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Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.


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TL;DR: In this paper, the authors carried out fully three-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a cold dark matter (CDM)-dominated Einstein-de Sitter universe.
Abstract: We carry out fully three-dimensional simulations of evolution from self-similar, spherically symmetric linear perturbations of a cold dark matter (CDM)-dominated Einstein-de Sitter universe. As a result of the radial orbit instability, the haloes which grow from such initial conditions are triaxial with major-to-minor axial ratios of the order of 3: 1. They nevertheless grow approximately self-similarly in time. In all cases, they have power-law density profiles and near-constant velocity anisotropy in their inner regions. Both the power-law index and the value of the velocity anisotropy depend on the similarity index of the initial conditions, the former as expected from simple scaling arguments. Halo structure is thus not 'universal' but remembers the initial conditions. On larger scales the density and anisotropy profiles show two characteristic scales, corresponding to particles at the first pericentre and at the first apocentre after infall. They are well approximated by the Navarro―Frenk―White model only for one value of the similarity index. In contrast, at all radii within the outer caustic the pseudo-phase-space density can be fitted by a single power law with an index which depends only very weakly on the similarity index of the initial conditions. This behaviour is very similar to that found for haloes formed from ACDM initial conditions and so can be considered approximately universal.

37 citations

Journal ArticleDOI
TL;DR: The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived in this paper for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension.
Abstract: The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov-Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multispecies case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution for a one-species, one-dimensional plasma is one of the general similarity solutions.

37 citations

Journal ArticleDOI
TL;DR: In this paper, a one-dimensional model for the bedload transport of sediment in a coastal-plain depositional system, such as a delta and a continental margin, is presented.
Abstract: Assuming that the sediment flux in the Exner equation can be linearly related to the local bed slope, we establish a one-dimensional model for the bed-load transport of sediment in a coastal-plain depositional system, such as a delta and a continental margin. The domain of this model is defined by two moving boundaries: the shoreline and the alluvial–bedrock transition. These boundaries represent fundamental transitions in surface morphology and sediment transport regime, and their trajectories in time and space define the evolution of the shape of the sedimentary prism. Under the assumptions of fixed bedrock slope and sea level the model admits a closed-form similarity solution for the movements of these boundaries. A mapping of the solution space, relevant to field scales, shows two domains controlled by the relative slopes of the bedrock and fluvial surface: one in which changes in environmental parameters are mainly recorded in the upstream boundary and another in which these changes are mainly recorded in the shoreline. We also find good agreement between the analytical solution and laboratory flume experiments for the movements of the alluvial–bedrock transition and the shoreline.

37 citations

Journal ArticleDOI
TL;DR: In this article, the existence of a solution of the nonlinear third-order differential equation over 0 < η < ∞ is established, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609-618).
Abstract: Consideration is given to a class of nonlinear third-order differential equations arising in fluid flow over a nonlinearly stretching sheet. Existence of a solution of the nonlinear third-order differential equation over 0<η<∞ is established in this paper, answering the open question of Vajravelu and Cannon (Appl. Math. Comput. 2006; 181:609–618). That is, we prove with estimates independent of R for solutions of the third-order differential equation on [0, R]. The existence of a solution on 0<η<∞ follows from the Ascoli–Arzela Theorem. Furthermore, numerical solutions are obtained and presented through graphs, and the influence of the physical parameter on the flow characteristics is discussed. Copyright © 2009 John Wiley & Sons, Ltd.

37 citations

Journal ArticleDOI
TL;DR: In this article, general slip boundary condition is used to solve the viscous incompressible flows induced by a stretching sheet and a similarity solution is developed by shooting method using Runge-Kutta algorithm.
Abstract: General slip boundary condition is used to solve the viscous incompressible flows induced by a stretching sheet. These flow problems corresponds to the planar and axisymmetric stretching. A similarity solution is developed by shooting method using Runge–Kutta algorithm. The results are graphically displayed and discussed under the influence of slip parameter and critical shear rate. The comparison of stretching flow problem subject to Navier's boundary condition in the planar case is made with the available numerical results in the literature.

37 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850