-6 as a means of accelerating charged particles, and this has recently been demonstrated7,8. Here we show that the charged particles can be trapped by relativistic plasma waves-a necessary condition for obtaining the maximum amount of energy theoretically possible for such schemes. In our experiments, plasma waves are excited in a hydrogen plasma by beats induced by two collinear laser beams, the difference in whose frequencies matches the plasma frequency. Electrons with an energy of 2 MeV are injected into the excited plasma, and the energy spectrum of the exiting electrons is analysed. We detect electrons with velocities exceeding that of the plasma wave, demonstrating that some electrons are 'trapped' by the wave potential and therefore move synchronously with the plasma wave. We observe a maximum energy gain of 28 MeV, corresponding to an acceleration rate of about 2.8 GeV m-1.
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
Coherent keV backscattering from plasma-wave boosted relativistic electron mirrors
Li, F Y; Chen, M; Wu, H C; Liu, Y; Meyer-ter-Vehn, J; Mori, W B; Zhang, J
2014-01-01
A new parameter regime of laser wakefield acceleration driven by sub-petawatt femotsecond lasers is proposed, which enables the generation of relativistic electron mirrors further accelerated by the plasma wave. Integrated particle-in-cell simulation including the mirror formation and Thomson scattering demonstrates that efficient coherent backscattering up to keV photon energy can be obtained with moderate driver laser intensities and high density gas targets.
Mao Jie-Jian; Yang Jian-Rong
2006-01-01
Using the solution of general Korteweg-de Vries (KdV) equation, the solutions of the generalized wriable coefficient Kadomtsev-Petviashvili (KP) equation are constructed, and then its new solitary wave-like solution and Jacobi clliptic function solution are obtained.
Sim, B. L.; Agterberg, F. P.
2006-07-01
If convection in the Earth's liquid outer core is disrupted, degrades to turbulence and begins to behave in a chaotic manner, it will destabilize the Earth's magnetic field and provide the seeds for kimberlite melts via turbulent jets of silicate rich core material which invade the lower mantle. These (proto-) melts may then be captured by extreme amplitude solitary nonlinear waves generated through interaction of the outer core surface with the base of the mantle. A pressure differential behind the wave front then provides a mechanism for the captured melt to ascend to the upper mantle and crust so quickly that emplacement may indirectly promote a type of impact fracture cone within the relatively brittle crust. These waves are very rare but of finite probability. The assumption of turbulence transmission between layers is justified using a simple three-layer liquid model. The core derived melts eventually become frozen in place as localised topographic highs in the Mohorovicic discontinuity (Moho), or as deep rooted intrusive events. The intrusion's final composition is a function of melt contamination by two separate sources: the core contaminated mantle base and subducted Archean crust. The mega-wave hypothesis offers a plausible vehicle for early stage emplacement of kimberlite pipes and explains the age association of diamondiferous kimberlites with magnetic reversals and tectonic plate rearrangements.
CHEN Jian-Hong; WEI Nan-Xia
2009-01-01
Taking into account the combined effects of the external magnetic field, adiabatic dust charge fluctuation and collisions occurring between the charged dust gains and neutral gas particles (dust-neutral collisions), the dust-acoustic solitary waves in three-dimensional uniform dusty plasmas are investigated analytically. By using the reductive perturbation method, the Korteweg-de Vries (KdV) equation governing the dust-acoustic solitary waves is obtained. The present analytical results show that only rarefactive solitary waves exist in this system. It is also found that the effects of the wave vector along the z-direction, dust charge variation, collisional frequency, the plasma density, and temperature ratio can significantly influence the characteristics of low-frequency wave modes. Moreover, for the collisional dusty plasmas, there is a certain critical value μc of the plasma density ratio #, if μ < μc, the width of the waves increases with μ, otherwise the width of waves decreases with μ.
Kh. H. EL-SHORBAGY
2008-01-01
The effect of a high frequency (HF) electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electro-static wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of rel-ativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.
Relativistic two-boson system in presence of electromagnetic plane waves
Droz-Vincent, Philippe
2015-01-01
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two conter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem concerning five degrees of freedom.
Terahertz radiation emission from plasma beat-wave interactions with a relativistic electron beam
Gupta, D. N.; Kulagin, V. V.; Suk, H.
