Kinetics of water flow through polymer gel

The water flow through the poly(acrylamide) gel under a constant water pressure is measured by newly designed apparatus. The time evolution of the water flow in the gel, is calculated based on the collective diffusion model of the polymer network coupled with the friction between the polymer network and the water. The friction coefficient are determined from the equilibrium velocity of water flow. The Young modulus and the Poisson's ratio of the rod shape gels are measured by the uni-axial elongation experiments, which determine the longitudinal modulus independently from the water flow experiments. With the values of the longitudinal modulus and of the friction determined by the experiments, the calculated results are compared with the time evolution of the flow experiments. We find that the time evolution of the water flow is well described by a single characteristic relaxation time predicted by the collective diffusion model coupled with the water friction.Comment: 7 pages, 5 figures, 27 references, Eqs adde

Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the attractors. A mutation introduces some new aspects: the emergence of structurally stable attractors, and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the mutataion rate -> +0 region.Comment: 4 pages, 9 figure

Two-population replicator dynamics and number of Nash equilibria in random matrix games

We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed points of the dynamics and the Nash equilibria. Except for the special case of zero-sum games one finds a transition as a function of the so-called co-operation pressure between a phase in which there is a unique stable fixed point of the dynamics coinciding with a unique Nash equilibrium, and an unstable phase in which there are exponentially many Nash equilibria with statistical properties different from the stationary state of the replicator equations. Our analytical results are confirmed by numerical simulations of the replicator dynamics, and by explicit enumeration of Nash equilibria.Comment: 9 pages, 2x2 figure

A Universal Lifetime Distribution for Multi-Species Systems

Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting systems, simple models having a rule for additions and deletions of entities are investigated. We found a quite universal lifetime distribution for various kinds of inter-entity interactions, and it is well fitted by a stretched-exponential function with an exponent close to 1/2. We propose a "modified Red-Queen" hypothesis to explain this distribution. We also review empirical studies on the lifetime distribution of social entities, and discussed the applicability of the model.Comment: 10 pages, 6 figures, Proceedings of Social Modeling and Simulations + Econophysics Colloquium 201

Mechanism of femtosecond laser nano-ablation for metals

Metals have three ablation threshold fluences (high,middle and low-threshold fluence, here called) forfemtosecond laser pulses. In order to investigatethe physics of metal ablation under an intenseoptical field, the ions emitted from a laserirradiatedcopper surface were studied by time-offlightenergy spectroscopy. The low laser fluenceat which ions are emitted, Fth,L is 0.028 J/cm2, andtwo higher emission thresholds were identified atfluences of Fth,M =0.195 J/cm2 and Fth,H =0.470J/cm2. The relation between the number of emittedions per pulse Ni and laser fluence F was in goodagreement with Ni ∝F4 for Fth,L - Fth,M, Ni ∝F3 forFth,M - Fth,H, and Ni ∝F2 for ≥ Fth,H. Thedependence of ion production on laser energyfluence is explained well by multiphotonabsorption and optical field ionization.For fluence levels near the middle to high ablationthreshold, the formation of grating structures onmetal surfaces has been observed. The interspacesof grating structures were shorter than the laserwavelength, and the interspaces depend on fluencefor Mo and W with a 160 fs laser pulse. Thisphenomenon is well explained by the parametricdecay model proposed by Sakabe et al

Statistical mechanics and stability of a model eco-system

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended, references adde