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Grand Free Energy Density of the Lattice Gas
, 2007
"... The grand free energy density A of the lattice gas, now with an explicit treatment 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 [1 ..."
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The grand free energy density A of the lattice gas, now with an explicit treatment 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
Freeenergy density functions for nematic elastomers
"... The recently proposed neoclassical theory for nematic elastomers is a molecularstatistical generalization of classical Gaussian network theory. The resulting freeenergy density predicts the phenomenon of soft elasticity—the ability of elastomers to undergo large deformations with zero force and ..."
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Cited by 2 (0 self)
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The recently proposed neoclassical theory for nematic elastomers is a molecularstatistical generalization of classical Gaussian network theory. The resulting freeenergy density predicts the phenomenon of soft elasticity—the ability of elastomers to undergo large deformations with zero force
Calculating the bending moduli of the Canham–Helfrich freeenergy density from a particular potential
"... The Canham–Helfrich freeenergy density for a lipid bilayer involves the mean and Gaussian curvatures of the midsurface of the bilayer. The splay and saddlesplay moduli κ and κ ̄ regulate the sensitivity of the freeenergy density to changes of these curvatures. Seguin and Fried derived the Canham ..."
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The Canham–Helfrich freeenergy density for a lipid bilayer involves the mean and Gaussian curvatures of the midsurface of the bilayer. The splay and saddlesplay moduli κ and κ ̄ regulate the sensitivity of the freeenergy density to changes of these curvatures. Seguin and Fried de
Distortional Lifshitz Vectors and Helicity in Nematic Free Energy Density
"... 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 pseudos ..."
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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
FreeEnergy Density of the ShapeMemory Alloy AuZn
"... The shapememory alloy AuZn transforms martensitically (T M ¼ 65 K) from a cubic B2 (Pm " 3 3m) to a rhombohedral Rphase (P3) through softening of the TA 2 [110] phonon branch. We report elastic constants, specific heat, and thermal expansivity measurements through the transition. A large ela ..."
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. On the basis of these measurements, combined with established grouptheoretical symmetry criteria, the freeenergy density is presented with atomic shuffle displacements as the primary order parameter, Q. We use this freeenergy model to explain the atomic displacements in the Rphase.
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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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
Geographyinformed Energy Conservation for Ad Hoc Routing
 ACM MOBICOM
, 2001
"... We introduce a geographical adaptive fidelity (GAF) algorithm that reduces energy consumption in ad hoc wireless networks. GAF conserves energy by identifying nodes that are equivalent from a routing perspective and then turning off unnecessary nodes, keeping a constant level of routing fidelity. GA ..."
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Cited by 1045 (21 self)
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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 fourfold increase in node density leads to network lifetime increase for 3 to 6
HEED: A Hybrid, EnergyEfficient, Distributed Clustering Approach for Ad Hoc Sensor Networks
 IEEE TRANS. MOBILE COMPUTING
, 2004
"... Topology control in a sensor network balances load on sensor nodes and increases network scalability and lifetime. Clustering sensor nodes is an effective topology control approach. In this paper, we propose a novel distributed clustering approach for longlived ad hoc sensor networks. Our proposed ..."
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Cited by 590 (1 self)
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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 EnergyEfficient Distributed clustering), that periodically selects cluster heads
Performance of optical flow techniques
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1994
"... While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, ..."
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Cited by 1325 (32 self)
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, matching, energybased and phasebased 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.
Results 1  10
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51,560