2017-10-01
We present a mechanism to generate terahertz radiation from laser-driven plasma beat-wave interacting with an electron beam. The theory of the energy transfer between the plasma beat-wave and terahertz radiation is elaborated through nonlinear coupling in the presence of a negative-energy relativistic electron beam. An expression of terahertz radiation field is obtained to find out the efficiency of the process. Our results show that the efficiency of terahertz radiation emission is strongly sensitive to the electron beam energy. Emitted field strength of the terahertz radiation is calculated as a function of electron beam velocity.
THE SIMULATION OF THE SAR IMAGE OF INTERNAL SOLITARY WAVES IN ALBORAN SEA
无
2001-01-01
SAR imaging mechanism of internal wave is studied. The numerical modelling of internal waves is obtained by the two-level scheme. The simulaed SAR images that have better expressed the features of internal waves are given by the internal waves SAR imaging theory and numerical modelling result.
Relativistic Covariance and Quark-Diquark Wave Functions
Dillig, M
2006-01-01
We derive covariant wave functions for hadrons composed of two constituents for arbitrary Lorentz boosts. Focussing explicitly on baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to covariant 3-dimensional forms by projecting on the relative quark-diquark energy. Guided by a phenomenological multi gluon exchange representation of covariant confining kernels, we derive explicit solutions for harmonic confinement and for the MIT Bag Model. We briefly sketch implications of breaking the spherical symmetry of the ground state and the transition from the instant form to the light cone via the infinite momentum frame.
Li, Shi-You; Deng, Xiao-Hua; Zhou, Meng; Yuan, Zhi-Gang; Wang, Jing-Fang; Lin, Xi; Lin, Min-Hui; Fu, Song
2010-01-01
Electrostatic solitary waves (ESWs) are observed in the vicinity of the magnetic null of the widely studied magnetic reconnection taking place at the near-earth tail when current sheet becomes dramatic thinning during substorm time on 1 October 2001. We use the Imada method for the 2-D reconnection model and study the characteristics of ESWs near the X-line region and the magnetic null points. The result shows that the amplitude of the observed ESWs in the vicinity of X-line region ranges from 0.1 mV/m to 5 mV/m, and the amplitude is larger near the magnetic null points. The generation mechanism and the role of ESWs associated with magnetic reconnection are also discussed.
Dokgo, Kyunghwan; Woo, Minho; Choi, Cheong-Rim; Min, Kyoung-Wook; Hwang, Junga
2016-09-01
Generation of coherent ion acoustic solitary waves (IASWs) in inhomogeneous plasmas by an odd eigenmode (OEM) of electron holes (EHs) is investigated using 1D electrostatic particle-in-cell (PIC) simulations. The OEM oscillates at a frequency comparable to the trapped electron bouncing frequency, as also demonstrated by Lewis' theoretical formalism about the linear eigenmode in Bernstein-Greene-Kruskal (BGK) equilibrium. The density gradient in the inhomogeneous plasmas causes asymmetry in the EH potential structure associated with the OEM, whose amplitude grows rapidly as it propagates through the density gradient region. As the ions interact with this asymmetric potential, which oscillates slowly enough for the ions to respond, they are ejected to the lower density side with a larger potential amplitude, forming a chain of IASWs coherently with the oscillation of the OEM.
Relativistic two-, three- and four-body wave equations in scalar QFT
Emami-Razavi, Mohsen; Darewych, Jurij W [Centre for Research in Earth and Space Science and Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3 (Canada)
2005-09-01
We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schroedinger non-relativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.
Theoretical analysis of a relativistic travelling wave tube filled with plasma
Xie Hong-Quan; Liu Pu-Kun
2007-01-01
A cold and uniform plasma-filled travelling wave tube with sinusoidally corrugated slow wave structure is driven by a finite thick annular intense relal:ivistic electron beam with the entire system immersed in a strong longitudinal magnetic field.By means of the linear field theory,the dispersion relation for the relativistic travelling wave tube (RTWT) is derived.By numerical computation,the dispersion characteristics of the RTWT are analysed in difierent cases of various geometric parameters of the slow wave structure and plasma densities.Also the gain versus frequency for three difierent plasma densities and the peak gain of the tube versus plasma density are analysed.Some useful results are obtained on the basis of the discussion.
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao
2017-09-01
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.
