Search results for "conservation law"
showing 10 items of 86 documents
Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier
2015
Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…
A Theoretical Approach to the Shift Mechanics of Rubber Belt Variators
2008
This paper proposes a theoretical description of the mechanical behavior of rubber belt variators during the speed ratio shift. Comparing with the steady operation, the mass conservation of the belt is completely reformulated considering an elementary dihedral control volume between two planes through the pulley axis and balancing the inside mass variation with the total mass flux through the control surface. On the other hand, the belt equilibrium conditions are similar to the steady case, as the inertia forces due to the shifting motion are negligible with respect to the other forces. Assuming a one-dimensional belt model, it is shown that adhesive regions may appear inside the arc of con…
Numerical Experiments with Multilevel Schemes for Conservation Laws
2001
Main steps of a point-value multilevel algorithm are presented and numerical results for a two dimensional test case of gas dynamics are discussed in terms of quality and efficiency.
Multiresolution-based adaptive schemes for Hyperbolic Conservation Laws
2006
Starting in the early nineties, wavelet and wavelet-like techniques have been successfully used to design adaptive schemes for the numerical solution of certain types of PDE. In this paper we review two representative examples of the development of such techniques for Hyperbolic Conservation Laws.
Representation of capacity drop at a road merge via point constraints in a first order traffic model
2018
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by c…
Historischer Überblick zur mathematischen Theorie von Unstetigkeitswellen seit Riemann und Christoffel
1981
We give a brief historical account of the development of the mathematical theory of propagation of discontinuities in gases, fluids or elastic materials. The theory was initiated by Riemann who investigated the propagation of shocks in one-dimensional isentropic gas flow. Riemann’s results were used by Christoffel to treat, more generally, the propagation of (first order) discontinuity surfaces in three-dimensional flows of perfect fluids. Subsequently Christoffel applied his general theory to first order waves in certain elastic materials. Independently of Riemann and Christoffel significant contributions were made by Hugoniot. The theory was completed in Hadamard’s celebrated monograph [3…
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Normal Coulomb Frames in $${\mathbb{R}}^{4}$$
2012
Now we consider two-dimensional surfaces immersed in Euclidean spaces \({\mathbb{R}}^{n+2}\) of arbitrary dimension. The construction of normal Coulomb frames turns out to be more intricate and requires a profound analysis of nonlinear elliptic systems in two variables. The Euler–Lagrange equations of the functional of total torsion are identified as non-linear elliptic systems with quadratic growth in the gradient, and, more exactly, the nonlinearity in the gradient is of so-called curl-type, while the Euler–Lagrange equations appear in a div-curl-form. We discuss the interplay between curvatures of the normal bundles and torsion properties of normal Coulomb frames. It turns out that such …
Entropy dissipation of moving mesh adaptation
2014
Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.
Infinite sets of conservation laws for linear and nonlinear field equations
1984
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the ‘coupling constant’) the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant u…