29,033 research outputs found
Thread-safe lattice Boltzmann for high-performance computing on GPUs
We present thread-safe, highly-optimized lattice Boltzmann implementations,
specifically aimed at exploiting the high memory bandwidth of GPU-based
architectures. At variance with standard approaches to LB coding, the proposed
strategy, based on the reconstruction of the post-collision distribution via
Hermite projection, enforces data locality and avoids the onset of memory
dependencies, which may arise during the propagation step, with no need to
resort to more complex streaming strategies. The thread-safe lattice Boltzmann
achieves peak performances, both in two and three dimensions and it allows to
sensibly reduce the allocated memory ( tens of GigaBytes for order billions
lattice nodes simulations) by retaining the algorithmic simplicity of standard
LB computing. Our findings open attractive prospects for high-performance
simulations of complex flows on GPU-based architectures
Soliton Gas: Theory, Numerics and Experiments
The concept of soliton gas was introduced in 1971 by V. Zakharov as an
infinite collection of weakly interacting solitons in the framework of
Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted
soliton gas, solitons with random parameters are almost non-overlapping. More
recently, the concept has been extended to dense gases in which solitons
strongly and continuously interact. The notion of soliton gas is inherently
associated with integrable wave systems described by nonlinear partial
differential equations like the KdV equation or the one-dimensional nonlinear
Schr\"odinger equation that can be solved using the inverse scattering
transform. Over the last few years, the field of soliton gases has received a
rapidly growing interest from both the theoretical and experimental points of
view. In particular, it has been realized that the soliton gas dynamics
underlies some fundamental nonlinear wave phenomena such as spontaneous
modulation instability and the formation of rogue waves. The recently
discovered deep connections of soliton gas theory with generalized
hydrodynamics have broadened the field and opened new fundamental questions
related to the soliton gas statistics and thermodynamics. We review the main
recent theoretical and experimental results in the field of soliton gas. The
key conceptual tools of the field, such as the inverse scattering transform,
the thermodynamic limit of finite-gap potentials and the Generalized Gibbs
Ensembles are introduced and various open questions and future challenges are
discussed.Comment: 35 pages, 8 figure
Tonelli Approach to Lebesgue Integration
Leonida Tonelli devised an interesting and efficient method to introduce the
Lebesgue integral. The details of this method can only be found in the original
Tonelli paper and in an old italian course and solely for the case of the
functions of one variable. We believe that it is woth knowing this method and
here we present a complete account for functions of every number of variables
Percentage ratios of cutting forces during high-reed face milling
This research paper is concerned with the experimental study of high-feed end milling of 1.4541 (X6CrNiTi18-10) stainless steel with replaceable cermet plates. Several machining operations were performed under different cutting conditions. The variable values were depth of cut, feed per tooth and cutting speed. The results were analyzed, and cutting forces were evaluated for dependence on cutting conditions (cutting speed, depth of cut, feed per tooth). The obtained data were statistically processed and plotted in graphs. It was found that the percentage distribution of cutting forces changed as the tool load increased. The ratio of forces acting in individual axes also changed with varying trends. An increasing trend was recorded in the x and y axes, while a decreasing trend was recorded in the z axis. Measured change, approximately 10%, can no longer be neglected as it can significantly influence the clamping stability of a part.IGA/FT/2023/005TBU of the Zlin Internal Grant Agency [IGA/FT/2023/005
Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms
In this paper we give a formula for the central value of the completed
-function , where and are Hilbert newforms,
by explicitly computing the local integrals appearing in the refined
Gan-Gross-Prasad conjecture for . We also work out
the rationality of this value in some special cases and give a conjecture for
the general case
Isotopic piecewise affine approximation of algebraic or varieties
We propose a novel sufficient condition establishing that a piecewise affine
variety has the same topology as a variety of the sphere defined
by positively homogeneous functions. This covers the case of
varieties in the projective space . We prove that this condition
is sufficient in the case of codimension one and arbitrary dimension. We
describe an implementation working for homogeneous polynomials in arbitrary
dimension and codimension and give experimental evidences that our condition
might still be sufficient in codimension greater than one
Efficient computation of the overpartition function and applications
In this paper we develop a method to calculate the overpartition function
efficiently using a Hardy-Rademacher-Ramanujan type formula, and we use this
method to find many new Ramanujan-style congruences whose existence is
predicted by Treneer and a few of which were first discovered by Ryan, Scherr,
Sirolli and Treneer
Genus character -functions of quadratic orders in an adelic way and maximal orders of matrix algebras
For a quadratic extension of , we consider orders in
that are not necessarily maximal and the ideal class group in the
narrow sense of proper ideals of . Characters of of order at most
two are traditionally called genus characters. Explicit description of such
characters is known classically, but explicit -functions associated to those
characters are only recently obtained partially by Chinta and Offen and
completely by Kaneko and Mizuno. As remarked in the latter paper, the present
author also obtained the formula of such -functions independently. Indeed,
here we will give a simple and transparent alternative proof of the formula by
rewriting explicit genus characters and their values in an adelic way starting
from scratch. We also add an explicit formula for the genus number in the wide
sense, which is maybe known but rarely treated. As an appendix we give an
ideal-theoretic characterization of isomorphism classes of maximal orders of
the matrix algebras over a number field up to and
conjugation respectively, and apply genus numbers to count them
when and is quadratic. To avoid any misconception, we include some
easy known details.Comment: 25 page
Computational approach to the Schottky problem
We present a computational approach to the classical Schottky problem based
on Fay's trisecant identity for genus . For a given Riemann matrix
, the Fay identity establishes linear dependence
of secants in the Kummer variety if and only if the Riemann matrix corresponds
to a Jacobian variety as shown by Krichever. The theta functions in terms of
which these secants are expressed depend on the Abel maps of four arbitrary
points on a Riemann surface. However, there is no concept of an Abel map for
general . To establish linear dependence of the
secants, four components of the vectors entering the theta functions can be
chosen freely. The remaining components are determined by a Newton iteration to
minimize the residual of the Fay identity. Krichever's theorem assures that if
this residual vanishes within the finite numerical precision for a generic
choice of input data, then the Riemann matrix is with this numerical precision
the period matrix of a Riemann surface. The algorithm is compared in genus 4
for some examples to the Schottky-Igusa modular form, known to give the Jacobi
locus in this case. It is shown that the same residuals are achieved by the
Schottky-Igusa form and the approach based on the Fay identity in this case. In
genera 5, 6 and 7, we discuss known examples of Riemann matrices and
perturbations thereof for which the Fay identity is not satisfied
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