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In this paper we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to…
A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…
Polymer models play the special role of elucidating the elementary features describing the physics of long molecules and become essential to interpret the measurements of their magnitudes. In this work the end-to-end distance of an…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, $w(t)\propto t^\beta$, is the classical means to have access…
We present a thermodynamic theory of plane coherent solid-solid interfaces in multicomponent systems subject to nonhydrostatic mechanical stresses. The interstitial and substitutional chemical components are treated separately using…
We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma…
We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity \eta is computed as a function of particle volume density \rho…
The surface exponents, the scaling behavior and the bulk porosity of a generalized ballistic deposition (GBD) model are studied. In nature, there exist particles with varying degrees of stickiness ranging from completely non-sticky to fully…
We revisit the scaling properties of a model for non-equilibrium wetting [Phys. Rev. Lett. 79, 2710 (1997)], correcting previous estimates of the critical exponents and providing a complete scaling scheme. Moreover, we investigate a special…
The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the…
This article explores the hysteretic behavior and the damping features of sheared granular media using discrete element method (DEM) simulations. We consider polydisperse non-cohesive frictional spherical particles, enclosed in a container…
Recent progress on studies of the nanoscale mechanical responses in disordered systems has highlighted a strong degree of heterogeneity in the elastic moduli. In this contribution, using computer simulations, we study the elastic…
An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip…
Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum…
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
We study the behavior of the elastic polymer, a model of a directed polymer in a continuous Gaussian random environment that is independent in time and correlated in space, as the dimension of the environment is taken to infinity. We give…