N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Higher-dimensional rotating charged black holes

Using the blackfold approach, we study new classes of higher-dimensional rotating black holes with electric charges and string dipoles, in theories of gravity coupled to a 2-form or 3-form field strength and to a dilaton with arbitrary coupling. The method allows to describe not only black holes with large angular momenta, but also other regimes that include charged black holes near extremality with slow rotation. We construct explicit examples of electric rotating black holes of dilatonic and non-dilatonic Einstein-Maxwell theory, with horizons of spherical and non-spherical topology. We also find new families of solutions with string dipoles, including a new class of prolate black rings. Whenever there are exact solutions that we can compare to, their properties in the appropriate regime are reproduced precisely by our solutions. The analysis of blackfolds with string charges requires the formulation of the dynamics of anisotropic fluids with conserved string-number currents, which is new, and is carried out in detail for perfect fluids. Finally, our results indicate new instabilities of near-extremal, slowly rotating charged black holes, and motivate conjectures about topological constraints on dipole hair.

Supergravity models of (3+1)-dimensional QCD

The most general black M5-brane solution of eleven-dimensional supergravity (with a flat R4 spacetime in the brane and a regular horizon) is characterized by charge, mass and two angular momenta. We use this metric to construct general dual models of large-N QCD (at strong coupling) that depend on two free parameters. The mass spectrum of scalar particles is determined analytically (in the WKB approximation) and numerically in the whole two-dimensional parameter space. We compare the mass spectrum with analogous results from lattice calculations, and find that the supergravity predictions are close to the lattice results everywhere on the two dimensional parameter space except along a special line. We also examine the mass spectrum of the supergravity Kaluza-Klein (KK) modes and find that the KK modes along the compact D-brane coordinate decouple from the spectrum for large angular momenta. There are however KK modes charged under a U(1)×U(1) global symmetry which do not decouple anywhere on the parameter space. General formulas for the string tension and action are also given.

Three-dimensional hydrodynamic numerical modelling of fold nappe formation, basement-cover deformation and slab detachment with applications to the helvetic nappe system (W Switzerland)

