Consumption processes and positively homogeneous projection properties

We constructively prove the existence of time-discrete consumption processes for stochastic money accounts that fulfill a pre-specified positively homogeneous projection property (PHPP) and let the account always be positive and exactly zero at the end. One possible example is consumption rates forming a martingale under the above restrictions. For finite spaces, it is shown that any strictly positive consumption strategy with restrictions as above possesses at least one corresponding PHPP and could be constructed from it. We also consider numeric examples under time-discrete and -continuous account processes, cases with infinite time horizons and applications to income drawdown and bonus theory.Comment: 24 pages, 2 figure

Croconaine-Based Polymer Particles as Contrast Agents for Photoacoustic Imaging

In the development and optimization of imaging methods, photoacoustic imaging (PAI) has become a powerful tool for preclinical biomedical diagnosis and detection of cancer. PAI probes can improve contrast and help identify pathogenic tissue. Such contrast agents must meet several requirements: they need to be biocompatible, and absorb strongly in the near-infrared (NIR) range, while relaxing the photoexcited state thermally and not radiatively. In this work, polymer nanoparticles are produced with croconaine as a monomer unit. Small molecular croconaine dyes are known to act as efficient pigments, which do not show photoluminescence. Here, for the first time croconaine copolymer nanoparticles are produced from croconic acid and a range of aromatic diamines. Following a dispersion polymerization protocol, this approach yields monodisperse particles of adjustable size. All synthesized polymers exhibit broad absorption within the NIR spectrum and therefore represent suitable candidates as contrast agents for PAI. The optical properties of these polymer particles are discussed with respect to the relation between particle size and outstanding photoacoustic performance. Biocompatibility of the polymer particles is demonstrated in cell viability experiments. © The Authors. Published by Wiley-VCH Gmb

Non-transitive maps in phase synchronization

Concepts from the Ergodic Theory are used to describe the existence of non-transitive maps in attractors of phase synchronous chaotic systems. It is shown that for a class of phase-coherent systems, e.g. the sinusoidally forced Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization implies that such maps exist. These ideas are also extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used to real time detection of phase synchronization in experimental systems

Non-perturbative Propagators, Running Coupling and Dynamical Quark Mass of Landau gauge QCD

The coupled system of renormalized Dyson-Schwinger equations for the quark, gluon and ghost propagators of Landau gauge QCD is solved within truncation schemes. These employ bare as well as non-perturbative ansaetze for the vertices such that the running coupling as well as the quark mass function are independent of the renormalization point. The one-loop anomalous dimensions of all propagators are reproduced. Dynamical chiral symmetry breaking is found, the dynamically generated quark mass agrees well with phenomenological values and corresponding results from lattice calculations. The effects of unquenching the system are small. In particular the infrared behavior of the ghost and gluon dressing functions found in previous studies is almost unchanged as long as the number of light flavors is smaller than four.Comment: 34 pages, 10 figures, version to be published by Phys. Rev.

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same behavior is obtained for the larger values of a^2q^2 (in units of the lattice spacing a), where it is otherwise swamped by the gauge field dynamics. Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II); references and comments on subsequent work on the subject added

On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory

We study the nature of the confinement phase transition in d=3+1 dimensions in various non-abelian gauge theories with the approach put forward in [1]. We compute an order-parameter potential associated with the Polyakov loop from the knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and Sp(2) we find a first-order phase transition in agreement with general expectations. Moreover our study suggests that the phase transition in E(7) Yang-Mills theory also is of first order. We find that it is weaker than for SU(N). We show that this can be understood in terms of the eigenvalue distribution of the order parameter potential close to the phase transition.Comment: 15 page

Roles of the color antisymmetric ghost propagator in the infrared QCD

The results of Coulomb gauge and Landau gauge lattice QCD simulation do not agree completely with continuum theory. There are indications that the ghost propagator in the infrared region is not purely color diagonal as in high energy region. After presenting lattice simulation of configurations produced with Kogut-Susskind fermion (MILC collaboration) and those with domain wall fermion (RBC/UKQCD collaboration), I investigate in triple gluon vertex and the ghost-gluon-ghost vertex how the square of the color antisymmetric ghost contributes. Then the effect of the vertex correction to the gluon propagator and the ghost propagator is investigated. Recent Dyson-Schwinger equation analysis suggests the ghost dressing function $G(0)=$ finite and no infrared enhancement or $\alpha_G=0$. But the ghost propagator renormalized by the loop containing a product of color antisymmetric ghost is expected to behave as $_r =-\frac{G(q^2)}{q^2}$ with $G(q^2)\propto q^{-2(1+\alpha_G)}$ with $\alpha_G = 0.5$, if the fixed point scenario is valid. I interpret the $\alpha_G=0$ solution should contain a vertex correction. The infrared exponent of our lattice Landau gauge gluon propagator of the RBC/UKQCD is $\kappa=\alpha_G=-0.5$ and that of MILC is about -0.7. The implication for the Kugo-Ojima color confinement criterion, QCD effective coupling and the Slavnov identity are given.Comment: 13 pages 10 figures, references added and revised. version to be published in Few-Body System

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite beta. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.Comment: 14 pages, 22 figures; minor changes, matches version to appear in Eur. Phys. J.