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We review some of the uncertainties in calculating nucleosynthetic yields, focusing on the explosion mechanism. Current yield calculations tend to either use a piston, energy injection, or enhancement of neutrino opacities to drive an…
This thesis mainly focuses on two problems in capital structure and individual's life-cycle portfolio choice. In the first problem, we derive a stochastic control model to optimize banks' dividend and recapitalization policies and calibrate…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age.…
High-tech systems are typically produced in two stages: 1) Production of components using specialized equipment and staff; 2) System assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of…
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…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
Supply chains are the backbone of the global economy. Disruptions to them can be costly. Centrally managed supply chains invest in ensuring their resilience. Decentralized supply chains, however, must rely upon the self-interest of their…
The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion (SALR) potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk.…
Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species…
Recognising changes in collective dynamics in complex systems is essential for predicting potential events and their development. Possessing intrinsic attractors with laws associated with scale invariance, self-organised critical dynamics…
Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of…
Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We…
The self-assembly of molecules at surfaces can be caused by a range of physical mechanisms. Assembly can be driven by intermolecular forces, or molecule-surface forces, or both; it can result in structures that are in equilibrium or that…
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity…
We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…
The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…
We survey our research on modeling the mechanisms of control of uniformity in growth of nanosize and colloid particles. The former are produced as nanocrystals, by burst-nucleation from solution. The latter, colloid-size particles, are…