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From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…
In this paper we study the Random energy model - so called toy model of the spin glass theory - where the underlying distributions are compactly supported. We prove a general theorem on the asymptotics of free energy and obtain formulae in…
We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be…
We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…
In connection with recent discussion of topological order and topological phase transitions in quantum systems, we reexamine circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local…
In a freely cooling granular material fluctuations in density and temperature cause position dependent energy loss. Due to strong local dissipation, pressure and energy drop rapidly and material moves from `hot' to `cold' regions, leading…
Spontaneous pattern formation from a uniform state is a widely studied nonlinear optical phenomenon that shares similarities with non-equilibrium pattern formation in other scientific domains. Here we show how a single layer of atoms in an…
Random pairwise encounters often occur in large populations, or groups of mobile agents, and various types of local interactions that happen at encounters account for emergent global phenomena. In particular, in the fields of swarm…
We use a simple mode-coupling approach to investigate glassy dynamics of partially pinned fluid systems. Our approach is different from the mode-coupling theory developed by Krakoviack [Phys. Rev. Lett. 94, 065703 (2005), Phys. Rev. E 84,…
Flocking is a prime example of how robust collective behavior can emerge from simple interaction rules. The flocking transition has been studied extensively since the inception of the original Vicsek model. Here, we introduce a novel…
Broken-symmetry-induced order parameters account for many phenomena in condensed matter physics. For spin glasses, such a framework dictates its theoretical construction, whereas experiments have only established dynamical behaviors such as…
Spin glasses are systems whose magnetic moments freeze at low temperature into random orientations without long-range order. It is generally accepted that both frustration and disorder are essential ingredients in all spin glasses, so it…
The random first-order transition (RFOT) theory of the structural glass transition is reviewed in a pedagogical fashion. The rigidity that emerges in crystals and glassy liquids is of the same fundamental origin. In both cases, it…
In these lectures I will present an introduction to the modern way of studying the properties of glassy systems. I will start from soluble models of increasing complications, the Random Energy Model, the $p$-spins interacting model and I…
We present a large-scale simulation of the three-dimensional and mean-field spin glasses down to a very low but finite temperature. We extrapolate pertinent observables, e.g., the disorder-averaged central weight to zero temperature,…
The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from…
We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly…
Using molecular dynamics simulation, we investigate the slow dynamics of a supercooled binary mixture of soft particles interacting with a generalized Hertzian potential. At low density, it displays typical slow dynamics near its glass…
This paper develops a game-theoretic model and an agent-based model to study group formation driven by resource pooling, spatial cohesion, and heterogeneity. We focus on cross-sector partnerships (CSPs) involving public, private, and…
We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. The simulations reveal that when the persistence time…