11,248 research outputs found
The large core limit of spiral waves in excitable media: A numerical approach
We modify the freezing method introduced by Beyn & Thuemmler, 2004, for
analyzing rigidly rotating spiral waves in excitable media. The proposed method
is designed to stably determine the rotation frequency and the core radius of
rotating spirals, as well as the approximate shape of spiral waves in unbounded
domains. In particular, we introduce spiral wave boundary conditions based on
geometric approximations of spiral wave solutions by Archimedean spirals and by
involutes of circles. We further propose a simple implementation of boundary
conditions for the case when the inhibitor is non-diffusive, a case which had
previously caused spurious oscillations.
We then utilize the method to numerically analyze the large core limit. The
proposed method allows us to investigate the case close to criticality where
spiral waves acquire infinite core radius and zero rotation frequency, before
they begin to develop into retracting fingers. We confirm the linear scaling
regime of a drift bifurcation for the rotation frequency and the core radius of
spiral wave solutions close to criticality. This regime is unattainable with
conventional numerical methods.Comment: 32 pages, 17 figures, as accepted by SIAM Journal on Applied
Dynamical Systems on 20/03/1
An efficient new route to dihydropyranobenzimidazole inhibitors of HCV replication.
A class of dihydropyranobenzimidazole inhibitors was recently discovered that acts against the hepatitis C virus (HCV) in a new way, binding to the IRES-IIa subdomain of the highly conserved 5' untranslated region of the viral RNA and thus preventing the ribosome from initiating translation. However, the reported synthesis of these compounds is lengthy and low-yielding, the intermediates are troublesome to purify, and the route is poorly structured for the creation of libraries. We report a streamlined route to this class of inhibitors in which yields are far higher and most intermediates are crystalline. In addition, a key variable side chain is introduced late in the synthesis, allowing analogs to be easily synthesized for optimization of antiviral activity
Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing
We study the excitation of spatial patterns by resonant, multi-frequency
forcing in systems undergoing a Hopf bifurcation to spatially homogeneous
oscillations. Using weakly nonlinear analysis we show that for small amplitudes
only stripe or hexagon patterns are linearly stable, whereas square patterns
and patterns involving more than three modes are unstable. In the case of
hexagon patterns up- and down-hexagons can be simultaneously stable. The
third-order, weakly nonlinear analysis predicts stable square patterns and
super-hexagons for larger amplitudes. Direct simulations show, however, that in
this regime the third-order weakly nonlinear analysis is insufficient, and
these patterns are, in fact unstable
Notes on the Norman vocabulary
The Norman Manuscript, containing- a vocabulary
and notes on customs in use among Tasmanian
Aboriginals, was recently discovered among the archives
deposited in the Tasmanian Museum, Hobart, and is now
published in full in the Transactions of the Royal Society
of Tasmania.
It is of great value, as containing what is probably
the only vocabulary now extant in the original manuscript,
and also a number of incidental notes written by
the same hand
Noise diffraction patterns eliminated in coherent optical systems
Lens rotation technique of noise diffraction pattern elimination spreads diffracted energy, normally concentrated over small area of image, over much larger annular area. Technique advantages include simplified lens selecting process, reduced clean room requirements, and low cost equipment requirements
Breakdown of the Fermi-liquid regime in the 2D Hubbard model from a two-loop field-theoretical renormalization group approach
We analyze the particle-hole symmetric two-dimensional Hubbard model on a
square lattice starting from weak-to-moderate couplings by means of the
field-theoretical renormalization group (RG) approach up to two-loop order.
This method is essential in order to evaluate the effect of the
momentum-resolved anomalous dimension which arises in the
normal phase of this model on the corresponding low-energy single-particle
excitations. As a result, we find important indications pointing to the
existence of a non-Fermi liquid (NFL) regime at temperature displaying
a truncated Fermi surface (FS) for a doping range exactly in between the
well-known antiferromagnetic insulating and the -wave singlet
superconducting phases. This NFL evolves as a function of doping into a
correlated metal with a large FS before the -wave pairing
susceptibility finally produces the dominant instability in the low-energy
limit.Comment: 9 pages, 9 figures; published in Phys. Rev.
Symmetries,Singularities and the De-Emergence of Space
Recent work has revealed intriguing connections between a
Belinsky-Khalatnikov-Lifshitz-type analysis of spacelike singularities in
General Relativity and certain infinite dimensional Lie algebras, and in
particular the `maximally extended' hyperbolic Kac--Moody algebra E10. In this
essay we argue that these results may lead to an entirely new understanding of
the (quantum) nature of space(-time) at the Planck scale, and hence -- via an
effective `de-emergence' of space near a singularity -- to a novel mechanism
for achieving background independence in quantum gravity.Comment: 10 page
Easy implementable algorithm for the geometric measure of entanglement
We present an easy implementable algorithm for approximating the geometric
measure of entanglement from above. The algorithm can be applied to any
multipartite mixed state. It involves only the solution of an eigenproblem and
finding a singular value decomposition, no further numerical techniques are
needed. To provide examples, the algorithm was applied to the isotropic states
of 3 qubits and the 3-qubit XX model with external magnetic field.Comment: 9 pages, 3 figure
Elimination of coherent noise in a coherent light imaging system
Optical imaging systems using coherent light introduce objectionable noise into the output image plane. Dust and bubbles on and in lenses cause most of the noise in the output image. This noise usually appears as bull's-eye diffraction patterns in the image. By rotating the lens about the optical axis these diffraction patterns can be essentially eliminated. The technique does not destroy the spatial coherence of the light and permits spatial filtering of the input plane
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