Related papers: Dynamics on the graph of the torus parametrisation

The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…

We consider several models whose motivation arises from statistical mechanics. We begin by investigating some families of distributions of translation invariant subgraphs of some Cayley graphs, and in particular subgraphs of the square…

Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Correlation of interacting particles is studied in their dynamics and localization in ideal and disordered lattice systems with the help of numerical tools. Both 1D and 2D systems are considered. In 1D lattices with long-range hopping,…

A number of successful theoretical models of hardness have been developed recently. A thermodynamic model of hardness, which supposes the intrinsic character of correlation between hardness and thermodynamic properties of solids, allows one…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and…

The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets of maximal tubings for the complete graph and the path…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

We discuss the use of a ferromagnetic spin model on a random graph to model granular compaction. A multi-spin interaction is used to capture the competition between local and global satisfaction of constraints characteristic for geometric…

This work presents a computational method for the design of architected truss lattice materials where each strut can be made of one of a set of available materials. We design the lattices to extremize effective properties. As customary in…

We consider so-called Leray regularization of the convective contributions. This gives rise to a subgrid parameterization which involves both explicit filtering and (approximate) inversion. The Leray model also arises from the…

The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be…

The uncertainties in material and other properties of structures are usually spatially correlated. We introduce an efficient technique for representing and processing spatially correlated random fields in robust topology optimisation of…

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…

The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…

The collective dynamics of topological structures have been of great interest from both fundamental and applied perspectives. For example, the studies of dynamical properties of magnetic vortices and skyrmions not only deepened the…

Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features. We propose a…