共查询到20条相似文献,搜索用时 62 毫秒
1.
Emrullah Yaşar 《Nonlinear dynamics》2008,54(4):307-312
We generate conservation laws for the Burridge–Knopoff equation which model nonlinear dynamics of earthquake faults by a new
conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation
(or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined
by the adjoint equations to the Burridge–Knopoff equation. 相似文献
2.
V. V. Alekhin B. D. Annin V. V. Ostapenko 《Journal of Applied Mechanics and Technical Physics》2008,49(4):580-586
The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along
which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static
equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be
similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved
with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations
are presented.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 74–80, July–August, 2008. 相似文献
3.
Yu. A. Chirkunov 《Journal of Applied Mechanics and Technical Physics》2009,50(3):413-418
A sufficient condition for the absence of tangent transformations admitted by second-order quasi-linear differential equations
and a sufficient condition for linear autonomy of operators of the Lie group of transformations admitted by second-order weakly
nonlinear differential equations are found. A theorem on the structure of the first-order conservation laws for second-order
weakly nonlinear differential equations is proved. A classification of second-order linear differential equations with two
independent variables in terms of first-order conservation laws is proposed.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 64–70, May–June, 2009. 相似文献
4.
The stored energy functional of a homogeneous isotropic elastic body is invariant with respect to translation and rotation
of a reference configuration. One can use Noether's Theorem to derive the conservation laws corresponding to these invariant
transformations. These conservation laws provide an alternative way of formulating the system of equations governing equilibrium
of a homogeneous isotropic body. The resulting system is mathematically identical to the system of equilibrium equations and
constitutive relations, generally, of another material. This implies that each solution of the system of equilibrium equations
gives rise to another solution, which describes the reciprocal deformation and solves the system of equilibrium equations
of another material. In this paper we derive conservation laws and prove the theorem on conjugate solutions for two models
of elastic homogeneous isotropic bodies – the model of a simple material and the model of a material with couple stress (Cosserat
continuum).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
5.
Fractal First-Order Partial Differential Equations 总被引:1,自引:0,他引:1
The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential
operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an
integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of
the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct
a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation
laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities
for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward
the entropy solution of the pure conservation law. 相似文献
6.
Nonlinear gas oscillations in a closed tube driven by the aperiodic motions of a piston as a result of the action of the external
and internal pressure drop are studied. The external pressure takes two values alternating at the moment of change of direction
of motion of the piston. Two models of the motion of the gas are considered. Model 1 is formed by a system of equations representing
the mass, momentum, and entropy conservation laws. As distinct from model 1, model 2 includes the total energy conservation
law in place of the entropy conservation laws.
Kazan’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 134–142, March–April, 1998.
The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 96-01-00484). 相似文献
7.
A system of equations of isentropic gas motion with n ⩾ 2 is classified in terms of zero-order conservation laws with the
use of the method of A-operators. New conservation laws are found to be valid only for potential isentropic motion of the Chaplygin gas. In this
case, the greatest number of nontrivial conservation laws is obtained, with n scalar conservation laws being nonlocal. Additional
properties of symmetry of the considered equations associated with these conservation laws are indicated. 相似文献
8.
Nicolas Besse 《Archive for Rational Mechanics and Analysis》2011,199(2):453-491
The aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags,
which can been viewed as an infinite dimensional system of first-order conservation laws. The waterbag model, which constitutes
a special class of exact weak solution of the Vlasov equation, is well known in plasma physics, and its applications in gyrokinetic
theory and laser–plasma interaction are very promising. The proof of the existence of a continuum of regular waterbags relies
on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations, some results in singular
integral operators theory and harmonic analysis, Riemann–Hilbert boundary value problems and energy estimates. 相似文献
9.
V. V. Ostapenko 《Journal of Applied Mechanics and Technical Physics》2007,48(6):795-812
A method for modeling the propagation of discontinuous waves over a dry bed using the first approximation of shallow water
theory is proposed. The method is based on a modified conservation law of total momentum that takes into account the concentrated
momentum losses due to the formation of local turbulent vortex structures in the fluid surface layer at a discontinuous-wave
front. A quantitative estimate of these losses is obtained by deriving the shallow water equations from the Navier-Stokes
equations with allowance for viscosity, which has a rapidly increasing effect in the turbulent flow regions described by discontinuous
waves. The stability of the discontinuous waves admitted by the modified system of conservation laws of shallow water theory
is examined. As an example, a comparative analysis is performed of the solutions of the dam-break problem obtained for the
classical and modified shallow water models.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 22–43, November–December, 2007 相似文献
10.
