相关论文: Coarse graining: lessons from simple examples

A complex compact surface which carries an automorphism of positive topological entropy has been proved by Cantat to be either a torus, a K3 surface, an Enriques surface or a rational surface. Automorphisms of rational surfaces are quite…

We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…

The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is…

We introduce a family of area preserving generalized baker's transformations acting on the unit square and having sharp polynomial rates of mixing for Holder data. The construction is geometric, relying on the graph of a single variable…

The Vlasov equation is analyzed for coarse grained distributions resembling a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the…

We study the gravitational collapse in modified gravitational theories. In particular, we analyze a general $f(R)$ model with uniformly collapsing cloud of self-gravitating dust particles. This analysis shares analogies with the formation…

Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process.…

We present an equation-free computational approach to the study of the coarse-grained dynamics of {\it finite} assemblies of {\it non-identical} coupled oscillators at and near full synchronization. We use coarse-grained observables which…

Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant finite decomposition complexity.

We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…

A polynomial automorphism of $\mathbb{A}^n$ over a field of characteristic zero is called co-tame if, together with the affine subgroup, it generates the entire tame subgroup. We prove some new classes of automorphisms, including…

We consider the problem of coarse-graining in the context of finite-volume fluid models. If a variable is defined on a high-resolution grid it may be coarse-grained so that it is defined on a grid of lower resolution. In general this will…

Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time. In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks.…

We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus…

Spontaneous stratification in granular mixtures has been recently reported by H. A. Makse et al. [Nature 386, 379 (1997)]. Here we study experimentally the dynamical processes leading to spontaneous stratification. Using a high-speed video…

We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…

Jet grooming has emerged as a necessary and vital tool for mitigating contamination radiation in jets. The additional restrictions on emissions imposed by the groomer can result in non-smooth behavior of resulting fixed-order distributions…