Nucleation of Instability of the Meissner State of 3-Dimensional Superconductors

This paper concerns a nonlinear partial differential system in a 3-dimensional domain involving the operator curl², which is a simplified model used to examine nucleation of instability of the Meissner state of a superconductor as the applied magnetic field reaches the superheating field. We derive a priori C ^2+α estimates for a weak solution H, the curl of the magnetic potential, and determine the location of the maximal points of |curlH| which correspond to the nucleation of instability of the Meissner state. We show that, if the penetration length is small, the solution exhibits a boundary layer. If the applied magnetic field is homogeneous, |curlH| is maximal around the points on the boundary where the applied field is tangential to the surface.     

An existence of universality in the dynamics of two types of glass-forming liquids - fragile liquids and strong liquids

By employing a simplified nonlinear memory function proposed recently by the present author, a universal equation for a collective-intermediate scattering function derived based on the time-convolutionless mode-coupling theory is numerically solved to study the dynamics of glass-forming liquids. The numerical calculation is done based on the simulation results performed on two types of liquids, fragile liquids and strong liquids. Those are then shown to be uniquely determined by the long-time collective diffusion coefficient $D(q_m)$, where $q_m$ is a first peak position of a static structure factor for a whole system. Thus, there exists such a universality that there is only one solution for different liquids of a same type at a given value of D. This may be consistent with the fact that strong liquids are structurally quite different from fragile liquids. Finally, it is emphasized that such a universality must be helpful to predict $q_m$ from experimental data.     

Four contemporary interpretations of the nature of science

Instrumentalism is an approach to science that treats a theory as a tool and only as a tool for computation; it dispenses with the concept of truth.Conventionalism treats a theory as true by convention if it forms a pattern of observations from which correct predictions can be made.Operationalism denies meaning to the concepts of a theory unless they can be defined operationally. It is argued in this paper that truth-value is indispensable to science, because a theory can be rejected only if an empirical consequence is false and if falsity of a conclusion entails falsity of a premise. This undermines the above positions. The fourth interpretation isinduction. Induction, by contrast, uses the notion of truth-value. What is focused on here is its reliance on the ultimacy ofobservation. The present thesis is that instrumentalism, conventionalism, and induction are different attempts to handle observations. The common problem is the gap between data and theory.All these interpretations share a philosophy of observationalism. The aim of this paper is to show that the several orthodox interpretations of science all fail to solve the problem of the data-theory gap, and to show that they all presuppose a philosophy of observation.     

Interaction of two superhigh-frequency fields with the resonance system of electron spins

Within the framework of the concept of a spin temperature in a steady-state regime, the interaction with a resonance medium of two superhigh-frequency fields, one of which is saturating and the other of which is trial, is considered theoretically in the general case without using a high-temperature approximation. The case where the absorption of a resonance medium vanishes at the trial-field frequency is investigated in detail. This occurs with an intensity of the saturating field lower than in the case of a high-temperature approximation. This intensity is estimated in the second and third orders by the parameter ω₀β_z/2, where ω₀ is the resonance frequency of the transition, β_z=ħ/(kT_z), T_z is the Zeeman-subsystem temperature, ħ is the Planck constant, and k is the Boltzmann constant. It is shown that the cooling of the dipole-dipole reservoir is more considerable than in the case of a high-temperature approximation. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 492–495, July–August, 2000.     

