1,211,082 research outputs found
Classical general relativity as BF-Plebanski theory with linear constraints
We investigate a formulation of continuum 4d gravity in terms of a
constrained BF theory, in the spirit of the Plebanski formulation, but
involving only linear constraints, of the type used recently in the spin foam
approach to quantum gravity. We identify both the continuum version of the
linear simplicity constraints used in the quantum discrete context and a linear
version of the quadratic volume constraints that are necessary to complete the
reduction from the topological theory to gravity. We illustrate and discuss
also the discrete counterpart of the same continuum linear constraints.
Moreover, we show under which additional conditions the discrete volume
constraints follow from the simplicity constraints, thus playing the role of
secondary constraints.Comment: 16 pages, revtex, changed one cross-reference in sect. IIIC to match
journal versio
Are Compact Hyperbolic Models Observationally Ruled Out?
We revisit the observational constraints on compact(closed) hyperbolic(CH)
models from cosmic microwave background(CMB). We carry out Bayesian analyses
for CH models with volume comparable to the cube of the present curvature
radius using the COBE-DMR data and show that a slight suppression in the
large-angle temperature correlations owing to the non-trivial topology explains
rather naturally the observed anomalously low quadrupole which is incompatible
with the prediction of the standard infinite Friedmann-Robertson-Walker models.
While most of positions and orientations are ruled out, the likelihoods of CH
models are found to be much better than those of infinite counterparts for some
specific positions and orientations of the observer, leading to less stringent
constraints on the volume of the manifolds. Even if the spatial geometry is
nearly flat as , suppression of the angular power on
large angular scales is still prominent for CH models with volume much less
than the cube of the present curvature radius if the cosmological constant is
dominant at present.Comment: 25 pages, 16 EPS figures Version accepted for publication in PT
Effects of geometric constraints on the nuclear multifragmentation process
We include in statistical model calculations the facts that in the nuclear
multifragmentation process the fragments are produced within a given volume and
have a finite size. The corrections associated with these constraints affect
the partition modes and, as a consequence, other observables in the process. In
particular, we find that the favored fragmenting modes strongly suppress the
collective flow energy, leading to much lower values compared to what is
obtained from unconstrained calculations. This leads, for a given total
excitation energy, to a nontrivial correlation between the breakup temperature
and the collective expansion velocity. In particular we find that, under some
conditions, the temperature of the fragmenting system may increase as a
function of this expansion velocity, contrary to what it might be expected.Comment: 16 pages, 5 figure
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
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