Genetic composition of an exponentially growing cell population

We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site-specific mutation rates. For illustration we estimate mutation rates in a lung adenocarcinoma

Logarithmic current fluctuations in non-equilibrium quantum spin chains

We study zero-temperature quantum spin chains which are characterized by a non-vanishing current. For the XX model starting from the initial state |... + + + - - - ...> we derive an exact expression for the variance of the total spin current. We show that asymptotically the variance exhibits an anomalously slow logarithmic growth; we also extract the sub-leading constant term. We then argue that the logarithmic growth remains valid for the XXZ model in the critical region.Comment: 9 pages, 4 figures, minor alteration

On the Role of External Constraints in a Spatially Extended Evolutionary Prisoner's Dilemma Game

We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T), and their total payoffs come from games with the nearest neighbors. During the random sequential updates the players adopt one of their neighboring strategies if the chosen neighbor has higher payoff. We compare the effect of two types of external constraints added to the Darwinian evolutionary processes. In both cases the strategy of a randomly chosen player is replaced with probability P by another strategy. In the first case, the strategy is replaced by a randomly chosen one among the two others, while in the second case the new strategy is always C. Using generalized mean-field approximations and Monte Carlo simulations the strategy concentrations are evaluated in the stationary state for different strength of external constraints characterized by the probability P.Comment: 19 pages, 10 figure

Guiding-fields for phase-separation: Controlling Liesegang patterns

Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicron lengthscales. Thus they have significant potential for technological applications provided adequate methods of control can be devised. Here we describe a simple, physically realizable pattern-control based on the notion of driven precipitation, meaning that the phase-separation is governed by a guiding field such as, for example, a temperature or a pH field. The phase-separation is modeled through a non-autonomous Cahn-Hilliard equation whose spinodal is determined by the evolving guiding field. Control over the dynamics of the spinodal gives control over the velocity of the instability front which separates the stable and unstable regions of the system. Since the wavelength of the pattern is largely determined by this velocity, the distance between successive precipitation bands becomes controllable. We demonstrate the above ideas by numerical studies of a 1D system with diffusive guiding field. We find that the results can be accurately described by employing a linear stability analysis (pulled-front theory) for determining the velocity -- local-wavelength relationship. From the perspective of the Liesegang theory, our results indicate that the so-called revert patterns may be naturally generated by diffusive guiding fields.Comment: Minor changes, to be published in Phys. Rev. E. 10 pages, 8 figure

INVESTIGATION OF HETEROGENEOUS CATALYSTS AND OF CATALYTIC HYDROGENATION IN GAS PHASE BY ELECTROCHEMICAL METHODS

A special electrochemical measuring cell was developed for the investigation of processes taking place on the surface of supported industrial metal catalysts above 100 ⁰C in the presence of hydrogen. The dependence of cell voltage on the partial pressure of hydrogen, the activation of catalysts, the hydrogenation of benzene and selective hydrogenation of phenol was investigated with this special measuring method