Early stages of laser graphitization of diamond

A mechanism for photographitization of a free diamond surface is proposed. The quantum-kinetic rate of this process is determined. The graphitization rate is close to zero if the activation energy of the graphitization process is taken as being equal to the binding energy of a carbon atom with the surface (i.e. equal to the sublimation energy of a carbon atom). On the contrary, if the activation energy is close to the energy of C–C bonds, the graphitization process may occur at a noticeable rate and be observed under ‘relatively smooth’ experimental conditions. The temperature rise leads to a considerable increase in the graphitization rates. Preliminary experimental data on the low-rate laser ablation of diamond are presented to support the proposed model of photographitization. An early stage of laser-induced graphitization in the bulk of diamond is also considered. It is found that the nucleation of a ‘tiny graphite drop’ is possible in the bulk of the diamond inside the focal area of a laser beam; the ‘graphite drop’ growth causing the appearance of mechanical stresses in the surrounding regions. The maximum size of the graphite drop is determined, which, when exceeded, leads to mechanical damage of the sample and to a change in the mechanism of laser graphitization. An evident mechanical criterion for laser-induced damage of diamond is proposed. Received: 2 October 2002 / Accepted: 5 October 2002 / Published online: 29 January 2003 RID="*" ID="*"Corresponding author. E-mail: stvn@stankin.ru     

Statistics of photocounts of blinking fluorescence of quantum dots

The blinking of quantum dots under the action of laser radiation is described based on a model of a binary (two-state) renewal process with on (fluorescent) and off (non fluorescent) states. The T _on and T _off sojourn times in the on and off states are random and power-law distributed with exponents 0 < α < 1 and 0 < β < 1; the averages of the on and off times are infinite. As a consequence of this, the Gaussian statistics is inapplicable and the process is described using a more general statistics. An equation for the density of distribution p(t _on|t) of the total on time during the observation time t is derived that contains derivatives of fractional orders α and β. A solution to this equation is found in terms of fractional stable distributions. The Poisson transform of the density p(t _on|t) leads to the photon counting distribution and determines the fluorescence statistics. It is demonstrated that, if a blinking process with exponents α < β is implemented, then, at fairly long times, the on time will considerably prevail over the off time, i.e., blinking will be suppressed. This behavior is evidenced by the types of distributions of the total fluorescence time, the decay of relative fluctuations, and the Monte Carlo simulated trajectories of the process.     

Dynamics of conservative peakons in a system of Popowicz

We consider a two-component Hamiltonian system of partial differential equations with quadratic nonlinearities introduced by Popowicz, which has the form of a coupling between the Camassa–Holm and Degasperis–Procesi equations. Despite having reductions to these two integrable partial differential equations, the Popowicz system itself is not integrable. Nevertheless, as one of the authors showed with Irle, it admits distributional solutions of peaked soliton (peakon) type, with the dynamics of N peakons being determined by a Hamiltonian system on a phase space of dimension 3N. As well as the trivial case of a single peakon ($N=1$), the case $N=2$ is Liouville integrable. We present the explicit solution for the two-peakon dynamics, and describe some of the novel features of the interaction of peakons in the Popowicz system.     

Limits of sensitivity of laser spectrometers

Theoretical considerations are given on the sensitivity of laser spectrometers in which the molecular transition is observed by a photoelectric detector, a photoconductive detector, or a diode. It is shown that the single-pass absorption spectrometer has extremely high sensitivity at a relatively high gas pressure and with optimum laser power. The holeburning spectrometer is less sensitive, though in offers much higher resolution of the homogeneous width at a low gas pressure. The nonlinear fluorescence method is characterized by both high resolution and high sensitivity, provided the fluorescence from the laser-excited level can be observed. The minimum detectable number of absorbing molecules is calculated to be 10² to 10⁶ depending on the parameters of the spectrometer. Thus a concentration of absorbing molecules lower than 10⁻¹² is expected to be detectable in some cases.     

Models of the universe

In this paper a theory of models of the universe is proposed. We refer to such models ascosmological models, where a cosmological model is defined as an Einstein-inextendible Einstein spacetime. A cosmological model isabsolute if it is a Lorentz-inextendible Einstein spacetime,predictive if it is globally hyperbolic, andnon-predictive if it is nonglobally-hyperbolic. We discuss several features of these models in the study of cosmology. As an example, any compact Einstein spacetime is always a non-predictive absolute cosmological model, whereas a noncompact complete Einstein spacetime is an absolute cosmological model which may be either predictive or non-predictive. We discuss the important role played by maximal Einstein spacetimes. In particular, we examine the possible proper Lorentz-extensions of such spacetimes, and show that a spatially compact maximal Einstein spacetime is exclusively either a predictive cosmological model or a proper sub-spacetime of a non-predictive cosmological model. Provided that the Strong Cosmic Censorship conjecture is true, a generic spatially compact maximal Einstein spacetime must be a predictive cosmological model. It isconjectured that the Strong Cosmic Censorship conjecture isnot true, and converting a vice to a virtue it is argued that the failure of the Strong Cosmic Censorship conjecture would point to what may be general relativity's greatest prediction of all, namely,that general relativity predicts that general relativity cannot predict the entire history of the universe.     

