Biomedical subjects

Joachim Krug

Publications and source records attributed to Joachim Krug.

5 recordsLinked to original sources

PubMed2006

Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes.

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length L. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance d(eff) up to which the population can spread in genotype space. For d(eff) = L, the deterministic quasi-species theory operates while for d(eff) < 1, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasi-species theory below a crossover time T(x) while above T(x) the population gets trapped at a local fitness peak and manages to find a better peak via either stochastic tunneling or double mutations. In the stochastic regime d(eff) < 1, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interpretation of evolution experiments with microbial populations.

Adaptation, Biological↗

PubMed2005

Complex shape evolution of electromigration-driven single-layer islands.

The shape evolution of two-dimensional islands through periphery diffusion biased by an electromigration force is studied numerically using a continuum approach. We show that the introduction of crystal anisotropy in the mobility of edge atoms induces a rich variety of migration modes, which include oscillatory and irregular behavior. A phase diagram in the plane of anisotropy strength and island size is constructed. The oscillatory motion can be understood in terms of stable facets that develop on one side of the island, and which the island then slides past. The facet orientations are determined analytically.

Journal Article↗

PubMed2005

Kinetics of step bunching during growth: a minimal model.

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio d of the attachment rate to the terrace diffusion coefficient. For generic parameters (d>0) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent beta approximately 0.38 . In the limit of infinitely fast terrace diffusion (d=0) linear coarsening (beta=1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when d=0 , whereas the speed vanishes with increasing size when d>0 . For d=0 an analytic description of the speed and profile of stationary bunches is developed, and a connection to the problem of front propagation into an unstable state is pointed out.

Journal Article↗

PubMed2005

Reaction kinetics in a tight spot.

The standard analysis of reaction networks based on deterministic rate equations fails in confined geometries, commonly encountered in fields such as astrochemistry, thin-film growth and cell biology. In these systems the small reactant population implies anomalous behavior of reaction rates, which can be accounted for only by following the full distribution of reactant numbers.

Catalysis↗

PubMed2003

Reaction kinetics in confined geometries: lonely adatoms in space.

There is a close relation between the problems of second-layer nucleation in epitaxial crystal growth and chemical surface reactions, such as hydrogen recombination, on interstellar dust grains. In both cases, standard rate equation analysis has been found to fail because the process takes place in a confined geometry, and under typical conditions the mean number of reactant particles on the surface is small compared to unity (the lonely adatom regime). Using scaling arguments developed in the context of second-layer nucleation, I present a simple derivation of the hydrogen recombination rate for small and large grains. I clarify the reasons for the failure of rate equations for small grains, and point out a logarithmic correction to the reaction rate when the reaction is limited by the desorption of hydrogen atoms (the second-order reaction regime).

Journal Article↗