Related papers: Dynamical Systems On Generalised Klein Bottles
We study a class of deterministic flows in ${\mathbb R}^{d\times k}$, parametrized by a random matrix ${\boldsymbol X}\in {\mathbb R}^{n\times d}$ with i.i.d. centered subgaussian entries. We characterize the asymptotic behavior of these…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Understanding transport processes in complex nanoscale systems, like ionic conductivities in nanofluidic devices or heat conduction in low dimensional solids, poses the problem of examining fluctuations of currents within nonequilibrium…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Existence of random dynamical systems for a class of coalescing stochastic flows on $\mathbb{R}$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential…
Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and…
Quantum dynamics of a general dissipative system investigated by its coupling to a Klein-Gordon type field as the environment by introducing a minimal coupling method. As an example, the quantum dynamics of a damped three dimensional…
We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…
Performing molecular dynamics simulations, we find that the structural relaxation dynamics of viscous silica, the prototype of a strong glass former, are spatially heterogeneous and cannot be understood as a statistical bond breaking…
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…
We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
We show that hydrodynamic diffusion is generically present in many-body interacting integrable models. We extend the recently developed generalised hydrodynamic (GHD) to include terms of Navier-Stokes type which lead to positive entropy…
Complex, oscillatory data arises from a large variety of biological, physical, and social systems. However, the inherent oscillation and ubiquitous noise pose great challenges to current methodology such as linear and nonlinear time series…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…