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We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for Stochastic Rotation Dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for…
The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general…
In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus on the characterization in terms of the existence of a…
Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these…
Due to the prohibitive cost of resolving all relevant scales, direct numerical simulations of turbulence remain unfeasible for most real-world applications. Consequently, dynamically simplified formulations are needed for coarse-grained…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
The eigenstates of d-dimensional quasicrystalline models with a separable Hamiltonian are studied within the tight-binding model. The approach is based on mathematical sequences, constructed by an inflation rule P = {w -> s, s -> sws^(b-1)}…
In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking…
Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…
A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{*}(\omega)$ calculated. Two non-trivial scaling regimes were observed,…
Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…
We consider the enstrophy cascade in forced two-dimensional turbulence with a linear drag force. In the presence of linear drag, the energy wavenumber spectrum drops with a power law faster than in the case without drag, and the vorticity…
We present a quantitative geometric rigidity estimate for special functions of bounded deformation in a planar setting generalizing the result by Friesecke, James, M\"uller obtained in nonlinear elasticity theory and the piecewise rigidity…
We theoretically study the electronic structure and spin properties of one-dimensional nanostructures of the prototypical bulk topological insulator Bi$_2$Se$_3$. Realistic models of experimentally observed Bi$_2$Se$_3$ nanowires and…
A molecular dynamics (MD) simulation of planar Couette flow is presented for the minimal channel in which turbulence structures can be sustained. Evolution over a single breakdown and regeneration cycle is compared to computational fluid…
We present a detailed study of the geometric and algebraic properties of the multidimensional quadrilateral lattice (a lattice whose elementary quadrilaterals are planar; the discrete analogue of a conjugate net) and of its basic…
We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers. These…