Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Deterministic diffusion in flower shape billiards

We propose a flower shape billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles of flower shape, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form by different schemes all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance to reproduce the precise parameter dependence of the diffusion coefficent.Comment: 8 pages (revtex) with 9 figures (encapsulated postscript

Understanding deterministic diffusion by correlated random walks

Low-dimensional periodic arrays of scatterers with a moving point particle are ideal models for studying deterministic diffusion. For such systems the diffusion coefficient is typically an irregular function under variation of a control parameter. Here we propose a systematic scheme of how to approximate deterministic diffusion coefficients of this kind in terms of correlated random walks. We apply this approach to two simple examples which are a one-dimensional map on the line and the periodic Lorentz gas. Starting from suitable Green-Kubo formulas we evaluate hierarchies of approximations for their parameter-dependent diffusion coefficients. These approximations converge exactly yielding a straightforward interpretation of the structure of these irregular diffusion coeficients in terms of dynamical correlations.Comment: 13 pages (revtex) with 5 figures (postscript

Qualität des Weidefutters in der ökologischen Milchviehhaltung

Grazing of dairy cows is mandatory in organic farming. However, as in conventional farming there is a tendency to increase milk yield per cows by employing other feeding strategies than grazing. On-farm research was initiated on organic dairy farms in Lower Saxony to investigate the current practice of grassland utilization and dairy husbandry and to explore the potential of grazing for milk production. The results show that with an increased focus on grazing of dairy cows there is considerable room for more milk being produced from grazed grass. An in-depth analysis of the spatio-temporal pattern of the quality of the herbage on offer revealed steadily high net energy and protein concentrations almost irrespective of the sward botanical composition and the season of sampling. Research is needed to improve grazing management strategies in organic farming to make better use of the high potential of grazed grasslands and thereby increase the sustainability of milk production

Methods of producing high quality alfalfa and prairie hay

The Oklahoma Cooperative Extension Service periodically issues revisions to its publications. The most current edition is made available. For access to an earlier edition, if available for this title, please contact the Oklahoma State University Library Archives by email at [email protected] or by phone at 405-744-6311

Studying the nuclear mass composition of Ultra-High Energy Cosmic Rays with the Pierre Auger Observatory

The Fluorescence Detector of the Pierre Auger Observatory measures the atmospheric depth, $X_{max}$, where the longitudinal profile of the high energy air showers reaches its maximum. This is sensitive to the nuclear mass composition of the cosmic rays. Due to its hybrid design, the Pierre Auger Observatory also provides independent experimental observables obtained from the Surface Detector for the study of the nuclear mass composition. We present $X_{max}$-distributions and an update of the average and RMS values in different energy bins and compare them to the predictions for different nuclear masses of the primary particles and hadronic interaction models. We also present the results of the composition-sensitive parameters derived from the ground level component.Comment: Proceedings of the 12th International Conference on Topics in Astroparticle and Underground Physics, TAUP 2011, Munich, German

Stationary states for underdamped anharmonic oscillators driven by Cauchy noise

Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the damping is strong enough, for potential wells which in the overdamped regime produce multimodal stationary states, stationary states in the underdamped regime can be multimodal with the same number of modes like in the overdamped regime. For the parabolic potential, the stationary density is always unimodal and it is given by the two dimensional $\alpha$-stable density. For the mixture of quartic and parabolic single-well potentials the stationary density can be bimodal. Nevertheless, the parabolic addition, which is strong enough, can destroy bimodlity of the stationary state.Comment: 9 page

Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a non-degenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$-function and find its behavior for small and large distances.Comment: 16 pages, 1 figur

The Nature of Actin-Family Proteins in Chromatin-Modifying Complexes

Actin is not only one of the most abundant proteins in eukaryotic cells, but also one of the most versatile. In addition to its familiar involvement in enabling contraction and establishing cellular motility and scaffolding in the cytosol, actin has well-documented roles in a variety of processes within the confines of the nucleus, such as transcriptional regulation and DNA repair. Interestingly, monomeric actin as well as actin-related proteins (Arps) are found as stoichiometric subunits of a variety of chromatin remodeling complexes and histone acetyltransferases, raising the question of precisely what roles they serve in these contexts. Actin and Arps are present in unique combinations in chromatin modifiers, helping to establish structural integrity of the complex and enabling a wide range of functions, such as recruiting the complex to nucleosomes to facilitate chromatin remodeling and promoting ATPase activity of the catalytic subunit. Actin and Arps are also thought to help modulate chromatin dynamics and maintain higher-order chromatin structure. Moreover, the presence of actin and Arps in several chromatin modifiers is necessary for promoting genomic integrity and an effective DNA damage response. In this review, we discuss the involvement of actin and Arps in these nuclear complexes that control chromatin remodeling and histone modifications, while also considering avenues for future study to further shed light on their functional importance