Influence of a small fraction of individuals with enhanced mutations on a population genetic pool

Computer simulations of the Penna ageing model suggest that already a small fraction of births with enhanced number of new mutations can negatively influence the whole population.Comment: 10 pages including 6 figures; draf

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Noise driven dynamic phase transition in a a one dimensional Ising-like model

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (henceforth referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model and $\beta \to \infty$ to the original model I. The equilibrium behaviour for any value of $\beta$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $\beta \neq 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $\beta = 0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}(\beta, L) = (\beta/L)^{\alpha}f(\beta)$, where $\alpha$ remains constant for all $\beta \neq 0$ supporting the existence of the dynamic phase transition at $\beta =0$. The scaling function $f(\beta)$ shows a crossover behaviour with $f(\beta) = \rm{constant}$ for $\beta <<1$ and $f(\beta) \propto \beta^{-\alpha}$ for $\beta >>1$.Comment: 4 pages, 5 figures, accepted version in Physical Review

Isostaticity of Constraints in Jammed Systems of Soft Frictionless Platonic Solids

The average number of constraints per particle $$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($\rightarrow 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming chain-like face-face clusters with finite extent form in these systems.Comment: 4 pages, 3 figures, 4 tabl