Related papers: A variational principle for nonlinear local pressu…
A comparison between the two possible variational principles for the study of a free falling spinless particle in a space-time with torsion is noted. It is well known that the autoparallel trajectories can be obtained from a variational…
This study focuses on the topological pressure of nonautonomous iterated function systems defined on a compact metric space. We establish an inequality relating two topological pressures associated with a factor map of nonautonomous…
As the motions of nonconservative autonomous systems are typically not periodic, the definition of nonlinear modes as periodic motions cannot be applied in the classical sense. In this paper, it is proposed 'make the motions periodic' by…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…
We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.
For a given topological dynamical system $(X,T)$ over a compact set $X$ with a metric $d$, the "variational principle" states that \begin{equation*} \sup_{\mu}h_\mu(T) = h(T) = h_d(T), \end{equation*} where $h_\mu(T)$ is the…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
For surfaces without boundary, nonlocal notions of directional and mean curvatures have been recently given. Here, we develop alternative notions, special cases of which apply to surfaces with boundary. Our main tool is a new fractional or…
The current noise in a multi-probe mesoscopic conductor can have a nonlinear dependence on the strength of driving bias voltage. This paper presents a theoretical formulation for the nonlinear noise spectra. We pay special attention to…
Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition, while it has required complicated…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
The hallmark feature of topological insulators renders edge transport virtually impervious to scattering at defects and lattice disorder. In our work, we experimentally demonstrate a topological system, using a photonic platform, in which…
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
The variational principle for linear stability of three-dimensional, inhomogenious, compressible, moving magnetized plasma is suggested. The principle is ``softer'' (easier to be satisfied) than all previously known variational stability…
We provide a suitable variational approach for a class of nonlocal problems involving the fractional laplacian and singular nonlinearities for which the standard techniques fail. As a corollary we deduce a characterization of the solutions.
We apply the variational approach to solitons in highly nonlocal nonlinear media in $D=1,2,3$ dimensions. We compare results obtained by the variational approach with those obtained in the accessible soliton approximation, by considering…
We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of "accessible solitons" and establishes an…