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Ladder polymers, known for their rigid, ladder-like structures, exhibit exceptional thermal stability and mechanical strength, positioning them as candidates for advanced applications. However, accurately determining their structure from…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
A numerical study of laminar flow through symmetric and slightly asymmetric sudden expansion, of expansion ratio 1:3, in channels with increasing cross section, is carried out using two different approaches - Conventional CFD and Lattice…
Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar…
We model Lagrangian lateral mixing and transport of passive scalars in meandering oceanic jet currents by two-dimensional advection equations with a kinematic stream function with a time-dependent amplitude of a meander imposed. The…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part and the projected image to the constraint, one can prove…
In diverse physical systems stable oscillatory solutions devolve into more complicated dynamical behaviour through border-collision bifurcations. Mathematically these occur when a stable fixed point of a piecewise-smooth map collides with a…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady state plastic flow,…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
We provide a survey of results on the statistics of random sections of holomorphic line bundles on K\"ahler manifolds, with an emphasis on the resulting asymptotics when a line bundle is raised to increasing tensor powers. We conclude with…
Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
We test the ability of a general low-dimensional model for turbulence to predict geometry-dependent dynamics of large-scale coherent structures, such as convection rolls. The model consists of stochastic ordinary differential equations,…
In this paper, we perform a detailed investigation on the various geometrical properties of trapped surfaces and the boundaries of trapped region in general relativity. This treatment extends earlier work on LRS II spacetimes to a general 4…