Metrics with Galilean Conformal Isometry

The Galilean Conformal Algebra (GCA) arises in taking the non-relativistic limit of the symmetries of a relativistic Conformal Field Theory in any dimensions. It is known to be infinite-dimensional in all spacetime dimensions. In particular, the 2d GCA emerges out of a scaling limit of linear combinations of two copies of the Virasoro algebra. In this paper, we find metrics in dimensions greater than two which realize the finite 2d GCA (the global part of the infinite algebra) as their isometry by systematically looking at a construction in terms of cosets of this finite algebra. We list all possible sub-algebras consistent with some physical considerations motivated by earlier work in this direction and construct all possible higher dimensional non-degenerate metrics. We briefly study the properties of the metrics obtained. In the standard one higher dimensional "holographic" setting, we find that the only non-degenerate metric is Minkowskian. In four and five dimensions, we find families of non-trivial metrics with a rather exotic signature. A curious feature of these metrics is that all but one of them are Ricci-scalar flat.Comment: 20 page

Influence of the Pressure on the Product Distribution in the Oxidative Dehydrogenation of Propane over a Ga2O3/MoO3 Catalyst

The yields and selectivities in both the catalyzed and non-catalyzed oxidative dehydrogenation of propane were found to increase with increasing pressure. The results showed that the maximum yields of valuable ODH products could be obtained by adjusting only reactants' partial pressure, while keeping their ratio constant

Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space

Lowest weight modules, in particular, Verma modules over the N = 1,2 super Schrodinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N = 1, 2 super Schrodinger algebras is also presented.Comment: 19 pages, no figur

SO(2,1) conformal anomaly: Beyond contact interactions

The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and special conformal charges is displayed for the two-dimensional inverse square potential. As a consequence, this anomaly appears to be a generic feature of conformal quantum mechanics and not merely an artifact of contact interactions. Moreover, a renormalization procedure traces the emergence of this conformal anomaly to the ultraviolet sector of the theory, within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio

Gravity duals for non-relativistic CFTs

We attempt to generalize the AdS/CFT correspondence to non-relativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and compute some two-point correlators. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.Comment: 12 pages; v2, v3, v4: added references, minor corrections; v3: cleaned up and generalized dust; v4: closer to published versio

Conformal symmetry transformations and nonlinear Maxwell equations

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October 29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer 201

Kennis- en innovatieagenda : creatieve industrie 2018-2021

De creatieve industrie versterkt het innovatievermogen van Nederland. Met haar innovatie- en verbeeldingskracht kan zij mensen verbinden, in beweging krijgen en vertrouwen geven in de wereld van morgen. De sector is een onmisbare schakel in het geven van antwoorden op grote maatschappelijke vraagstukken en het bieden van een zinvolle betekenis aan nieuwe technologische mogelijkheden. Om deze impact te realiseren, maakt de creatieve professional gebruik van een kennisbasis van Key Enabling Methodologies; strategieën, methoden en modellen die structuur geven aan het creatieve proces en deze valideren. In deze methodologieën stelt de professional de mens centraal en is hij in staat om nieuwe werelden en visies te verbeelden en technologieën en actoren uit verschillende hoeken bij elkaar te brengen. De samenleving is het speelveld van de creatieve professional. In deze tijd, waarin transities in de maatschappij gaande zijn, verandert de manier waarop de professional werkt en samenwerkt. De rol van de creatieve professional is meer fluïde dan voorheen. Tegelijkertijd wordt er meer verwacht van de onderbouwing van ontwikkelde interventies en neemt de complexiteit van vraagstukken en oplossingen toe. Om de creatieve professional hierin te ondersteunen, is samenwerking tussen creatieve industrie en kennisinstellingen cruciaal

Fluiddynamik des Kammerwassers beim chronischen einfachen Glaukom: Mechanismen der Drucknormalisierung durch ein künstliches Abflusssystem

Zusammenfassung: Die Wechselwirkung zwischen Kräften, Verteilung und Absorption des Kammerwassers im subkonjunktivalen Gewebe wird anhand eines kürzlich publizierten theoretischen Modells untersucht, das die Produktion von Flüssigkeit im Auge und deren Eliminierung durch das Trabekelwerk, das uveosklerale Gewebe und einen Shunt beschreibt. Zielgröße dabei ist der intraokulare Druck. Die Mechanismen von neu geschaffenen Abflusswegen werden mithilfe der Theorie der porösen Medien dargestellt, die sich auf ein Sickerkissen beziehen, das unter dem subkonjunktivalen Gewebe liegt. Die rechnerische Analyse basiert auf der Geometrie und den Parametern, die das Zu- und Abflusssystem charakterisieren. Diese sind durch die Produktion von Kammerwasser, den chirurgisch angelegten Abflusskanal, sodann durch die Resorption in den episkleralen Gefäßen und durch die hydraulischen Eigenschaften des subkonjunktivalen Gewebes und des Sickerkissens sowie durch dessen Geometrie gegeben. Anhand parametrischer Untersuchungen können klinische Befunde physikalisch begründet werde