L. A. Spodareva 《Journal of Applied Mechanics and Technical Physics》1999,40(6):1111-1115
An inertial flow of a granular material can be described by the laws of conservation of mass, momentum, and energy of random
motion of solid particles by invoking some closing relations. In this work, these closing relations are inferred from the
dimensional theory. The system of equations obtained is used to determine characteristics of a steady flow of a bed of a granular
material down an inclined surface with a microrelief for various Richardson numbers and finite contact times of the particles
during their collisions.
Novosibirsk Military Institute, Novosibirsk 630103. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40,
No. 6, pp. 128–132, November–December, 1999. 相似文献
11.
V. V. Ostapenko 《Journal of Applied Mechanics and Technical Physics》1999,40(5):796-804
A well-posedness criterion for a complete system of conservation laws is proposed that assumes maximum compatibility of the
convexity domain of the closing conservation law with the domain of hyperbolicity of the model used. This criterion is used
to obtain well-posed complete systems of conservation laws for the models of two-layer shallow water with a free-surface (model
I) and with a rigid lid (model II).
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 23–32, September–October, 1999. 相似文献
12.
G. Wolansky 《Archive for Rational Mechanics and Analysis》2009,193(1):57-115
The process of coagulation is associated with scalar conservation laws, where the adhesion particle dynamics results from
shock waves. Conversely, the fragmentation of a massive particle into a number of smaller ones, or into a continuous (dust)
distribution, is associated with rarefaction waves. It is generally agreed that a reversible solution of a conservation law
can include neither shock waves nor the spontaneous emergence of rarefaction waves. The present paper is an attempt to demonstrate
that both coagulation and fragmentation may coexist for a reversible solution, under a natural generalization of the system
of conservation law. This is done by introducing an action principle which includes, in addition to the inertial (kinetic
energy) term, also an appropriately defined internal energy. The above generalization of the system of conservation law appears
as the Euler–Lagrange equations for this action. 相似文献
13.
V. M. Teshukov 《Journal of Applied Mechanics and Technical Physics》1999,40(2):263-275
Generalized characteristics and Riemann invariants that are preserved along the characteristics are found for a kinetic model
of motion of bubbles in a fluid. Conditions that ensure the hyperbolicity of a set of equations of a bubbly flow are obtained.
It is shown that the set of equations of motion has an infinite number of conservation laws. An infinite series of generalized
symmetries admitted by the equations is constructed. Solutions that are invariant under the generalized symmetries of solution
and describe the propagation of running and simple waves in a bubbly fluid are found.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No., 2. pp. 86–100, March–April, 1999. 相似文献
14.
Björn Johannesson 《Transport in Porous Media》2010,85(2):565-592
A numerical scheme for the transient solution of a generalized version of the Poisson–Nernst–Planck (PNP) equations is presented.
The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present
problem iteratively. The PNP equations represent a set of diffusion equations for charged species, i.e. dissolved ions, present
in the pore solution of a rigid porous material in which the surface charge can be assumed neglectable. These equations are
coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst–Planck equations describing
the diffusion of the ionic species and Gauss’ law in use are, however, coupled in both directions. The governing set of equations
is derived from a simplified version of the so-called hybrid mixture theory (HMT). The simplifications used here mainly concerns
ignoring the deformation and stresses in the porous material in which the ionic diffusion occurs. The HMT is a special version
of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macroscale and that
it includes the volume fractions of phases in its structure. The background to the PNP equations can by the HMT approach be
described by using the postulates of mass conservation of constituents together with Gauss’ law used together with consistent
constitutive laws. The HMT theory includes the constituent forms of the quasistatic version of Maxwell’s equations making
it suitable for analyses of the kind addressed in this work. Within the framework of HTM, constitutive equations have been
derived using the postulate of entropy inequality together with the technique of identifying properties by Lagrange multipliers.
These results will be used in obtaining a closed set of equations for the present problem. 相似文献
15.
