3,464 research outputs found
Internal state of granular assemblies near random close packing
The structure of random sphere packings in mechanical equilibrium in
prescribed stress states, as studied by molecular dynamics simulations,
strongly depends on the assembling procedure. Frictionless packings in the
limit of low pressure are devoid of dilatancy, and consequently share the same
random close packing density, but exhibit fabric anisotropy related to stress
anisotropy. Efficient compaction methods can be viewed as routes to circumvent
the influence of friction. Simulations designed to resemble two such
procedures, lubrication and vibration (or ``tapping'') show that the resulting
granular structures differ, the less dense one having, remarkably, the larger
coordination number. Density, coordination number and fabric can thus vary
independently. Calculations of elastic moduli and comparisons with experimental
results suggest that measurable elastic properties provide information on those
important internal state variables.Comment: March 12, 200
Density profiles in a classical Coulomb fluid near a dielectric wall. II. Weak-coupling systematic expansions
In the framework of the grand-canonical ensemble of statistical mechanics, we
give an exact diagrammatic representation of the density profiles in a
classical multicomponent plasma near a dielectric wall. By a reorganization of
Mayer diagrams for the fugacity expansions of the densities, we exhibit how the
long-range of both the self-energy and pair interaction are exponentially
screened at large distances from the wall. However, the self-energy due to
Coulomb interaction with images still diverges in the vicinity of the
dielectric wall and the variation of the density is drastically different at
short or large distances from the wall. This variation is involved in the
inhomogeneous Debye-H\"uckel equation obeyed by the screened pair potential.
Then the main difficulty lies in the determination of the latter potential at
every distance. We solve this problem by devising a systematic expansion with
respect to the ratio of the fundamental length scales involved in the two
coulombic effects at stake. (The application of this method to a plasma
confined between two ideally conducting plates and to a quantum plasma will be
presented elsewhere). As a result we derive the exact analytical perturbative
expressions for the density profiles up to first order in the coupling between
charges. The mean-field approach displayed in Paper I is then justified.Comment: 37 pages, 5 figure
Density profiles in a classical Coulomb fluid near a dielectric wall. I. Mean-field scheme
The equilibrium density profiles in a classical multicomponent plasma near a
hard wall made with a dielectric material characterized by a relative
dielectric constant \ew are studied from the first Born-Green-Yvon equation
combined with Poisson equation in a regime where Coulomb coupling is weak
inside the fluid. In order to prevent the collapse between charges with
opposite signs or between each charge and its dielectric image inside the wall
when \ew >1, hard-core repulsions are added to the Coulomb pair interaction.
The charge-image interaction cannot be treated perturbatively and the density
profiles vary very fast in the vicinity of the wall when \ew \neq 1. The
formal solution of the associated inhomogeneous Debye-H\"uckel equations will
be given in Paper II, together with a systematic fugacity expansion which
allows to retrieve the results obtained from the truncated \bgy hierarchy. In
the present paper the exact density profiles are calculated analytically up to
first order in the coupling parameter. The expressions show the interplay
between three effects~: the geometric repulsion from the impenetrable wall; the
electrostatic effective attraction (\ew >1) or repulsion (\ew <1) due to
its dielectric response; and the Coulomb interaction between each charge and
the potential drop created by the electric layer which appears as soon as the
system is not symmetric. We exhibit how the charge density profile evolves
between a structure with two oppositely-charged layers and a three-layer
organization when \ew varies. (The case of two ideally conducting walls will
be displayed elsewhere)Comment: 32 pages, 11 figure
Synthesis of New Chiral N-Heterocyclic Carbenes and Abnormal Carbenes
Chapter 1
Carbenes have fascinated organic chemists ever since the first evidence of their existence. The
isolation and first crystallographic analysis of a stable NHC by Arduengo, in 1991, has had a major
impact on the application of NHCs in chemistry. NHCs are widely used as ligands for transition
metals, but also as catalysts in their own right.
The aim of this project is to synthesise novel monodentate chiral NHCs 1 in order
to induce a high level of stereocontrol in a selection of asymmetric reactions. The
rigid ring structure, C2 symmetry and the presence of bulky groups (R) that
project directly toward the reactive centre are important concepts in the design of
our molecules.