Many three-dimensional (3-D) structures in rock, which formed during the deformation of the Earth's crust and lithosphere, are controlled by a difference in mechanical strength between rock units and are often the result of a geometrical instability. Such structures are, for example, folds, pinch-and-swell structures (due to necking) or cuspate-lobate structures (mullions). These struc-tures occur from the centimeter to the kilometer scale and the related deformation processes con-trol the formation of, for example, fold-and-thrust belts and extensional sedimentary basins or the deformation of the basement-cover interface. The 2-D deformation processes causing these structures are relatively well studied, however, several processes during large-strain 3-D defor-mation are still incompletely understood. One of these 3-D processes is the lateral propagation of these structures, such as fold and cusp propagation in a direction orthogonal to the shortening direction or neck propagation in direction orthogonal to the extension direction. Especially, we are interested in fold nappes which are recumbent folds with amplitudes usually exceeding 10 km and they have been presumably formed by ductile shearing. They often exhibit a constant sense of shearing and a non-linear increase of shear strain towards their overturned limb. The fold axes of the Morcles fold nappe in western Switzerland plunges to the ENE whereas the fold axes in the more eastern Doldenhorn nappe plunges to the WSW. These opposite plunge direc-tions characterize the Rawil depression (Wildstrubel depression). The Morcles nappe is mainly the result of layer parallel contraction and shearing. During the compression the massive lime-stones were more competent than the surrounding marls and shales, which led to the buckling characteristics of the Morcles nappe, especially in the north-dipping normal limb. The Dolden-horn nappe exhibits only a minor overturned fold limb. There are still no 3-D numerical studies which investigate the fundamental dynamics of the formation of the large-scale 3-D structure including the Morcles and Doldenhorn nappes and the related Rawil depression. We study the 3-D evolution of geometrical instabilities and fold nappe formation with numerical simulations based on the finite element method (FEM). Simulating geometrical instabilities caused by sharp variations of mechanical strength between rock units requires a numerical algorithm that can accurately resolve material interfaces for large differences in material properties (e.g. between limestone and shale) and for large deformations. Therefore, our FE algorithm combines a nu-merical contour-line technique and a deformable Lagrangian mesh with re-meshing. With this combined method it is possible to accurately follow the initial material contours with the FE mesh and to accurately resolve the geometrical instabilities. The algorithm can simulate 3-D de-formation for a visco-elastic rheology. The viscous rheology is described by a power-law flow law. The code is used to study the 3-D fold nappe formation, the lateral propagation of folding and also the lateral propagation of cusps due to initial half graben geometry. Thereby, the small initial geometrical perturbations for folding and necking are exactly followed by the FE mesh, whereas the initial large perturbation describing a half graben is defined by a contour line inter-secting the finite elements. Further, the 3-D algorithm is applied to 3-D viscous nacking during slab detachment. The results from various simulations are compared with 2-D resulats and a 1-D analytical solution. -- On retrouve beaucoup de structures en 3 dimensions (3-D) dans les roches qui ont pour origines une déformation de la lithosphère terrestre. Ces structures sont par exemple des plis, des boudins (pinch-and-swell) ou des mullions (cuspate-lobate) et sont présentés de l'échelle centimétrique à kilométrique. Mécaniquement, ces structures peuvent être expliquées par une différence de résistance entre les différentes unités de roches et sont généralement le fruit d'une instabilité géométrique. Ces différences mécaniques entre les unités contrôlent non seulement les types de structures rencontrées, mais également le type de déformation (thick skin, thin skin) et le style tectonique (bassin d'avant pays, chaîne d'avant pays). Les processus de la déformation en deux dimensions (2-D) formant ces structures sont relativement bien compris. Cependant, lorsque l'on ajoute la troisiéme dimension, plusieurs processus ne sont pas complètement compris lors de la déformation à large échelle. L'un de ces processus est la propagation latérale des structures, par exemple la propagation de plis ou de mullions dans la direction perpendiculaire à l'axe de com-pression, ou la propagation des zones d'amincissement des boudins perpendiculairement à la direction d'extension. Nous sommes particulièrement intéressés les nappes de plis qui sont des nappes de charriage en forme de plis couché d'une amplitude plurikilométrique et étant formées par cisaillement ductile. La plupart du temps, elles exposent un sens de cisaillement constant et une augmentation non linéaire de la déformation vers la base du flanc inverse. Un exemple connu de nappes de plis est le domaine Helvétique dans les Alpes de l'ouest. Une de ces nap-pes est la Nappe de Morcles dont l'axe de pli plonge E-NE tandis que de l'autre côté de la dépression du Rawil (ou dépression du Wildstrubel), la nappe du Doldenhorn (équivalent de la nappe de Morcles) possède un axe de pli plongeant O-SO. La forme particulière de ces nappes est due à l'alternance de couches calcaires mécaniquement résistantes et de couches mécanique-ment faibles constituées de schistes et de marnes. Ces différences mécaniques dans les couches permettent d'expliquer les plissements internes à la nappe, particulièrement dans le flanc inver-se de la nappe de Morcles. Il faut également noter que