Guo, Shimin; Mei, Liquan; He, Ya-Ling; Ma, Chenchen; Sun, Youfa
2016-10-01
The nonlinear behavior of an ion-acoustic wave packet is investigated in a three-component plasma consisting of warm ions, nonthermal electrons and positrons. The nonthermal components are assumed to be inertialess and hot where they are modeled by the kappa distribution. The relevant processes, including the kinematic viscosity amongst the plasma constituents and the collision between ions and neutrals, are taken into consideration. It is shown that the dynamics of the modulated ion-acoustic wave is governed by the generalized complex Ginzburg-Landau equation with a linear dissipative term. The dispersion relation and modulation instability criterion for the generalized complex Ginzburg-Landau equation are investigated numerically. In the general dissipation regime, the effect of the plasma parameters on the dissipative solitary (dissipative soliton) and shock waves is also discussed in detail. The project is supported by NSF of China (11501441, 11371289, 11371288), National Natural Science Foundation of China (U1261112), China Postdoctoral Science Foundation (2014M560756), and Fundamental Research Funds for the Central Universities (xjj2015067).
2006-06-01
sech2 wave form is used because the amplitude and horizontal displacement are solutions of the Korteweg de Vries ( KdV ) non linear wave equation which...a solution to the KDV wave equation . After making the frozen field approximation, the soliton can be represented by the following mathematical...scattering. 3. The Gaussian Soliton As discussed, the sech2 form of a soliton is chosen because it is an exact solution to the KDV wave equation . For
Analytic Representation of Relativistic Wave Equations I The Dirac Case
Tepper, L; Zachary, W W
2003-01-01
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the wave functions, as is done by the Foldy-Wouthuysen method, and reveals the nonlocal time behavior of the particle-antiparticle relationship. It is well known that the Foldy-Wouthuysen transformation leads to a diagonalization that is nonlocal in space. We interpret the zitterbewegung, and the result that a velocity measurement (of a Dirac particle) at any instant in time is +(-)c, as reflections of the fact that the Dirac equation makes a spatially extended particle appear as a point in the present by forcing it to oscillate between the past and future at speed c. This suggests that although the Dirac Hamiltonian and the square-root Hamiltonian, are mathematically, they are not physically, equivalent. Furthermore, we see that alt! ho! ugh the form of the Dirac equation serve...
Ion-acoustic rogue waves and breathers in relativistically degenerate electron-positron plasmas
Abdikian, A.; Ismaeel, S.
2017-08-01
In this paper, we employ a weakly relativistic fluid model to study the nonlinear amplitude modulation of electrostatic waves in an unmagnetized electron-positron-ion plasma. It is assumed that the degeneracy pressure law for electrons and positrons follows the Chandrasekhar limit of state whereas ions are warm and classical. The hydrodynamic approach along with the perturbation method have been applied to obtain the corresponding nonlinear Schrödinger equation (NLSE) in which nonlinearity is in balance with the dispersive terms. Using the NLSE, we could evaluate the modulational instability to show that various types of localized ion acoustic excitations exist in the form of either bright-type envelope solitons or dark-type envelope solitons. The regions of the stable and unstable envelope wave have been confined punctually for various regimes. Furthermore, it is proposed that the exact solutions of the NLSE for breather waves are the rogue waves (RWs), Akhmediev breather (AB), and Kuznetsov-Ma breather (KM) soliton. In order to show that the characteristics of breather structures is influenced by the plasma parameters (namely, relativistic parameter, positron concentration, and ionic temperature), the relevant numerical analysis of the NLSE is examined. In particular, it is observed that by increasing the values of the mentioned plasma parameters, the amplitude of the RWs will be decreased. Our results help researchers to explain the formation and dynamics of nonlinear electrostatic excitations in super dense astrophysical regimes.
Touil, B.; Bendib, A.; Bendib-Kalache, K.
2017-02-01
The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.
Relativistic electron beam driven longitudinal wake-wave breaking in a cold plasma
Bera, Ratan Kumar; Sengupta, Sudip; Das, Amita
2016-01-01
Space-time evolution of relativistic electron beam driven wake-field in a cold, homogeneous plasma, is studied using 1D-fluid simulation techniques. It is observed that the wake wave gradu- ally evolves and eventually breaks, exhibiting sharp spikes in the density profile and sawtooth like features in the electric field profile [1]. It is shown here that the excited wakefield is a longitudi- nal Akhiezer-Polovin mode [2] and its steepening (breaking) can be understood in terms of phase mixing of this mode, which arises because of relativistic mass variation effects. Further the phase mixing time (breaking time) is studied as a function of beam density and beam velocity and is found to follow the well known scaling presented in ref.[3].
