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Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio
http://hdl.handle.net/10993/32622
Title: Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio
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<br/>Author, co-author: Heymans, Sven; Schilling, Tanja
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<br/>Abstract: We present a Monte Carlo simulation study of suspensions of hard ellipsoids of revolution. Based on the
spatial fluctuations of the orientational order, we have computed the Frank elastic constants for prolate and oblate
ellipsoids and compared them to the affine transformation model. The affine transformation model predicts the
right order of magnitude of the twist and bend constant but not of the splay constant. In addition, we report
the observation of a stable nematic phase at an aspect ratio as low as 2.5.Small-angle neutron scattering modeling of spin disorder in nanoparticles
http://hdl.handle.net/10993/32610
Title: Small-angle neutron scattering modeling of spin disorder in nanoparticles
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<br/>Author, co-author: Vivas, Laura G.; Yanes, Rocio; Michels, AndreasMagnetic SANS as a probe to disclose internal interfaces and the spin structure of nanoparticles
http://hdl.handle.net/10993/32609
Title: Magnetic SANS as a probe to disclose internal interfaces and the spin structure of nanoparticles
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<br/>Author, co-author: Michels, AndreasOn the Concept of a Filtered Bundle
http://hdl.handle.net/10993/32603
Title: On the Concept of a Filtered Bundle
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<br/>Author, co-author: Bruce, Andrew; Grabowska, Katarzyna; Grabowski, Janusz
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<br/>Abstract: We present the notion of a filtered bundle as a generalization of a graded bundle. In
particular, we weaken the necessity of the transformation laws for local coordinates
to exactly respect the weight of the coordinates by allowing more general polynomial
transformation laws. The key examples of such bundles include affine bundles and various
jet bundles, both of which play fundamental roles in geometric mechanics and classical
field theory. We also present the notion of double filtered bundles which provide natural
generalizations of double vector bundles and double affine bundles. Furthermore, we show
that the linearization of a filtered bundle — which can be seen as a partial polarization
of the admissible changes of local coordinates — is well defined.On a geometric framework for Lagrangian supermechanics
http://hdl.handle.net/10993/32598
Title: On a geometric framework for Lagrangian supermechanics
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<br/>Author, co-author: Bruce, Andrew; Grabowska, Katarzyna; Moreno, Giovanni
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<br/>Abstract: We re--examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, we use arbitrary supermanifolds by following the categorical approach to supermanifolds.Hall measurements on low-mobility thin films
http://hdl.handle.net/10993/32597
Title: Hall measurements on low-mobility thin films
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<br/>Author, co-author: Werner, FlorianRemarks on Contact and Jacobi Geometry
http://hdl.handle.net/10993/32596
Title: Remarks on Contact and Jacobi Geometry
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<br/>Author, co-author: Bruce, Andrew; Grabowska, Katarzyna; Grabowski, Janusz
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<br/>Abstract: We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,ℝ)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory.Calculs de paramètres RMN de fluorures inorganiques cristallisés
http://hdl.handle.net/10993/32581
Title: Calculs de paramètres RMN de fluorures inorganiques cristallisés
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<br/>Author, co-author: Bernard, Nicolas
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<br/>Abstract: The goal of this work was to compute the NMR parameters of some crystalline inorganic fluorides using the Gipaw method as implemented in Quantum-Espresso. Notably, we were interested in reproducing (or not) some published results [16, 17] that had been obtained using Castep.Enumerating quasitrivial semigroups
http://hdl.handle.net/10993/32555
Title: Enumerating quasitrivial semigroups
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<br/>Author, co-author: Devillet, Jimmy; Couceiro, Miguel; Marichal, Jean-Luc