Detection of small traces of 15N2 and 14N2 by Faraday LMR spectroscopy of the corresponding isotopomers of nitric oxide

15 N₂ in a gas phase sample is described. The nitrogen is transformed by a microwave discharge into nitric oxide NO. The latter is analyzed by recording both a ¹⁵NO and a ¹⁴NO Faraday LMR signal. The determination of the transformation rate from N₂ into NO is described. The method of measurement and the achieved sensitivity (∼0.1 ppm ¹⁵N₂≈4 nanomoles ¹⁵N₂/litergas) of the spectrometer are discussed. An application in pharmacology, where ¹⁵N is used as a tracer for metabolism is indicated. First experiments with the exhalation of a rat show that the apparatus is useful to give a new quality of results. Received: 30 April 1996/Revised version: 29 July 1996     

The effect of the heat capacity of the liquid phase on the heat of fusion liquidus equation of compound semiconductors

We have critically examined the assumptions involved in the derivation of Vieland's widely used heat of fusion liquidus equation for binary compounds and conclude that the thermodynamic form of this equation ignores the relative partial molar heat capacity of the liquid solution. Taking into account this quantity, we obtain the generalized heat of fusion equation which is exact and show its complete equivalence to its alternative, the heat of formation equation. The generalized result provides a correction term to Vieland's equation which can be expressed as a function of the activity coefficients at the compound composition. Applying the correction term to the activity coefficients derived for a number of useful solution models, we find that the regular solution form of Vieland's equation is exact, as shown previously, if α (interchange energy) is a constant or a linear function of temperature. But when α is expanded as an nth order polynomial in temperature (simple solution), Vieland's equation is inexact for n ? 2. In addition, it is demonstrated that for a regular associated solution and for Darken's quadratic representation, Vieland's thermodynamic equation is exact only with certain restrictions, while for a quasi-chemical solution it is invalid.     

Runaway of electrons in dense gases and mechanism of generation of high-power subnanosecond beams

New understanding of mechanism of the runaway electrons beam generation in gases is presented. It is shown that the Townsend mechanism of the avalanche electron multiplication is valid even for the strong electric fields when the electron ionization friction on gas may be neglected. A non-local criterion for a runaway electron generation is proposed. This criterion results in the universal two-valued dependence of critical voltage U _cr on pd for a certain gas (p is a pressure, d is an interelectrode distance). This dependence subdivides a plane (U _cr , pd) onto the area of the efficient electron multiplication and the area where the electrons leave the gas gap without multiplication. On the basis of this dependence analogs of Paschen’s curves are constructed, which contain an additional new upper branch. This brunch demarcates the area of discharge and the area of e-beam. The mechanism of the formation of the recently created atomospheric pressure subnanosecond e-beams is discussed. It is shown that the beam of the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the runaway electrons is formed at an instant when the plasma of the discharge gap approaches to the anode. In this case a basic pulse of the electron beam is formed according to the non-local criterion of the runaway electrons generation. The role of the discharge gap preionization by the fast electrons, emitted from the plasma non-uniformities on the cathode, as well as a propagation of an electron multiplication wave from cathode to anode in a dense gas are considered.     