le développement du flanc inverse des nappes n'est pas le même des deux côtés de la dépression de Rawil. Ainsi la nappe de Morcles possède un important flanc inverse alors que la nappe du Doldenhorn en est presque dépour-vue. A l'heure actuelle, aucune étude numérique en 3-D n'a été menée afin de comprendre la dynamique fondamentale de la formation des nappes de Morcles et du Doldenhorn ainsi que la formation de la dépression de Rawil. Ce travail propose la première analyse de l'évolution 3-D des instabilités géométriques et de la formation des nappes de plis en utilisant des simulations numériques. Notre modèle est basé sur la méthode des éléments finis (FEM) qui permet de ré-soudre avec précision les interfaces entre deux matériaux ayant des propriétés mécaniques très différentes (par exemple entre les couches calcaires et les couches marneuses). De plus nous utilisons un maillage lagrangien déformable avec une fonction de re-meshing (production d'un nouveau maillage). Grâce à cette méthode combinée il nous est possible de suivre avec précisi-on les interfaces matérielles et de résoudre avec précision les instabilités géométriques lors de la déformation de matériaux visco-élastiques décrit par une rhéologie non linéaire (n>1). Nous uti-lisons cet algorithme afin de comprendre la formation des nappes de plis, la propagation latérale du plissement ainsi que la propagation latérale des structures de type mullions causé par une va-riation latérale de la géométrie (p.ex graben). De plus l'algorithme est utilisé pour comprendre la dynamique 3-D de l'amincissement visqueux et de la rupture de la plaque descendante en zone de subduction. Les résultats obtenus sont comparés à des modèles 2-D et à la solution analytique 1-D. -- Viele drei dimensionale (3-D) Strukturen, die in Gesteinen vorkommen und durch die Verfor-mung der Erdkruste und Litosphäre entstanden sind werden von den unterschiedlichen mechani-schen Eigenschaften der Gesteinseinheiten kontrolliert und sind häufig das Resulat von geome-trischen Istabilitäten. Zu diesen strukturen zählen zum Beispiel Falten, Pich-and-swell Struktu-ren oder sogenannte Cusbate-Lobate Strukturen (auch Mullions). Diese Strukturen kommen in verschiedenen Grössenordungen vor und können Masse von einigen Zentimeter bis zu einigen Kilometer aufweisen. Die mit der Entstehung dieser Strukturen verbundenen Prozesse kontrol-lieren die Entstehung von Gerbirgen und Sediment-Becken sowie die Verformung des Kontaktes zwischen Grundgebirge und Stedimenten. Die zwei dimensionalen (2-D) Verformungs-Prozesse die zu den genannten Strukturen führen sind bereits sehr gut untersucht. Einige Prozesse wäh-rend starker 3-D Verformung sind hingegen noch unvollständig verstanden. Einer dieser 3-D Prozesse ist die seitliche Fortpflanzung der beschriebenen Strukturen, so wie die seitliche Fort-pflanzung von Falten und Cusbate-Lobate Strukturen senkrecht zur Verkürzungsrichtung und die seitliche Fortpflanzung von Pinch-and-Swell Strukturen othogonal zur Streckungsrichtung. Insbesondere interessieren wir uns für Faltendecken, liegende Falten mit Amplituden von mehr als 10 km. Faltendecken entstehen vermutlich durch duktile Verscherung. Sie zeigen oft einen konstanten Scherungssinn und eine nicht-lineare zunahme der Scherverformung am überkipp-ten Schenkel. Die Faltenachsen der Morcles Decke in der Westschweiz fallen Richtung ONO während die Faltenachsen der östicher gelegenen Doldenhorn Decke gegen WSW einfallen. Diese entgegengesetzten Einfallrichtungen charakterisieren die Rawil Depression (Wildstrubel Depression). Die Morcles Decke ist überwiegend das Resultat von Verkürzung und Scherung parallel zu den Sedimentlagen. Während der Verkürzung verhielt sich der massive Kalkstein kompetenter als der Umliegende Mergel und Schiefer, was zur Verfaltetung Morcles Decke führ-te, vorallem in gegen Norden eifallenden überkippten Schenkel. Die Doldenhorn Decke weist dagegen einen viel kleineren überkippten Schenkel und eine stärkere Lokalisierung der Verfor-mung auf. Bis heute gibt es keine 3-D numerischen Studien, die die fundamentale Dynamik der Entstehung von grossen stark verformten 3-D Strukturen wie den Morcles und Doldenhorn Decken sowie der damit verbudenen Rawil Depression untersuchen. Wir betrachten die 3-D Ent-wicklung von geometrischen Instabilitäten sowie die Entstehung fon Faltendecken mit Hilfe von numerischen Simulationen basiert auf der Finite Elemente Methode (FEM). Die Simulation von geometrischen Instabilitäten, die aufgrund von Änderungen der Materialeigenschaften zwischen verschiedenen Gesteinseinheiten entstehen, erfortert einen numerischen Algorithmus, der in der Lage ist die Materialgrenzen mit starkem Kontrast der Materialeigenschaften (zum Beispiel zwi-schen Kalksteineinheiten und Mergel) für starke Verfomung genau aufzulösen. Um dem gerecht zu werden kombiniert unser FE Algorithmus eine numerische Contour-Linien-Technik und ein deformierbares Lagranges Netz mit Re-meshing. Mit dieser kombinierten Methode ist es mög-lich den anfänglichen Materialgrenzen mit dem FE Netz genau zu folgen und die geometrischen Instabilitäten genügend aufzulösen. Der Algorithmus ist in der Lage visko-elastische 3-D Ver-formung zu rechnen, wobei die viskose Rheologie mit Hilfe eines power-law Fliessgesetzes beschrieben wird. Mit dem numerischen Algorithmus untersuchen wir die Entstehung von 3-D Faltendecken, die seitliche Fortpflanzung der Faltung sowie der Cusbate-Lobate Strukturen die sich durch die Verkürzung eines mit Sediment gefüllten Halbgraben bilden. Dabei werden die anfänglichen geometrischen Instabilitäten der Faltung exakt mit dem FE Netz aufgelöst wäh-rend die Materialgranzen des Halbgrabens die Finiten Elemente durchschneidet. Desweiteren wird der 3-D Algorithmus auf die Einschnürung während der 3-D viskosen Plattenablösung und Subduktion angewandt. Die 3-D Resultate werden mit 2-D Ergebnissen und einer 1-D analyti-schen Lösung verglichen.

