318 research outputs found
Commutative association schemes
Association schemes were originally introduced by Bose and his co-workers in
the design of statistical experiments. Since that point of inception, the
concept has proved useful in the study of group actions, in algebraic graph
theory, in algebraic coding theory, and in areas as far afield as knot theory
and numerical integration. This branch of the theory, viewed in this collection
of surveys as the "commutative case," has seen significant activity in the last
few decades. The goal of the present survey is to discuss the most important
new developments in several directions, including Gelfand pairs, cometric
association schemes, Delsarte Theory, spin models and the semidefinite
programming technique. The narrative follows a thread through this list of
topics, this being the contrast between combinatorial symmetry and
group-theoretic symmetry, culminating in Schrijver's SDP bound for binary codes
(based on group actions) and its connection to the Terwilliger algebra (based
on combinatorial symmetry). We propose this new role of the Terwilliger algebra
in Delsarte Theory as a central topic for future work.Comment: 36 page
Mesoscopic simulation study of wall roughness effects in micro-channel flows of dense emulsions
We study the Poiseuille flow of a soft-glassy material above the jamming
point, where the material flows like a complex fluid with Herschel- Bulkley
rheology. Microscopic plastic rearrangements and the emergence of their spatial
correlations induce cooperativity flow behavior whose effect is pronounced in
presence of confinement. With the help of lattice Boltzmann numerical
simulations of confined dense emulsions, we explore the role of geometrical
roughness in providing activation of plastic events close to the boundaries. We
probe also the spatial configuration of the fluidity field, a continuum
quantity which can be related to the rate of plastic events, thereby allowing
us to establish a link between the mesoscopic plastic dynamics of the jammed
material and the macroscopic flow behaviour
A walk in the noncommutative garden
This text is written for the volume of the school/conference "Noncommutative
Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in
noncommutative geometry, based on a discussion of significant examples of
noncommutative spaces in geometry, number theory, and physics. The paper also
contains an outline (the ``Tehran program'') of ongoing joint work with Consani
on the noncommutative geometry of the adeles class space and its relation to
number theoretic questions.Comment: 106 pages, LaTeX, 23 figure
On dense granular flows
The behaviour of dense assemblies of dry grains submitted to continuous shear
deformation has been the subject of many experiments and discrete particle
simulations. This paper is a collective work carried out among the French
research group GDR Milieux Divis\'es. It proceeds from the collection of
results on steady uniform granular flows obtained by different groups in six
different geometries both in experiments and numerical works. The goal is to
achieve a coherent presentation of the relevant quantities to be measured i.e.
flowing thresholds, kinematic profiles, effective friction, etc. First, a
quantitative comparison between data coming from different experiments in the
same geometry enforces the robust features in each case. Second, a transversal
analysis of the data across the different configurations, allows us to identify
the relevant dimensionless parameters, the different flow regimes and to
propose simple interpretations. The present work, more than a simple
juxtaposition of results, underlines the richness of granular flows and
enhances the open problem of defining a single rheologyComment: collectif paper written by the GdR Milieux divises (submitted the
12/12/03
Two-Loop String Theory on Null Compactifications
We compute the two-loop contributions to the free energy in the null
compactification of perturbative string theory at finite temperature. The cases
of bosonic, Type II and heterotic strings are all treated. The calculation
exploits an explicit reductive parametrization of the moduli space of
infinite-momentum frame string worldsheets in terms of branched cover
instantons. Various arithmetic and physical properties of the instanton sums
are described. Applications to symmetric product orbifold conformal field
theories and to the matrix string theory conjecture are also briefly discussed.Comment: 41 pages, 1 figur
Dry granular flows: rheological measurements of the -Rheology
Granular materials do not flow homogeneously like fluids when submitted to
external stress,but often form rigid regions that are separated by narrow shear
bands where the material yields and flows. This shear localization impacts
their apparent rheology, which makes it difficult to infer a constitutive
behaviour from conventional rheometric measurements. Moreover, they present a
dilatant behaviour, which makes their study in classical fixedvolume geometries
difficult. These features led to perform extensive studies with inclined plane
flows, which were of crucial importance for the development and the validation
of the rheology. Our aim is to develop a method to characterize
granular materials with rheometrical tools. Using unusual rheometry
measurements in an annular shear cell adapted from Boyer et al. (2011), dense
granular flows are studied. A focus is placed on the comparison between the
present results and the -rheology
Layer-by-layer growth of complex-shaped three-dimensional nanostructures with focused electron beams
The fabrication of three-dimensional (3D) nanostructures is of great interest to many areas of nanotechnology currently challenged by fundamental limitations of conventional lithography. One of the most promising direct-write methods for 3D nanofabrication is focused electron beam-induced deposition (FEBID), owing to its high spatial resolution and versatility. Here we extend FEBID to the growth of complex-shaped 3D nanostructures by combining the layer-by-layer approach of conventional macroscopic 3D printers and the proximity effect correction of electron beam lithography. This framework is based on the continuum FEBID model and is capable of adjusting for a wide range of effects present during deposition, including beam-induced heating, defocussing and gas flux anisotropies. We demonstrate the capabilities of our platform by fabricating free-standing nanowires, surfaces with varying curvatures and topologies, and general 3D objects, directly from standard stereolithography (STL) files and using different precursors. Real 3D nanoprinting as demonstrated here opens up exciting avenues for the study and exploitation of 3D nanoscale phenomena
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