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<br/>Abstract: We investigate the class of binary associative and quasitrivial operations on a given finite set. Here quasitriviality (also known as conserva-tiveness) means that the operation always outputs one of its input values. We also examine the special situations where the operations are commutative and nondecreasing. In the latter case, these operations reduce to discrete uninorms, which are discrete fuzzy connectives that play an important role in fuzzy logic. As we will see nondecreasing, associative and quasitrivial operations are chara-cterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black. This will enable visual interpretaions of the above mentioned algebraic properties. Motivated by these results, we will also address a number of counting issues: we enumerate all binary associative and quasitrivial operations on a given finite set as well as of those operations that are commutative, are nondecreasing, have neutral and/or annihilator elements. As we will see, these considerations lead to several, previously unknown, integer sequences.Structure of Hecke algebras of modular forms modulo $p$
http://hdl.handle.net/10993/32527
Title: Structure of Hecke algebras of modular forms modulo $p$
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<br/>Author, co-author: Deo, ShaunakStep-edge sputtering through grazing incidence ions investigated by scanning tunneling microscopy and molecular dynamics simulations
http://hdl.handle.net/10993/32482
Title: Step-edge sputtering through grazing incidence ions investigated by scanning tunneling microscopy and molecular dynamics simulations
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<br/>Author, co-author: Redinger, Alex; Rosandi, Yudi; Urbassek, Herbert M.; Thomas, Michely
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<br/>Abstract: Scanning tunneling microscopy is used to quantify step-edge sputtering of Pt(111) at 550 K by grazing incidence ion bombardment with 5 keV Ar(+) ions. For bombardment conditions causing negligible erosion on terraces, damage features associated with step bombardment allow us to visualize step retraction and thus to quantify the step-edge sputtering yield. An alternative method for step-edge yield determination, which is applicable under more general conditions, is the analysis of the concentration of ascending steps together with the removed amount as a function of ion fluence. Interestingly, the azimuthal direction of the impinging ions with respect to the surface significantly changes the sputtering yield at step edges. This change is attributed to the orientation dependence of subsurface channeling. Atomistic insight into step-edge sputtering and its azimuthal dependence is given by molecular dynamics simulations of ion impacts at 0 and 550 K. The simulations also demonstrate a strong dependence of the step-edge sputtering yield on temperature.Spiral growth and step edge barriers
http://hdl.handle.net/10993/32481
Title: Spiral growth and step edge barriers
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<br/>Author, co-author: Redinger, Alex; Ricken, Oliver; Kuhn, Philipp; Raetz, Andreas; Voigt, Axel; Krug, Joachim; Michely, Thomas
<br/>
<br/>Abstract: The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both structures attain the same large scale shape when a significant step-edge barrier suppresses interlayer transport. The higher vertical growth rate of the spiral mounds on Pt(111) reflects the different incorporation mechanisms for atoms in the top region and can be formally represented by an enhanced apparent step-edge barrier.Competition of terrace and step-edge sputtering under oblique-incidence ion impact on a stepped Pt(111) surface
http://hdl.handle.net/10993/32480
Title: Competition of terrace and step-edge sputtering under oblique-incidence ion impact on a stepped Pt(111) surface
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<br/>Author, co-author: Rosandi, Yudi; Redinger, Alex; Michely, Thomas; M., Urbassek Herbert
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<br/>Abstract: Using molecular-dynamics simulation, we study the sputtering of a Pt(111) surface under oblique and glancing incidence 5 keV Ar ions. For incidence angles larger than a critical angle theta(c), the projectile is reflected off the surface and the sputter yield is zero. We discuss the azimuth dependence of the critical angle theta(c) with the help of the surface corrugation felt by the impinging ion. If a step exists on the surface, sputtering occurs also for glancing incidence theta > theta(c). We demonstrate that for realistic step densities, the total sputtering of a stepped surface may be sizable even at glancing incidence. (C) 2009 Elsevier B.V. All rights reserved.
