Spin-Foam Models and the Physical Scalar Product

This paper aims at clarifying the link between Loop Quantum Gravity and Spin-Foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl($\Gamma$), where $\Gamma$ is the 4-simplex graph, such that its ma- trix elements are, up to some normalization factors, the vertex amplitude of Spin-Foam models. The Spin-Foam models we are considering are the topological model, the Barrett-Crane model and the Engle-Pereira-Rovelli model. The operator P is usually called the "projector" into physical states and its matrix elements gives the physical scalar product. Therefore, we relate the physical scalar product of Loop Quantum Gravity to vertex amplitudes of some Spin-Foam models. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.Comment: 24 page

Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging

We introduce a new dynamic light scattering method, termed photon correlation imaging, which enables us to resolve the dynamics of soft matter in space and time. We demonstrate photon correlation imaging by investigating the slow dynamics of a quasi two-dimensional coarsening foam made of highly packed, deformable bubbles and a rigid gel network formed by dilute, attractive colloidal particles. We find the dynamics of both systems to be determined by intermittent rearrangement events. For the foam, the rearrangements extend over a few bubbles, but a small dynamical correlation is observed up to macroscopic length scales. For the gel, dynamical correlations extend up to the system size. These results indicate that dynamical correlations can be extremely long-ranged in jammed systems and point to the key role of mechanical properties in determining their nature.Comment: Published version (Phys. Rev. Lett. 102, 085702 (2009)) The Dynamical Activity Mapsprovided as Supplementary Online Material are also available on http://w3.lcvn.univ-montp2.fr/~lucacip/dam/movies.ht

Spherical Foams in Flat Space

Regular tesselations of space are characterized through their Schlafli symbols {p,q,r}, where each cell has regular p-gonal sides, q meeting at each vertex, and r meeting on each edge. Regular tesselations with symbols {p,3,3} all satisfy Plateau's laws for equilibrium foams. For general p, however, these regular tesselations do not embed in Euclidean space, but require a uniform background curvature. We study a class of regular foams on S^3 which, through conformal, stereographic projection to R^3 define irregular cells consistent with Plateau's laws. We analytically characterize a broad classes of bulk foam bubbles, and extend and explain recent observations on foam structure and shape distribution. Our approach also allows us to comment on foam stability by identifying a weak local maximum of A^(3/2)/V at the maximally symmetric tetrahedral bubble that participates in T2 rearrangements.Comment: 4 pages, 4 included figures, RevTe

Space-Time Foam and Cosmic-Ray Interactions

It has been proposed that propagation of cosmic rays at extreme-energy may be sensitive to Lorentz-violating metric fluctuations (``foam''). We investigate the changes in interaction thresholds for cosmic-rays and gamma-rays interacting on the CMB and IR backgrounds, for a class of stochastic models of spacetime foam. The strength of the foam is characterized by the factor (E/M_P)^a, where ``a'' is a phenomenological suppression parameter. We find that there exists a critical value of ``a'' (dependent on the particular reaction), below which the threshold energy can only be lowered, and above which the threshold energy may be raised, but at most by a factor of two. Thus, it does not appear possible in this class of models to extend cosmic-ray spectra significantly beyond their classical absorption energies. However, the lower thresholds resulting from foam may have signatures in the cosmic-ray spectrum. We also find that cosmic-ray energies cannot exceed the fundamental Planck scale, and so set a lower bound of 10^8 TeV on the context of this model for the scale of gravity. Finally, we comment in the apparent non-conservation of particle energy-momentum, and speculate on its re-emergence as dark energy in the foamy vacuum.Comment: 27 pages, 13 figures. Author added (Buniy), appendix added, and new section added, corrections made. To appear in Astroparticle Physic

Impact of Low-Energy Constraints on Lorentz Violation

We extend previous analyses of the violation of Lorentz invariance induced in a non-critical string model of quantum space-time foam, discussing the propagation of low-energy particles through a distribution of non-relativistic D-particles.We argue that nuclear and atomic physics experiments do not constitute sensitive probes of this approach to quantum gravity due to a difference in the dispersion relations for massive probes as compared to those for massless ones, predicted by the model.Comment: 4 pages revte

