共查询到20条相似文献,搜索用时 31 毫秒
1.
The influence of magnetic field on the process of steepening or flattening of the characteristic wave fronts in a plane and cylindrically symmetric motion of an ideal plasma is investigated. This aspect of the problem has not been considered until now. Remarkable differences between plane, cylindrical diverging, and cylindrical converging waves are discovered. For instance, when the adiabatic index γ is 2, the magnetic field does not affect the behaviour of plane waves, but does affect cylindrical waves. As the field strength increases, the time tc taken for the shock formation varies monotonically for plane waves, while for cylindrical waves, in some situations tc exhibits a unique minimum for diverging waves and a unique maximum for converging waves. For cylindrical converging waves, a shock formation takes place if and only if, γ and the field strength are restricted to certain finite intervals. Moreover, tc is bounded in all cases except for cylindrical diverging waves. The discontinuity in the velocity gradient at the wave front is shown to satisfy a Bernoulli-type equation. The discussion of the solutions of such equations reported in the literature is shown to be incomplete, and three general theorems are established. 相似文献
2.
S. A. Aldashev 《Journal of Mathematical Sciences》2011,173(2):150-154
It is known that waves (acoustic waves, radio waves, elastic waves, and electric waves) in cylindrical tubes are described by the wave equation. In the theory of hyperbolic-type partial differential equations, boundary-value problems with data on the whole boundary serve as examples of ill-posedness of the posed problems. In this work, it is shown that the Poincar´e problem in a cylindrical domain for the higher-dimensional wave equation is uniquely solvable. A uniqueness criterion for a regular solution is also obtained. 相似文献
3.
Shalini Bagchi Kasturi Roychowdhury A.P. Mishra A. Roy Chowdhury 《Communications in Nonlinear Science & Numerical Simulation》2010,15(2):275-280
Excitation of nonlinear waves in a quantum dusty plasma with various effects is analyzed when the geometry is cylindrical.This introduces the effect of finite boundary conditions on the solitary waves so generated. it is observed that the nonlinear equation deduced is cylindrical KP–Burger type leading to the generation of Shock Wave. Different situations which arises in various parameter regions are considered separately and the form of the nonlinear excitations are obtained explicitly. 相似文献
4.
I.G. Khusainov 《Journal of Applied Mathematics and Mechanics》2013,77(3):321-329
The reflection and transmission of harmonic waves and waves of finite duration through the boundary of the perforated part of a cylindrical channel (a lined borehole), filled with a fluid and surrounded by a permeable porous medium, is investigated. A model of the plane time-varying fluid flow in the cylindrical channel in a quasi-one-dimensional approximation and of the seepage absorption of the fluid in the porous medium surrounding the channel is presented. The effect of the collector characteristics of the porous medium surrounding the channel and the quality of the perforation (the length of the perforation channels) on the evolution of the waves when they are reflected from the boundary of the perforated part of the wall are investigated. 相似文献
5.
A. R. Snitser 《Journal of Mathematical Sciences》2001,107(6):4386-4394
Biot [5] examined the propagation of waves along the free surface of a cylindrical cavity in an elastic body of infinite extent and obtained a dispersion relation for the velocity of this wave in terms of the ratio of the wavelength to the cavity diameter. This paper contains solutions for waves in a semiinfinite elastic medium with a cylindrical cavity with axially symmetric harmonic loading of the plane surface. The solutions are expressed in terms of Lame potentials which are represented by combinations of integrals containing trigonometric kernels and kernels of Weber transforms. A solution is obtained for volume waves and Biot waves. The relative velocity and relative length of surface waves are studied as functions of the loading frequency. 相似文献
6.