[Co(en)(3)][Sb12S19]: a new antimony sulfide with a zeolite-like structure containing one-dimensional channels

Solvothermal synthesis affords access to the first truly three-dimensional anti mony-sufide framework which contains one-dimensional circular channels.

On instabilities in data assimilation algorithms

Data assimilation algorithms are a crucial part of operational systems in numerical weather prediction, hydrology and climate science, but are also important for dynamical reconstruction in medical applications and quality control for manufacturing processes. Usually, a variety of diverse measurement data are employed to determine the state of the atmosphere or to a wider system including land and oceans. Modern data assimilation systems use more and more remote sensing data, in particular radiances measured by satellites, radar data and integrated water vapor measurements via GPS/GNSS signals. The inversion of some of these measurements are ill-posed in the classical sense, i.e. the inverse of the operator H which maps the state onto the data is unbounded. In this case, the use of such data can lead to significant instabilities of data assimilation algorithms. The goal of this work is to provide a rigorous mathematical analysis of the instability of well-known data assimilation methods. Here, we will restrict our attention to particular linear systems, in which the instability can be explicitly analyzed. We investigate the three-dimensional variational assimilation and four-dimensional variational assimilation. A theory for the instability is developed using the classical theory of ill-posed problems in a Banach space framework. Further, we demonstrate by numerical examples that instabilities can and will occur, including an example from dynamic magnetic tomography.

A three-dimensional network constructed from the assembly of 1,3-diaminopropane-copper(II) and tetracyanopalladate(II) moieties

The coordination polymer [Cu(Pd(CN)(4))(pn)](n) (pn = 1,3-diaminopropane) has been synthesized and characterized by elemental analysis, infrared spectroscopy and single-crystal X-ray diffraction. The crystal structure showed that three cyano groups of each [Pd(CN)(4)] unit bridge Cu(II) centers leading to the formation of a three-dimensional network. A series of bifurcated hydrogen bonds between the amino groups of the diamine and the nonbridging cyano groups of the cyanometallate result in the organization of suprarnolecular chains and rings along the polymer. (c) 2008 Elsevier B.V. All rights reserved.

A three-dimensional network constructed from the assembly of 1,3-diaminopropane-copper(II) and tetracyanopalladate(II) moieties

The coordination polymer [Cu(Pd(CN)(4))(pn)](n) (pn = 1,3-diaminopropane) has been synthesized and characterized by elemental analysis, infrared spectroscopy and single-crystal X-ray diffraction. The crystal structure showed that three cyano groups of each [Pd(CN)(4)] unit bridge Cu(II) centers leading to the formation of a three-dimensional network. A series of bifurcated hydrogen bonds between the amino groups of the diamine and the nonbridging cyano groups of the cyanometallate result in the organization of suprarnolecular chains and rings along the polymer. (c) 2008 Elsevier B.V. All rights reserved.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Synergistic Anti-Inflammatory Activity of the Antimicrobial Peptides Human Beta-Defensin-3 (hBD-3) and Cathelicidin (LL-37) in a Three-Dimensional Co-Culture Model of Gingival Epithelial Cells and Fibroblasts