During the first part of my thesis, we developed a one-pot synthesis of allylic chlorides from
benzaldehyde. A mechanistic study was carried out, as well as studying the scope of the reaction.
We then achieved the synthesis of the desired NHCs precursors in 13 or 14 steps and carried out
studies of their coordination and application in asymmetric α-arylation and allylic alkylation.
Chapter 2
Recently novel coordination modes have been noted for NHCs. The so-called “abnormal” NHCs, due
to their isomeric relationship between C2- and C4-bound imidazolylidene ligands are one type of
relatively unexplored ligand. We have therefore developed a strategy to access chiral abnormal
NHCs.
Two
different chiral abnormal NHC precursors: 1,2,3-triazolidinenes 2 and isomeric Hartwig’s NHCs 3
were synthesised via a short synthesis (2 or 3 steps) and metallated with a transition metal
The critical merger distance between two co-rotating quasi-geostrophic vortices
This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.Publisher PDFPeer reviewe
Nonlinear evolution of a morphological instability in a strained epitaxial film
A strained epitaxial film deposited on a deformable substrate undergoes a
morphological instability relaxing the elastic energy by surface diffusion. The
nonlinear and nonlocal dynamical equations of such films with wetting
interactions are derived and solved numerically in two and three dimensions.
Above some critical thickness, the surface evolves towards an array of islands
separated by a wetting layer. The island chemical potential decreases with its
volume, so that the system experiences a non-interrupted coarsening described
by power laws with a marked dimension dependence.Comment: 4 pages, 6 figure
Heated granular fluids: the random restitution coefficient approach
We introduce the model of inelastic hard spheres with random restitution
coefficient , in order to account for the fact that, in a vertically
shaken granular system interacting elastically with the vibrating boundary, the
energy injected vertically is transferred to the horizontal degrees of freedom
through collisions only, which leads to heating through collisions, i.e. to
inelastic horizontal collisions with an effective restitution coefficient that
can be larger than 1. This allows the system to reach a non-equilibrium steady
state, where we focus in particular on the single particle velocity
distribution in the horizontal plane, and on its deviation from a
Maxwellian. Molecular Dynamics simulations and Direct Simulation Monte Carlo
(DSMC) show that, depending on the distribution of , different shapes
of can be obtained, with very different high energy tails. Moreover, the
fourth cumulant of the velocity distribution quantifying the deviations from
Gaussian statistics is obtained analytically from the Boltzmann equation and
successfully tested against the simulations.Comment: 14 pages, 9 eps figure
Hierarchical Parallel Matrix Multiplication on Large-Scale Distributed Memory Platforms
Matrix multiplication is a very important computation kernel both in its own
right as a building block of many scientific applications and as a popular
representative for other scientific applications. Cannon algorithm which dates
back to 1969 was the first efficient algorithm for parallel matrix
multiplication providing theoretically optimal communication cost. However this
algorithm requires a square number of processors. In the mid 1990s, the SUMMA
algorithm was introduced. SUMMA overcomes the shortcomings of Cannon algorithm
as it can be used on a non-square number of processors as well. Since then the
number of processors in HPC platforms has increased by two orders of magnitude
making the contribution of communication in the overall execution time more
significant. Therefore, the state of the art parallel matrix multiplication
algorithms should be revisited to reduce the communication cost further. This
paper introduces a new parallel matrix multiplication algorithm, Hierarchical
SUMMA (HSUMMA), which is a redesign of SUMMA. Our algorithm reduces the
communication cost of SUMMA by introducing a two-level virtual hierarchy into
the two-dimensional arrangement of processors. Experiments on an IBM BlueGene-P
demonstrate the reduction of communication cost up to 2.08 times on 2048 cores
and up to 5.89 times on 16384 cores.Comment: 9 page
ASCIE: An integrated experiment to study CSI in large segmented optical systems
A description of the advanced structures/control integrated experiment (ASCIE) experimental setup, a generic test bed for several essential technologies was presented. In particular its multi-input, multi-output, non-collocated control system and its complex structural dynamics, characteristic of large segmented systems make it an ideal test bed for Control-Structure Interaction (CSI) experiments. The high accuracy of its measurement system will make it possible to investigate the dynamics of microvibrations and its implication for the CSI phenomenon
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