107 research outputs found
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
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
Density functional theory for dense nematics with steric interactions
The celebrated work of Onsager on hard particle systems, based on the
truncated second order virial expansion, is valid at relatively low volume
fractions for large aspect ratio particles. While it predicts the
isotropic-nematic phase transition, it fails to provide a realistic equation of
state in that the pressure remains finite for arbitrarily high densities. In
this work, we derive a mean field density functional form of the Helmholtz free
energy for nematics with hard core repulsion. In addition to predicting the
isotropic-nematic transition, the model provides a more realistic equation of
state. The energy landscape is much richer, and the orientational probability
distribution function in the nematic phase possesses a unique feature: it
vanishes on a nonzero measure set in orientational space
A confined rod: mean field theory for hard rod-like particles
In this paper, we model the configurations of a system of hard rods by
viewing each rod in a cell formed by its neighbors. By minimizing the free
energy in the model and performing molecular dynamics, where, in both cases,
the shape of the cell is a free parameter, we obtain the equilibrium
orientational order parameter, free energy and pressure of the system. Our
model enables the calculation of anisotropic stresses exerted on the walls of
the cell due to shape change of the rod in photoisomerization. These results
are a key step towards understanding molecular shape change effects in
photomechanical systems under illumination.Comment: 15 pages, 8 figure
Leaky cell model of hard spheres
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan–Starling and Percus–Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials
Leaky Cell Model of Hard Spheres
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without touching another sphere. We compute these free volumes using a leaky cell model, in which the accessible space accounts for the possibility that spheres may escape from the local cage of lattice neighbors. We describe how elementary geometry may be used to calculate the free volume exactly for this leaky cell model in two- and three-dimensional lattice packings and compare the results to the well-known Carnahan–Starling and Percus–Yevick liquid models. We provide formulas for the free volumes of various lattices and use the common tangent construction to identify several phase transitions between them in the leaky cell regime, indicating the possibility of coexistence in crystalline materials
Is it still worth searching for lepton flavor violation in rare kaon decays?
Prospective searches for lepton flavor violation (LFV) in rare kaon decays at
the existing and future intermediate-energy accelerators are considered. The
proposed studies are complementary to LFV searches in muon-decay experiments
and offer a unique opportunity to probe models with approximately conserved
fermion-generation quantum number with sensitivity superior to that in other
processes. Consequently, new searches for LFV in kaon decays are an important
and independent part of the general program of searches for lepton flavor
violation in the final states with charged leptons.Comment: 30 pages, 10 figures. An extended version of the talk given at the
Chicago Flavor Seminar, February 27, 2004. In the new version some misprints
were corrected and some new data for LFV-processes were added. The main
content of the paper was not changed. The paper is published in Yad. Fiz. 68,
1272 (2005
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