LISA sensitivities to gravitational waves from relativistic metric theories of gravity
Tinto, Massimo; Alves, Márcio Eduardo Da Silva
2010-12-01
The direct observation of gravitational waves will provide a unique tool for probing the dynamical properties of highly compact astrophysical objects, mapping ultrarelativistic regions of space-time, and testing Einstein’s general theory of relativity. LISA (Laser Interferometer Space Antenna), a joint National Aeronautics and Space Administration and European Space Agency mission to be launched in the next decade, will perform these scientific tasks by detecting and studying low-frequency cosmic gravitational waves through their influence on the phases of six modulated laser beams exchanged between three remote spacecraft. By directly measuring the polarization components of the waves LISA will detect, we will be able to test Einstein’s theory of relativity with good sensitivity. Since a gravitational wave signal predicted by the most general relativistic metric theory of gravity accounts for six polarization modes (the usual two Einstein’s tensor polarizations as well as two vector and two scalar wave components), we have derived the LISA time-delay interferometric responses and estimated their sensitivities to vector- and scalar-type waves. We find that (i) at frequencies larger than roughly the inverse of the one-way light time (≈6×10-2Hz), LISA is more than ten times sensitive to scalar-longitudinal and vector signals than to tensor and scalar-transverse waves, and (ii) in the low part of its frequency band is equally sensitive to tensor and vector waves and somewhat less sensitive to scalar signals.
Hughes, Stephen Fôn; Thomas-Wright, Samantha Jayne; Banwell, Joseph; Williams, Rachel; Moyes, Alyson Jayne; Mushtaq, Sohail; Abdulmajed, Mohamed; Shergill, Iqbal
2015-01-01
The number of patients undergoing shock wave lithotripsy (SWL) in the UK for solitary unilateral kidney stones is increasing annually. The development of postoperative complications such as haematuria and sepsis following SWL is likely to increase. Comparing a range of biological markers with the aim of monitoring or predicting postoperative complications following SWL has not been extensively researched. The main purpose of this pilot-study was to test the hypothesis that SWL results in changes to haemostatic function. Subsequently, this pilot-study would form a sound basis to undertake future investigations involving larger cohorts. Twelve patients undergoing SWL for solitary unilateral kidney stones were recruited. From patients (8 male and 4 females) aged between 31-72 years (median-43 years), venous blood samples were collected pre-operatively (baseline), at 30, 120 and 240 minutes postoperatively. Specific haemostatic biomarkers [platelet counts, prothrombin time (PT), activated partial thromboplastin time (aPTT), fibrinogen, D-dimer, von Willebrand Factor (vWF), sE-selectin and plasma viscosity (PV)] were measured. Platelet counts and fibrinogen concentration were significantly decreased following SWL (p = 0.027 and p = 0.014 respectively), while D-dimer and vWF levels significantly increased following SWL (p = 0.019 and p = 0.001 respectively). PT, APTT, sE-selectin and PV parameters were not significantly changed following SWL (p>0.05). Changes to specific biomarkers such as plasma fibrinogen and vWF suggest that these represent a more clinically relevant assessment of the extent of haemostatic involvement following SWL. Analysis of such markers, in the future, may potentially provide valuable data on "normal" response after lithotripsy, and could be expanded to identify or predict those patients at risk of coagulopathy following SWL. The validation and reliability will be assessed through the assessment of larger cohorts.
