2,031 research outputs found
Concavity analysis of the tangent method
The tangent method has recently been devised by Colomo and Sportiello
(arXiv:1605.01388 [math-ph]) as an efficient way to determine the shape of
arctic curves. Largely conjectural, it has been tested successfully in a
variety of models. However no proof and no general geometric insight have been
given so far, either to show its validity or to allow for an understanding of
why the method actually works. In this paper, we propose a universal framework
which accounts for the tangency part of the tangent method, whenever a
formulation in terms of directed lattice paths is available. Our analysis shows
that the key factor responsible for the tangency property is the concavity of
the entropy (also called the Lagrangean function) of long random lattice paths.
We extend the proof of the tangency to -deformed paths.Comment: published version, 22 page
Exact mean-field solution of a spin chain with short-range and long-range interactions
We consider the transverse field Ising model with additional all-to-all
interactions between the spins. We show that a mean-field treatment of this
model becomes exact in the thermodynamic limit, despite the presence of 1D
short-range interactions. This is established by looking for eigenstates as
coherent states with an amplitude that varies through the Hilbert space. We
study then the thermodynamics of the model and identify the different phases.
Among its peculiar features, this 1D model possesses a second-order phase
transition at finite temperature and exhibits inverse melting.Comment: 27 page
Hamilton decompositions of regular bipartite tournaments
A regular bipartite tournament is an orientation of a complete balanced
bipartite graph where every vertex has its in- and outdegree both
equal to . In 1981, Jackson conjectured that any regular bipartite
tournament can be decomposed into Hamilton cycles. We prove this conjecture for
all sufficiently large bipartite tournaments. Along the way, we also prove
several further results, including a conjecture of Liebenau and Pehova on
Hamilton decompositions of dense bipartite digraphs.Comment: 119 pages, 4 figure
On tidal capture of primordial black holes by neutron stars
The fraction of primordial black holes (PBHs) of masses g
in the total amount of dark matter may be constrained by considering their
capture by neutron stars (NSs), which leads to the rapid destruction of the
latter. The constraints depend crucially on the capture rate which, in turn, is
determined by the energy loss by a PBH passing through a NS. Two alternative
approaches to estimate the energy loss have been used in the literature: the
one based on the dynamical friction mechanism, and another on tidal
deformations of the NS by the PBH. The second mechanism was claimed to be more
efficient by several orders of magnitude due to the excitation of particular
oscillation modes reminiscent of the surface waves. We address this
disagreement by considering a simple analytically solvable model that consists
of a flat incompressible fluid in an external gravitational field. In this
model, we calculate the energy loss by a PBH traversing the fluid surface. We
find that the excitation of modes with the propagation velocity smaller than
that of PBH is suppressed, which implies that in a realistic situation of a
supersonic PBH the large contributions from the surface waves are absent and
the above two approaches lead to consistent expressions for the energy loss.Comment: 7 page
Enhanced transmission of slit arrays in an extremely thin metallic film
Horizontal resonances of slit arrays are studied. They can lead to an
enhanced transmission that cannot be explained using the single-mode
approximation. A new type of cavity resonance is found when the slits are
narrow for a wavelength very close to the period. It can be excited for very
low thicknesses. Optimization shows these structures could constitute
interesting monochromatic filters
Large-Eddy Simulation and experimental study of cycle-to-cycle variations of stable and unstable operating points in a spark ignition engine
This article presents a comparison between experiments and Large-Eddy Simulation (LES) of a spark ignition engine on two operating points: a stable one characterized by low cycle-to-cycle variations (CCV) and an unstable one with high CCV. In order to match the experimental cycle sample, 75 full cycles (with combustion) are computed by LES. LES results are compared with experiments by means of pressure signals in the intake and exhaust ducts, in-cylinder pressure, chemiluminescence and OH Planar Laser Induced Fluorescence (PLIF). Results show that LES is able to: (1) reproduce the flame behavior in both cases (low and high CCV) in terms of position, shape and timing; (2) distinguish a stable point from an unstable one; (3) predict quantitatively the CCV levels of the two fired operating points. For the unstable case, part of the observed CCV is due to incomplete combustion. The results are then used to analyze the incomplete combustion phenomenon which occurs for some cycles of the unstable point and propose modification of the spark location to control CCV
Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model
International audienceThis paper considers the problem of a fluid-driven fracture propagating in a permeable poroelastic medium. We develop a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model and the flow within the fracture by the lubrication equation. The hydro-mechanical equations are solved with a fully coupled approach, using the developed zero-thickness element for the propagating fracture and conventional bulk finite elements for the surrounding medium. The numerical results are compared to analytical asymptotic solutions under zero fluid lag assumption in the four following limiting propagation regimes: toughness-fracture storage, toughness-leak-off, viscosity-fracture storage and viscosity-leak-off dominated. We demonstrate the ability of our cohesive zone model in simulating the hydraulic fracture in all these propagation regimes
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