364 research outputs found
Manners and method in classical criticism of the early eighteenth century
This article explores a neglected period in the history of classical scholarship: the first decades of the eighteenth century. It focuses on the tension between an evolving idea of method, and the tradition of personal polemic which had been an important part of the culture of scholarship since the Renaissance. There are two case studies: the conflict between Jean Le Clerc and Pieter Burman, and the controversy that followed Richard Bentley's edition of Horace's Odes. Both demonstrate the need to revise current paradigms for writing the history of scholarship, and invite us to reconsider the role of methodology in producing of scholarly authority
Non-negative mixed finite element formulations for a tensorial diffusion equation
We consider the tensorial diffusion equation, and address the discrete
maximum-minimum principle of mixed finite element formulations. In particular,
we address non-negative solutions (which is a special case of the
maximum-minimum principle) of mixed finite element formulations. The discrete
maximum-minimum principle is the discrete version of the maximum-minimum
principle.
In this paper we present two non-negative mixed finite element formulations
for tensorial diffusion equations based on constrained optimization techniques
(in particular, quadratic programming). These proposed mixed formulations
produce non-negative numerical solutions on arbitrary meshes for low-order
(i.e., linear, bilinear and trilinear) finite elements. The first formulation
is based on the Raviart-Thomas spaces, and is obtained by adding a non-negative
constraint to the variational statement of the Raviart-Thomas formulation. The
second non-negative formulation based on the variational multiscale
formulation.
For the former formulation we comment on the affect of adding the
non-negative constraint on the local mass balance property of the
Raviart-Thomas formulation. We also study the performance of the active set
strategy for solving the resulting constrained optimization problems. The
overall performance of the proposed formulation is illustrated on three
canonical test problems.Comment: 40 pages using amsart style file, and 15 figure
Where are the missing gamma ray burst redshifts?
In the redshift range z = 0-1, the gamma ray burst (GRB) redshift
distribution should increase rapidly because of increasing differential volume
sizes and strong evolution in the star formation rate. This feature is not
observed in the Swift redshift distribution and to account for this
discrepancy, a dominant bias, independent of the Swift sensitivity, is
required. Furthermore, despite rapid localization, about 40-50% of Swift and
pre-Swift GRBs do not have a measured redshift. We employ a heuristic technique
to extract this redshift bias using 66 GRBs localized by Swift with redshifts
determined from absorption or emission spectroscopy. For the Swift and
HETE+BeppoSAX redshift distributions, the best model fit to the bias in z < 1
implies that if GRB rate evolution follows the SFR, the bias cancels this rate
increase. We find that the same bias is affecting both Swift and HETE+BeppoSAX
measurements similarly in z < 1. Using a bias model constrained at a 98% KS
probability, we find that 72% of GRBs in z < 2 will not have measurable
redshifts and about 55% in z > 2. To achieve this high KS probability requires
increasing the GRB rate density in small z compared to the high-z rate. This
provides further evidence for a low-luminosity population of GRBs that are
observed in only a small volume because of their faintness.Comment: 5 pages, submitted to MNRA
An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems
Heterogeneous anisotropic diffusion problems arise in the various areas of
science and engineering including plasma physics, petroleum engineering, and
image processing. Standard numerical methods can produce spurious oscillations
when they are used to solve those problems. A common approach to avoid this
difficulty is to design a proper numerical scheme and/or a proper mesh so that
the numerical solution validates the discrete counterpart (DMP) of the maximum
principle satisfied by the continuous solution. A well known mesh condition for
the DMP satisfaction by the linear finite element solution of isotropic
diffusion problems is the non-obtuse angle condition that requires the dihedral
angles of mesh elements to be non-obtuse. In this paper, a generalization of
the condition, the so-called anisotropic non-obtuse angle condition, is
developed for the finite element solution of heterogeneous anisotropic
diffusion problems. The new condition is essentially the same as the existing
one except that the dihedral angles are now measured in a metric depending on
the diffusion matrix of the underlying problem. Several variants of the new
condition are obtained. Based on one of them, two metric tensors for use in
anisotropic mesh generation are developed to account for DMP satisfaction and
the combination of DMP satisfaction and mesh adaptivity. Numerical examples are
given to demonstrate the features of the linear finite element method for
anisotropic meshes generated with the metric tensors.Comment: 34 page
The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations
The cutoff method, which cuts off the values of a function less than a given
number, is studied for the numerical computation of nonnegative solutions of
parabolic partial differential equations. A convergence analysis is given for a
broad class of finite difference methods combined with cutoff for linear
