Related papers: Linking microscopic and macroscopic response in di…
Particle based methods such as the Discrete Element Method and the Lattice Spring Method may be used for describing the behaviour of isotropic linear elastic materials. However, the common bond models employed to describe the interaction…
Normal modes provide a fundamental basis for understanding crucial properties of solids, such as the thermal conductivity, the heat capacity and the sound propagation. While the normal modes are excellently described by plane waves in…
This report presents a systematic understanding of the nature behind the unusual behavior of a nanosolid, and a surface as well, in mechanics, thermodynamics, acoustics, optoelectronics, magnetism, dielectrics, atomic diffusivity and…
Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P,…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic…
A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on a ribbon is given by the moduli space of semi-stable…
We study the interplay between structural and conductivity (composite) disorder and the collective electrical response in random networks models. Translating the problem of time-dependent electrical response (resonance and transient…
Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state-variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by…
Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to…
Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…
We study dense, disordered stacks of elastic macroscopic fibers. These stacks often exhibit non-linear elasticity, due to the coupling between the applied stress and the internal distribution of fiber contacts. We propose a theoretical…
Torsional oscillator experiments show evidence of mass decoupling in solid 4He. This decoupling is amplitude dependent, suggesting a critical velocity for supersolidity. We observe similar behavior in the elastic shear modulus. By measuring…
A fundamental challenge for disordered solids is predicting macroscopic yield from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic…
We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local…
The aim of this paper is to offer an analytic theory of the shear banding instability in amorphous solids that are subjected to athermal quasi-static shear. To this aim we derive nonlinear equations for the displacement field, including the…
We consider local invariants of general connections (with torsion). The group of origin-preserving diffeomorphisms acts on a space of jets of general connections. Dimensions of moduli spaces of generic connections are calculated. Poincar\'e…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…