2,953 research outputs found
Integration-free Learning of Flow Maps
We present a method for learning neural representations of flow maps from
time-varying vector field data. The flow map is pervasive within the area of
flow visualization, as it is foundational to numerous visualization techniques,
e.g. integral curve computation for pathlines or streaklines, as well as
computing separation/attraction structures within the flow field. Yet
bottlenecks in flow map computation, namely the numerical integration of vector
fields, can easily inhibit their use within interactive visualization settings.
In response, in our work we seek neural representations of flow maps that are
efficient to evaluate, while remaining scalable to optimize, both in
computation cost and data requirements. A key aspect of our approach is that we
can frame the process of representation learning not in optimizing for samples
of the flow map, but rather, a self-consistency criterion on flow map
derivatives that eliminates the need for flow map samples, and thus numerical
integration, altogether. Central to realizing this is a novel neural network
design for flow maps, coupled with an optimization scheme, wherein our
representation only requires the time-varying vector field for learning,
encoded as instantaneous velocity. We show the benefits of our method over
prior works in terms of accuracy and efficiency across a range of 2D and 3D
time-varying vector fields, while showing how our neural representation of flow
maps can benefit unsteady flow visualization techniques such as streaklines,
and the finite-time Lyapunov exponent
Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH
In this paper we discuss the treatment of discontinuities in Smoothed
Particle Hydrodynamics (SPH) simulations. In particular we discuss the
difference between integral and differential representations of the fluid
equations in an SPH context and how this relates to the formulation of dissip
ative terms for the capture of shocks and other discontinuities.
This has important implications for many problems, in particular related to
recently highlighted problems in treating Kelvin-Helmholtz instabilities across
entropy gradients in SPH. The specific problems pointed out by Agertz et al.
(2007) are shown to be related in particular to the (lack of) treatment of
contact discontinuities in standard SPH formulations which can be cured by the
simple application of an artificial thermal conductivity term. We propose a new
formulation of artificial thermal conductivity in SPH which minimises
dissipation away from discontinuities and can therefore be applied quite
generally in SPH calculations.Comment: 31 pages, 10 figures, submitted to J. Comp. Phys. Movies + hires
version available at http://www.astro.ex.ac.uk/people/dprice/pubs/kh/ . v3:
modified as per referee's comments - comparison with Ritchie & Thomas
formulation added, quite a few typos fixed. No major change in metho
Gauge Theories of Gravitation
During the last five decades, gravity, as one of the fundamental forces of
nature, has been formulated as a gauge theory of the Weyl-Cartan-Yang-Mills
type. The present text offers commentaries on the articles from the most
prominent proponents of the theory. In the early 1960s, the gauge idea was
successfully applied to the Poincar\'e group of spacetime symmetries and to the
related conserved energy-momentum and angular momentum currents. The resulting
theory, the Poincar\'e gauge theory, encompasses Einstein's general relativity
as well as the teleparallel theory of gravity as subcases. The spacetime
structure is enriched by Cartan's torsion, and the new theory can accommodate
fermionic matter and its spin in a perfectly natural way. This guided tour
starts from special relativity and leads, in its first part, to general
relativity and its gauge type extensions \`a la Weyl and Cartan. Subsequent
stopping points are the theories of Yang-Mills and Utiyama and, as a particular
vantage point, the theory of Sciama and Kibble. Later, the Poincar\'e gauge
theory and its generalizations are explored and special topics, such as its
Hamiltonian formulation and exact solutions, are studied. This guide to the
literature on classical gauge theories of gravity is intended to be a
stimulating introduction to the subject.Comment: 169 pages, pdf file, v3: extended to a guide to the literature on
classical gauge theories of gravit
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
MAGMA: a 3D, Lagrangian magnetohydrodynamics code for merger applications
We present a new, completely Lagrangian magnetohydrodynamics code that is
based on the SPH method. The equations of self-gravitating hydrodynamics are
derived self-consistently from a Lagrangian and account for variable smoothing
length (``grad-h''-) terms in both the hydrodynamic and the gravitational
acceleration equations. The evolution of the magnetic field is formulated in
terms of so-called Euler potentials which are advected with the fluid and thus
guarantee the MHD flux-freezing condition. This formulation is equivalent to a
vector potential approach and therefore fulfills the
-constraint by construction. Extensive tests in
one, two and three dimensions are presented. The tests demonstrate the
excellent conservation properties of the code and show the clear superiority of
the Euler potentials over earlier magnetic SPH formulations.Comment: 18 pages, 17 Figures, a high resolution copy of the paper can be
found at http://www.faculty.iu-bremen.de/srosswog/MAGMA.pd
Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics
After recalling episodes from Pascual Jordan's biography including his
pivotal role in the shaping of quantum field theory and his much criticized
conduct during the NS regime, I draw attention to his presentation of the first
phase of development of quantum field theory in a talk presented at the 1929
Kharkov conference. He starts by giving a comprehensive account of the
beginnings of quantum theory, emphasising that particle-like properties arise
as a consequence of treating wave-motions quantum-mechanically. He then goes on
to his recent discovery of quantization of ``wave fields'' and problems of
gauge invariance. The most surprising aspect of Jordan's presentation is
however his strong belief that his field quantization is a transitory not yet
optimal formulation of the principles underlying causal, local quantum physics.
The expectation of a future more radical change coming from the main architect
of field quantization already shortly after his discovery is certainly quite
startling. I try to answer the question to what extent Jordan's 1929
expectations have been vindicated. The larger part of the present essay
consists in arguing that Jordan's plea for a formulation without ``classical
correspondence crutches'', i.e. for an intrinsic approach (which avoids
classical fields altogether), is successfully addressed in past and recent
publications on local quantum physics.Comment: More biographical detail, expansion of the part referring to Jordan's
legacy in quantum field theory, 37 pages late
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