Stephen Fôn Hughes
Full Text Available PURPOSE: The number of patients undergoing shock wave lithotripsy (SWL in the UK for solitary unilateral kidney stones is increasing annually. The development of postoperative complications such as haematuria and sepsis following SWL is likely to increase. Comparing a range of biological markers with the aim of monitoring or predicting postoperative complications following SWL has not been extensively researched. The main purpose of this pilot-study was to test the hypothesis that SWL results in changes to haemostatic function. Subsequently, this pilot-study would form a sound basis to undertake future investigations involving larger cohorts. METHODS: Twelve patients undergoing SWL for solitary unilateral kidney stones were recruited. From patients (8 male and 4 females aged between 31-72 years (median-43 years, venous blood samples were collected pre-operatively (baseline, at 30, 120 and 240 minutes postoperatively. Specific haemostatic biomarkers [platelet counts, prothrombin time (PT, activated partial thromboplastin time (aPTT, fibrinogen, D-dimer, von Willebrand Factor (vWF, sE-selectin and plasma viscosity (PV] were measured. RESULTS: Platelet counts and fibrinogen concentration were significantly decreased following SWL (p = 0.027 and p = 0.014 respectively, while D-dimer and vWF levels significantly increased following SWL (p = 0.019 and p = 0.001 respectively. PT, APTT, sE-selectin and PV parameters were not significantly changed following SWL (p>0.05. CONCLUSIONS: Changes to specific biomarkers such as plasma fibrinogen and vWF suggest that these represent a more clinically relevant assessment of the extent of haemostatic involvement following SWL. Analysis of such markers, in the future, may potentially provide valuable data on "normal" response after lithotripsy, and could be expanded to identify or predict those patients at risk of coagulopathy following SWL. The validation and reliability will be assessed through the assessment of
Chen, Zaigao; Wang, Jianguo; Wang, Yue; Qiao, Hailiang; Zhang, Dianhui; Guo, Weijie
2013-11-01
Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.
Observation of Self-Sustaining Relativistic Ionization Wave Launched by a Sheath Field
McCormick, M.; Arefiev, A. V.; Quevedo, H. J.; Bengtson, R. D.; Ditmire, T.
2014-01-01
We present experimental evidence supported by simulations of a relativistic ionization wave launched into a surrounding gas by the sheath field of a plasma filament with high energy electrons. Such a filament is created by irradiating a clustering gas jet with a short pulse laser (115 fs) at a peak intensity of 5×1017 W/cm2. We observe an ionization wave propagating radially through the gas for about 2 ps at 0.2-0.5 c after the laser has passed, doubling the initial radius of the filament. The gas is ionized by the sheath field, while the longevity of the wave is explained by a moving field structure that traps the high energy electrons near the boundary, maintaining a strong sheath field despite the significant expansion of the plasma.
Observation of Self-Sustaining Relativistic Ionization Wave Launched by Sheath Field
McCormick, M W; Quevedo, H J; Bengtson, R D; Ditmire, T
2013-01-01
We present experimental evidence supported by simulations of a relativistic ionization wave launched into surrounding gas by the sheath field of a plasma filament with high energy electrons. Such filament is created by irradiating a clustering gas jet with a short pulse laser ($\\sim$115 fs) at a peak intensity of $5 \\times 10^{17}$ W/cm$^2$. We observe an ionization wave propagating radially through the gas for about 2 ps at 0.2-0.5 $c$ after the laser has passed, doubling the initial radius of the filament. The gas is ionized by the sheath field, while the longevity of the wave is explained by a moving field structure that traps the high energy electrons near the boundary, maintaining a strong sheath field despite the significant expansion of the plasma.
Caballero, J.A. [Univ. de Sevilla (Spain). Dept. de Fisica Atomica, Molecular y Nucl.]|[Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Donnelly, T.W. [Centre for Theoretical Physics, Laboratory for Nuclear Science and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (United States); Moya de Guerra, E. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Udias, J.M. [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040 (Spain)
1998-03-23
The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function. (orig.). 30 refs.
Strumik, Marek; Stasiewicz, Krzysztof
2017-02-01
We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge-Kutta advancing in time and Kurganov-Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.
A five-wave Harten-Lax-van Leer Riemann solver for relativistic magnetohydrodynamics
Mignone, A.; Ugliano, M.; Bodo, G.
2009-03-01
We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.
Modified ion-acoustic solitary waves in plasmas with field-aligned shear flows
Saleem, H. [Department of Space Science, Institute of Space Technology, 1-Islamabad Highway, Islamabad (Pakistan); Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); Ali, S. [Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); National Centre for Physics (NCP) at Quaid-i-Azam University Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Haque, Q. [Theoretical Research Institute, Pakistan Academy of Sciences, 3-Constitution Avenue G-5/3, Islamabad (Pakistan); National Centre for Physics (NCP) at Quaid-i-Azam University Campus, Shahdra Valley Road, Islamabad 44000 (Pakistan); Theoretical Physics Division, PINSTECH, P.O. Nilore, Islamabad (Pakistan)
2015-08-15
The nonlinear dynamics of ion-acoustic waves is investigated in a plasma having field-aligned shear flow. A Korteweg-deVries-type nonlinear equation for a modified ion-acoustic wave is obtained which admits a single pulse soliton solution. The theoretical result has been applied to solar wind plasma at 1 AU for illustration.