Given the spread of antibiotic resistance in bacterial pathogens, antimicrobial peptides that can also modulate the immune response may be a novel approach for effectively controlling periodontal infections. In the present study, we used a three-dimensional (3D) co-culture model of gingival epithelial cells and fibroblasts stimulated with Aggregatibacter actinomycetemcomitans lipopolysaccharide (LPS) to investigate the anti-inflammatory properties of human beta-defensin-3 (hBD-3) and cathelicidin (LL-37) and to determine whether these antimicrobial peptides can act in synergy. The 3D co-culture model composed of gingival fibroblasts embedded in a collagen matrix overlaid with gingival epithelial cells had a synergistic effect with respect to the secretion of IL-6 and IL-8 in response to LPS stimulation compared to fibroblasts and epithelial cells alone. The 3D co-culture model was stimulated with non-cytotoxic concentrations of hBD-3 (10 and 20 mu M) and LL-37 (0.1 and 0.2 mu M) individually and in combination in the presence of A. actinomycetemcomitans LPS. A multiplex ELISA assay was used to quantify the secretion of 41 different cytokines. hBD-3 and LL-37 acted in synergy to reduce the secretion of GRO-alpha, G-CSF, IP-10, IL-6, and MCP-1, but only had an additive effect on reducing the secretion of IL-8 in response to A. actinomycetemcomitans LPS stimulation. The present study showed that hBD-3 acted in synergy with LL-37 to reduce the secretion of cytokines by an LPS-stimulated 3D model of gingival mucosa. This combination of antimicrobial peptides thus shows promising potential as an adjunctive therapy for treating inflammatory periodontitis.

Green tea polyphenol epigallocatechin-3-gallate and cranberry proanthocyanidins act in synergy with cathelicidin (LL-37) to reduce the LPS-induced inflammatory response in a three-dimensional co-culture model of gingival epithelial cells and fibroblasts

Objectives: The human antimicrobial peptide cathelicidin (LL-37) possesses anti-inflammatory properties that may contribute to attenuating the inflammatory process associated with chronic periodontitis. Plant polyphenols, including those from cranberry and green tea, have been reported to reduce inflammatory cytokine secretion by host cells. In the present study, we hypothesized that A-type cranberry proanthocyanidins (AC-PACs) and green tea epigallocatechin-3-gallate (EGCG) act in synergy with LL-37 to reduce the secretion of inflammatory mediators by oral mucosal cells. Methods: A three-dimensional (3D) co-culture model of gingival epithelial cells and fibroblasts treated with non-cytotoxic concentrations of AC-PACs (25 and 50 mg/ml), EGCG (1 and 5 mg/ml), and LL-37 (0.1 and 0.2 mM) individually and in combination (AC-PACs + LL-37 and EGCG + LL-37) were stimulated with Aggregatibacter actinomycetemcomitans lipopolysaccharide (LPS). Multiplex ELISA assays were used to quantify the secretion of 54 host factors, including chemokines, cytokines, growth factors, matrix metalloproteinases (MMPs), and tissue inhibitors of metalloproteinases (TIMPs). Results: LL-37, AC-PACs, and EGCG, individually or in combination, had no effect on the regulation of MMP and TIMP secretion but inhibited the secretion of several cytokines. ACPACs and LL-37 acted in synergy to reduce the secretion of CXC-chemokine ligand 1 (GRO-a), granulocyte colony-stimulating factor (G-CSF), and interleukin-6 (IL-6), and had an additive effect on reducing the secretion of interleukin-8 (IL-8), interferon-g inducible protein 10 (IP-10), and monocyte chemoattractant protein-1 (MCP-1) in response to LPS stimulation. EGCG and LL-37 acted in synergy to reduce the secretion of GRO-a, G-CSF, IL-6, IL-8, and IP-10, and had an additive effect on MCP-1 secretion. Conclusion: The combination of LL-37 and natural polyphenols from cranberry and green tea acted in synergy to reduce the secretion of several cytokines by an LPS-stimulated 3D coculture model of oral mucosal cells. Such combinations show promising results as potential adjunctive therapies for treating inflammatory periodontitis.

Toroidal solitons in 3+1 dimensional integrable theories

We analyze the integrability properties of models defined on the symmetric space SU(2)/U(1) in 3 + 1 dimensions, using a recently proposed approach for integrable theories in any dimension. We point out the key ingredients for a theory to possess an infinite number of local conservation laws, and discuss classes of models with such property, We propose a 3 + 1-dimensional, relativistic invariant field theory possessing a toroidal soliton solution carrying a unit of topological charge given by the Hopf map. Construction of the action is guided by the requirement that the energy of static configuration should be scale invariant. The solution is constructed exactly. The model possesses an infinite number of local conserved currents. The method is also applied to the Skyrme-Faddeev model, and integrable submodels are proposed. (C) 1999 Elsevier B.V. B.V. All rights reserved.