Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially filled with D$_2$O, were examined with NMR (nuclear magnetic resonance) microscopy for rendering proton spin density maps. The propagating proton/deuteron inter-diffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk, $d_w$, evaluated from the diffusion measurements on the one hand and the fractal dimension, $d_f$, deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

HKT Geometry and Fake Five Dimensional Supergravity

Recent results on the relation between hyper-Kahler geometry with torsion and solutions admitting Killing spinors in minimal de sitter supergravity are extended to more general supergravity models with vector multiplets.Comment: 14 pages, latex. Minor typos corrected, references adde

Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry

At arbitrary temperature $T$, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants $J_1$, or on an isosceles triangle with a third, different exchange constant $J_2$. As T\rightrarrow\infty, the Fourier transforms and long-time asymptotic behaviors of the two-spin time correlation functions are evaluated exactly. The lack of translational symmetry on a chain or an isosceles triangle yields time correlation functions that differ strikingly from those on an equilateral trinagle with $J_1=J_2$. At low $T$, the Fourier transforms of the two autocorrelation functions with $J_1\ne J_2$ show one and four modes, respectively. For a semi-infinite $J_2/J_1$ range, one mode is a central peak. At the origin of this range, this mode has a novel scaling form.Comment: 9 pages, 14 figures, accepted for publication in Phys. Rev.

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0, \beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $\alpha$ on the phase boundary.Comment: 4 pages REVTEX, 4 figure

A New Derivation of the Picard-Fuchs Equations for Effective N=2N = 2 Super Yang-Mills Theories

A new method to obtain the Picard-Fuchs equations of effective $N = 2$ supersymmetric gauge theories in 4 dimensions is developed. It includes both pure super Yang-Mills and supersymmetric gauge theories with massless matter hypermultiplets. It applies to all classical gauge groups, and directly produces a decoupled set of second-order, partial differential equations satisfied by the period integrals of the Seiberg-Witten differential along the 1-cycles of the algebraic curves describing the vacuum structure of the corresponding $N = 2$ theory.Comment: Latex version, 43 pages, a few cosmetic changes and some references adde

Supersymmetric gyratons in five dimensions

We obtain the gravitational and electromagnetic field of a spinning radiation beam-pulse (a gyraton) in minimal five-dimensional gauged supergravity and show under which conditions the solution preserves part of the supersymmetry. The configurations represent generalizations of Lobatchevski waves on AdS with nonzero angular momentum, and possess a Siklos-Virasoro reparametrization invariance. We compute the holographic stress-energy tensor of the solutions and show that it transforms without anomaly under these reparametrizations. Furthermore, we present supersymmetric gyratons both in gauged and ungauged five-dimensional supergravity coupled to an arbitrary number of vector supermultiplets, which include gyratons on domain walls.Comment: 25 pages, no figures, uses JHEP3.cls. Final version to appear in CQ

Two antisymmetric hypermultiplets in N=2 SU(N) gauge theory: Seiberg-Witten curve and M-theory interpretation

The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric hypermultiplets and N_f \leq 3 hypermultiplets in the defining representation. Using methods developed for the instanton expansion of non-hyperelliptic curves, we construct an effective quartic Seiberg-Witten curve that generates this one-instanton prepotential. We then interpret this curve in terms of an M-theoretic picture involving NS 5-branes, D4-branes, D6-branes, and orientifold sixplanes, and show that for consistency, an infinite chain of 5-branes and orientifold sixplanes is required, corresponding to a curve of infinite order.Comment: 30 pages; 3 figures; LaTeX; minor typos correcte

Mirror Symmetry, Mirror Map and Applications to Calabi-Yau Hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.Comment: 59 pages. Some changes in the references, a few minor points have been clarifie

Pathological regional blood flow in opiate-dependent patients during withdrawal: A HMPAO-SPECT study

The aims of the present study were to investigate regional cerebral blood flow (rCBF) in heroin-dependent patients during withdrawal and to assess the relation between these changes and duration of heroin consumption and withdrawal data. The rCBF was measured using brain SPECT with Tc-99m-HMPAO in 16 heroin-dependent patients during heroin withdrawal. Thirteen patients received levomethadone at the time of the SPECT scans. The images were analyzed both visually and quantitatively, a total of 21 hypoperfused brain regions were observed in 11 of the 16 patients. The temporal lobes were the most affected area, hypoperfusions of the right and left temporal lobe were observed in 5 and 5 patients, respectively. Three of the patients had a hypoperfusion of the right frontal lobe, 2 patients showed perfusion defects in the left frontal lobe, right parietal lobe and left parietal lobe. The results of the quantitative assessments of the rCBF were consistent with the results of the qualitative findings. The stepwise regression analysis showed a significant positive correlation (r = 0.54) between the dose of levomethadone at the time of the SPECT scan and the rCBF of the right parietal lobe. Other significant correlations between clinical data and rCBF were not found. The present results suggest brain perfusion abnormalities during heroin withdrawal in heroin-dependent patients, which are not due to the conditions of withdrawal