Boundary terms in the Barrett-Crane spin foam model and consistent gluing

We extend the lattice gauge theory-type derivation of the Barrett-Crane spin foam model for quantum gravity to other choices of boundary conditions, resulting in different boundary terms, and re-analyze the gluing of 4-simplices in this context. This provides a consistency check of the previous derivation. Moreover we study and discuss some possible alternatives and variations that can be made to it and the resulting models.Comment: 10 pages, 2 figures, revtex; v2: typos in some formulas corrected, version appeared in journa

Validation of the immersed boundary surface method in computational fluid dynamics

Cilj ovog rada je predstaviti teorijsku i praktičnu pozadinu metode uronjene granice implementirane u foam-extend 4.1, odnosno njene prednosti i nedostatke. Glavni cilj metode uronjene granice je pojednostavljenje izrade mreža u računalnoj dinamici fluida, što može dovesti do značajnog smanjenja količine ljudskog rada koji se mora uložiti pri pripremanju simulacija u računalnoj dinamici fluida, pogotovo kod simulacija sa složenim geometrijama. Također, metoda uronjene granice može donijeti određene prednosti kod simulacija s pomičnim mrežama, u vidu smanjenja računalne zahtjevnosti takvih simulacija. Glavni nedostatak metode uronjene granice je smanjenje točnosti rješenja na uronjenim granicama (površinama simuliranih objekata). Metoda uronjene granice implementirana u foam-extend 4.1 je ovdje validirana na trima slučajevima: unutarnje strujanje u 2-D slučaju u cijevi sa naglim proširenjem, vanjsko strujanje oko Onera M6 krila i strujanje u Francisovoj turbini, što je pogotovo zanimljiv slučaj za metodu uronjene granice. Rezultati simulacija izvedenih uporabom metodom uronjene granice su uspoređeni sa rezultatima simulacija izvedenim konvencionalnim načinom izrade mreže. Rezultati simulacija su zadovoljavajući, odnosno, smanjenje točnosti rješenja na uronjenim granicama je dovoljno maleno da implementaciju metode uronjene granice u foam-extend 4.1 možemo ocjeniti kao dobru.The aim of this thesis is to describe the Immersed Boundary Method version implemented in foam-extend 4.1, both its advantages and shortcomings. The main goal of the Immersed Boundary Method is to simplify the mesh generation process in Computational Fluid Dynamics, which can lead to drastic reductions of human time needed for setting up simulations, especially for simulations with complex geometries. Additionally, it can offer certain advantages in simulations with moving meshes, as it can decrease the computational requirements of such cases. The main shortcoming of the Immersed Boundary Method is loss of solution accuracy on immersed boundaries (surfaces of simulated objects). The foam-extend 4.1 Immersed Boundary Method is here validated on three cases: internal 2-D flow over a backward facing step, external flow around the Onera M6 wing, and the flow in a model Francis turbine, which is an especially interesting case, concerning the Immersed Boundary Method. The results of the Immersed Boundary Method simulations are compared to the results of equivalent body-fitted (conventional) simulations. The simulation results are generally satisfactory, as the loss of accuracy was modest enough to assess the foam-extend 4.1 implementation of the Immersed Boundary Method as successful

FoamVis, A Visualization System for Foam Research: Design and Implementation

Liquid foams are used in areas such as mineral separation, oil recovery, food and beverage production, sanitation and fire fighting. To improve the quality of products and the efficiency of processes in these areas, foam scientists wish to understand and control foam behaviour. To this end, foam scientists have used foam simulations to model foam behaviour; however, analysing these simulations presents difficult challenges. We describe the main foam research challenges and present the design of FoamVis, the only existing visualization, exploration and analysis application created to address them. We describe FoamVis’ main features, together with relevant design and implementation notes. Our goal is to provide a global overview and individual feature implementation details that would allow a visualization scientist to extend the FoamVis system with new algorithms and adapt it to new requirements. The result is a detailed presentation of the software that is not provided in previous visualization research papers