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Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…
The behavior of identical particles interacting through the harmonic-repulsive pair potential has been studied in 3D using molecular dynamics simulations at a number of different densities. We found that at many densities, as the…
Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely…
It has been well known for some time that for strictly stationary Markov chains that are ``reversible'', that special symmetry provides special extra features in the mathematical theory. This paper here is primarily a purely expository…
We use a mixed-spin model, with aperiodic ferromagnetic exchange interactions and crystalline fields, to investigate the effects of deterministic geometric fluctuations on first-order transitions and tricritical phenomena. The interactions…
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is…
The local structure of disordered jammed packings of monodisperse spheres without friction, generated by the Lubachevsky-Stillinger algorithm, is studied for packing fractions above and below 64%. The structural similarity of the particle…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
It has recently been shown that one-dimensional Ising problems can have degenerate, disordered ground states (GSs) over a finite range of coupling onstants, ie, without `fine tuning'. The disorder is however of a special kind, consisting of…
Disordered magnets, martensitic mixed crystals, and glassy solids can be irreversibly deformed by subjecting them to external deformation. The deformation produces a smooth, reversible response punctuated by abrupt relaxation "glitches".…
We consider Markov chains that obey the following general non-linear state space model: $\Phi_{k+1} = F(\Phi_k, \alpha(\Phi_k, U_{k+1}))$ where the function $F$ is $C^1$ while $\alpha$ is typically discontinuous and $\{U_k: k \in…
Chromonic liquid crystals constitute a novel lyotropic phase, whose elastic properties have so far been modeled within the classical Oseen-Frank theory, provided that the twist constant is assumed to be considerably smaller than the…
In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a $C^{1+\alpha}$ and there is a hyperbolic ergodic…
A spacetime crystal is a phase of matter that spontaneously develops periodic order in both space and time. Spacetime crystals have been experimentally observed in microscopic quantum many-body systems and, very recently, in a mesoscopic…
A mathematical framework is developed to describe tilted perovskites using a tensor description of octahedral deformations. The continuity of octahedral tilts through the crystal is described using an operator which relates the deformations…
A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform…
A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to…
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a…
We consider a phenomenological continuum theory for an extensile, overdamped active nematic liquid crystal, applicable in the dense regime. Constructed from general principles, the theory is universal, with parameters independent of any…
Upon melting, the molecules in the crystal explore numerous configurations, reflecting an increase in disorder. The molar entropy of disorder can be defined by Bolzmann's formula dSd = Rln(Wd) where Wd is the increase in the number of…