Onsager's missing steps retraced

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles) Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities

Dimensional Analysis and the Time Required to Urinate

According to the recently discovered 'Law of Urination', mammals, ranging in size from mice to elephants, take, on the average, 21s to urinate. We attempt to gain insights into the physical processes responsible for this uniformity using simple dimensional analysis. We assume that the biological apparatus for urination in mammals simply scales with linear size, and consider the scenarios where the driving force is gravity or elasticity, and where the response is dominated by inertia or viscosity. We ask how the time required for urination depends on the length scale, and find that for the time to be independent of body size, the dominant driving force must be elasticity, and the dominant response viscosity. Our note demonstrates that dimensional analysis can indeed readily give insights into complex physical and biological processes

Future Reference in Hungarian with and without Future Marking

There are two main expressions which can give rise to future-oriented interpretations in Hungarian. The fog construction, which consists of an auxiliary verb and an infinitival main verb is obligatorily associated with future interpretations. The second expression, the non-past, consists of a verb inflected for person and number, with no grammatical marker of temporal reference. Interestingly, atelic predicates give rise to event-in-progress readings and telic non-past predicates give rise to future readings in the absence of future-oriented contexts or adverbs. I provide a semantics of fog and the non-past construction that accounts for these patterns through the interaction of the situation aspect of the predicate with temporal properties of the constructions in question. I argue that fog is a simple existential quantifier over future intervals, whereas the non-past restricts the time that the predicate can hold to the interval extending from now to infinitely in the future. There are three logical possibilities for how an atelic predicate like ”john run” can hold of this interval. Either the predicate holds only over the the moment of speech, P holds over some interval after speech time, or P holds of the interval where John’s running would begin at speech time and extend into the future. I argue that because telic predicates do not have the Subinterval Property, they cannot hold punctually of now, and so do not give rise to ongoing readings

Contributions of Repulsive and Attractive Interactions to Nematic Order

Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular interactions in a unified theory. This attempt is not unprecedented; what is perhaps new is the focus on the understanding of nematics in the high density limit. There, the orientational probability distribution is shown to exhibit a unique feature: it has compact support on configuration space. As attractive interactions are turned on, the behavior changes, and at a critical attractive interaction strength, thermotropic behavior of the Maier-Saupe type is attained.Comment: 14 pages, 4 figure

Director dynamics in liquid-crystal physical gels

Nematic liquid-crystal (LC) elastomers and gels have a rubbery polymer network coupled to the nematic director. While LC elastomers show a single, non-hydrodynamic relaxation mode, dynamic light-scattering studies of self-assembled liquid-crystal gels reveal orientational fluctuations that relax over a broad time scale. At short times, the relaxation dynamics exhibit hydrodynamic behavior. In contrast, the relaxation dynamics at long times are non-hydrodynamic, highly anisotropic, and increase in amplitude at small scattering angles. We argue that the slower dynamics arise from coupling between the director and the physically associated network, which prevents director orientational fluctuations from decaying completely at short times. At long enough times the network restructures, allowing the orientational fluctuations to fully decay. Director dynamics in the self-assembled gels are thus quite distinct from those observed in LC elastomers in two respects: they display soft orientational fluctuations at short times, and they exhibit at least two qualitatively distinct relaxation processes

St. Petersburg Paradox and Failure Probability

The St. Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The St. Petersburg model may be useful in a variety fields where failure and reliability are critical