共查询到20条相似文献,搜索用时 437 毫秒
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Inna K. Shingareva Carlos Lizárraga-Celaya 《Journal of Applied Mathematics and Computing》2014,44(1-2):167-186
Applying perturbation methods, symbolic computation, and generalizing the solution method, higher-order asymptotic solutions are constructed in Lagrangian variables for several models describing 2D standing wave motions in fluids of various configurations. Three main parameters of the fluid configuration, depth, capillarity, and stratification layer, are considered. The frequency-amplitude dependences are obtained and compared with those known in the literature in Eulerian and Lagrangian variables. The comparison shows that the analytical frequency-amplitude dependences are in complete agreement with previous results known in the literature and with the results obtained for other models. A generalization allows us to investigate critical phenomena for standing waves in fluids of various configurations. Namely, special attention is focused on critical values of one parameter, the fluid depth. The frequency-amplitude dependences are analyzed from the point of view of critical values: critical points and critical curves are determined for several models describing standing waves in fluids of various configurations. 相似文献
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In structural dynamics, energy dissipative mechanisms with nonviscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary functions. Combination of damping parameters in the dissipative model can lead the system to be overdamped in some (or all) modes. In the domain of the damping parameters, the thresholds between induced oscillatory and non-oscillatory motion are named critical damping surfaces (or critical manifolds, since several parameters can be involved). In this paper the theoretical foundations to determine critical damping surfaces in nonviscously damped systems are established. In addition, a numerical method to obtain critical curves is developed. The approach is based on the transformation of the algebraic equations, which define implicitly the critical curves, into a system of differential equations. The derivations are validated with three numerical methods covering single and multiple degree of freedom systems. 相似文献
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A. G. Chentsov 《Proceedings of the Steklov Institute of Mathematics》2010,268(1):32-48
The topological classification is discussed for real polynomials of degree 4 in two real independent variables whose critical
points and critical values are all different. It is proved that among the 17 746 topological types of smooth functions with
the same number of critical points, at most 426 types are realizable by polynomials of degree 4. 相似文献
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Yang Cao 《Journal of Differential Equations》2009,246(12):4568-4590
This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations. After establishing the necessary existence, uniqueness and comparison principle for mild solutions, which are also classical ones provided that the initial data are appropriately smooth, we investigate large time behavior of solutions. It is shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations. 相似文献
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An efficient algorithm is described for calculating stationary one-dimensional transonic outflow solutions of the compressible Euler equations with gravity and heat source terms. The stationary equations are solved directly by exploiting their dynamical system form. Transonic expansions are the stable manifolds of saddle-point-type critical points, and can be obtained efficiently and accurately by adaptive integration outward from the critical points. The particular transonic solution and critical point that match the inflow boundary conditions are obtained by a two-by-two Newton iteration which allows the critical point to vary within the manifold of possible critical points. The proposed Newton Critical Point (NCP) method typically converges in a small number of Newton steps, and the adaptively calculated solution trajectories are highly accurate. A sample application area for this method is the calculation of transonic hydrodynamic escape flows from extrasolar planets and the early Earth. The method is also illustrated for an example flow problem that models accretion onto a black hole with a shock. 相似文献
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In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory. 相似文献
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We consider in this paper the propagation of neutral modes along a vortex with velocity profile being the radial coordinate. In the linear stability theory governing such flows, the boundary in parameter space separating stable and unstable regions is usually comprised of modes that are singular at some value of r denoted rc , the critical point. The singularity can be dealt with by adding viscous and/or nonlinear effects within a thin critical layer centered on the critical point. At high Reynolds numbers, the case of most interest in applications, nonlinearity is essential, but it develops that viscosity, treated here as a small perturbation, still plays a subtle role. After first presenting the scaling for the general case, we formulate a nonlinear critical layer theory valid when the critical point occurs far enough from the center of the vortex so that the vorticity there is small. Solutions are found having no phase change across the critical layer thus permitting the existence of modes not possible in a linear theory. It is found that both the axial and azimuthal mean vorticity are different on either side of the critical layer as a result of the wave–mean flow interaction. A long wave analysis with O (1) vorticity leads to similar conclusions. 相似文献
