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Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in…

In this paper we investigate the statistical behavior of an annealed continuous damage model. For different model variations we study distributions of times to failure and compare these results with the classical case of metastable…

Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to Poisson default shock jointly sets its dividend policy and capital structure to maximize the expected…

The model of binary aggregation with constant kernel is subjected to stochastic resetting: aggregates of any size explode into monomers at independent stochastic times. These resetting times are Poisson distributed, and the rate of the…

First order phase transitions proceed via nucleation. The rate of nucleation varies exponentially with the free-energy barrier to nucleation, and so is highly sensitive to variations in this barrier. In practice, very few systems are…

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In…

We use neuroevolutionary learning to identify time-dependent protocols for low-dissipation self-assembly in a model of generic active particles with interactions. When the time allotted for assembly is sufficiently long, low-dissipation…

We use analytic theory and computer simulation to study patterns formed during the growth of two-component assemblies in 2D and 3D. We show that these patterns undergo a nonequilibrium phase transition, at a particular growth rate, between…

Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly…

The two-state Togashi-Kaneko model demonstrates how, at finite system sizes, autocatalysis can lead to noise-induced bistability between the cellular concentrations of different molecular species. Here, we show that, in the biologically…

Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…

We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites…

Multifarious assembly models consider multiple structures assembled from a shared set of components, reflecting the efficient usage of components in biological self-assembly. These models are subject to a high-dimensional parameter space,…

We explore the use of templated self-assembly to facilitate the formation of complex target structures made from patchy particles. First, we consider the templating of high-symmetry shell structures around a spherical core particle. We find…

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of…

We solve the stochastic equations for a cluster of parallel bonds with shared constant loading, rebinding and the completely dissociated state as an absorbing boundary. In the small force regime, cluster lifetime grows only logarithmically…

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however,…

For most organisms with viscous population structure, spatially localized growth drives the invasive advance of a favorable mutation. We model a two-allele competition where recurrent mutation introduces a genotype with a rate of local…

This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like…

The biological processes that execute complex multiple functions, such as cell cycle, must ensure the order of sequential events and keep the dynamic robustness against various fluctuations. Here, we examine the dynamic mechanism and the…