Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems

Computer modeling of multicellular systems has been a valuable tool for interpreting and guiding in vitro experiments relevant to embryonic morphogenesis, tumor growth, angiogenesis and, lately, structure formation following the printing of cell aggregates as bioink particles. Computer simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in explaining and predicting the resulting stationary structures (corresponding to the lowest adhesion energy state). Here we present two alternatives to the MMC approach for modeling cellular motion and self-assembly: (1) a kinetic Monte Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC, both KMC and CPD methods are capable of simulating the dynamics of the cellular system in real time. In the KMC approach a transition rate is associated with possible rearrangements of the cellular system, and the corresponding time evolution is expressed in terms of these rates. In the CPD approach cells are modeled as interacting cellular particles (CPs) and the time evolution of the multicellular system is determined by integrating the equations of motion of all CPs. The KMC and CPD methods are tested and compared by simulating two experimentally well known phenomena: (1) cell-sorting within an aggregate formed by two types of cells with different adhesivities, and (2) fusion of two spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev

Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde

Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential

Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating soliton-like wave packet and the wave front is wedge shaped. In a statistical mechanics framework our solution represents the partition sum of a directed polymer subjected to a potential layer with alternating (attractive and repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon request at [email protected] . Physical Review Letter

Equilibrium of anchored interfaces with quenched disordered growth

The roughening behavior of a one-dimensional interface fluctuating under quenched disorder growth is examined while keeping an anchored boundary. The latter introduces detailed balance conditions which allows for a thorough analysis of equilibrium aspects at both macroscopic and microscopic scales. It is found that the interface roughens linearly with the substrate size only in the vicinity of special disorder realizations. Otherwise, it remains stiff and tilted.Comment: 6 pages, 3 postscript figure

The dynamics of coset dimensional reduction

The evolution of multiple scalar fields in cosmology has been much studied, particularly when the potential is formed from a series of exponentials. For a certain subclass of such systems it is possible to get `assisted` behaviour, where the presence of multiple terms in the potential effectively makes it shallower than the individual terms indicate. It is also known that when compactifying on coset spaces one can achieve a consistent truncation to an effective theory which contains many exponential terms, however, if there are too many exponentials then exact scaling solutions do not exist. In this paper we study the potentials arising from such compactifications of eleven dimensional supergravity and analyse the regions of parameter space which could lead to scaling behaviour.Comment: 27 pages, 4 figures; added citation

Stochastic strength prediction of masonry structures: a methodological approach or a way forward?

Today, there are several computational models to predict the mechanical behaviour of masonry structures subjected to external loading. Such models require the input of material parameters to describe the mechanical behaviour and strength of masonry constructions. Although such masonry material parameters are characterised by stochastic-probabilistic nature, engineers are assigning the same material properties throughout the structure to be analysed. The aim of this paper is to propose a methodology which considers material spatial variability and stochastic strength prediction for masonry structures. The methodology is illustrated on a case study covering the in-plane behaviour of a low bond strength masonry wall panel containing an opening. A 2D non-linear computational model based on the Discrete Element Method (DEM) is used. The computational results are compared against those obtained from the experimental findings in terms of failure mode and structural capacity. It is shown that computational models which consider the spatial variability of masonry material properties better predict the load carrying capacity, stiffness and failure mode of the masonry structures. These observations provide new insights into structural behaviour of masonry constructions and lead to suggestions for improving assessment techniques for masonry structures

Quantum interface unbinding transitions

We consider interfacial phenomena accompanying bulk quantum phase transitions in presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature T_c down to T=0. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations, where the bulk order sets in discontinuously at T=0, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\geq 2$ and extract the values of the exponents describing the interfacial singularities in $d\geq 3$

Non-locality and short-range wetting phenomena

We propose a non-local interfacial model for 3D short-range wetting at planar and non-planar walls. The model is characterized by a binding potential \emph{functional} depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tube-like fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories, and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong non-perturbative influence of non-locality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let

Network formation of tissue cells via preferential attraction to elongated structures

Vascular and non-vascular cells often form an interconnected network in vitro, similar to the early vascular bed of warm blooded embryos. Our time-lapse recordings show that the network forms by extending sprouts, i.e., multicellular linear segments. To explain the emergence of such structures, we propose a simple model of preferential attraction to stretched cells. Numerical simulations reveal that the model evolves into a quasi-stationary pattern containing linear segments, which interconnect above the critical volume fraction of 0.2. In the quasi-stationary state the generation of new branches offset the coarsening driven by surface tension. In agreement with empirical data, the characteristic size of the resulting polygonal pattern is density-independent within a wide range of volume fractions

The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model

A formula for the mass-gap of the supersymmetric \CP^{n-1} sigma model ($n > 1$) in two dimensions is derived: $m/\Lambda_{\overline{\rm MS}}=\sin(\pi\Delta)/(\pi\Delta)$ where $\Delta=1/n$ and $m$ is the mass of the fundamental particle multiplet. This result is obtained by comparing two expressions for the free-energy density in the presence of a coupling to a conserved charge; one expression is computed from the exact S-matrix of K\"oberle and Kurak via the thermodynamic Bethe ansatz and the other is computed using conventional perturbation theory. These calculations provide a stringent test of the S-matrix, showing that it correctly reproduces the universal part of the beta-function and resolving the problem of CDD ambiguities.Comment: Plain TeX (macro included), CERN-TH.7426/94, SWAT/93-94/4