Search results for " Nonlinear"
showing 10 items of 1224 documents
Energy dissipative solutions to the Kobayashi-Warren-Carter system
2017
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which dissipate the associated energy functional. We obtain existence of this type of solutions via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some $\Gamma$-convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions togethe…
Nonradial normalized solutions for nonlinear scalar field equations
2018
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
Porosities and dimensions of measures
1999
We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measures: measures on $R^n$ which satisfy the doubling condition and strongly porous measures on $R$.
Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture
1995
Abstract We have performed a molecular dynamics computer simulation study to investigate the dynamical behavior of a supercooled simple liquid for comparison with the predictions of mode-coupling theory (MCT). By scaling the intermediate scattering function by the α-relaxation time r we find that the correlators fall onto a master curve extending over several decades in time. Thus we find that the time temperature superposition principle holds. In the late β-relaxation regime this master curve can be fitted very well by a master curve predicted by the idealized version MCT. However, there is no evidence for the presence of the critical decay predicted by the theory for the early part of the…
Bifurcations of links of periodic orbits in non-singular Morse - Smale systems on
1997
The set of periodic orbits of a non-singular Morse - Smale (NMS) flow on defines a link; a characterization of all possible links of NMS flows on has been developed by Wada. In the frame of codimension-one bifurcations, this characterization allows us to study the restrictions a link requires for suffering a given bifurcation. We also derive the topological description of the new link and the possibility of relating links by a chain of this type of bifurcation.
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
One-dimensional families of projections
2008
Let m and n be integers with 0 < m < n. We consider the question of how much the Hausdorff dimension of a measure may decrease under typical orthogonal projections from onto m-planes provided that the dimension of the parameter space is one. We verify the best possible lower bound for the dimension drop and illustrate the sharpness of our results by examples. The question stems naturally from the study of measures which are invariant under the geodesic flow.
Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions
2023
This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see…
Convergence of KAM iterations for counterterm problems
1998
Abstract We analyse two iterative KAM methods for counterterm problems for finite-dimensional matrices. The starting point for these methods is the KAM iteration for Hamiltonians linear in the action variable in classical mechanics. We compare their convergence properties when a perturbation parameter is varied. The first method has no fixed points beyond a critical value of the perturbation parameter. The second one has fixed points for arbitrarily large perturbations. We observe different domains of attraction separated by Julia sets.
Filter approach to the stochastic analysis of MDOF wind-excited structures
1999
Abstract In this paper, an approach useful for stochastic analysis of the Gaussian and non-Gaussian behavior of the response of multi-degree-of-freedom (MDOF) wind-excited structures is presented. This approach is based on a particular model of the multivariate stochastic wind field based upon a particular diagonalization of the power spectral density (PSD) matrix of the fluctuating part of wind velocity. This diagonalization is performed in the space of eigenvectors and eigenvalues that are called here wind-eigenvalues and wind-eigenvectors, respectively. From the examination of these quantities it can be recognized that the wind-eigenvectors change slowly with frequency while the first wi…