Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Magnetic properties of amorphous alloys

The magnetic properties of existing amorphous iron based materials, i.e., Fe--metalloid, Fe--early transition metals and Fe--rare earth alloys, are briefly discussed for some representative alloys. The spin orientation of amorphous Fe--metalloid alloys has been determined by the angular dependence of hyperfine interactions. It is shown that in iron--early transition metals ferromagnetic order is not long-ranged, but determined by magnetic clusters. The magnetic hyperfine field distributions of Fe-rich iron--early transition metals consist of a high and a low field tail. The magnetic structure has been investigated for two representative Fe--RE (RE = Er, Ce) amorphous alloys. For the first time, the magnetic coupling phenomenon in amorphous/crystalline multilayers has been discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal diffusivity measurements in porous ceramics by photothermal methods

Received: 16 September 1996/Accepted: 6 January 1997     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx     

An improved injector bunching geometry for ATLAS

The bunching system of the ATLAS positive ion injector (PII) has been improved by relocating the harmonic buncher to a point significantly closer to the second stage sine-wave buncher and the injector LINAC. The longitudinal optics design has also been modified and now employs a virtual waist from the harmonic buncher feeding the second stage sine-wave buncher. This geometry improves the handling of space charge for high-current beams, significantly increases the capture fraction into the primary rf bucket and reduces the capture fraction of the unwanted parasitic rf bucket. Total capture and transport through the PII has been demonstrated as high as 80% of the injected dc beam while the population of the parasitic, unwanted rf bucket is typically less than 3% of the total transported beam. To remove this small residual parasitic component a new traveling-wave transmission-line chopper has been developed reducing both transverse and longitudinal emittance growth from the chopping process. This work was supported by the U.S. Department of Energy under contract W-31-109-ENG-38.     

Simultaneous determination of cloramphenicol, salicylic acid and resorcinol by capillary zone electrophoresis and its application to pharmaceutical dosage forms

This study demonstrates the separation of active ingredients in acne formulations (salicylic acid, cloramphenicol and resorcinol in presence of azulene) by capillary zone electrophoresis. Factors affecting their separations were the buffer pH and concentration, applied voltage, sample preparation, and presence of additives. Optimun results were obtained with a 50 mM sodium tetraborate-50 mM sodium phosphate, pH 9.0. The carrier electrolyte gave baseline separation with good resolution, short migration times (<6 min), great reproducibility and accuracy. Calibration plots were linear over at least three orders of magnitude of analyte concentrations, the lower limits of detection being within the range 0.39-1.25 μg ml⁻¹. The procedure was fast and reliable and commercial pharmaceuticals could be analysed without prior sample clean-up procedure.     

Ocean surface films measured by interferential microwave probe

Summary Measurements on sea surface films were conducted during five separate experimental periods in the following marine areas: the Sicilian Channel, the Gulf of Maine (spring and fall periods), Bermuda, and the Pacific Ocean West of Southern California. The measurements consisted in surface elevation sampling using an interferential microwave probe with frequency spectra evaluation. Wave spectra were performed for both clean and film-covered sea surface conditions to determine the wave attenuation ratio within the 2–20 Hz spectral range. The method is able to detect, chart and characterize sea surface films. Theoretical analyses of the results yield several viscoelastic film parameters: the modulus of elasticity, the relaxation frequency and the maximum of the damping ratio as a function of wave frequency. The analysed data are interpreted to infer film weathering effects, surface concentration of film-forming constituents, and compactness of the organic sea surface film.