5,052 research outputs found
Finite element differential forms on curvilinear cubic meshes and their approximation properties
We study the approximation properties of a wide class of finite element
differential forms on curvilinear cubic meshes in n dimensions. Specifically,
we consider meshes in which each element is the image of a cubical reference
element under a diffeomorphism, and finite element spaces in which the shape
functions and degrees of freedom are obtained from the reference element by
pullback of differential forms. In the case where the diffeomorphisms from the
reference element are all affine, i.e., mesh consists of parallelotopes, it is
standard that the rate of convergence in L2 exceeds by one the degree of the
largest full polynomial space contained in the reference space of shape
functions. When the diffeomorphism is multilinear, the rate of convergence for
the same space of reference shape function may degrade severely, the more so
when the form degree is larger. The main result of the paper gives a sufficient
condition on the reference shape functions to obtain a given rate of
convergence.Comment: 17 pages, 1 figure; v2: changes in response to referee reports; v3:
minor additional changes, this version accepted for Numerische Mathematik;
v3: very minor updates, this version corresponds to the final published
versio
Information decomposition of multichannel EMG to map functional interactions in the distributed motor system
The central nervous system needs to coordinate multiple muscles during postural control. Functional coordination is established through the neural circuitry that interconnects different muscles. Here we used multivariate information decomposition of multichannel EMG acquired from 14 healthy participants during postural tasks to investigate the neural interactions between muscles. A set of information measures were estimated from an instantaneous linear regression model and a time-lagged VAR model fitted to the EMG envelopes of 36 muscles. We used network analysis to quantify the structure of functional interactions between muscles and compared them across experimental conditions. Conditional mutual information and transfer entropy revealed sparse networks dominated by local connections between muscles. We observed significant changes in muscle networks across postural tasks localized to the muscles involved in performing those tasks. Information decomposition revealed distinct patterns in task-related changes: unimanual and bimanual pointing were associated with reduced transfer to the pectoralis major muscles, but an increase in total information compared to no pointing, while postural instability resulted in increased information, information transfer and information storage in the abductor longus muscles compared to normal stability. These findings show robust patterns of directed interactions between muscles that are task-dependent and can be assessed from surface EMG recorded during static postural tasks. We discuss directed muscle networks in terms of the neural circuitry involved in generating muscle activity and suggest that task-related effects may reflect gain modulations of spinal reflex pathways
Flux through a time-periodic gate: Monte Carlo test of a homogenization result
We investigate via Monte Carlo numerical simulations and theoretical
considerations the outflux of random walkers moving in an interval bounded by
an interface exhibiting channels (pores, doors) which undergo an open/close
cycle according to a periodic schedule. We examine the onset of a limiting
boundary behavior characterized by a constant ratio between the outflux and the
local density, in the thermodynamic limit. We compare such a limit with the
predictions of a theoretical model already obtained in the literature as the
homogenization limit of a suitable diffusion problem
Origin of the orbital and spin orderings in rare-earth titanates
Rare-earth titanates RTiO are Mott insulators displaying a rich physical
behavior, featuring most notably orbital and spin orders in their ground state.
The origin of their ferromagnetic to antiferromagnetic transition as a function
of the size of the rare-earth however remains debated. Here we show on the
basis of symmetry analysis and first-principles calculations that although
rare-earth titanates are nominally Jahn-Teller active, the Jahn-Teller
distortion is negligible and irrelevant for the description of the ground state
properties. At the same time, we demonstrate that the combination of two
antipolar motions produces an effective Jahn-Teller-like motion which is the
key of the varying spin-orbital orders appearing in titanates. Thus, titanates
are prototypical examples illustrating how a subtle interplay between several
lattice distortions commonly appearing in perovskites can produce orbital
orderings and insulating phases irrespective of proper Jahn-Teller motions.Comment: Accepted in Physical Review
A consistent interpretation of recent CR nuclei and electron spectra
We try to interpret the recently updated measurement of the cosmic ray
electron (CRE) spectrum observed by Fermi-LAT, together with PAMELA data on
positron fraction, in a single-component scenario adopting different
propagation setups; we find that the model is not adequate to reproduce the two
datasets, so the evidence of an extra primary component of electrons and
positrons is strengthened. Instead, a double component scenario computed in a
Kraichnan-like diffusion setup (which is suggested by B/C and data)
gives a satisfactory fit of all exisiting measurements. We confirm that nearby
pulsars are good source candidates for the required extra-component and
we show that the predicted CRE anisotropy in our scenario is compatible with
Fermi-LAT recently published constraints.Comment: Accepted for the publication in the proceedings of the ICATPP
Conference on Cosmic Rays for Particle and Astroparticle Physics, Villa Olmo
(Como), Oct. 201
Neutrino oscillation phase dynamically induced by f(R)-gravity
The gravitational phase shift of neutrino oscillation can be discussed in the
framework of f(R)-gravity. We show that the shift of quantum mechanical phase
can depend on the given f(R)-theory that we choose. This fact is general and
could constitute a fundamental test to discriminate among the various
alternative relativistic theories of gravity. Estimations of ratio between the
gravitational phase shift and the standard phase are carried out for the
electronic Solar neutrinos.Comment: 4 page
Quantum Mechanics on SO(3) via Non-commutative Dual Variables
We formulate quantum mechanics on SO(3) using a non-commutative dual space
representation for the quantum states, inspired by recent work in quantum
gravity. The new non-commutative variables have a clear connection to the
corresponding classical variables, and our analysis confirms them as the
natural phase space variables, both mathematically and physically. In
particular, we derive the first order (Hamiltonian) path integral in terms of
the non-commutative variables, as a formulation of the transition amplitudes
alternative to that based on harmonic analysis. We find that the non-trivial
phase space structure gives naturally rise to quantum corrections to the action
for which we find a closed expression. We then study both the semi-classical
approximation of the first order path integral and the example of a free
particle on SO(3). On the basis of these results, we comment on the relevance
of similar structures and methods for more complicated theories with
group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam
models.Comment: 29 pages; matches the published version plus footnote 7, a journal
reference include
Performance of Reynolds Averaged Navier-Stokes Models in Predicting Separated Flows: Study of the Hump Flow Model Problem
Separation can be seen in most aerodynamic flows, but accurate prediction of separated flows is still a challenging problem for computational fluid dynamics (CFD) tools. The behavior of several Reynolds Averaged Navier-Stokes (RANS) models in predicting the separated ow over a wall-mounted hump is studied. The strengths and weaknesses of the most popular RANS models (Spalart-Allmaras, k-epsilon, k-omega, k-omega-SST) are evaluated using the open source software OpenFOAM. The hump ow modeled in this work has been documented in the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control. Only the baseline case is treated; the slot flow control cases are not considered in this paper. Particular attention is given to predicting the size of the recirculation bubble, the position of the reattachment point, and the velocity profiles downstream of the hump
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