derivation of the

The grand free energy density A of the lattice gas, now with an explicit treat-ment of excluded volume effects is: A = −kBT logZ = U − TS (7) where: U = c1(z1eψ − µ1) + c2(z2eψ − µ2) + c3(z3eψ − µ3) −TS = kBT a3 {c1a3 ln (c1a3/k) + c2a3 ln (c2a3) + c3a3 ln (c3a3) +k[1 − (c1a3/k) − c2a3 − c3a3] ln

The recently proposed neo-classical theory for nematic elastomers is a molecular-statistical generalization of classical Gaussian network theory. The resulting free-energy density pre-dicts the phenomenon of soft elasticity—the ability of elastomers to undergo large deforma-tions with zero force

The Canham–Helfrich free-energy density for a lipid bilayer involves the mean and Gaussian curvatures of the midsurface of the bilayer. The splay and saddle-splay moduli κ and κ ̄ regulate the sensitivity of the free-energy density to changes of these curvatures. Seguin and Fried de

Abstract: Here we discuss the free energy of nematic liquid crystals using two vectors and the helicity, with the aim of having a compact form of its density. The two vectors are due to the splay and bend distortions of the director field. They have a polar nature, whereas the helicity is a

. On the basis of these measurements, combined with established group-theoretical symmetry criteria, the freeenergy density is presented with atomic shuffle displacements as the primary order parameter, Q. We use this free-energy model to explain the atomic displacements in the R-phase.

that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve

studies of GAF show that it can consume 40% to 60% less energy than an unmodified ad hoc routing protocol. Moreover, simulations of GAF suggest that network lifetime increases proportionally to node density; in one example, a four-fold increase in node density leads to network lifetime increase for 3 to 6

proposed approach does not make any assumptions about the presence of infrastructure or about node capabilities, other than the availability of multiple power levels in sensor nodes. We present a protocol, HEED (Hybrid Energy-Efficient Distributed clustering), that periodically selects cluster heads

, matching, energy-based and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.