Related papers: Duality Structure, Asymptotic analysis and Emergen…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is…
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following the work of Bouchut and James (Comm. Partial Diff. Eq., 24, 1999), a notion of duality solution for…
Power-law sensitivity to initial conditions, characterizing the behaviour of dynamical systems at their critical points (where the standard Liapunov exponent vanishes), is studied in connection with the family of nonlinear 1D logistic-like…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…
It is argued that the formal rules of correspondence between local observation procedures and observables do not exhaust the entire physical content of generally covariant quantum field theory. This result is obtained by expressing the…
A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…
Dualities are mathematical mappings that reveal unexpected links between apparently unrelated systems or quantities in virtually every branch of physics. Systems that are mapped onto themselves by a duality transformation are called…
System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and…
We consider transformations of deterministic and random signals governed by simple dynamical mappings. It is shown that the resulting signal can be a random process described in terms of fractal distributions and fractal domain integrals.…
The weak correlation between spatiotemporal fluctuations in nonequilibrium complex systems is shown to govern the fluctuation distribution, maximizing the conditional entropy associated with such fluctuations. The result is illustrated in…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
We consider solutions to nonlinear hyperbolic systems of balance laws with stiff relaxation and formally derive a parabolic-type effective system describing the late-time asymptotics of these solutions. We show that many examples from…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
This is the first of two papers devoted to the asymptotic structure of space-time in the presence of a non-negative cosmological constant $\Lambda$. This first paper is concerned with the case of $\Lambda =0$. Our approach is fully based on…