parabolic equations. Two applications are investigated, linear anisotropic
diffusion problems satisfying the setting of the convergence analysis and
nonlinear lubrication-type equations for which it is unclear if the convergence
analysis applies. The numerical results are shown to be consistent with the
theory and in good agreement with existing results in the literature. The
convergence analysis and applications demonstrate that the cutoff method is an
effective tool for use in the computation of nonnegative solutions. Cutoff can
also be used with other discretization methods such as collocation, finite
volume, finite element, and spectral methods and for the computation of
positive solutions.Comment: 19 pages, 41 figure
EAGLE multi-object AO concept study for the E-ELT
EAGLE is the multi-object, spatially-resolved, near-IR spectrograph
instrument concept for the E-ELT, relying on a distributed Adaptive Optics,
so-called Multi Object Adaptive Optics. This paper presents the results of a
phase A study. Using 84x84 actuator deformable mirrors, the performed analysis
demonstrates that 6 laser guide stars and up to 5 natural guide stars of
magnitude R<17, picked-up in a 7.3' diameter patrol field of view, allow us to
obtain an overall performance in terms of Ensquared Energy of 35% in a 75x75
mas^2 spaxel at H band, whatever the target direction in the centred 5' science
field for median seeing conditions. The computed sky coverage at galactic
latitudes |b|~60 is close to 90%.Comment: 6 pages, to appear in the proceedings of the AO4ELT conference, held
in Paris, 22-26 June 200
Probing the low-luminosity GRB population with new generation satellite detectors
We compare the detection rates and redshift distributions of low-luminosity
(LL) GRBs localized by Swift with those expected to be observed by the new
generation satellite detectors on GLAST (now Fermi) and, in future, EXIST.
Although the GLAST burst telescope will be less sensitive than Swift's in the
15--150 keV band, its large field-of-view implies that it will double Swift's
detection rate of LL bursts. We show that Swift, GLAST and EXIST should detect
about 1, 2 & 30 LL GRBs, respectively, over a 5-year operational period. The
burst telescope on EXIST should detect LL GRBs at a rate of more than an order
of magnitude greater than that of Swift's BAT. We show that the detection
horizon for LL GRBs will be extended from for Swift to in the EXIST era. Also, the contribution of LL bursts to the observed GRB
redshift distribution will contribute to an identifiable feature in the
distribution at .Comment: 6 pages, 4 figures, accepted by MNRA
Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids
In this paper, we consider anisotropic diffusion with decay, and the
diffusivity coefficient to be a second-order symmetric and positive definite
tensor. It is well-known that this particular equation is a second-order
elliptic equation, and satisfies a maximum principle under certain regularity
assumptions. However, the finite element implementation of the classical
Galerkin formulation for both anisotropic and isotropic diffusion with decay
does not respect the maximum principle.
We first show that the numerical accuracy of the classical Galerkin
formulation deteriorates dramatically with increase in the decay coefficient
for isotropic medium and violates the discrete maximum principle. However, in
the case of isotropic medium, the extent of violation decreases with mesh
refinement. We then show that, in the case of anisotropic medium, the classical
Galerkin formulation for anisotropic diffusion with decay violates the discrete
maximum principle even at lower values of decay coefficient and does not vanish
with mesh refinement. We then present a methodology for enforcing maximum
principles under the classical Galerkin formulation for anisotropic diffusion
with decay on general computational grids using optimization techniques.
Representative numerical results (which take into account anisotropy and
heterogeneity) are presented to illustrate the performance of the proposed
formulation
Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement
We present a new model and a novel loosely coupled partitioned numerical
scheme modeling fluid-structure interaction (FSI) in blood flow allowing
non-zero longitudinal displacement. Arterial walls are modeled by a {linearly
viscoelastic, cylindrical Koiter shell model capturing both radial and
longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes
equations for an incompressible, viscous fluid. The two are fully coupled via
kinematic and dynamic coupling conditions. Our numerical scheme is based on a
new modified Lie operator splitting that decouples the fluid and structure
sub-problems in a way that leads to a loosely coupled scheme which is
{unconditionally} stable. This was achieved by a clever use of the kinematic
coupling condition at the fluid and structure sub-problems, leading to an
implicit coupling between the fluid and structure velocities. The proposed
scheme is a modification of the recently introduced "kinematically coupled
scheme" for which the newly proposed modified Lie splitting significantly
increases the accuracy. The performance and accuracy of the scheme were studied
on a couple of instructive examples including a comparison with a monolithic
scheme. It was shown that the accuracy of our scheme was comparable to that of
the monolithic scheme, while our scheme retains all the main advantages of
partitioned schemes, such as modularity, simple implementation, and low
computational costs
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