Related papers: The Cellular Potts Model on Disordered Lattices
We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
We develop a mesoscopic lattice model to study the morphology formation in interacting ternary mixtures with evaporation of one component. As concrete application of our model, we wish to capture morphologies as they are typically arising…
Haldane's tight-binding model, which describes a Chern insulator in a two-dimensional hexagonal lattice, exhibits quantum Hall conductivity without an external magnetic field. Here, we explore an $\alpha -T_{3}$ lattice subjected to…
We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that…
We examine the order of the phase transition in the Potts model by using the graph representation for the partition function, which allows treating a non-integer number of Potts states. The order of transition is determined by the analysis…
An infinite system of nonlocal, individually confining solitons is considered as a model of high-density nuclear matter. The soliton-lattice problem is discussed in the Wigner-Seitz approximation. The cell size is varied to study the…
A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective two-dimensional lattice…
Biological cells are able to generate intricate structures and respond to external stimuli, sculpting their membrane from within. Simplified biomimetic systems can aid in understanding the principles which govern these shape changes and…
A lattice Boltzmann model for amphiphilic fluid dynamics is presented. It is a ternary model, in that it conserves mass separately for each chemical species present (water, oil, amphiphile), and it maintains an orientational degree of…
Confluent populations of elongated cells give rise to ordered patterns seen in nematic phase liquid crystals. We correlate cell elongation and intercellular distance with intercellular alignment using an amorphous spin glass model. We…
Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by…
We investigate the connection between the geometry of Favoured Local Structures (FLS) in liquids and the associated liquid and solid properties. We introduce a lattice spin model - the FLS model on a face-centered cubic lattice - where this…
In vivo and in vitro cells rely on the support of an underlying biocompatible substrate, such as the extracellular matrix or a culture substrate, to spread and proliferate. The mechanical and chemical properties of such structures play a…
A new class of bootstrap percolation models in which particle culling occurs only for certain numbers of nearest neighbours is introduced and studied on a Bethe lattice. Upon increasing the density of initial configuration they undergo…
In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…
The first aim of this work is to characterize when the lattice of all submodules of a module is a direct product of two lattices. In particular, which decompositions of a module $M$ produce these decompositions: the \emph{lattice…
The dynamics of dry active matter have implications for a diverse collection of biological phenomena spanning a range of length and time scales, such as animal flocking, cell tissue dynamics, and swarming of inserts and bacteria. Uniting…
A lattice Boltzmann model with interacting particles was developed in order to simulate the magneto-rheological characteristics of magnetic fluids. In the frame of this model, $6\, +\,1$ species of particles are allowed to move across a…
Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized…