Vector-axialvector mixing from a chiral effective field theory at finite temperature

We study the vector-axialvector mixing in a hot medium and its evolution toward the chiral phase transition using different symmetry restoration scenarios based on the generalized hidden local symmetry framework. We show that the presence of the $a_1$ meson reduces the vector spectral function around $\rho$ meson mass and enhances it around $a_1$ meson mass. The coupling strength of $a_1$ to $\rho$ and $\pi$ vanishes at the critical temperature due to the degenerate $\rho$-$a_1$ masses. This feature holds rigorously in the chiral limit and still stays intact to good approximation for the physical pion mass.Comment: v2:11 pages, 6 figures, reorganized and expanded the text, new plots and references added, main result and conclusions unchange

Coagulation kinetics beyond mean field theory using an optimised Poisson representation

Binary particle coagulation can be modelled as the repeated random process of the combination of two particles to form a third. The kinetics can be represented by population rate equations based on a mean field assumption, according to which the rate of aggregation is taken to be proportional to the product of the mean populations of the two participants. This can be a poor approximation when the mean populations are small. However, using the Poisson representation it is possible to derive a set of rate equations that go beyond mean field theory, describing pseudo-populations that are continuous, noisy and complex, but where averaging over the noise and initial conditions gives the mean of the physical population. Such an approach is explored for the simple case of a size-independent rate of coagulation between particles. Analytical results are compared with numerical computations and with results derived by other means. In the numerical work we encounter instabilities that can be eliminated using a suitable 'gauge' transformation of the problem [P. D. Drummond, Eur. Phys. J. B38, 617 (2004)] which we show to be equivalent to the application of the Cameron-Martin-Girsanov formula describing a shift in a probability measure. The cost of such a procedure is to introduce additional statistical noise into the numerical results, but we identify an optimised gauge transformation where this difficulty is minimal for the main properties of interest. For more complicated systems, such an approach is likely to be computationally cheaper than Monte Carlo simulation

Scattering of dislocated wavefronts by vertical vorticity and the Aharonov-Bohm effect II: Dispersive waves

Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order in the ratio of depth to wavelength. The dislocation of the incident wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short wavelengths the scattering is qualitatively similar to the nondispersive case. At moderate wavelengths, however, there are two markedly different scattering regimes according to wether the capillary length is smaller or larger than $\sqrt{3}$ times depth. The dislocation is characterized by a parameter that depends both on phase and group velocity. The validity range of the calculation is the same as in the shallow water case: wavelengths small compared to vortex radius, and low Mach number. The implications of these limitations are carefully considered.Comment: 30 pages, 11 figure

Optimal flexibility for conformational transitions in macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge''. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo'' attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices.Comment: 4 pages, 4 figure

Towards generalized measures grasping CA dynamics

In this paper we conceive Lyapunov exponents, measuring the rate of separation between two initially close configurations, and Jacobians, expressing the sensitivity of a CA's transition function to its inputs, for cellular automata (CA) based upon irregular tessellations of the n-dimensional Euclidean space. Further, we establish a relationship between both that enables us to derive a mean-field approximation of the upper bound of an irregular CA's maximum Lyapunov exponent. The soundness and usability of these measures is illustrated for a family of 2-state irregular totalistic CA

Lattice extraction of K→ππ K \to \pi \pi amplitudes to NLO in partially quenched and in full chiral perturbation theory

We show that it is possible to construct $\epsilon^\prime/\epsilon$ to NLO using partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable on the lattice. We demonstrate that none of the needed amplitudes require three-momentum on the lattice for either the full theory or the partially quenched theory; non-degenerate quark masses suffice. Furthermore, we find that the electro-weak penguin ($\Delta I=3/2$ and 1/2) contributions to $\epsilon^\prime/\epsilon$ in PQChPT can be determined to NLO using only degenerate ($m_K=m_\pi$) $K\to\pi$ computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of $K\to\pi\pi$ at unphysical kinematics are plagued with enhanced finite volume effects in the (partially) quenched theory, but in simulations when the sea quark mass is equal to the up and down quark mass the enhanced finite volume effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and Pallante. With one version (the "PQS") of the QCD penguin, the inputs needed from the lattice for constructing $K\to\pi\pi$ at NLO in PQChPT coincide with those needed for the full theory. Explicit expressions for the finite logarithms emerging from our NLO analysis to the above amplitudes are also given.Comment: 54 pages, 3 figures; Important revisions: Corrections to formulas for K->pi pi with degenerate quark masses have been mad

Spontaneous emergence of spatial patterns ina a predator-prey model

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays travelling waves solutions, clustering and uniform distributions, all related to the parameters values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plants, regulated the presence of predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure

Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.Comment: 8 pages, 3 figure

Consequences Of Fully Dressing Quark-Gluon Vertex Function With Two-Point Gluon Lines

We extend recent studies of the effects of quark-gluon vertex dressing upon the solutions of the Dyson-Schwinger equation for the quark propagator. A momentum delta function is used to represent the dominant infrared strength of the effective gluon propagator so that the resulting integral equations become algebraic. The quark-gluon vertex is constructed from the complete set of diagrams involving only 2-point gluon lines. The additional diagrams, including those with crossed gluon lines, are shown to make an important contribution to the DSE solutions for the quark propagator, because of their large color factors and the rapid growth in their number