On the relevance of q-distribution functions: The return time distribution of restricted random walker

There exist a large literature on the application of $q$-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, $P_R(0,t)$, of a random walk on the set of integers $\{0,1,2,...,L\}$ with a position dependent transition probability given by $|n/L|^a$. We find that for all values of $a\in[0,2]$ $P_R(0,t)$ can be fitted by $q$-exponentials, but only for $a=1$ is $P_R(0,t)$ given exactly by a $q$-exponential in the limit $L\rightarrow\infty$. This is a remarkable result since the exact analytical solution of the corresponding continuum model represents $P_R(0,t)$ as a sum of Bessel functions with a smooth dependence on $a$ from which we are unable to identify $a=1$ as of special significance. However, from the high precision numerical iteration of the discrete Master Equation, we do verify that only for $a=1$ is $P_R(0,t)$ exactly a $q$-exponential and that a tiny departure from this parameter value makes the distribution deviate from $q$-exponential. Further research is certainly required to identify the reason for this result and also the applicability of $q$-statistics and its domain.Comment: 14 pages, 3 figures. The replacement correct that two papers in the reference list were not mentioned in the tex

Anatomy of three-body decay II. Decay mechanism and resonance structure

We use the hyperspherical adiabatic expansion method to discuss the the two mechanisms of sequential and direct three-body decay. Both short-range and Coulomb interactions are included. Resonances are assumed initially populated by a process independent of the subsequent decay. The lowest adiabatic potentials describe the resonances rather accurately at distances smaller than the outer turning point of the confining barrier. We illustrate with realistic examples of nuclei from neutron ($^{6}$He) and proton ($^{17}$Ne) driplines as well as excited states of beta-stable nuclei ($^{12}$C).Comment: To be published in Nuclear Physics

Connectivity-Driven Coherence in Complex Networks

We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the coupling function. These findings predict that in random graphs, the enhancement of coherence is proportional to the mean degree. In locally connected networks, coherence is no longer controlled by the mean degree, but rather on how the mean degree scales with the network size. In these networks, even when the coherence is absent, adding a fraction s of random connections leads to an enhancement of coherence proportional to s. Our results provide a way to control the emergent properties by the manipulation of the dynamics of the elements and the network connectivity.Comment: 4 pages, 2 figure

Can on-farm bioenergy production make organic farming more sustainable? - A model for energy balance, nitrogen losses, and green house gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated bioenergy production

Can biogas and bioethanol production make organic farming more sustainable? - Results from a model for the fossil energy balance, Nitrogen losses, and greenhouse gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated biogas and bioethanol production. Dalgaard T1, Pugesgaard S1, Jørgensen U1, Olesen JE1, Møller HB1 and Jensen ES2 1) Dept. Agroecology and Environment. Faculty of Agricultural Sciences (DJF), University of Aarhus. DK-8830 Tjele. Denmark. Contact: [email protected] 2) Biosystems Department, Risø DTU, The National Laboratory for Sustainable Energy, The Technical University of Denmark DK-4000 Roskilde, Denmark The vision of organic farming systems, independent of fossil energy resources, with significantly lower nutrient losses, and no net contribution to the greenhouse gas emissions might be fulfilled via the integration of biogas production. This is an important hypothesis investigated in the www.bioconcens.elr.dk/uk/ research project. This poster illustrates preliminary results from a model for the fossil energy balance, Nitrogen losses, and greenhouse gas emissions in a 1000 ha energy catchment with organic dairy farming and integrated biogas production in Denmark. The model will draw on results from previous models (e.g the farmGHG model), and includes a number of organic dairy farm type components, including information on livestock production, housing, manure storage, manure and fodder import/export, crop rotations, yield levels, and soil types. In addition, a biogas plant model component evaluates effects of the inclusion of variable amounts of manures and crop residues from the specified farm types, into the biogas energy production. The model is intended to result in an overall catchment balance for the following three types of indicators: 1) the fossil energy use – i.e. the net fossil energy use minus the bioenergy production, 2) losses of Nitrogen in the form of nitrates, ammonia and nitrous oxide, and 3) the emission of the three main greenhouse gasses from agriculture: carbon dioxide, nitrous oxide and methane, measured in carbon dioxide equivalents. Moreover, these indicator values are specified for each of the farm types included in the model, and for the biogas plant component. Finally, selected model results are discussed in relation to the overall hypothesis of the research project, and it is discussed how the integration of biogas production in organic farming, can help to improve the self-sufficiency in Nitrogen, and thereby reduce the import of nutrients to the organic farming systems

The Optically Unbiased GRB Host (TOUGH) survey. IV. Lyman-alpha emitters

We report the results of a spectroscopic search for Lyman-alpha emission from gamma-ray burst host galaxies. Based on the well-defined TOUGH sample of 69 X-ray selected Swift GRBs, we have targeted the hosts of a subsample of 20 GRBs known from afterglow spectroscopy to be in the redshift range 1.8-4.5. We detect Lya emission from 7 out of the 20 hosts, with the typical limiting 3sigma line flux being 8E-18 erg/cm2/s, corresponding to a Lya luminosity of 6E41 erg/s at z=3. The Lya luminosities for the 7 hosts in which we detect Lya emission are in the range (0.6-2.3)E42 erg/s corresponding to star-formation rates of 0.6-2.1 Msun/yr (not corrected for extinction). The rest-frame Lya equivalent widths (EWs) for the 7 hosts are in the range 9-40A. For 6 of the 13 hosts for which Lya is not detected we place fairly strong 3sigma upper limits on the EW (<20A), while for others the EW is either unconstrained or has a less constraining upper limit. We find that the distribution of Lya EWs is inconsistent with being drawn from the Lya EW distribution of bright Lyman break galaxies at the 98.3% level, in the sense that the TOUGH hosts on average have larger EWs than bright LBGs. We can exclude an early indication, based on a smaller, heterogeneous sample of pre-Swift GRB hosts, that all GRB hosts are Lya emitters. We find that the TOUGH hosts on average have lower EWs than the pre-Swift GRB hosts, but the two samples are only inconsistent at the 92% level. The velocity centroid of the Lya line is redshifted by 200-700 km/s with respect to the systemic velocity, similar to what is seen for LBGs, possibly indicating star-formation driven outflows from the host galaxies. There seems to be a trend between the Lya EW and the optical to X-ray spectral index of the afterglow (beta_OX), hinting that dust plays a role in the observed strength and even presence of Lya emission. [ABRIDGED]Comment: ApJ accepted (v2: minor changes in the Subject headings and reference list

Remarks on certain composita of fields

Let $L$ and $M$ be two algebraically closed fields contained in some common larger field. It is obvious that the intersection $C=L\cap M$ is also algebraically closed. Although the compositum $LM$ is obviously perfect, there is no reason why it should be algebraically closed except when one of the two fields is contained in the other. We prove that if the two fields are strictly larger that $C$, and linearly disjoint over $C$, then the compositum $LM$ is not algebraically closed; in fact we shall prove that the Galois group of the maximal abelian extension of $LM$ is the free pro-abelian group of rank $|LM|$, and that the free pro-nilpotent group of rank $|C|$ can be realized as a Galois group over $LM$. The above results may be considered as the main contribution of this article but we obtain some additional results on field composita that might be of independent interest