2,765 research outputs found
Quasi-Topological Ricci Polynomial Gravities
Quasi-topological terms in gravity can be viewed as those that give no
contribution to the equations of motion for a special subclass of metric
ans\"atze. They therefore play no r\^ole in constructing these solutions, but
can affect the general perturbations. We consider Einstein gravity extended
with Ricci tensor polynomial invariants, which admits Einstein metrics with
appropriate effective cosmological constants as its vacuum solutions. We
construct three types of quasi-topological gravities. The first type is for the
most general static metrics with spherical, toroidal or hyperbolic isometries.
The second type is for the special static metrics where is
constant. The third type is the linearized quasi-topological gravities on the
Einstein metrics. We construct and classify results that are either dependent
on or independent of dimensions, up to the tenth order. We then consider a
subset of these three types and obtain Lovelock-like quasi-topological
gravities, that are independent of the dimensions. The linearized gravities on
Einstein metrics on all dimensions are simply Einstein and hence ghost free.
The theories become quasi-topological on static metrics in one specific
dimension, but non-trivial in others. We also focus on the quasi-topological
Ricci cubic invariant in four dimensions as a specific example to study its
effect on holography, including shear viscosity, thermoelectric DC
conductivities and butterfly velocity. In particular, we find that the
holographic diffusivity bounds can be violated by the quasi-topological terms,
which can induce an extra massive mode that yields a butterfly velocity unbound
above.Comment: Latex, 56 pages, discussion on shear viscosity revise
Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel
The numerical simulation of steady planar two-dimensional, laminar flow of an incompressible fluid through an abruptly contracting channel using spectral domain decomposition methods is described. The key features of the method are the decomposition of the flow region into a number of rectangular subregions and spectral approximations which are pointwise C(1) continuous across subregion interfaces. Spectral approximations to the solution are obtained for Reynolds numbers in the range 0 to 500. The size of the salient corner vortex decreases as the Reynolds number increases from 0 to around 45. As the Reynolds number is increased further the vortex grows slowly. A vortex is detected downstream of the contraction at a Reynolds number of around 175 that continues to grow as the Reynolds number is increased further
Multi-Trace Superpotentials vs. Matrix Models
We consider N = 1 supersymmetric U(N) field theories in four dimensions with
adjoint chiral matter and a multi-trace tree-level superpotential. We show that
the computation of the effective action as a function of the glueball
superfield localizes to computing matrix integrals. Unlike the single-trace
case, holomorphy and symmetries do not forbid non-planar contributions.
Nevertheless, only a special subset of the planar diagrams contributes to the
exact result. Some of the data of this subset can be computed from the large-N
limit of an associated multi-trace Matrix model. However, the prescription
differs in important respects from that of Dijkgraaf and Vafa for single-trace
superpotentials in that the field theory effective action is not the derivative
of a multi-trace matrix model free energy. The basic subtlety involves the
correct identification of the field theory glueball as a variable in the Matrix
model, as we show via an auxiliary construction involving a single-trace matrix
model with additional singlet fields which are integrated out to compute the
multi-trace results. Along the way we also describe a general technique for
computing the large-N limits of multi-trace Matrix models and raise the
challenge of finding the field theories whose effective actions they may
compute. Since our models can be treated as N = 1 deformations of pure N =2
gauge theory, we show that the effective superpotential that we compute also
follows from the N = 2 Seiberg-Witten solution. Finally, we observe an
interesting connection between multi-trace local theories and non-local field
theory.Comment: 35 pages, LaTeX, 6 EPS figures. v2: typos fixed, v3: typos fixed,
references added, Sec. 5 added explaining how multi-trace theories can be
linearized in traces by addition of singlet fields and the relation of this
approach to matrix model
Vortex crystals
Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.published or submitted for publicationis peer reviewe
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