Approximate solution for Fokker-Planck equation

In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schr\"{o}dinger type equation with a partially confining and symmetrical potential. To estimate the accuracy of the solution, a function error obtained from the original Fokker-Planck equation is suggested. Two examples, a truncated harmonic potential and non-harmonic polynomial, are analyzed using the proposed method. For the truncated harmonic potential, the system behavior as a function of temperature is also discussed.Comment: 12 pages, 8 figure

Brownian motion of black holes in stellar systems with non-Maxwellian distribution for the stars field

A massive black hole at the center of a dense stellar system, such as a globular cluster or a galactic nucleus, is subject to a random walk due gravitational encounters with nearby stars. It behaves as a Brownian particle, since it is much more massive than the surrounding stars and moves much more slowly than they do. If the distribution function for the stellar velocities is Maxwellian, there is a exact equipartition of kinetic energy between the black hole and the stars in the stationary state. However, if the distribution function deviates from a Maxwellian form, the strict equipartition cannot be achieved. The deviation from equipartition is quantified in this work by applying the Tsallis q-distribution for the stellar velocities in a q-isothermal stellar system and in a generalized King model.Comment: Presented at XXVI Int. Astronomical Union General Assembly, Symp. 238, Prague, Czech Republic, Aug 21-25 200

Polyethylene naphthalate film as a wavelength shifter in liquid argon detectors

Liquid argon-based scintillation detectors are important for dark matter searches and neutrino physics. Argon scintillation light is in the vacuum ultraviolet region, making it hard to be detected by conventional means. Polyethylene naphthalate (PEN), an optically transparent thermoplastic polyester commercially available as large area sheets or rolls, is proposed as an alternative wavelength shifter to the commonly-used tetraphenyl butadiene (TPB). By combining the existing literature data and spectrometer measurements relative to TPB, we conclude that the fluorescence yield and timing of both materials may be very close. The evidence collected suggests that PEN is a suitable replacement for TPB in liquid argon neutrino detectors, and is also a promising candidate for dark matter detectors. Advantages of PEN are discussed in the context of scaling-up existing technologies to the next generation of very large ktonne-scale detectors. Its simplicity has a potential to facilitate such scale-ups, revolutionizing the field.Comment: 6 pages, 3 figure

Smooth rationally connected threefolds contain all smooth curves

We show that if X is a smooth rationally connected threefold and C is a smooth projective curve then C can be embedded in X. Furthermore, a version of this property characterises rationally connected varieties of dimension at least 3. We give some details about the toric case.Comment: Version 1 was called "Any smooth toric threefold contains all curves". This version is completely rewritten and proves a much stronger result, following suggestions of Janos Kolla

Cerebral and cardiovascular effects of analgesic doses of ketamine during a target controlled general anesthesia: a prospective randomized study

Introduction: Ketamine is increasingly being used in various pain settings. The purpose of this study was to assess the effect of an analgesic dose of ketamine in the bispectral index (BIS), spectral edge frequency (SEF-95), density spectral array (DSA), cerebral oximetry (rSO2) and mean arterial pressure (MAP) during general anaesthesia with a target controlled infusion. Methods: A prospective, single-blinded and randomized study on adult patients scheduled for elective spine surgery was carried out. After anaesthesia induction with propofol, remifentanil and rocuronium, when a stable BIS value (45-55) was achieved, an automatic recording of BIS, SEF-95, rSO2 and MAP values during 9 min was performed to establish patients baseline values. Subsequently, patients were randomly assigned to receive a ketamine bolus dose of 0.2 mg/kg, 0.5 mg/kg or 1 mg/kg; all variables were recorded for additional 9 min after the ketamine bolus, in the absence of any surgical stimulus. A p-value <0.05 was considered significant in the statistical analysis. Results and discussion: Thirty-nine patients were enrolled in the study. Our results show a dose-related increase of SEF-95 and BIS values. DSA demonstrate a shift in the frequency range and power distribution towards higher frequencies. Our results do not show significant differences in MAP and rSO2 values. Conclusion: When ketamine is used intraoperatively in analgesic doses, the anaesthetist should anticipate an increase in SEF-95 and BIS values which will not be associated with the level of anaesthesia.info:eu-repo/semantics/publishedVersio