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Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
The emergence of dynamical structures in multi-agent systems is analysed. Three different mechanisms are identified, namely: (1) sensitive-dependence and convex coupling, (2) sensitive-dependence and extremal dynamics and (3) interaction…
Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Disordered many-body systems exhibit a wide range of emergent phenomena across different scales. These complex behaviors can be utilized for various information processing tasks such as error correction, learning, and optimization. Despite…
Bivalency confers several concentration-dependent phenomena, including avidity, competitive exchange and multi-site competitive exchange. Since these concepts are crucial for a wide variety of topics in cell and molecular biology, their…
Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Biological systems exhibit large-scale self-organized dynamics and structures which enable organisms to perform the functions of life. The field of active matter strives to develop and understand microscopically-driven nonequilibrium…
Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self propelling…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
A particular case of a causal set is considered that is a directed dyadic acyclic graph. This is a model of a discrete pregeometry on a microscopic scale. The dynamics is a stochastic sequential growth of the graph. New vertexes of the…
We investigate the role of nondeterminism in Winfree's abstract Tile Assembly Model (aTAM), which was conceived to model artificial molecular self-assembling systems constructed from DNA. Of particular practical importance is to find tile…
In equilibrium self-assembly, microscopic building blocks spontaneously self-organize into stable structures as dictated by their interaction potentials, which limits the accessible structural features to those that correspond to global…
Active nematics are out-of-equilibrium systems in which energy injection at the microscale drives emergent collective behaviors, from spontaneous flows to active turbulence. While the dynamics of these systems have been extensively studied,…
Long-range interactions and electric response are essential for accurate modeling of condensed-phase systems, but capturing them efficiently remains a challenge for atomistic machine learning. Traditionally, these two phenomena can be…
Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…