Related papers: Force rearrangements and statistics of hyperstatic…
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
The distribution P(F) of contact forces F in a homogeneous isotropic disordered granular sample subject to uniform triaxial stress field is studied using a model where forces propagate and collide. Collisions occur at grain and obey given…
A polymer chain pinned in space exerts a fluctuating force on the pin point in thermal equilibrium. The average of such fluctuating force is well understood from statistical mechanics as an entropic force, but little is known about the…
Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has…
Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow…
The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between…
The mechanics of granular media at low liquid saturation levels remain poorly understood. Macroscopic mechanical properties are affected by microscale forces and processes, such as capillary forces, inter-particle friction, liquid flows,…
Geometric graph models of systems as diverse as proteins, robots, and mechanical structures from DNA assemblies to architected materials point towards a unified way to represent and control them in space and time. While much work has been…
The experiments involving a slider moving on top of granular media consisting of photoelastic particles in two dimensions have uncovered elaborate dynamics that may vary from continuous motion to crackling, periodic motion, and stick-slip…
Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality.…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
In a recent paper [Phys. Rev. X 12, 031021], we reported experimental observations of ``ultrastable'' states in a shear-jammed granular system subjected to small-amplitude cyclic shear. In such states, all the particle positions and contact…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
The effect of increasing structural disorder on the distribution of contact forces P(f), inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a…
In polycrystalline materials, grain boundaries are sites of enhanced atomic motion, but the complexity of the atomic structures within a grain boundary network makes it difficult to link the structure and atomic dynamics. Here we use a…
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both illustrate general principles, and for their…