21,368 research outputs found
Gutzwiller description of non-magnetic Mott insulators: a dimer lattice model
We introduce a novel extension of the Gutzwiller variational wavefunction
able to deal with insulators that escape any mean-field like description, as
for instance non-magnetic insulators. As an application, we study the Mott
transition from a paramagnetic metal into a non-magnetic Peierls, or
valence-bond, Mott insulator. We analyze this model by means of our Gutzwiller
wavefunction analytically in the limit of large coordination lattices, where we
find that: (1) the Mott transition is first order; (2) the Peierls gap is large
in the Mott insulator, although it is mainly contributed by the electron
repulsion; (3) singlet-superconductivity arises around the transition.Comment: 15 pages, 9 figure
The influence of convective exchanges on coandã effect
Modeling Coandã effect has been a fundamental issue in fluid dynamic research in the XX century. It has lost some interest because of the improvement in CFD, even if it could be still important in the area of the preliminary design of aerodynamic devices that benefits of fluid deflection by convex surfaces. An effective model of Coandã effect has not been defined, and fundamental questions are still open. The influence of convective heat exchange on Coandã adhesion of a fluid stream on a convex surface in the presence of a temperature gradient between the fluid and the convex surface is a problem, which affects many practical cases, but it is still marginally approached by scientific literature. This paper aims to start an effective research direction on the effects of convective heat exchange on Coandã effect. It approaches the problem with a set of CFD simulations. It analyses the previous hypotheses, which are based on Prandtl number and evidences the need of a more effective model that accounts also for the Reynolds number
Some Preconditioning Techniques for Saddle Point Problems
Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to saddle point systems. This paper provides a concise overview of iterative approaches for the solution of such systems which are of particular importance in the context of large scale computation. In particular we describe some of the most useful preconditioning techniques for Krylov subspace solvers applied to saddle point problems, including block and constrained preconditioners.\ud
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The work of Michele Benzi was supported in part by the National Science Foundation grant DMS-0511336
Curve counting, instantons and McKay correspondences
We survey some features of equivariant instanton partition functions of
topological gauge theories on four and six dimensional toric Kahler varieties,
and their geometric and algebraic counterparts in the enumerative problem of
counting holomorphic curves. We discuss the relations of instanton counting to
representations of affine Lie algebras in the four-dimensional case, and to
Donaldson-Thomas theory for ideal sheaves on Calabi-Yau threefolds. For
resolutions of toric singularities, an algebraic structure induced by a quiver
determines the instanton moduli space through the McKay correspondence and its
generalizations. The correspondence elucidates the realization of gauge theory
partition functions as quasi-modular forms, and reformulates the computation of
noncommutative Donaldson-Thomas invariants in terms of the enumeration of
generalized instantons. New results include a general presentation of the
partition functions on ALE spaces as affine characters, a rigorous treatment of
equivariant partition functions on Hirzebruch surfaces, and a putative
connection between the special McKay correspondence and instanton counting on
Hirzebruch-Jung spaces.Comment: 79 pages, 3 figures; v2: typos corrected, reference added, new
summary section included; Final version to appear in Journal of Geometry and
Physic
Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
We use the recently proposed Kaluza-Klein (KK) reduction over the time
dimension, within an effective field theory (EFT) approach, to calculate the
next to leading order (NLO) gravitational spin1-spin2 interaction between two
spinning compact objects. It is shown here that to NLO in the spin1-spin2
interaction, the reduced KK action within the stationary approximation is
sufficient to describe the gravitational interaction, and that it simplifies
calculation substantially. We also find here that the gravito-magnetic vector
field defined within the KK decomposition of the metric mostly dominates the
mediation of the interaction. Our results coincide with those calculated in the
ADM Hamiltonian formalism, and we provide another explanation for the
discrepancy with the result previously derived within the EFT approach, thus
demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the
EFT action approach.Comment: 12 pages, revtex4-1, 3 figures; v2: reference added; v3: edited,
section 3 elaborated; v4: publishe
Bayesian inference for pulsar timing models
The extremely regular, periodic radio emission from millisecond pulsars makes
them useful tools for studying neutron star astrophysics, general relativity,
and low-frequency gravitational waves. These studies require that the observed
pulse times of arrival be fit to complex timing models that describe numerous
effects such as the astrometry of the source, the evolution of the pulsar's
spin, the presence of a binary companion, and the propagation of the pulses
through the interstellar medium. In this paper, we discuss the benefits of
using Bayesian inference to obtain pulsar timing solutions. These benefits
include the validation of linearized least-squares model fits when they are
correct, and the proper characterization of parameter uncertainties when they
are not; the incorporation of prior parameter information and of models of
correlated noise; and the Bayesian comparison of alternative timing models. We
describe our computational setup, which combines the timing models of Tempo2
with the nested-sampling integrator MultiNest. We compare the timing solutions
generated using Bayesian inference and linearized least-squares for three
pulsars: B1953+29, J2317+1439, and J1640+2224, which demonstrate a variety of
the benefits that we posit.Comment: 13 pages, 4 figures, RevTeX 4.1. Revised in response to referee's
suggestions; contains a broader discussion of model comparison, revised Monte
Carlo runs, improved figure
General contact mechanics theory for randomly rough surfaces with application to rubber friction
We generalize the Persson contact mechanics and rubber friction theory to the
case where both surfaces have surface roughness. The solids can be rigid,
elastic or viscoelastic, and can be homogeneous or layered. We calculate the
contact area, the viscoelastic contribution to the friction force, and the
average interfacial separation as a function of the sliding speed and the
nominal contact pressure. We illustrate the theory with numerical results for a
rubber block sliding on a road surface. We find that with increasing sliding
speed, the influence of the roughness on the rubber block decreases, and for
typical sliding speeds involved in tire dynamics it can be neglected
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