Relativistic quantum mechanical spin-1 wave equation in 2+1 dimensional spacetime
Dernek, Mustafa; Sucu, Yusuf; Unal, Nuri
2016-01-01
In the study, we introduce a relativistic quantum mechanical wave equation of the spin-1 particle as an excited state of the zitterbewegung and show that it is consistent with the 2+1 dimensional Proca theory. At the same time, we see that this equation has two eigenstates, particle and antiparticle states or negative and positive energy eigenstates, respectively, in the rest frame and the spin-1 matrices satisfy $SO(2,1)$ spin algebra. As practical applications, we derive the exact solutions of the equation in the presence of a constant magnetic field and a curved spacetime. From these solutions, we construct the current components of the spin-1 particle.
Hadron Mass Spectra and Decay Rates in a Potential Model with Relativistic Wave Equations.
Namgung, Wuk
Hadron properties of mass spectra and decay rates are calculated in a quark potential model. Wave equations based on the Klein-Gordon and Todorov equations both of which incorporate the feature of relativistic two-body kinematics are used. The wave equations are modified to contain potentials which transform either like a Lorentz scalar or like a time-component of a four-vector. Potentials based on the Fogleman-Lichtenberg-Wills potential which has the properties suggested by QCD of both confinement and asymptotic freedom are used. The potentials, motivated by QCD but otherwise phenomenological, are further generalized to forms which can apply to any color representation. To break the degeneracy between vector and pseudoscalar mesons or between spin-3/2 and spin-1/2 baryons, the essential feature of spin dependence is included in the potentials. The masses of vector and pseudoscalar mesons are calculated with only a small number of adjustable parameters, and good qualitative agreement with experiment is obtained for both heavy and light mesons. Baryons are treated in this framework by making use of a quark-diquark two-body model of baryons. First, diquark properties are calculated without any additional parameters. The g-factors of diquarks and spin-flavor configuration of baryons, which are necessary for the calculation of baryons, are given. Then baryon masses are calculated also without additional parameters. The results of the masses of ground-state baryons are in good qualitative agreement with experiment. Also effective constituent quark masses are obtained using current quark masses as input. The calculated effective constituent quark masses are in the right range of the values that most theoretical estimates have given. The general qualitative features of hadron spectra are similar with the two relativistic wave equations, although there are differences in detail. The Van Royen-Weisskopf formula for electromagnetic decay widths of vector mesons into lepton
J. S. Pickett
2009-06-01
Full Text Available Electrostatic Solitary Waves (ESWs have been observed by several spacecraft in the current layers of Earth's magnetosphere since 1982. ESWs are manifested as isolated pulses (one wave period in the high time resolution waveform data obtained on these spacecraft. They are thus nonlinear structures generated out of nonlinear instabilities and processes. We report the first observations of ESWs associated with the onset of a super-substorm that occurred on 24 August 2005 while the Cluster spacecraft were located in the magnetotail at around 18–19 R_{E} and moving northward from the plasma sheet to the lobes. These ESWs were detected in the waveform data of the WBD plasma wave receiver on three of the Cluster spacecraft. The majority of the ESWs were detected about 5 min after the super-substorm onset during which time 1 the PEACE electron instrument detected significant field-aligned electron fluxes from a few 100 eV to 3.5 keV, 2 the EDI instrument detected bursts of field-aligned electron currents, 3 the FGM instrument detected substantial magnetic fluctuations and the presence of Alfvén waves, 4 the STAFF experiment detected broadband electric and magnetic waves, ion cyclotron waves and whistler mode waves, and 5 CIS detected nearly comparable densities of H+ and O+ ions and a large tailward H+ velocity. We compare the characteristics of the ESWs observed during this event to those created in the laboratory at the University of California-Los Angeles Plasma Device (LAPD with an electron beam. We find that the time durations of both space and LAPD ESWs are only slightly larger than the respective local electron plasma periods, indicating that electron, and not ion, dynamics are responsible for generation of the ESWs. We have discussed possible mechanisms for generating the ESWs in space, including the beam and kinetic Buneman type instabilities and the acoustic instabilities. Future studies will examine these mechanisms in
Zhang, Hong Lin; Sampson, D.H. (Pennsylvania State Univ., University Park, PA (USA). Dept. of Astronomy)
1990-10-22
The rapid relativistic distorted wave method of Zhang et al for excitation, which uses the atomic structure data of Sampson et al, has been extended to ionization. In this approach the same Dirac-Fock-Slater potential evaluated using a single mean configuration is used in calculating the orbitals of all electrons bound and free. Values for the cross sections Q for ionization of various ions have been calculated and generally good agreement is obtained with other recent relativistic calculations. When results are expressed in terms of the reduced ionization cross section Q{sub R}, which is proportional to I{sup 2}Q, they are close to the non-relativistic Coulomb-Born-Exchange values of Moores et al for hydrogenic ions except for high Z and/or high energies. This suggests that fits of the Q{sub R} to simple functions of the impact electron energy in threshold units with coefficients that are quite slowly varying functions of an effective Z can probably be made. This would be convenient for plasma modeling applications. 24 refs., 2 tabs.