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M. V. Komarova D. M. Krasnov M. Yu. Nalimov 《Theoretical and Mathematical Physics》2011,169(1):1441-1449
We propose a model for studying the mutual influence of critical fluctuations in the vicinity of the critical point of phase
transition to a superfluid state and the velocity fluctuations in the developed turbulence regime. We demonstrate the presence
of two different regimes: the turbulence regime and the equilibrium regime. We show that the standard critical behavior can
break in the turbulence regime. The viscosity becomes an infrared-irrelevant parameter in the equilibrium regime. We justify
the assumption that the viscosity critical dimension in this regime is determined by critical indices of the critical behavior
statistical model, which are currently known with sufficient accuracy. 相似文献
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We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is sufficiently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered. 相似文献
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H. L. Skudlarek 《Mathematische Nachrichten》1980,96(1):33-34
In [5], [7] is was shown that the operator of KLEIN-GORDON type is a spectral operator with critical points. In this paper we estimate where the critical points can be found. We are especially interested in finding sufficient conditions for the absence of singular critical points. 相似文献
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Ivan Tafteberg Jakobsen 《Discrete Mathematics》1974,9(3):265-276
It is shown that the number of vertices of valency 2 in a critical graph with chromatic index 4 is at most 1/3 of the total number of vertices, and that there exist critical graphs with just one vertex of valency 2, but none with exactly two vertices of valency 2. From this bounds for the number of edges are deduced. The paper ends with a presentation of a catalogue of all critical graphs with chromatic index 4 and at most 8 vertices, and all simple critical graphs with chromatic index 4 and at most 10 vertices. 相似文献
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A new approach to the investigation of the stability of nonlinear nonautonomous differential equations with impulse effects in critical cases is proposed. The approach is based on the direct method of Lyapunov with the use of piecewise differentiable functions. The sufficient conditions of the asymptotic stability of the critical position of equilibrium in one case are obtained. The case is analogous to Kamenkov’s critical case. 相似文献
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This paper is concerned with characterizations of nonsmooth saddle critical points for numerical algorithm design. Most characterizations
for nonsmooth saddle critical points in the literature focus on existence issue and are converted to solve global minimax
problems. Thus they are not helpful for numerical algorithm design. Inspired by the results on computational theory and methods
for finding multiple smooth saddle critical points in [14, 15, 19, 21, 23], a local minimax characterization for multiple
nonsmooth saddle critical points in either a Hilbert space or a reflexive Banach space is established in this paper to provide
a mathematical justification for numerical algorithm design. A local minimax algorithm for computing multiple nonsmooth saddle
critical points is presented by its flow chart.
Dedicated to Terry Rockafellar on his 70th birthday 相似文献
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Jinge Yang Sining Zheng Chengyuan Qu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(2):311-319
This paper deals with the Fujita phenomenon for the Cauchy problem of an inhomogeneous fast diffusion system. Both the critical exponent and the second exponent are obtained. We observe that the inhomogeneous terms in the system substantially contribute to the critical exponent, in that the blow-up exponent region is obviously enlarged, with keeping the second critical exponent unchanged for small inhomogeneous sources. 相似文献
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In this paper, we study the critical metrics for quadratic curvature functionals involving the Ricci curvature and scalar curvature in the space of Riemannian metrics with unit volume. For these functionals, Einstein metrics are always critical metrics. However, a converse problem is not always true. The purpose of this paper is to show that, under the condition that the critical metrics are Bach-flat, a partial converse is true. 相似文献
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In 1968, Vizing made the following two conjectures for graphs which are critical with respect to the chromatic index: (1) every critical graph has a 2‐factor, and (2) every independent vertex set in a critical graph contains at most half of the vertices. We prove both conjectures for critical graphs with many edges, and determine upper bounds for the size of independent vertex sets in those graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 113–118, 2004 相似文献