1,520 research outputs found
Uniqueness and Non-uniqueness in the Einstein Constraints
The conformal thin sandwich (CTS) equations are a set of four of the Einstein
equations, which generalize the Laplace-Poisson equation of Newton's theory. We
examine numerically solutions of the CTS equations describing perturbed
Minkowski space, and find only one solution. However, we find {\em two}
distinct solutions, one even containing a black hole, when the lapse is
determined by a fifth elliptic equation through specification of the mean
curvature. While the relationship of the two systems and their solutions is a
fundamental property of general relativity, this fairly simple example of an
elliptic system with non-unique solutions is also of broader interest.Comment: 4 pages, 4 figures; abstract and introduction rewritte
Counting Points on Genus 2 Curves with Real Multiplication
We present an accelerated Schoof-type point-counting algorithm for curves of
genus 2 equipped with an efficiently computable real multiplication
endomorphism. Our new algorithm reduces the complexity of genus 2 point
counting over a finite field (\F_{q}) of large characteristic from
(\widetilde{O}(\log^8 q)) to (\widetilde{O}(\log^5 q)). Using our algorithm we
compute a 256-bit prime-order Jacobian, suitable for cryptographic
applications, and also the order of a 1024-bit Jacobian
Microscopic formulation of the Zimm-Bragg model for the helix-coil transition
A microscopic spin model is proposed for the phenomenological Zimm-Bragg
model for the helix-coil transition in biopolymers. This model is shown to
provide the same thermophysical properties of the original Zimm-Bragg model and
it allows a very convenient framework to compute statistical quantities.
Physical origins of this spin model are made transparent by an exact mapping
into a one-dimensional Ising model with an external field. However, the
dependence on temperature of the reduced external field turns out to differ
from the standard one-dimensional Ising model and hence it gives rise to
different thermophysical properties, despite the exact mapping connecting them.
We discuss how this point has been frequently overlooked in the recent
literature.Comment: 11 pages, 2 figure
Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
We describe how the iterative technique used by Isenberg and Moncrief to
verify the existence of large sets of non constant mean curvature solutions of
the Einstein constraints on closed manifolds can be adapted to verify the
existence of large sets of asymptotically hyperbolic non constant mean
curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure
Cantor type functions in non-integer bases
Cantor's ternary function is generalized to arbitrary base-change functions
in non-integer bases. Some of them share the curious properties of Cantor's
function, while others behave quite differently
Trapped Surfaces in Vacuum Spacetimes
An earlier construction by the authors of sequences of globally regular,
asymptotically flat initial data for the Einstein vacuum equations containing
trapped surfaces for large values of the parameter is extended, from the time
symmetric case considered previously, to the case of maximal slices. The
resulting theorem shows rigorously that there exists a large class of initial
configurations for non-time symmetric pure gravitational waves satisfying the
assumptions of the Penrose singularity theorem and so must have a singularity
to the future.Comment: 14 page
Testing Hardy nonlocality proof with genuine energy-time entanglement
We show two experimental realizations of Hardy ladder test of quantum
nonlocality using energy-time correlated photons, following the scheme proposed
by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)].
Unlike, previous energy-time Bell experiments, these tests require precise
tailored nonmaximally entangled states. One of them is equivalent to the
two-setting two-outcome Bell test requiring a minimum detection efficiency. The
reported experiments are still affected by the locality and detection
loopholes, but are free of the post-selection loophole of previous energy-time
and time-bin Bell tests.Comment: 5 pages, revtex4, 6 figure
Membranes in rod solutions: a system with spontaneously broken symmetry
We consider a dilute solution of infinitely rigid rods near a curved,
perfectly repulsive surface and study the contribution of the rod depletion
layer to the bending elastic constants of membranes. We find that a spontaneous
curvature state can be induced by exposure of BOTH sides of the membrane to a
rod solution. A similar result applies for rigid disks with a diameter equal to
the rod's length. We also study the confinement of rods in spherical and
cylindrical repulsive shells. This helps elucidate a recent discussion on
curvature effects in confined quantum mechanical and polymer systems.Comment: 10 pages, 2 figures, 1 table; submitted to PR
Competition for hydrogen bond formation in the helix-coil transition and protein folding
The problem of the helix-coil transition of biopolymers in explicit solvents,
like water, with the ability for hydrogen bonding with solvent is addressed
analytically using a suitably modified version of the Generalized Model of
Polypeptide Chains. Besides the regular helix-coil transition, an additional
coil-helix or reentrant transition is also found at lower temperatures. The
reentrant transition arises due to competition between polymer-polymer and
polymer-water hydrogen bonds. The balance between the two types of hydrogen
bonding can be shifted to either direction through changes not only in
temperature, but also by pressure, mechanical force, osmotic stress or other
external influences. Both polypeptides and polynucleotides are considered
within a unified formalism. Our approach provides an explanation of the
experimental difficulty of observing the reentrant transition with pressure;
and underscores the advantage of pulling experiments for studies of DNA.
Results are discussed and compared with those reported in a number of recent
publications with which a significant level of agreement is obtained.Comment: 21 pages, 3 figures, submitted to Phys Rev
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