Self-consistent check of the validity of Gibbs calculus using dynamical variables

The high- and low-energy limits of a chain of coupled rotators are integrable and correspond respectively to a set of free rotators and to a chain of harmonic oscillators. For intermediate values of the energy, numerical calculations show the agreement of finite time averages of physical observables with their Gibbsian estimate. The boundaries between the two integrable limits and the statistical domain are analytically computed using the Gibbsian estimates of dynamical observables. For large energies the geometry of nonlinear resonances enables the definition of relevant 1.5-degree-of-freedom approximations of the dynamics. They provide resonance overlap parameters whose Gibbsian probability distribution may be computed. Requiring the support of this distribution to be right above the large-scale stochasticity threshold of the 1.5-degree-of-freedom dynamics yields the boundary at the large-energy limit. At the low-energy limit, the boundary is shown to correspond to the energy where the specific heat departs from that of the corresponding harmonic chain.     

Comparison of beaked whale detection algorithms

Due to recent advances in passive acoustic monitoring techniques, beaked whales are now more effectively detected acoustically than visually during vessel-based (e.g. line-transect) surveys. Beaked whales signals can be discriminated from those of other cetaceans by the unique characteristics of their echolocation clicks (e.g. duration >175 μs, center frequencies between 30 and 40 kHz, inter-click intervals between 0.2 and 0.4 s and frequency upsweeps). Furthermore, these same characteristics make these signals ideal candidates for testing automated detection and classification algorithms. There are several different beaked whale automated detectors currently available for use. However, no comparative analysis of detectors exists. Therefore, comparison between studies and datasets is difficult. The purpose of this study was to test, validate, and compare algorithms for detection of beaked whales in acoustic line-transect survey data. Six different detection algorithms (XBAT, Ishmael, PAMGUARD, ERMA, GMM and FMCD) were evaluated and compared. Detection trials were run on three sample days of towed-hydrophone array recordings collected by NOAA Southwest Fisheries Science Center (SWFSC) during which were confirmed visual sightings of beaked whales (Ziphius cavirostris and Mesoplodon peruvianus). Detections also were compared to human verified acoustic detections for a subset of these data. In order to measure the probabilities of false detection, each detector was also run on three sample recordings containing clicks from another species: Risso’s dolphin (Grampus griseus). Qualitative and quantitative comparisons and the detection performance of the different algorithms are discussed.     

Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from the Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the large-value tail of the inter-tracer distance probability distribution. At large times this tail is found to be closer to a pure exponential than to the form obtained from the Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson’s distribution.     

Numerical simulation of process dynamics during laser beam drilling with short pulses

In the last years, laser beam drilling became increasingly important for many technical applications as it allows the contactless production of high quality drill holes. So far, mainly short laser pulses are of industrial relevance, as they offer a good compromise between precision and efficiency and combine high ablation efficiency with low thermal damage of the workpiece. Laser beam drilling in this pulse length range is still a highly thermal process. There are two ablation mechanisms: evaporation and melt expulsion. In order to achieve high quality processing results, a basic process understanding is absolutely necessary. Yet, process observations in laser beam drilling suffer from both the short time scales and the restricted accessibility of the interaction zone. Numerical simulations offer the possibility to acquire additional knowledge of the process as they allow a direct look into the drill hole during the ablation process. In this contribution, a numerical finite volume multi-phase simulation model for laser beam drilling with short laser pulses shall be presented. The model is applied for a basic study of the ablation process with μs and ns laser pulses. The obtained results show good qualitative correspondence with experimental data.     

Dynamical quantities and their numerical analysis by saddle periodic orbits

We study estimators for dynamical quantities such as the topological entropy and the topological pressure which are based on numerical computations on periodic orbits. For the particular case of the Hénon family for some parameter ranges we find a reasonable convergence of the entropy, the pressure, and Birkhoff averages of test functions. However, pointing out possible pitfalls of such an analysis, we show that the evaluation by means of saddle orbits alone can be misleading if, for example, chaotic saddles and attractors coexist.     

A multiple recursive non-linear congruential pseudo random number generator

On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n0, the sequence of non-negative integers with x_N(n)0 (mod p). The non-linear generator is defined by z_nx_N(n)+1·x _N(n) ^–1 (mod p), n0, where x _N(n) ^–1 denotes the inverse element of x_N(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length p^r and all (p–1)^r r-tupels (y₁,...,y_r) with 1y₁,...,y_rp are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2].     

Nuclear charge radii of Sc,V, Fe,Co, Ni,Cu and Zn from elastic electron scattering at 60 MeV

Elastic electron scattering cross sections have been measured at 60 MeV for scattering angles between 45 and 153 degrees relative to⁴⁶Ti (for⁴⁵Sc),⁵⁰Ti (for⁵¹V) and¹²C (for the other nuclei). The following rms radii (in fm) have been deduced with a Fermi-type charge distribution (skin thickness 2.5 fm):⁴⁵Sc: 3.52(9);⁵¹V:3.62 (9); Fe: 3.71 (11);⁵⁹Co: 3.77 (5); Ni: 3.78 (8); Cu: 3.85 (5); Zn: 3.90 (5). The present uncertainty of the rms radius of¹²C increases the errors given by 0.01 fm. The rms radius differences 0.04 (5) fm for⁴⁶Ti-⁴⁵Sc and 0.06 (5) for⁵¹V-⁵⁰Ti were measured directly.