441 research outputs found
A non-hybrid method for the PDF equations of turbulent flows on unstructured grids
In probability density function (PDF) methods of turbulent flows, the joint
PDF of several flow variables is computed by numerically integrating a system
of stochastic differential equations for Lagrangian particles. A set of
parallel algorithms is proposed to provide an efficient solution of the PDF
transport equation, modeling the joint PDF of turbulent velocity, frequency and
concentration of a passive scalar in geometrically complex configurations. An
unstructured Eulerian grid is employed to extract Eulerian statistics, to solve
for quantities represented at fixed locations of the domain (e.g. the mean
pressure) and to track particles. All three aspects regarding the grid make use
of the finite element method (FEM) employing the simplest linear FEM shape
functions. To model the small-scale mixing of the transported scalar, the
interaction by exchange with the conditional mean model is adopted. An adaptive
algorithm that computes the velocity-conditioned scalar mean is proposed that
homogenizes the statistical error over the sample space with no assumption on
the shape of the underlying velocity PDF. Compared to other hybrid
particle-in-cell approaches for the PDF equations, the current methodology is
consistent without the need for consistency conditions. The algorithm is tested
by computing the dispersion of passive scalars released from concentrated
sources in two different turbulent flows: the fully developed turbulent channel
flow and a street canyon (or cavity) flow. Algorithmic details on estimating
conditional and unconditional statistics, particle tracking and particle-number
control are presented in detail. Relevant aspects of performance and
parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200
Higher-degree supersingular group actions
International audienceWe investigate the isogeny graphs of supersingular elliptic curves over equipped with a -isogeny to their Galois conjugate. These curves are interesting because they are, in a sense, a generalization of curves defined over , and there is an action of the ideal class group of on the isogeny graphs. We investigate constructive and destructive aspects of these graphs in isogeny-based cryptography, including generalizations of the CSIDH cryptosystem and the Delfs-Galbraith algorithm
Refined geometric transition and -characters
We show the refinement of the prescription for the geometric transition in
the refined topological string theory and, as its application, discuss a
possibility to describe -characters from the string theory point of view.
Though the suggested way to operate the refined geometric transition has passed
through several checks, it is additionally found in this paper that the
presence of the preferred direction brings a nontrivial effect. We provide the
modified formula involving this point. We then apply our prescription of the
refined geometric transition to proposing the stringy description of doubly
quantized Seiberg--Witten curves called -characters in certain cases.Comment: 44 pages, 11 figures; v2: references corrected, text corrected,
published in JHE
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