Poincare recurrences and transient chaos in systems with leaks

In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient chaos. This expression improves previous estimates based on the properties of the closed system and explains dependencies on the position and size of the leak and on the initial ensemble. With a subtle choice of the initial ensemble, we obtain an equivalence to the classical problem of Poincare recurrences in closed systems, which is treated in the same framework. Finally, we show how our results apply to weakly chaotic systems and justify a split of the invariant saddle in hyperbolic and nonhyperbolic components, related, respectively, to the intermediate exponential and asymptotic power-law decays of the survival probability.Comment: Corrected version, as published. 12 pages, 9 figure

Affine T-varieties of complexity one and locally nilpotent derivations

Let X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-Limanov invariant of such varieties. In particular we exhibit a family of non-rational varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo

New Langevin and Gradient Thermostats for Rigid Body Dynamics

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.Comment: 16 pages, 4 figure

Prevalence of marginally unstable periodic orbits in chaotic billiards

The dynamics of chaotic billiards is significantly influenced by coexisting regions of regular motion. Here we investigate the prevalence of a different fundamental structure, which is formed by marginally unstable periodic orbits and stands apart from the regular regions. We show that these structures both {\it exist} and {\it strongly influence} the dynamics of locally perturbed billiards, which include a large class of widely studied systems. We demonstrate the impact of these structures in the quantum regime using microwave experiments in annular billiards.Comment: 6 pages, 5 figure

GNO Solar Neutrino Observations: Results for GNOI

We report the first GNO solar neutrino results for the measuring period GNOI, solar exposure time May 20, 1998 till January 12, 2000. In the present analysis, counting results for solar runs SR1 - SR19 were used till April 4, 2000. With counting completed for all but the last 3 runs (SR17 - SR19), the GNO I result is [65.8 +10.2 -9.6 (stat.) +3.4 -3.6 (syst.)]SNU (1sigma) or [65.8 + 10.7 -10.2 (incl. syst.)]SNU (1sigma) with errors combined. This may be compared to the result for Gallex(I-IV), which is [77.5 +7.6 -7.8 (incl. syst.)] SNU (1sigma). A combined result from both GNOI and Gallex(I-IV) together is [74.1 + 6.7 -6.8 (incl. syst.)] SNU (1sigma).Comment: submitted to Physics Letters B, June 2000. PACS: 26.65. +t ; 14.60 Pq. Corresponding author: [email protected] ; [email protected]

Poincare recurrences from the perspective of transient chaos

We obtain a description of the Poincar\'e recurrences of chaotic systems in terms of the ergodic theory of transient chaos. It is based on the equivalence between the recurrence time distribution and an escape time distribution obtained by leaking the system and taking a special initial ensemble. This ensemble is atypical in terms of the natural measure of the leaked system, the conditionally invariant measure. Accordingly, for general initial ensembles, the average recurrence and escape times are different. However, we show that the decay rate of these distributions is always the same. Our results remain valid for Hamiltonian systems with mixed phase space and validate a split of the chaotic saddle in hyperbolic and non-hyperbolic components.Comment: 4 pages and 4 figures, final published versio

Complete results for five years of GNO solar neutrino observations

We report the complete GNO solar neutrino results for the measuring periods GNO III, GNO II, and GNO I. The result for GNO III (last 15 solar runs) is [54.3 + 9.9 - 9.3 (stat.)+- 2.3 (syst.)] SNU (1 sigma) or [54.3 + 10.2 - 9.6 (incl. syst.)] SNU (1 sigma) with errors combined. The GNO experiment is now terminated after altogether 58 solar exposure runs that were performed between May 20, 1998 and April 9, 2003. The combined result for GNO (I+II+III) is [62.9 + 5.5 - 5.3 (stat.) +- 2.5 (syst.)] SNU (1 sigma) or [62.9 + 6.0 - 5.9] SNU (1 sigma) with errors combined in quadrature. Overall, gallium based solar observations at LNGS (first in GALLEX, later in GNO) lasted from May 14, 1991 through April 9, 2003. The joint result from 123 runs in GNO and GALLEX is [69.3 +- 5.5 (incl. syst.)] SNU (1 sigma). The distribution of the individual run results is consistent with the hypothesis of a neutrino flux that is constant in time. Implications from the data in particle- and astrophysics are reiterated.Comment: 22 pages incl. 9 Figures and 8 Tables. to appear in: Physics Letters B (accepted April 13, 2005) PACS: 26.65.+t ; 14.60.P

Serum neurofilament light chain withstands delayed freezing and repeated thawing

Serum neurofilament light chain (sNfL) and its ability to expose axonal damage in neurologic disorders have solicited a considerable amount of attention in blood biomarker research. Hence, with the proliferation of high-throughput assay technology, there is an imminent need to study the pre-analytical stability of this biomarker. We recruited 20 patients with common neurological diagnoses and 10 controls (i.e. patients without structural neurological disease). We investigated whether a variation in pre-analytical variables (delayed freezing up to 24 h and repeated thawing/freezing for up to three cycles) affects the measured sNfL concentrations using state of the art Simoa technology. Advanced statistical methods were applied to expose any relevant changes in sNfL concentration due to different storing and processing conditions. We found that sNfL concentrations remained stable when samples were frozen within 24 h (mean absolute difference 0.2 pg/ml; intraindividual variation below 0.1%). Repeated thawing and re-freezing up to three times did not change measured sNfL concentration significantly, either (mean absolute difference 0.7 pg/ml; intraindividual variation below 0.2%). We conclude that the soluble sNfL concentration is unaffected at 4–8 °C when samples are frozen within 24 h and single aliquots can be used up to three times. These observations should be considered for planning future studies

An example of Mirror Symmetry for Fano threefolds

In this note we illustrate the Fanosearch programme of Coates, Corti, Galkin, Golyshev, and Kasprzyk in the example of the anticanonical cone over the smooth del Pezzo surface of degree 6.Comment: 13 pages, 2 figure