Gamayunov, K. V.; Khazanov, G. V.
2007-01-01
We consider the effect of oblique EMIC waves on relativistic electron scattering in the outer radiation belt using simultaneous observations of plasma and wave parameters from CRRES. The main findings can be s ummarized as follows: 1. In 1comparison with field-aligned waves, int ermediate and highly oblique distributions decrease the range of pitc h-angles subject to diffusion, and reduce the local scattering rate b y an order of magnitude at pitch-angles where the principle absolute value of n = 1 resonances operate. Oblique waves allow the absolute va lue of n > 1 resonances to operate, extending the range of local pitc h-angle diffusion down to the loss cone, and increasing the diffusion at lower pitch angles by orders of magnitude; 2. The local diffusion coefficients derived from CRRES data are qualitatively similar to the local results obtained for prescribed plasma/wave parameters. Conseq uently, it is likely that the bounce-averaged diffusion coefficients, if estimated from concurrent data, will exhibit the dependencies similar to those we found for model calculations; 3. In comparison with f ield-aligned waves, intermediate and highly oblique waves decrease th e bounce-averaged scattering rate near the edge of the equatorial lo ss cone by orders of magnitude if the electron energy does not excee d a threshold (approximately equal to 2 - 5 MeV) depending on specified plasma and/or wave parameters; 4. For greater electron energies_ ob lique waves operating the absolute value of n > 1 resonances are more effective and provide the same bounce_averaged diffusion rate near the loss cone as fiel_aligned waves do.
Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB
Khazanov, G. V.; Gamayunov, K. V.
2007-01-01
We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.
Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun
In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.
Uday Narayan Ghosh; Prasantha Chatterjee; Deb Kumar Ghosh
2013-10-01
Interaction of nonplanar ion-acoustic solitary waves is an important source of information for studying the nature and characteristics of ion-acoustic solitary waves (IASWs). The head-on collision between two cylindrical/spherical IASWs in un-magnetized plasmas comprising of nonthermal distributed electrons and warm ions is investigated using the extended version of Poincaré–Lighthill–Kuo (PLK) perturbation method. How the interactions are taking place in cylindrical and spherical geometries are shown numerically. Analytical phase shifts are derived for nonplanar geometry. The effects of the ion to electron temperature parameter and the nonthermal electrons parameter on the phase shift are studied. It is shown that the properties of the interaction of IASWs in different geometries are very different.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Terahertz relativistic spatial solitons in doped graphene metamaterials
Dong, Haiming; Biancalana, Fabio
2011-01-01
We propose an electrically tunable graphene-based metamaterial showing a large nonlinear optical response at THz frequencies, which we calculate analytically for the first time to our knowledge and arises from the intraband current. The structure sustains a novel type of stable two-dimensional spatial solitary wave, a relativistic version of the Townes soliton. These results can be also applied to any material exhibiting a conical dispersion with massless Dirac fermions.
Hafez, M. G.; Roy, N. C.; Talukder, M. R.; Hossain Ali, M.
