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In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
We derive the mean-field theory of disordered block-copolymers composed of two monomeric species, combining Edwards' functional method with the replica technique of disordered systems. In the absence of disorder we recover the canonical…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
We investigate the growth of a film of some element B on a substrate made of another substrance A in a model of molecular beam epitaxy. A vertical exchange mechanism allows the A-atoms to stay on the growing surface with a certain…
Understanding grain-surface processes is crucial to interpreting the chemistry of the ISM. However, accurate surface chemistry models are computationally expensive and are difficult to integrate with gas-phase simulations. A new…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
In this paper we study the asymptotic nonlinear dynamics of scalar semilinear parabolic problems reaction-diffusion type when the diffusion coefficient becomes large in a subregion which is interior to the domain. We obtain, under suitable…
Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active…
We study one-dimensional models of particle diffusion and attachment/detachment from islands where the detachment rates gamma(m) of particles at the cluster edges increase with cluster mass m. They are expected to mimic the effects of…
We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur…
The self-consistency of a thermodynamical theory for hadronic sys- tems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if…
The distribution of capture zones formed during the nucleation and growth of point islands on a one-dimensional substrate during monomer deposition is considered for general critical island size $i$. A fragmentation theory approach yields…
A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…
We generalize the standard computation of homogeneous nucleation theory at zero temperature to a scenario in which the bubble shape is determined self-consistently with its quantum fluctuations. Studying two scalar models in 1+1 dimensions,…
What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(\lambda, F)$ plane, where $\lambda$…
It has been experimentally established in numerous cases that precipitation of monodispersed colloids from homogeneous solutions is a complex process. Specifically, it was found that in many systems nuclei, produced rapidly in a…
Co-assembly of inorganic nanoparticles (NPs) and nanostructured polymer matrix represents an intricate interplay of enthalpic or entropic forces. Particle size largely affects the phase behavior of the nanocomposite. Theoretical studies…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…