Ignition of a vapor-gas mixture by a moving small-size source

A theoretical analysis of the ignition of a liquid fuel vapor-air mixture by a moving small source of heating was performed. A gas-phase model of the ignition with consideration given to heat transfer, liquid fuel evaporation, diffusion and convective motion of fuel vapor in the oxidizer medium, crystallization of the heating source, kinetics of the vaporization and ignition processes, temperature dependence of the thermophysical characteristics of the interacting substances, and character of motion of the heating source in the vapor-gas mixture was developed. The values of the ignition delay time τ _d , the main characteristic of the process, were determined. It was established how τ _d depends on the initial temperature, heating source sizes, velocity and trajectory of the heating source, and ambient air temperature.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

Drift theory of charged-particle motion for a strong electric field in a weakly relativistic approximation

Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v²/c². The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished [2] in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is v_E v, where v is the characteristic velocity of the particle. For a strong electric field,v _Ev.The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1–3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2–4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v²/c², where c is the velocity of light. Also hf fields may be present.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–9, September, 1981.     

Direct observation of intracluster reactions induced in (CF<Subscript>3</Subscript>I)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters by femtosecond ultraviolet radiation

Intracluster reactions that are induced in (CF₃I) _n clusters by femtosecond ultraviolet radiation, including the reaction of the formation of the I₂⁺ molecular ion, have been directly observed. It has been shown that there are two channels of the formation of I₂⁺ ions with the characteristic times τ₁ ≈ 1 ps and τ₂ ≈ 7 ps. A model of these reactions has been proposed that is in good agreement with the experimental data.     

Energy losses of high-energy muons and τ-leptons in inelastic scattering by nuclei

A hybrid model is used to calculate the losses of muons and τ-leptons in inelastic scattering by nuclei in water and in ground. The model includes soft and semihard photoprocesses and also hard scattering with an exchange by a γ-photon and a Z₀-boson. In the calculations, nuclear effects, such as shading and antiscreening of nucleons, the EMC effect, and the Fermi motion of nucleons in a nucleus, are considered. The distinction in scattering between a particle and an antiparticle, conditioned by an admixture of a weak neutral current, is discussed. Comparison with other calculations is given. Formulas for the coefficients of energy losses of muons and τ-leptons in water and in ground are obtained which approximate the calculation results over a wide interval of energies: 10²–10⁹ GeV. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 82–86, March, 2006.     

Quantum Brownian Motion in a Simple Model System

We consider a quantum particle coupled (with strength λ) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the motion of the particle is diffusive at large times for small, but finite λ. Our proof relies on an expansion around the kinetic scaling limit ( l\searrow 0{\lambda \searrow 0}, while time and space scale as λ⁻²) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of O(λ²).     

Frequency stability of a mercury ion frequency standard

Observation with an improved signal-to-noise ratio of the hyperfine resonance pattern of¹⁹⁹Hg⁺ stored in a radiofrequency trap is reported. A frequency control loop which locks the frequency of a 5MHz quartz crystal oscillator to the hyperfine transition of stored mercury ions, close to 40.5 GHz, is described. In this system, pulses delivered by the photomultiplier are processed digitally. Optimal conditions for the interrogation of the hyperfine transition are specified. A fractional frequency stability σ_y(τ)=3.6×10⁻¹¹τ^−1/2 for 10s<τ<3500s has been obtained. This frequency stability is comparble to that of commercially available cesium beam frequency standards. Prospect for improvement by a factor of at least 10 are discussed. This work has been sponsored by DRET     

Defect entropies and enthalpies in BaF<Subscript>2</Subscript>

Various experimental techniques have revealed that the predominant intrinsic point defects in BaF₂ are anion Frenkel defects. Their formation, enthalpy and entropy, as well as the corresponding parameters for the fluorine vacancy and fluorine interstitial motion have been determined. In addition, low temperature dielectric relaxation measurements in BaF₂doped with uranium leads to the parameters τ₀, E in the Arrhenius relation τ = τ₀ exp(E/k _B T) for the relaxation time τ. For the relaxation peak associated with a single tetravalent uranium, the migration entropy deduced from the pre-exponential factor τ₀ is smaller than the anion Frenkel defect formation entropy by almost two orders of magnitude. We show that, despite their great variation, the defect entropies and enthalpies are interconnected through a model based on anharmonic properties of the bulk material which have been recently studied by employing density-functional theory and density-functional perturbation theory.     

