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We study the evolution of one-dimensional quantum lattice systems when the ground state is perturbed by altering one site in the middle of the chain. For a large class of models, we observe a similar pattern of entanglement growth during…
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on…
For an ordered array of critical volatile wetting droplets the formation of a super lattice by an Ostwald-ripening like competition process is considered. The underlying diffusion problem is treated within a quasistatic approximation and to…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
The method of molecular dynamics is used to investigate the distribution of DOBAMBC molecules in a capsule with the fixed border layer. Change of an arrangement of molecules in smectic layers depending on an inclination of molecules on…
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain…
In this work, we investigate the shape evolution of rotated, embedded, initially cylindrical grains (with [001] cylinder axis) in Ni under an applied synthetic driving force via molecular dynamics simulations and a continuum,…
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a…
The density of states of disordered hopping models generically exhibits an essential singularity around the edges of its support, known as a Lifshitz tail. We study this phenomenon on the Bethe lattice, i.e. for the large-size limit of…
A closure endomorphism of a Hilbert algebra A is a mapping that is simultaneously an endomorphism of and a closure operator on A. It is known that the set CE of all closure endomorphisms of A is a distributive lattice where the meet of two…
We study the dynamics of upper and lower bounds of squared concurrence.Our results are similar to that of Konard et al. and can help the estimation of high-dimension bipartite entanglement in experiments.
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential…
Mechanical interactions among cells in a growing microbial colony can significantly influence the colony's spatial genetic structure and, thus, evolutionary outcomes such as the fates of rare mutations. Here, we computationally investigate…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
We study theoretically the structure of sliding grafted polymer layers or SGP layers. These interfacial structures are built by attaching each polymer to the substrate with a ring-like molecule such as cyclodextrins. Such a topological…
Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…
We consider two constructions of an envelope for a finite locally distributive strong upper semilattice. The first is based on Birkhoff's representation of finite distributive lattices and the second on valuations on lattices. We show that…
Directed growth, anisotropic cell shapes, and confinement drive self-organization in multicellular systems. We investigate the influence of particle shape on the distribution and dynamics of nematic microdomains in a minimal in-silico model…