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<br/>Commentary: 23rd International Conference on Atomic Collisions in Solids Phalaborwa, SOUTH AFRICA, AUG 17-22, 2008Rapid Coarsening of Ion Beam Ripple Patterns by Defect Annihilation
http://hdl.handle.net/10993/32479
Title: Rapid Coarsening of Ion Beam Ripple Patterns by Defect Annihilation
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<br/>Author, co-author: Hansen, Henri; Redinger, Alex; Messlinger, Sebastian; Georgiana, Stoian; Krug, Joachim; Michely, Thomas
<br/>
<br/>Abstract: Ripple patterns formed on Pt(111) through grazing incidence ion beam erosion coarsen rapidly. At and below 450 K coarsening of the patterns is athermal and kinetic, unrelated to diffusion and surface free energy. Similar to the situation for sand dunes, coarsening takes place through annihilation reactions of mobile defects in the pattern. The defect velocity derived on the basis of a simple model agrees quantitatively with the velocity of monatomic steps illuminated by the ion beam.Influence of a single adatom on sputtering at grazing incidence - A molecular-dynamics case study of 5 keV Ar impact on Pt (111)
http://hdl.handle.net/10993/32478
Title: Influence of a single adatom on sputtering at grazing incidence - A molecular-dynamics case study of 5 keV Ar impact on Pt (111)
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<br/>Author, co-author: Rosandi, Yudi; Redinger, Alex; Michely, Thomas; M., Urbassek Herbert
<br/>
<br/>Abstract: Grazing incidence ion impact on a flat terrace lets the projectile reflect specularly off the surface, leading to little or no damage production or sputtering. The presence of isolated surface defects may change this behaviour drastically. We investigate this phenomenon for the specific case of 5 keV Ar ions impinging at 83 degrees towards the surface normal onto the Pt (111) surface. Molecular-dynamics simulations allow to study the influence of isolated adatoms in detail. The scattering of the projectile from the adatom can redirect the projectile, or let the adatom recoil, such that either of them deposits considerable energy in the target surface, leading to abundant damage production and sputtering. Two distinct collision zones are identified: (i) When the projectile hits the surface in front of the adatom, it may collide with the adatom indirectly (after being specularly reflected off the surface); (ii) alternatively, it may hit the adatom directly. We quantify our results by measuring the zone of influence (congruent to 13 angstrom(2)) around the adatom, into which the projectile must hit in order to collide with the adatom, and by the sputter cross section of roughly 110 angstrom(2). The data compare well with previous simulation results of sputtering from an atomically rough surface. (C) 2008 Elsevier B.V. All rights reserved.Trails of Kilovolt Ions Created by Subsurface Channeling
http://hdl.handle.net/10993/32477
Title: Trails of Kilovolt Ions Created by Subsurface Channeling
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<br/>Author, co-author: Redinger, Alex; Standop, Sebastian; Michely, Thomas; Yudi, Rosandi; Urbassek, Herbert M.
<br/>
<br/>Abstract: Using scanning tunneling microscopy, we observe the damage trails produced by keV noble-gas ions incident at glancing angles onto Pt(111). Surface vacancies and adatoms aligned along the ion trajectory constitute the ion trails. Atomistic simulations reveal that these straight trails are produced by nuclear (elastic) collisions with surface layer atoms during subsurface channeling of the projectiles. In a small energy window around 5 keV, Xe(+) ions create vacancy grooves that mark the ion trajectory with atomic precision. The asymmetry of the adatom production on the two sides of the projectile path is traced back to the asymmetry of the ion's subsurface channel.Sputtering at grazing ion incidence: Influence of adatom islands
http://hdl.handle.net/10993/32476
Title: Sputtering at grazing ion incidence: Influence of adatom islands
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<br/>Author, co-author: Rosandi, Yudi; Redinger, Alex; Michely, Thomas; M., Urbassek Herbert
<br/>
<br/>Abstract: When energetic ions impinge at grazing incidence onto an atomically flat terrace, they will not sputter. However, when adatom islands (containing N atoms) are deposited on the surface, they induce sputtering. We investigate this effect for the specific case of 83 degrees-incident 5 keV Ar ions on a Pt (111) surface by means of molecular-dynamics simulation and experiment. We find that-for constant coverage Theta-the sputter yield has a maximum at island sizes of N congruent to 10-20. A detailed picture explaining the decline of the sputter yield toward larger and smaller island sizes is worked out. Our simulation results are compared with dedicated sputtering experiments, in which a coverage 0.09 of Pt adatoms are deposited onto the Pt (111) surface and form islands with a broad distribution around a most probable size of N congruent to 20.Molecular structure of the H2O wetting layer on Pt(111)
http://hdl.handle.net/10993/32475
Title: Molecular structure of the H2O wetting layer on Pt(111)