This work deals with the analytical and numerical simulation of the loads on cylindrical offshore structures due to breaking waves. We investigate breaking waves impact on a cylindrical structure on the surface of the water by using a multiphase flow model of immiscible fluids based on the Volume of Fluid (VOF) method. Different numerical schemes are applied to identify the sharp interface between water and gas. The results are compared as well with the already existing experimental, analytical and numerical studies by [1-3]. The agreement shows that the analytical and numerical models are suited to describe the experimental results. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Alexander A. Chernitskii 《Advances in Applied Clifford Algebras》2005,15(1):27-54
Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered.
Functional product and infinitesimal operators for translation and rotation groups are introduced, where unit pseudoscalar
or hyperimaginary unit is used instead of imaginary unit. Basic systems of orthogonal functions (plane waves, cylindrical,
and spherical) for space-time multivectors are built by using the introduced infinitesimal operators. Appropriate orthogonal
decompositions for electromagnetic field are presented. These decompositions are applied to nonlinear electrodynamics. Appropriate
first order equation systems for cylindrical and spherical radial functions are obtained. Plane waves, cylindrical, and spherical
solutions to the linear electrodynamics are represented by using the introduced orthogonal functions. A decomposition of a
plane wave in terms of the introduced spherical harmonics is obtained. 相似文献
8.
9.
V.O. Kalvine P. Neittaanmaki B.A. Plamenevskii 《Journal of Mathematical Sciences》2004,122(3):3212-3245
In a domain with finitely many cylindrical ends at infinity, we consider dissipative and formally selfadjoint elliptic problems for systems of differential equations of arbitrary order. As is known, one can regard cylindrical ends as waveguides and introduce families of incoming and outgoing waves. The amplitudes of such waves can grow at infinity at power or even exponential rate. The scattering matrices account finitely many waves. We suggest and justify a numerical method for finding such scattering matrices. Bibliography: 18 titles. 相似文献
10.
Rotary gravity waves in a partially filled vertical cylindrical container excited by a rotating disc at the top of the cylinder are investigated. Analytical results for the growth rate of the waves are reported. Moreover, the development of the wave is shown in an experiment. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Interference attenuating waves traveling in a cylindrical elastic waveguide, placed in an elastic medium, are considered. The group velocity of these waves is intermediate between that of the P wave and that of the S wave; the phase velocity equals that of the P wave. The frequency of the waves is almost constant and is determined by the requirement of constructive interference. The dispersion and attenuation of these waves are described. Bibliography: 3 titles. 相似文献
12.
Scattering of waves obliquely incident on small cylindrical undulations at the bottom of a two-layer fluid wherein the upper layer has a free surface and the lower layer has an undulating bottom, is investigated here assuming linear theory. There exists two modes of time-harmonic waves propagating at each of the free surface and the interface. Due to an obliquely incident wave of a particular mode, reflected and transmitted waves of both the modes are created in general by the bottom undulations. For small undulations, a simplified perturbation analysis is used to obtain first-order reflection and transmission coefficients of both the modes due to oblique incidence of waves of again both modes, in terms of integrals involving the shape function describing the bottom. For sinusoidal undulations, these coefficients are plotted graphically to illustrate the energy transfer between the waves of different modes induced by the bottom undulations. 相似文献
13.
Elastic wave propagation in a cylindrical bore situated in a micropolar elastic medium with stretch 总被引:2,自引:0,他引:2
Propagation of surface elastic waves in a cylindrical bore through a micropolar elastic medium with stretch is analysed in
two cases. In the first case, the cylindrical bore is considered empty while in the second case, the bore is filled with homogeneous
inviscid liquid. In both the problems, period equations are obtained in closed form. The problem of Banerji and Sengupta [2,3]
has been reduced as a special case. Numerical calculations have been performed for a particular model and results obtained
are presented graphically. It is noticed that the effect of micropolarity on dispersion curve is significant while the effect
of micro-stretch on dispersion curve is not appreciable. 相似文献
14.
