Elastic Effects in Disordered Nematic Networks

Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit unusual soft mechanical response against stretching. It arises from gradual alignment of orientationally correlated regions that are elongated along the director. A sharp crossover to a macroscopically aligned state is obtained on further stretching. The effect of random internal stress is also discussed.Comment: 5 pages, 5 figure

Timelike Infinity and Asymptotic Symmetry

By extending Ashtekar and Romano's definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike 3-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on asymptotically flat spacetimes at timelike infinity. Asymptotic flatness is characterized by the fall-off rate of the energy-momentum tensor at timelike infinity, which makes it easier to understand physically what spacetimes are investigated. The notion of the order of the asymptotic flatness is naturally introduced from the rate. The definition gives a systematized picture of hierarchy in the asymptotic structure, which was not clear in the previous works. It is found that if the energy-momentum tensor falls off at a rate faster than $\sim t^{-2}$, the spacetime is asymptotically flat and asymptotically stationary in the sense that the Lie derivative of the metric with respect to \ppp_t falls off at the rate $\sim t^{-2}$. It also admits an asymptotic symmetry group similar to the Poincar\'e group. If the energy-momentum tensor falls off at a rate faster than $\sim t^{-3}$, the four-momentum of a spacetime may be defined. On the other hand, angular momentum is defined only for spacetimes in which the energy-momentum tensor falls off at a rate faster than $\sim t^{-4}$.Comment: 19 pages, LaTex, the final version to appear in J. Math. Phy

The evolution of cooperation by social exclusion

The exclusion of freeriders from common privileges or public acceptance is widely found in the real world. Current models on the evolution of cooperation with incentives mostly assume peer sanctioning, whereby a punisher imposes penalties on freeriders at a cost to itself. It is well known that such costly punishment has two substantial difficulties. First, a rare punishing cooperator barely subverts the asocial society of freeriders, and second, natural selection often eliminates punishing cooperators in the presence of non-punishing cooperators (namely, "second-order" freeriders). We present a game-theoretical model of social exclusion in which a punishing cooperator can exclude freeriders from benefit sharing. We show that such social exclusion can overcome the above-mentioned difficulties even if it is costly and stochastic. The results do not require a genetic relationship, repeated interaction, reputation, or group selection. Instead, only a limited number of freeriders are required to prevent the second-order freeriders from eroding the social immune system.Comment: 28 pages, 3 figures, supplementary material (materials and methods, and 6 supplementary figures

Optimal Timber Rotation on Multiple Stands with an Asymmetric Externality

Replaced with revised version of paper 07/28/05.forest economics, multiple stands, non-timber goods, flood risk, spatial externality, additivity properties, Resource /Energy Economics and Policy, Q23, Q57,

Synchronization in A Carpet of Hydrodynamically Coupled Rotors with Random Intrinsic Frequency

We investigate synchronization caused by long-range hydrodynamic interaction in a two-dimensional, substrated array of rotors with random intrinsic frequencies. The rotor mimics a flagellated bacterium that is attached to the substrate ("bacterial carpet") and exerts an active force on the fluid. Transition from coherent to incoherent regimes is studied numerically, and the results are compared to a mean-field theory. We show that quite a narrow distribution of the intrinsic frequency is required to achieve collective motion in realistic cases. The transition is gradual, and the critical behavior is qualitatively different from that of the conventional globally coupled oscillators. The model not only serves as a novel example of non-locally coupled oscillators, but also provides insights into the role of intrinsic heterogeneities in living and artificial microfluidic actuators.Comment: 5 pages, 5 figure

Quantum Radion on de Sitter branes

The quantum fluctuation of the relative location of two (n-1)-dimensional de Sitter branes (i.e., of n spacetime dimensions) embedded in the (n+1)-dimensional anti-de Sitter bulk, which we shall call the quantum radion, is investigated at the linear perturbation level. The quantization of the radion is done by deriving the effective action of the radion. Assuming the positive tension brane is our universe, the effect of the quantum radion is evaluated by using the effective Einstein equations on the brane in which the radion contributes to the effective energy momentum tensor at the linear order of the radion amplitude. Specifically, the rms effective energy density arising from the quantum radion is compared with the background energy density. It is found out that this ratio remains small for reasonable values of the parameters of the model even without introducing a stabilizing mechanism for radion, although the radion itself has a negative mass squared and is unstable. The reason behind this phenomenon is also discussed.Comment: 17 pages, no figure