Effect of intrinsic degrees of freedom on the quantum tunneling of a collective variable

The effect of intrinsic degrees of freedom on tunneling through a potential barrier is discussed using a BKW-like approximation. In the present work intrinsic degrees of freedom are represented by a single harmonic oscillator. The theory leads to a formula for the effect of the coupling on the decay width Γ of a metastable state. When the frequency ω of the intrinsic degree of freedom is large, then Γ → Γ_ad where Γ_ad is the decay width calculated with the adiabatic barrier. An inequality Γ ≤ Γ_ad is proved for any form of the coupling hamitonian. Corrections are discussed and are shown to be of order $\text{1}\text{M}$ where M is the mass of the tunneling coordinate. An application to fission is considered. The generalization of our formula for Γ to the case of many intrinsic degrees of freedom is given explicitly.     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998     

Theoretical investigation of plasmonic enhancement of silica-coated gold nanorod on molecular fluorescence

The plasmonic enhancement or quenching effects of a silica-coated gold nanorod (GNR@SiO₂) on the fluorescence of a molecule doped in the silica layer are studied using the multiple multipole method. The enhancement factors (EF) of a GNR with a typical aspect ratio of 3 coated by a 13 nm silica layer upon the fluorescence of a molecule embedded at different locations with various orientations irradiated by a plane wave are analyzed, particularly at the longitudinal surface plasmon resonance (SPR) of GNR. The numerical results show that the EF of a GNR@SiO₂ on the fluorescence is sensitive to the molecular location and orientation. Furthermore, an effective EF (EEF), which is an average of EF over all possible orientations at a specific location, is calculated. According to EEF, the proximities of the end-caps of a GNR are strong enhancing zones. In contrast, the waist area is the weak zone. Moreover, a bigger GNR (a=10 nm) possesses a higher EEF than a smaller one (a=7 nm) for the same aspect ratio and the molecular relative location. Hence, a strong enhancement on the fluorescence is obtained using bigger GNR, if the molecule is near the end-cup and the dipole orientation is along the long axis. On the contrary, the consequence could be quenching, if the molecule is near the waist of a small GNR. The Stokes shift of fluorescence can also affect the EF, except the excitation wavelength.     

Method of systems of equations of P-adic coverages for fractal analysis of events

Self-similarity in high-energy multiparticle production processes is discussed. A parton shower and hadronization are assumed to give rise to a set of particle with a fractal structure. It is noted that the box counting (BC) and P-adic coverage (PaC) methods determine the fractal dimension with permissible 1/k ranges. A new method of systems of equations of P-adic coverages (SePaC) is proposed that extends the PaC method to fractals with permissible m/k ranges. The SePaC method is shown to determine the fractal dimension of a shower with a prescribed accuracy, the number of fractal levels, the type of the cascade (random or regular), and its structure.     

Theoretical study of the temperature dependence of the width of magnetic domain walls

The temperature dependence of magnetic domain walls in ferromagnetic systems with strong exchange coupling and weak lattice anisotropy is studied assuming that the thermal influence results mainly from the temperature dependence of the magnetization. We obtain that in lattices with an uniaxial symmetry like Co the wall width increases with temperature, but stays finite up to the Curie temperature T_c. In contrary, for a cubic lattice like Fe the wall width diverges for T → T_c, if only the lattice anisotropy is taken into account. The shape of the domain walls is not conserved, since at T_c the wall is determined only by the lowest order of anisotropy. In addition, the temperature dependence of a domain wall width for a thin magnetic film is determined. Using a special symmetry, we obtain a diverging wall width at a temperature markedly lower than T_c. However, the consideration of additional domain wall modes should modify this result.     

Representation of solutions of the Burgers equation using functional integrals

In the paper, a representation of a solution of the Burgers equation in ℝ ⁿ is obtained by using integrals with respect to the Wiener measure on the space of trajectories in ℝ ⁿ . The Burgers equation is considered in a rigged Hilbert space. It is proved that, in the infinite-dimensional case, there is an analog of the Cole-Hopf transformation relating the Burgers equation and an analog of the heat equation with respect to measures. The Feynman-Kac formula for the heat equation (with potential) with respect to measures in a rigged Hilbert space is obtained.