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Domain Growth, Budding, and Fission in Phase Separating Self-Assembled Fluid Bilayers
A systematic investigation of the phase separation dynamics in self-assembled
multi-component bilayer fluid vesicles and open membranes is presented. We use
large-scale dissipative particle dynamics to explicitly account for solvent,
thereby allowing for numerical investigation of the effects of hydrodynamics
and area-to-volume constraints. In the case of asymmetric lipid composition, we
observed regimes corresponding to coalescence of flat patches, budding,
vesiculation and coalescence of caps. The area-to-volume constraint and
hydrodynamics have a strong influence on these regimes and the crossovers
between them. In the case of symmetric mixtures, irrespective of the
area-to-volume ratio, we observed a growth regime with an exponent of 1/2. The
same exponent is also found in the case of open membranes with symmetric
composition
Why do axons differ in caliber?
CNS axons differ in diameter (d) by nearly 100-fold (∼0.1-10 μm); therefore, they differ in cross-sectional area (d(2)) and volume by nearly 10,000-fold. If, as found for optic nerve, mitochondrial volume fraction is constant with axon diameter, energy capacity would rise with axon volume, also as d(2). We asked, given constraints on space and energy, what functional requirements set an axon's diameter? Surveying 16 fiber groups spanning nearly the full range of diameters in five species (guinea pig, rat, monkey, locust, octopus), we found the following: (1) thin axons are most numerous; (2) mean firing frequencies, estimated for nine of the identified axon classes, are low for thin fibers and high for thick ones, ranging from ∼1 to >100 Hz; (3) a tract's distribution of fiber diameters, whether narrow or broad, and whether symmetric or skewed, reflects heterogeneity of information rates conveyed by its individual fibers; and (4) mitochondrial volume/axon length rises ≥d(2). To explain the pressure toward thin diameters, we note an established law of diminishing returns: an axon, to double its information rate, must more than double its firing rate. Since diameter is apparently linear with firing rate, doubling information rate would more than quadruple an axon's volume and energy use. Thicker axons may be needed to encode features that cannot be efficiently decoded if their information is spread over several low-rate channels. Thus, information rate may be the main variable that sets axon caliber, with axons constrained to deliver information at the lowest acceptable rate
Finite Volume Chiral Partition Functions and the Replica Method
In the framework of chiral perturbation theory we demonstrate the equivalence
of the supersymmetric and the replica methods in the symmetry breaking classes
of Dyson indices \beta=1 and \beta=4. Schwinger-Dyson equations are used to
derive a universal differential equation for the finite volume partition
function in sectors of fixed topological charge, \nu. All dependence on the
symmetry breaking class enters through the Dyson index \beta. We utilize this
differential equation to obtain Virasoro constraints in the small mass
expansion for all \beta and in the large mass expansion for \beta=2 with
arbitrary \nu. Using quenched chiral perturbation theory we calculate the first
finite volume correction to the chiral condensate demonstrating how, for all
\betathere exists a region in which the two expansion schemes of quenched
finite volume chiral perturbation theory overlap.Comment: RevTeX, 18 pages. Some typos corrected and a note added in the
introduction to section III. To appear in Phys. Rev.
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