The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling

We study the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. We find that the Hartree approximation is remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by numerically solving the equations of motion in light-cone coordinates for a broad range of initial conditions and energy densities.The time evolution is described by several stages with a cascade of energy towards the ultraviolet. After a transient stage, the spatio-temporal gradient terms become larger than the nonlinear term and a stage of universal cascade emerges.This cascade starts at a time scale t_0 independent of the initial conditions (except for very low energy density). Here the power spectra feature universal scaling behavior and the front of the cascade k(t) grows as a power law k(t) sim t^alpha with alpha lesssim 0.25. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium (LTE) with all correlations being determined by the equilibrium functional form with an effective time dependent temperatureTeff(t) which slowly decreases as sim t^{-alpha}.Two well separated time scales emerge while Teff(t) varies slowly, the wavectors in the wake with k < k(t) attain LTE on much shorter time scales.This universal scaling stage ends when the front of the cascade reaches the cutoff at a time t_1 sim a^{-1/alpha}. Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale.Comment: relevance for quantum field theory discussed providing validity criteria. To appear in Phys. Rev.

Size of coronal structures in active stellar coronae from the detection of X-ray resonant scattering

We have analyzed high-resolution X-ray spectra of a large sample of active stars observed with the High Energy Transmission Grating Spectrometer on Chandra in order to investigate the properties of optical thickness of the coronal plasma. The analysis of Lyman series lines arising from hydrogen-like oxygen and neon ions shows in the coronae of the active RS CVn-type binaries II Peg and IM Peg significant decrements in the Ly alpha/Ly beta ratios as compared with theoretical predictions and with the same ratios observed in similar active binaries. We interpret these depletions in terms of resonance scattering of line photons out of the line-of-sight. These observations present the first strong evidence for this effect in active stellar coronae. The net line photon loss implies a non-uniform and asymmetric surface distribution of emitting structures on these stars. Escape probability arguments imply typical line-of-sight sizes of the coronal structures that dominate the X-ray emission of 10(10) cm at temperatures of 3 x 10(6) K and 10(10) cm at 10(7) K. These sizes are an order of magnitude larger than predicted by simple quasi-static coronal loop models, but are still very small compared to the several 10(11) cm radii of the stars

Prior chemotherapy does not prevent effective mobilisation by G-CSF of peripheral blood progenitor cells.

In this study we demonstrate that the hemopoietic growth factor, G-CSF successfully mobilised progenitor cell populations into the peripheral blood in a population of patients despite intensive pretreatment with chemotherapy. Administration of G-CSF increased the numbers of peripheral blood progenitor cells (PBPC) by a median of 76-fold above basal levels. Maximal levels of PBPC were observed on days 5 and 6 after G-CSF treatment. In two patients a second cycle of G-CSF mobilised PBPC to levels comparable with those seen after the first cycle of G-CSF treatment. An earlier hemopoietic cell population (pre-CFC's) was also mobilised with levels increased up to 50-fold above basal levels. Using a standard mononuclear cell leukapheresis technique the PBPC were collected extremely efficiently (essentially 100%) and could be further successfully enriched by separation using a Ficoll gradient. For patients who underwent the optimal collection protocol (i.e. leukapheresis on days 5, 6 and 7) a total of 32 +/- 6 x 10(4) GM-CFC kg-1 were collected. The ability to mobilise PBPC using G-CSF alone and to successfully and efficiently harvest these cells has important implications for the future of transplantation and high dose chemotherapy procedures

Universality of rain event size distributions

We compare rain event size distributions derived from measurements in climatically different regions, which we find to be well approximated by power laws of similar exponents over broad ranges. Differences can be seen in the large-scale cutoffs of the distributions. Event duration distributions suggest that the scale-free aspects are related to the absence of characteristic scales in the meteorological mesoscale.Comment: 16 pages, 10 figure

Relaxation of classical many-body hamiltonians in one dimension

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.Comment: 9 pag. 6 figs. To appear in Phys.Rev.

Clinical measurement of patellar tendon: accuracy and relationship to surgical tendon dimensions.

Patellar tendon width and length are commonly used for preoperative planning for anterior cruciate ligament reconstruction (ACLR). In the study reported here, we assessed the accuracy of preoperative measurements made by palpation through the skin, and correlated these measurements with the actual dimensions of the tendons at surgery. Before making incisions in 53 patients undergoing ACLR with patellar tendon autograft, we measured patellar tendon length with the knee in full extension and in 90° of flexion, and tendon width with the knee in 90° of flexion. The tendon was then exposed, and its width was measured with the knee in 90° of flexion. The length of the central third of the tendon was measured after the graft was prepared. Mean patellar tendon length and width with the knee in 90° of flexion were 39 mm and 32 mm, respectively. No clinical difference was found between the estimated pre-incision and surgical widths. However, the estimated pre-incision length with the knee in full extension and in 90° of flexion was significantly shorter than the surgical length. Skin measurements can be used to accurately determine patellar tendon width before surgery, but measurements of length are not as reliable