We introduce a game form that captures a non-cooperative dimension of the consistency property of bankruptcy rules. Any consistent and monotone rule is fully characterized by a bilateral principle and consistency. Like the consistency axiom, our game form, together with a bilateral principle, yields the respective consistent bankruptcy rule as a result of a unique outcome of subgame perfect equilibria. The result holds for a large class of consistent and monotone rules, including the Constrained Equal Award, the Proportional and many other well-known rules. Moreover, for a large class of rules, all the subgame perfect equilibria are coalition-proof.

We consider the effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of ‘‘bimolecular’’ combination processes L + L’ –> (L + L’) and ‘‘unimolecular’’ fragmentations L –> L’ + (L - L’). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalescence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size (LBAR) evaluated as a function of the Peclet number P, i.e., the dimensionless ratio of flow rate-gamma and rotational diffusion coefficient D(r). For sufficiently dilute solutions, we find only a weak dependence of LBAR on P. In the semidilute regime, however, an apparent divergence in LBAR at P congruent-to 1 suggests a flow-induced first-order gelation phenomenon.

In this paper we present a rigid-rod model (involving a restricted set of orientations) which is solved first with mean-field theory and then by Monte Carlo simulation. It is shown that both interparticle attractions and anisotropic adsorption energies are necessary in order for two successive fluid-fluid transitions to occur. The first is basically a gas-liquid condensation of ‘‘lying down’’ rods in the plane of the surface, and the second involves a ‘‘standing up’’ of the particles. A close qualitative correspondence is established between the results obtained in the mean-field and Monte Carlo descriptions. The role of biaxial states, i.e., in-plane orientational ordering, is also discussed in both contexts. To this end, we develop an analogy between our one-component rod monolayer and a bidisperse system of interconverting isotropic particles.

We present a statistical-thermodynamic theory that associates fracture of a solid with the approach of a spinodal upon increasing stress. This formulation is illustrated by a one-dimensional model, and the temperature dependence of the nonlinear stress-strain relation and fracture stress is obtained. A two-dimensional network model is treated by both effective-medium theory and Monte Carlo simulations, showing metastability and the nucleation of microcracks.

Within the framework of two complementary models, we show that the densities and patterns of defects in amphiphile-water systems with lamellar organization are coupled to the strength of the bilayer-bilayer interactions and hence to the overall surfactant concentration. We consider defects which introduce curvature (i.e., larger head-group area per molecule) while preserving the integrity of stacked bilayers at surfactant volume fractions of several tenths. These features are favored if the molecules comprising the lamellae are preferentially packed with a nonplanar aggregate-water interface: curvature defects lower the local free energy in systems constrained by aggregate-aggregate interactions to lamellar geometry. As the amphiphile volume fraction is increased-and the bilayer-bilayer spacing thereby decreased-we predict phase transitions between lamellar phases of different defect patterns on the bilayer surface, with concurrent decrease in the defect area fraction per bilayer. Specifically, there is a progression from a stripe-like pattern of parallel channels to a random network of line defects to a pore phase, with the latter appearing at the highest amphiphile concentrations but characterized by the lowest density of defects. Connection is made with experimental work which has recently suggested various departures from classical lamellar structure.

The steady-state bimolecular annihilation reaction A + B –> 0 on two-dimensional surfaces is studied via computer simulations. In the simulations A and B are randomly adsorbed on vacant sites, and reaction takes place whenever A and B reach nearest-neighbor sites, either directly following adsorption or through diffusion. It is found that both with and without diffusion the reactants segregate into separate islands of A’s and B’s. The islands vary in size and exhibit highly ramified shapes. Moreover, the islands are self-similar with a fractal dimension D = 1.89 (similar to percolation, but also other clusters). D is found to be independent of the diffusion rate K. Other fractal dimensions, e.g., of the ‘‘hull’’ differ from those of percolating clusters. The steady-state coverage theta* = theta*A + theta*B decreases with K, as expected (theta*A = theta*B, corresponding to equal fluxes of A and B is the only physical solution). For systems with immobile particles (K = 0) we find theta* congruent-to 0.59 and theta* congruent-to 0.49 for the square and the triangular lattices, respectively, similar to the percolation thresholds on these lattices. The long-time characteristics of the system (D, theta*, etc.) are independent of the initial conditions of the simulation, indicating that the system reaches a stable steady state. Furthermore, for the large systems simulated (typically 500 x 500 lattice sites) it was found that the long-time behavior is independent of the input mode. Namely, the same results are obtained for conserved (i.e., exactly balanced) and nonconserved (statistically balanced) A,B input mechanisms, indicating that on the time scale of the simulations (approximately 10(4) Monte Carlo steps) the apparent steady state (for nonconserved input) is essentially identical with the true steady state (for the conserved input).

A mean field theory of chain packing in amphiphilic aggregates is used to calculate conformational and thermodynamic properties of the inverse hexagonal phase. These properties are compared with those for planar bilayers and curved monolayers. Calculated bond order parameters reveal that chains packed in the hexagonal arrangement have more conformational freedom than chains packed in a bilayer. The calculated order parameters are in good agreement with recent experimental results. Free energy calculations are also presented. It is found that for small areas per head group the packing free energy of amphiphiles in a bilayer is considerably higher than in the hexagonal phase.