Junbao Li Song Shen Min Li Xijun Liu 《Communications in Nonlinear Science & Numerical Simulation》2013,18(7):1710-1724
This paper presents an experimental investigation on nonlinear low frequency gravity water waves in a partially filled cylindrical shell subjected to high frequency horizontal excitations. The characteristics of natural frequencies and mode shapes of the water–shell coupled system are discussed. The boundaries for onset of gravity waves are measured and plotted by curves of critical excitation force magnitude with respect to excitation frequency. For nonlinear water waves, the time history signals and their spectrums of motion on both water surface and shell are recorded. The shapes of water surface are also measured using scanning laser vibrometer. In particular, the phenomenon of transitions between different gravity wave patterns is observed and expressed by the waterfall graphs. These results exhibit pronounced nonlinear properties of shell–fluid coupled system. 相似文献
15.
16.
The propagation of the weak discontinuities in binary non-reacting mixtures of classical ideal monoatomic gases is analyzed. The normal speeds of propagation are determined and compared with those of a single fluid. The differential equation governing the growth and the decay of the acceleration waves is obtained and the solutions for plane, cylindrical and spherical waves are shown. The influence of the different atomic masses of the constituents is also investigated. 相似文献
17.
A new class of exact solutions is obtained for the diffraction of waves on a nonsymmetric nonuniform cylindrical scatterer whose properties depend on two coordinates, radial and angular. 相似文献
18.
P. N. Soroka 《Journal of Mathematical Sciences》1993,66(2):2187-2192
A ray method based on geometrical optics is applied to solve the problem of propagation of harmonic elastic waves excited by the perturbation of the surface of a noncircular cylindrical cavity. Stresses are computed under plane strain conditions for a cavity in the form of a parabolic cylinder and for a cylindrical cavity with a Munger oval section subjected to a uniform, surface load or a surface load which is a cosinusoidal function of the angle.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 75–82, 1987. 相似文献
19.
Roger Grimshaw 《Studies in Applied Mathematics》2019,143(2):176-191
In this paper, we find suitable initial conditions for the cylindrical Korteweg‐de Vries equation by first solving exactly the initial‐value problem for localized solutions of the underlying axisymmetric linear long‐wave equation. The far‐field limit of the solution of this linear problem then provides, through matching, an initial condition for the cylindrical Korteweg‐de Vries equation. This initial condition is associated only with the leading wave front of the far‐field limit of the linear solution. The main motivation is to resolve the discrepancy between the exact mass conservation law, and the “mass” conservation law for the cylindrical Korteweg‐de Vries equation. The outcome is that in the linear initial‐value problem all the mass is carried behind the wave front, and then the “mass” in the initial condition for the cylindrical Korteweg‐de Vries equation is zero. Hence, the evolving solution in the cylindrical Korteweg‐de Vries equation has zero “mass.” This situation arises because, unlike the well‐known unidirectional Korteweg‐de Vries equation, the solution of the initial‐value problem for the axisymmetric linear long‐wave problem contains both outgoing and ingoing waves, but in the cylindrical geometry, the latter are reflected at the origin into outgoing waves, and eventually the total outgoing solution is a combination of these and those initially generated. 相似文献
20.
Permeable and slotted breakwaters are becoming more popular, in order to reduce the drawback of rigid coastal structures: namely large reflections, forces and overtopping. The linearized theory of water waves is used to examine the diffraction of incident regular waves by a vertically slotted cylindrical breakwater that consists of a number of distinct rigid cylindrical panels. Under the assumption that the wavelength is much greater than the thickness, each segment is replaced by a thin structure and the permeability is modelled by suitable boundary conditions. The first condition is the matching pressure and normal velocity conditions between two internal and external fluid regions and the second condition is zero normal velocity on rigid panels. The mixed boundary–value problem is transformed to dual series relations and the least–square method is applied to get the forces on the structure. The results are presented to illustrate the effects of permeability. Numerical results compare well with McCamy and Fuchs predictions for the limiting case of an impermeable rigid cylinder. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献