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<br/>Author, co-author: Standop, Sebastian; Redinger, Alex; Morgenstern, Markus; Michely, Thomas; Busse, Carsten
<br/>
<br/>Abstract: The molecular structure of the wetting layer of ice on Pt(111) is resolved using scanning tunneling microscopy. Two structures observed previously by diffraction techniques are imaged for coverages at or close to completion of the wetting layer. At 140 K only a root 37 x root 37R25.3 degrees superstructure can be established while at 130 K also a root 39 x root 39R16.1 degrees superstructure with slightly higher molecular density is formed. In the temperature range under concern the superstructures reversibly transform into each other by slight changes in coverage through adsorption or desorption. The superstructures exhibit a complex pattern of molecules in different geometries.Mechanisms of pattern formation in grazing-incidence ion bombardment of Pt(111)
http://hdl.handle.net/10993/32474
Title: Mechanisms of pattern formation in grazing-incidence ion bombardment of Pt(111)
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<br/>Author, co-author: Hansen, Henri; Redinger, Alex; Messlinger, Sebastian; Georgiana, Stoian; Rosandi, Yudi; Urbassek, Herbert M.; Linke, Udo; Michely, Thomas
<br/>
<br/>Abstract: Ripple patterns forming on Pt(111) due to 5 keV Ar(+) grazing-incidence ion bombardment were investigated by scanning tunneling microscopy in a broad temperature range from 100 to 720 K and for ion fluences up to 3x10(20) ions/m(2). A detailed morphological analysis together with molecular dynamics simulations of single ion impacts allow us to develop atomic scale models for the formation of these patterns. The large difference in step edge versus terrace damage is shown to be crucial for ripple formation under grazing incidence. The importance of distinct diffusion processes-step adatom generation at kinks and adatom lattice gas formation-for temperature dependent transitions in the surface morphology is highlighted. Surprisingly, ion bombardment effects like thermal spike induced adatom production and planar subsurface channeling are important for pattern ordering.Kusuoka-Stroock type bounds for densities related to low-dimensional projections of high-dimensional SDE
http://hdl.handle.net/10993/32467
Title: Kusuoka-Stroock type bounds for densities related to low-dimensional projections of high-dimensional SDE
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<br/>Author, co-author: Ledent, Antoine Patrick Isabelle Eric
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<br/>Abstract: One of the purposes of this thesis is to use Malliavin calculus and
Stochastic Taylor expansions to study the densities of interacting
systems of stochastic differential equations (SDE), seen as
projections of SDE onto a low-dimensional space, and to control the
dependence of the constants on the dimension of the background
space. The setting includes time-dependent SDE and a relatively large
class of path-dependent SDE. Several results also shed light on the
classical theory of SDE, independently of the control on the
constants.
In Part 1, assuming the system satisfies suitably defined projected
equivalents of the classic ellipticity or weak Hörmander conditions,
we prove Gaussian estimates in terms of the Euclidean distance where,
provided natural assumptions, for a fixed target-space
dimension, the constants depend polynomially on the background dimension, and, in the elliptic case, on the number of
driving Brownian motions.
In Part 2, we first define suitable generalisations of
(time-dependent) control distances and prove Kusuoka-Stroock type
results without control on the constants.
In particular, we obtain a time-dependent extension of a result of
Léandre about SDE with non-trivial drifts, i.e., drifts which are not
uniformly contained in the span of the other vector fields.
Then, we introduce a condition which we call the `Progressive
Hörmander condition' and prove similar control-type estimates valid
under this assumption, with polynomial control on the growth
of the constants with background space dimension. The condition is of independent interest in the
study of SDE, and shows the connection between the classic
works of Ben Arous, Kusuoka, Léandre and Stroock, and the more recent
works of Bally, Caramellino, Delarue, Menozzi and Pigato. To main
technique required is the study of density and scaling properties of
some careful choice of linear combinations of terms of the signature
of the driving path.
In Part 3, we introduce a stricter condition called the `separated
progressive Hörmander condition', and prove lower bounds and local
strict positivity under this assumption. (By `local' we mean local
around the solution of the deterministic ODE driven by a null control,
rather than local round the initial point.) The main technical
difficulty is the identification of points contained in the interior
of the support of the log-signature of the path in
the d dimensional Euclidean space composed of d Brownian motions and a deterministic linear
component.
The purpose of Part 4 is to use some results and techniques of the
rest of the thesis to prove extensions of a theorem of Löcherbach
about uniformly elliptic interacting branching diffusions.