2,630 research outputs found
Stable multispeed lattice Boltzmann methods
We demonstrate how to produce a stable multispeed lattice Boltzmann method
(LBM) for a wide range of velocity sets, many of which were previously thought
to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method
operates stably for almost zero viscosity, has second-order accuracy,
suppresses typical spurious oscillation (only a modest Gibbs effect is present)
and introduces no artificial viscosity. There is almost no computational cost
for this innovation.
DISCLAIMER: Additional tests and wide discussion of this preprint show that
the claimed property of coupled steps: no artificial dissipation and the
second-order accuracy of the method are valid only on sufficiently fine grids.
For coarse grids the higher-order terms destroy coupling of steps and
additional dissipation appears.
The equations are true.Comment: Disclaimer about the area of applicability is added to abstrac
On the numerical evaluation of algebro-geometric solutions to integrable equations
Physically meaningful periodic solutions to certain integrable partial
differential equations are given in terms of multi-dimensional theta functions
associated to real Riemann surfaces. Typical analytical problems in the
numerical evaluation of these solutions are studied. In the case of
hyperelliptic surfaces efficient algorithms exist even for almost degenerate
surfaces. This allows the numerical study of solitonic limits. For general real
Riemann surfaces, the choice of a homology basis adapted to the
anti-holomorphic involution is important for a convenient formulation of the
solutions and smoothness conditions. Since existing algorithms for algebraic
curves produce a homology basis not related to automorphisms of the curve, we
study symplectic transformations to an adapted basis and give explicit formulae
for M-curves. As examples we discuss solutions of the Davey-Stewartson and the
multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure
Reconsidering the substance of digital video from a Sadrian perspective
The digitisation process is debated as video’s deficiency, where pixels are conceived as isolated fragments without an existential link to the source image. This article explores the ontology of digital-video through Mulla Sadrā’s (1571–1641) theory of Substantial Motion. Sadrā, a Persian-Islamic existentialist, proposed that substance (material/visible and immaterial/invisible) undergoes an internal change. Through imperceptible internal change, intimate connections exist between the smallest parts and the One, visible and invisible. We can think of these dynamic connections in terms of pixels and frames. From the view of Sadrā’s substance, pixels are explored as open to change. The apparent weaknesses of digital materiality become potentials towards understanding its existence in time
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