2016-09-01
This work investigates the oblique nonlinear propagation of ion acoustic (IA) shock waves for both weakly and highly relativistic plasmas composed of nonthermal electrons and positrons with relativistic thermal ions. The KdVB-like equation, involving dispersive, weakly transverse dispersive, nonlinearity and dissipative coefficients, is derived employing the well known reductive perturbation method. The integration of this equation is carried out by the {tanh} method taking the stable shock formation condition into account. The effects of nonthermal electrons and positrons, nonthermal electrons with isothermal positrons, isothermal electrons with nonthermal positrons, and isothermal electrons and positrons on oblique propagation of IA shock waves in weakly relativistic regime are described. Furthermore, the effects of plasma parameters on oblique propagation of IA shock waves in highly relativistic regime are discussed and compared with weakly relativistic case. It is seen that the plasma parameters within certain limits significantly modify the structures of the IA shock waves in both cases. The results may be useful for better understanding of the interactions of charged particles with extra-galactic jets as well as astrophysical compact objects.
Wen－QingLu
1993-01-01
A boundary element method has been developed for analysing heat transport phenomena in solitary wave on falling thin liquid films at high Reynolds numbers.The divergence theorem is applied to the non-linear convective volume integral of the boundary element formulation with the pressure penalty function.Consequently,velocity and temperature gradients are dliminated.and the complete formulation is written in terms of velocity and temperature,This provides considerable reduction is storage and computational requirements while improving accuracy.The non-linear equation systems of boundary element discretization are solved by the quasi-Nweton iterative scheme with Broyden's update.The streamline maps and the temperature distributions in solitary wave and wavy film flow have been obtained,and the variations of Nusselt numbers along the wall-liquid interface are also given.There are large cross-flow velocities and S-shape temperature distributions in the recirculating region of solitary wave.This special flow and thermal process can be a mechanism to enhance heat transport.
Investigation of a K-band large coaxial relativistic backward wave oscillator
Zeng, Fanzheng, E-mail: zengfanzheng92@163.com; Du, Guangxing; Wang, Honggang; Shi, Difu [College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China)
2016-01-15
A K-band large coaxial relativistic backward wave oscillator has been investigated by the 2.5-D particle-in-cell code. This device can generate high-power microwave at a constant frequency with a constant efficiency by increasing the radius of the electron beam and the average radius of the slow-wave structure. The simulation results show that the power conversion efficiency can reach 38.8% at the frequency of 25.48 GHz with the output power of 1.65 GW, while the electron beam has the energy of 196 kV and carries the current of 21.6 kA guided by the magnetic field of 2.5 T.
A compact relativistic backward-wave oscillator with metallized plastic components
Ge, Xingjun; Zhang, Jun; Zhong, Huihuang; Qian, Baoliang
2014-09-01
This letter presents the mechanism and realization of a compact relativistic backward-wave oscillator with metallized plastic components. The physical idea, specific structure, and the main testing results are presented. The three periods slow-wave structures with both inner and outer ripples and the coaxial extractor are designed to reduce the volume and increase the efficiency of the device. The metallized plastic components replacing the stainless steel components in the high power microwave (HPM) sources are put forward to reduce the device weight. In the initial experiment, a microwave with frequency of 1.54 GHz, power of 1.97 GW, efficiency of 33.5%, and pulse duration above 47 ns is generated, which proves that this technical route is feasible. Undoubtedly, the technical route can provide a guide to design other types of HPM sources and be benefit to the practical application of the compact HPM systems.
A viscous blast-wave model for relativistic heavy-ion collisions
Jaiswal, Amaresh
2015-01-01
Using a viscosity-based survival scale for geometrical perturbations formed in the early stages of relativistic heavy-ion collisions, we model the radial flow velocity during freeze-out. Subsequently, we employ the Cooper-Frye freeze-out prescription, with first-order viscous corrections to the distribution function, to obtain the transverse momentum distribution of particle yields and flow harmonics. For initial eccentricities, we use the results of Monte Carlo Glauber model. We fix the blast-wave model parameters by fitting the transverse momentum spectra of identified particles at the Large Hadron Collider (LHC) and demonstrate that this leads to a fairly good agreement with transverse momentum distribution of elliptic and triangular flow for various centralities. Within this viscous blast-wave model, we estimate the shear viscosity to entropy density ratio $\\eta/s\\simeq 0.24$ at the LHC.