Non-dynamical stochastic resonance: Theory and experiments with white and various coloured noises

Summary We describe the simplest system which shows stochastic resonance. A linear(ized) theory for white and (almost) arbitrarily coloured noise is presented. The presented new system has new, unique properties which originate from itsnon-dynamical character; for example, the strength and phase shift of periodic response of the system is independent of the frequency. Experiments have been carried out with the following noise processes: (physical) white noise, (physical) Lorentzian noise and (physical) 1/f noise. With a small extension of the system, its linear-response regime can be significantly increased. As the system is similar to some simple models of neurones, the new results might have not only physical but also biological importance. Paper presented at the International Workshop “Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena”, Elba, 5–10 June 1994.     

Discrete Green's Function for Lattice Random Walk

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U(1) symmetry in the current algebra and N-fermionic massless Thirring model

Local U(1) symmetry in current algebra constructed by fermions has been found. The symmetry is related to the simplest q-deformation of N-fermions. We give the physical interpretation through the N-fermionic massless Thirring model. The Bethe ansatz wavefunction is also given.     

Synthesizing 0.9PZN–0.1BT by mechanically activating mixed oxides

0.9Pb(Zn_1/3Nb_2/3)–0.1BaTiO₃ (0.9PZN–0.1BT) of perovskite structure has been successfully prepared by mechanically activating mixed oxides of PbO, ZnO, Nb₂O₅, BaO and TiO₂. The novel mechanochemical technique skips the phase-forming calcination step at an intermediate temperature that is always required in both the conventional solid state reaction and chemistry-based precursor routes. Ultrafine 0.9PZN–0.1BT particles of perovskite structure were formed when the constituent oxides were mechanically activated for more than 10 h. The powder was sintered to a density of 96% theoretical density at 1100°C for 1 h. The sintered 0.9PZN–0.1BT exhibits perovskite structure and a peak dielectric constant of 8800 at the Curie temperature of 60°C when measured at a frequency of 100 Hz.     

Magnetization of an electron plasma by microwave pulses: Faraday induction

It has been argued theoretically that the recently proposed vacuum fieldB ⁽³⁾ is not accompanied by a real electric fieldE ⁽³⁾ . Experimental evidence for this interence is available in the data reported by Deschampset al. [10], using microwave magnetization of an electron plasma set up in helium gas. Faraday induction due toB ⁽³⁾ does not occur in the inert gas and is not observed experimentally in the absence of free electrons. WheneverB ⁽³⁾ interacts with free electrons, however, Faraday induction occurs through a pulse of induced magnetization (i.e., induced orbital electronic angular momentum).     

Fluorescence lifetimes of diphenylhexatriene-containing probes reflect local probe concentrations: Application to the measurement of membrane fusion

An important process in the life of a cell is fusion between cellular membranes. This is the process by which two cellular compartments surrounded by different membranes join to become a single compartment surrounded by a single membrane, without significant loss of compartment contents. To demonstrate fusion, the cell biophysicist must demonstrate all three critical aspects of the process: (1) mixing of membrane components, (2) mixing of compartment contents; and (3) retention of compartment contents. Most commonly, accomplishing this involves the use of fluorescence probes. The general theme to the methods described involves some form of concentration-dependent quenching. An unique method developed in our laboratory utilizes the concentration dependence of the fluorescence lifetime of a phosphatidylcholine containing carboxyethyl diphenylhexatriene at position 2 and palmitic acid at position 1 of glycerol (DPHpPC). The fluorescence lifetime of this molecule and that of its parent fluorophore diphenylhexatriene (DPH) shorten dramatically as their two-dimensional concentrations in a membrane increase. This lifetime quenching can be described by dimer formation that reduces the symmetry of the DPH excited state. This phenomenon allows one to use the fluorescence lifetime to gain insight into the local concentration of probe in microscopic regions of a membrane. One application of this is in distinguishing lipid transfer between the outer leaflets of two contacting membrane bilayers from fusion between these membranes that leads to mixing of lipids in both the inner and outer leaflets of the membrane bilayers. This allows a single measurement to demonstrate fusion between membrane pairs.Abbreviations PEG poly(ethylene glycol) - Na₂EDTA ethyiene-diamine-tetraacedic acid, disodium salt - LUV large, unilamellar vesicles made by rapid extrusion technique - DPH 1,6-diphenyl-trans-1,3,5-hexatriene - DPHpPC 1-palmitoyl-2-[[[2-[4- (phenyl-trans-1,3,5-hexatrienyl)phenyl]ethyl]oxy]carbonyl]-3-sn-phosphatidylcholine - DPPC 1,2-dipalmitoyl-3-sn-phosphatidylcholine - PA palmitic acid - NBD-PE N-(7-nitro-2,1,3-benzoxadiazol-4-yl)-PE - Rh-PE N-(lissamine Rhodamine B sulfoyl)-PE - R₁₈ octadecyl Rhodamine B chloride - ANTS 1-aminonaphthalene-3,6,8-trisulfonic acid - DPX N,N-p-xylylene-bis(pyradinium bromide)     

Confined electron and shallow donor states in graded GaAs/Al Ga As spherical quantum dots

A theoretical study is performed on the confined electron and shallow donor states properties in graded GaAs/Al_xGa_1-xAs spherical quantum dots. The two lowest energy levels of a confined electron are obtained taking into account the dependence of the electron effective mass on the spatial profile of the Al molar fraction. The ground state of a single Si shallow donor, which may be located at an arbitrary position in the structure, is calculated through a variational approach. Depending on the dot interface width and localization, we find that the energy levels of the electron and donor states for the system under study can be blue or red shifted appreciably in comparison to those calculated within the sharp interface picture. We show that it is necessary to have accurate information concerning the interface of semiconductor dots whose samples are used in the experiments, in order to achieve a better understanding of their optical properties. Received 31 May 1999     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

The Spearman footrule and a Markov chain property

An equivalent representation of the Spearman footrule is considered and a characterization in terms of a Markov chain is established. A martingale approach is thereby incorporated in the study of the asymptotic normality of the statistics.     

On the order of composite multistep methods for ordinary differential equations

Summary In this paper, a general class ofk-step methods for the numerical solution of ordinary differential equations is discussed. It is shown that methods with order of consistencyq have order of convergence (q+1) if a very simple condition is satisfied. This result gives a new aspect to previous results of Spijker; it also serves as a starting point for a new theory of cyclick-step methods, completing an approach of Donelson and Hansen. It facilitates the practical determination of high-order cyclick-step methods, especially of stiffly stable,k-step methods.