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Nanoscale electronics and novel fabrication technologies bear unique opportunities for self-assembling multi-billion component systems in a largely random manner, which would likely lower fabrication costs significantly compared to a…
The self-assembly of anisotropic building blocks into complex spatial architectures is an important design strategy in material science but the mechanisms by which the anisotropic interactions influence the early-stage growth and formation…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
We investigate general properties of non-deterministic self-assembly with asymmetric interactions, using a computational model and DNA tile assembly experiments. By contrasting symmetric and asymmetric interactions we show that the latter…
The sustenance of life depends on the high degree of organization that prevails through different levels of living organisms, from subcellular structures such as biomolecular complexes and organelles to tissues and organs. The physical…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
In this paper, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical…
Self-assembly processes in biological and synthetic biomolecular systems are often governed by the spatial separation of biochemical processes. While previous work has focused on optimizing self-assembly through fine-tuned reaction…
Two simple kinetic models of Quantum Size Effect-directed nanocluster self-assembly in circular atomic corrals are discussed. The models correspond to an adsorption (either a physisorption or a chemisorption) and an adsorption-diffusion…
Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise…
Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…
Motivated by recent experimental findings in chemical synthesis of colloidal particles, we draw an analogy between self-assembly processes occurring in biological systems (e.g. protein folding) and a new exciting possibility in the field of…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
Within a mathematical model, the metabolic process of glycolysis is studied. The general scheme of glycolysis is considered as a natural result of the biochemical evolution. By using the theory of dissipative structures, the conditions of…
Long-range interactions often proceed as a sequence of hopping through intermediate, statistically-favored events. Here, we identify a widely-overlooked mechanism for the mechanical motion of particles that arises from the Lorentz force and…
Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al.,…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
Spontaneous directed motion, a hallmark of cell biology, is unusual in classical statistical physics. Here we study, using both numerical and analytical methods, organized motion in models of the cytoskeleton in which constituents are…