A large class of wave equations, with dissipation and source terms (Gordon type equations), are analysed using a symmetry
approach and constructing conservation laws. We obtain some, previously unknown, relationships between the conservation laws
and symmetries in the former case. In the latter case, we use the multiplier (and homotopy) approach to construct conservation
laws from which some surprisingly, interesting higher-order variational symmetries and corresponding conserved quantities
are obtained for a large class of Gordon type equations similar to those of the sine-Gordon equation. 相似文献
16.
S. Mizzi R. W. Barber D. R. Emerson J. M. Reese S. K. Stefanov 《Continuum Mechanics and Thermodynamics》2007,19(5):273-283
This paper presents a new technique that combines Grad’s 13-moment equations (G13) with a phenomenological approach to rarefied
gas flows. This combination and the proposed solution technique capture some important non-equilibrium phenomena that appear
in the early continuum-transition flow regime. In contrast to the fully coupled 13-moment equation set, a significant advantage
of the present solution technique is that it does not require extra boundary conditions explicitly; Grad’s equations for viscous
stress and heat flux are used as constitutive relations for the conservation equations instead of being solved as equations
of transport. The relative computational cost of this novel technique is low in comparison to other methods, such as fully
coupled solutions involving many moments or discrete methods. In this study, the proposed numerical procedure is tested on
a planar Couette flow case, and the results are compared to predictions obtained from the direct simulation Monte Carlo method.
This test case highlights the presence of normal viscous stresses and tangential heat fluxes that arise from non-equilibrium
phenomena, which cannot be captured by the Navier–Stokes–Fourier constitutive equations or phenomenological modifications.
相似文献
17.
We propose a non-oscillatory balanced numerical scheme for a simplified tropical climate model with a crude vertical resolution,
reduced to the barotropic and the first baroclinic modes. The two modes exchange energy through highly nonlinear interaction
terms. We consider a periodic channel domain, oriented zonally and centered around the equator and adopt a fractional stepping–splitting
strategy, for the governing system of equations, dividing it into three natural pieces which independently preserve energy.
We obtain a scheme which preserves geostrophic steady states with minimal ad hoc dissipation by using state of the art numerical
methods for each piece: The f-wave algorithm for conservation laws with varying flux functions and source terms of Bale et al. (2002) for the advected
baroclinic waves and the Riemann solver-free non-oscillatory central scheme of Levy and Tadmor (1997) for the barotropic-dispersive
waves. Unlike the traditional use of a time splitting procedure for conservation laws with source terms (here, the Coriolis
forces), the class of balanced schemes to which the f-wave algorithm belongs are able to preserve exactly, to the machine precision, hydrostatic (geostrophic) numerical-steady
states. The interaction terms are gathered into a single second order accurate predictor-corrector scheme to minimize energy
leakage. Validation tests utilizing known exact solutions consisting of baroclinic Kelvin, Yanai, and equatorial Rossby waves
and barotropic Rossby wave packets are given. 相似文献
18.
Dai Tian-min 《应用数学和力学(英文版)》2003,24(12):1369-1374
The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass
and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the
line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented.
Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived
in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories
is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum
and energy may be obtained by the usual localization.
Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM
Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001)
Biography: DAI Tian-min (1931≈) 相似文献
19.
We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with
the fluid, in the whole plane. The fluid motion is described by the Navier–Stokes equations and the motion of the rigid body
by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate,
as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of
the Navier–Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the
centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory. 相似文献
20.
We study the model describing thermal motion of gas in the rarefied space. This model can be used, in particular, in the study of the state of the medium behind the front of shock wave after very strong blast, in the study of the processes taking place inside of tornado, in the study of the motion of the gas in outer space. For any given initial distribution of the pressure a specific selection of mass Lagrange variables leads to reduction of the system of differential equations describing this motion to the system, for which the number of independent variables is less on the unit. For the obtained system we found all nontrivial conservation laws of the first order. In addition to the classical conservation laws the system has other conservation laws, which generalizes the energy conservation law. We obtained the exact solutions of this system. These solutions describe a variety of different physical processes taking place in the rarefied medium. Using the symmetry properties of the system we got the generating formulas for the receipt of the new solutions using already found earlier solutions of the system. 相似文献