Related papers: Nonintegrability, Chaos, and Complexity
Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure…
A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Riemann invariants. Exact solutions described by these…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
The complex spaciotemporal patterns of atmospheric flows that result from the cooperative existence of fluctuations ranging in size from millimetres to thousands of kilometres are found to exhibit long-range spacial and temporal…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an…
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…
In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly…
One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion…
We introduce a dissipative particle dynamics scheme for the dynamics of non-ideal fluids. Given a free-energy density that determines the thermodynamics of the system, we derive consistent conservative forces. The use of these effective,…