scholarly journals Continuum approximations for lattice-free multi-species models of collective cell migration

2017 ◽  
Author(s):  
Oleksii M Matsiaka ◽  
Catherine J Penington ◽  
Ruth E Baker ◽  
Matthew J Simpson
Keyword(s):  
Cell Migration ◽  
Discrete Model ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Collective Cell Migration ◽  
Moment Equations ◽  
The Mean ◽  
Continuum Description ◽  
The Moment ◽  
Adhesive Forces

AbstractCell migration within tissues involves the interaction of many cells from distinct subpopulations. In this work, we present a discrete model of collective cell migration where the motion of individual cells is driven by random forces, short range repulsion forces to mimic crowding, and longer range attraction forces to mimic adhesion. This discrete model can be used to simulate a population of cells that is composed of K ≥ 1 distinct subpopulations. To analyse the discrete model we formulate a hierarchy of moment equations that describe the spatial evolution of the density of agents, pairs of agents, triplets of agents, and so forth. To solve the hierarchy of moment equations we introduce two forms of closure: (i) the mean field approximation, which effectively assumes that the distributions of individual agents are independent; and (ii) a moment dynamics description that is based on the Kirkwood superposition approximation. The moment dynamics description provides an approximate way of incorporating spatial patterns, such as agent clustering, into the continuum description. Comparing the performance of the two continuum descriptions confirms that both perform well when adhesive forces are sufficiently weak. In contrast, the moment dynamics description outperforms the mean field model when adhesive forces are sufficiently large. This is a first attempt to provide an accurate continuum description of a lattice-free, multi-species model of collective cell migration.

scholarly journals Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics

2017 ◽  
Author(s):  
Oleksii M Matsiaka ◽  
Catherine J Penington ◽  
Ruth E Baker ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Cell Migration ◽  
Stochastic Model ◽  
Cell Size ◽  
Mitomycin C ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Langevin Equations ◽  
Collective Cell Migration ◽  
Scratch Assay

AbstractScratch assays are routinely used to study the collective spreading of cell populations. In general, the rate at which a population of cells spreads is driven by the combined effects of cell migration and proliferation. To examine the effects of cell migration separately from the effects of cell proliferation, scratch assays are often performed after treating the cells with a drug that inhibits proliferation. Mitomycin-C is a drug that is commonly used to suppress cell proliferation in this context. However, in addition to suppressing cell proliferation, Mitomycin-C also causes cells to change size during the experiment, as each cell in the population approximately doubles in size as a result of treatment. Therefore, to describe a scratch assay that incorporates the effects of cell-to-cell crowding, cell-to-cell adhesion, and dynamic changes in cell size, we present a new stochastic model that incorporates these mechanisms. Our agent-based stochastic model takes the form of a system of Langevin equations that is the system of stochastic differential equations governing the evolution of the population of agents. We incorporate a time-dependent interaction force that is used to mimic the dynamic increase in size of the agents. To provide a mathematical description of the average behaviour of the stochastic model we present continuum limit descriptions using both a standard mean-field approximation, and a more sophisticated moment dynamics approximation that accounts for the density of agents and density of pairs of agents in the stochastic model. Comparing the accuracy of the two continuum descriptions for a typical scratch assay geometry shows that the incorporation of agent growth in the system is associated with a decrease in accuracy of the standard mean-field description. In contrast, the moment dynamics description provides a more accurate prediction of the evolution of the scratch assay when the increase in size of individual agents is included in the model.

scholarly journals The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

scholarly journals Locating the critical end point using the linear sigma model coupled to quarks.

2018 ◽  
Vol 172 ◽  
pp. 02003
Author(s):  
Alejandro Ayala ◽  
J. A. Flores ◽  
L. A. Hernández ◽  
S. Hernández-Ortiz
Keyword(s):  
Sigma Model ◽  
Chemical Potential ◽  
Potential Temperature ◽  
Mean Field ◽  
Field Approximation ◽  
Baryon Density ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
End Point ◽  
The Mean

We use the linear sigma model coupled to quarks to compute the effective potential beyond the mean field approximation, including the contribution of the ring diagrams at finite temperature and baryon density. We determine the model couplings and use them to study the phase diagram in the baryon chemical potential-temperature plane and to locate the Critical End Point.

scholarly journals UNDERSTANDING MAGNETIC INSTABILITY IN GAPLESS SUPERCONDUCTORS

2006 ◽  
Vol 21 (04) ◽  
pp. 910-913 ◽  
Author(s):  
Mei Huang
Keyword(s):  
Superconducting State ◽  
Phase Fluctuation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Bcs Theory ◽  
Magnetic Instability ◽  
Fermi Surfaces ◽  
Strong Phase ◽  
The Mean

Magnetic instability in gapless superconductors still remains as a puzzle. In this article, we point out that the instability might be caused by using BCS theory in mean-field approximation, where the phase fluctuation has been neglected. The mean-field BCS theory describes very well the strongly coherent or rigid superconducting state. With the increase of mismatch between the Fermi surfaces of pairing fermions, the phase fluctuation plays more and more important role, and "soften" the superconductor. The strong phase fluctuation will eventually quantum disorder the superconducting state, and turn the system into a phase-decoherent pseudogap state.

Quartetting in Fermionic Matter and Alpha-Particle Condensation in Nuclear Systems

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2513-2546 ◽  
Author(s):  
G. Röpke ◽  
P. Schuck
Keyword(s):  
Nuclear Matter ◽  
Cluster Formation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Density Region ◽  
Nuclear Matter Density ◽  
Nuclear Systems ◽  
The Mean ◽  
Finite Nuclei

Quantum condensates in nuclear matter are treated beyond the mean-field approximation, with the inclusion of cluster formation. The occurrence of a separate binding pole in the four-particle propagator in nuclear matter is investigated with respect to the formation of a condensate of α-like particles (quartetting), which is dependent on temperature and density. Due to Pauli blocking, the formation of an α-like condensate is limited to the low-density region. Consequences for finite nuclei are considered. In particular, excitations of self-conjugate 2n-Z–2n-N nuclei near the n-α-breakup threshold are candidates for quartetting. We review some results and discuss their consequences. Exploratory calculations are performed for the density dependence of the α condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density.

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