Survival Probabilities at Spherical Frontiers

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: $R(t)=R_0(1+t/t^*)^{\Theta}$, where $\Theta$ is a growth exponent, $R_0$ is the initial radius, and $t^*$ is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters $t^*$ and $\Theta$ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary $\Theta$. We compare our results to simulations of linearly inflating expansions ($\Theta=1$ spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations ($\Theta=0$, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" $(\Theta=1/2)$ expansions.Comment: 35 pages, 11 figures, revised versio

Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory

We propose a new Monte-Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.Comment: 12 pages, 6 figures, accepted in Int. J. Mod. Phys.

Thermogravimetric Analysis of Indicators of the Paste Based on Sour Cream

For forming structural-mechanical properties of sour milk pastes and guaranteeing their stability at storage, it is promising to use non-fried buckwheat in their recipes that allows to raise the food value of products additionally. The aim of the researches was the study of features of the condition of moisture of sour milk pastes, based on sour cream with introducing non-fried buckwheat in the amount 5,0 % of the mixture mass. A sample with modified starch Е 1410 was taken as a control in the amount 1,3 %.The study of the moisture condition was realized by the thermogravimetric method using a derivatograph Q-1500D (Paulik-Erdey) (Hungry). It was established, that the content of adsorptive moisture of the sour milk paste was 34,0 %, whereas in the control – 34,5 %, that confirm the effectiveness of using non-fried buckwheat as a moisture-binding component. Such properties of non-fried buckwheat may be explained by the presence of starch compounds and easily accessible protein in its composition, able to hydration in the process of preparation of a component and to keeping moisture at further storage of a product

Lassoing saddle splay and the geometrical control of topological defects

Systems with holes, such as colloidal handlebodies and toroidal droplets, have been studied in the nematic liquid crystal (NLC) 4-cyano-4'-pentylbiphenyl (5CB): both point and ring topological defects can occur within each hole and around the system, while conserving the system's overall topological charge. However, what has not been fully appreciated is the ability to manipulate the hole geometry with homeotropic (perpendicular) anchoring conditions to induce complex, saddle-like deformations. We exploit this by creating an array of holes suspended in an NLC cell with oriented planar (parallel) anchoring at the cell boundaries. We study both 5CB and a binary mixture of bicyclohexane derivatives (CCN-47 and CCN-55). Through simulations and experiments, we study how the bulk saddle deformations of each hole interact to create novel defect structures, including an array of disclination lines, reminiscent of those found in liquid crystal blue phases. The line locations are tunable via the NLC elastic constants, the cell geometry, and the size and spacing of holes in the array. This research lays the groundwork for the control of complex elastic deformations of varying length scales via geometrical cues in materials that are renowned in the display industry for their stability and easy manipulability.Comment: 9 pages, 7 figures, 1 supplementary figur

Coarse Graining RNA Nanostructures for Molecular Dynamics Simulations

A series of coarse-grained models have been developed for the study of the molecular dynamics of RNA nanostructures. The models in the series have one to three beads per nucleotide and include different amounts of detailed structural information. Such a treatment allows us to reach, for the systems of thousands of nucleotides, a time scale of microseconds (i.e. by three orders of magnitude longer than in the full atomistic modelling) and thus to enable simulations of large RNA polymers in the context of bionanotechnology. We find that the 3-beads-per-nucleotide models, described by a set of just a few universal parameters, are able to describe different RNA conformations and are comparable in structural precision to the models where detailed values of the backbone P-C4' dihedrals taken from a reference structure are included. These findings are discussed in the context of the RNA conformation classes

Integrable Systems and Metrics of Constant Curvature

In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature. Kaup-Boussinesq system has three local Hamiltonian structures and one nonlocal Hamiltonian structure associated with metric of constant curvature. Darboux theorem (reducing Hamiltonian structures to canonical form ''d/dx'' by differential substitutions and reciprocal transformations) for these Hamiltonian structures is proved

Quintessence Models and the Cosmological Evolution of alpha

The cosmological evolution of a quintessence-like scalar field, phi, coupled to matter and gauge fields leads to effective modifications of the coupling constants and particle masses over time. We analyze a class of models where the scalar field potential V(phi) and the couplings to matter B(phi) admit common extremum in phi, as in the Damour-Polyakov ansatz. We find that even for the simplest choices of potentials and B(phi), the observational constraints on delta alpha/alpha coming from quasar absorption spectra, the Oklo phenomenon and Big Bang nucleosynthesis provide complementary constraints on the parameters of the model. We show the evolutionary history of these models in some detail and describe the effects of a varying mass for dark matter.Comment: 26 pages, 20 eps figure