Scaling laws of electron acceleration driven by an intense laser pulse

We studied the scaling laws for slow-electron acceleration driven by an intense laser pulse in a vacuum, the ponderomotive acceleration scenario (PAS) scheme. With 3D test particle simulation by numerically solving the relativistic Lorentz–Newton equation of motion, the maximum electron energy gain was found to be proportional to the laser intensity (a₀), the laser beam width (w₀), and inversely proportional to the laser pulse duration (τ). Theoretical analyses and a physical explanation based on the ponderomotive potential model (PPM) are presented. PACS 42.50.Vk; 41.75.Jv; 42.60.Jf     

KdV-soliton dynamics in a random field

We consider the interaction between soliton and a spatially uniform external random field within the framework of the forced Korteweg-de Vries equation. In the general case, the averaged soliton field is transformed to a Gaussian pulse whose amplitude falls off with time as t^−α, while its width increases as t^α, where the parameter α is characterized by the statistical properties of the external force. We obtain an analytical solution for α = 2, which corresponds to the limiting case of an infinitely long correlation time (τ₀ → ∞). The obtained solution is compared with the well-known Wadati solution for the case of a delta-correlated external force (τ₀ → 0) where the soliton is transformed to a Gaussian pulse with amplitude falling off at a lower rate α = 3/2. The numerical solutions of the forced Korteweg-de Vries equation, which demonstrate an increase in the parameter α from 3/2 to 2 with increasing correlation time, are given for the intermediate case corresponding to 0 < τ₀ < ∞. It is shown that the amplitude of the averaged soliton in a periodic random field falls off as t⁻¹ for the long times t. In this case, two pulses propagating in different directions are formed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 599–606, July 2006.     

Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

1H relaxation study in (NH4)2SbF5

¹H spin-lattice relaxation rate (T ₁ ⁻¹ ) has been measured using inversion recovery technique in polycrystalline (NH₄)₂SbF₅ system in the temperature range 140–400 K. From the plot of log (M ₀−M) againstτ, we have estimated two differentT ₁ corresponding to two inequivalent ammonium ions in the unit cell. Temperature-dependence ofT ₁ in each case exhibits features of double minima indicating the influence of different correlation times corresponding to different types of motion. Activation energies at different temperature regions have been estimated. Some features of dynamics of motion of the different groups of ions across the phase transitions have been discussed.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Electromagnetic pulse amplification in a Cherenkov laser

An investigation is made of the amplification of a Gaussian electromagnetic pulse in a Cherenkov waveguide laser for the cases of long and short waveguides. It is shown that in the first case, the concept of a characteristic pulse duration τ ₀ can be introduced. It is established that when the pulse duration is short (τ<τ ₀) the gain is determined only by its spectral width, and the amplification process leads to a change in the pulse envelope. It is shown that in a short waveguide pulse amplification can be achieved without any change in shape. Zh. Tekh. Fiz. 69, 79–83 (April 1999)     

Quantum and Classical Disparity and Accord

Discrepancies and accords between quantum (QM) and classical mechanics (CM) related to expectation values and periods are generally found for both the harmonic oscillator (SHO) and a free particle in a box (FPB), which may apply generally. These indicate non-locality is expected throughout QM. The FPB energy states violate the Correspondence Principle. Previously unexpected accords are found and proven that 〈x ²〉 _CM =〈x ²〉 _QM and τ _CM =τ _QMb (beat period i.e. beats between the phases for adjoining energy states) for the SHO for all quantum numbers, n. However, for the FPB the beat periods differ at small n. It is shown that a particle’s velocity in an infinite square well varies, no matter how wide the box, nor how far the particle is from the walls. The quantum free particle variances share an indirect commonality with the Aharonov-Bohm and Aharonov-Casher effects in that there is a quantum action in the absence of a force. The concept of an “Expectation Value over a Partial Well Width” is introduced. This paper raises the question as to whether these inconsistencies are undetectable, or can be empirically ascertained. These inherent variances may need to be fixed, or nature is manifestly more non-classical than expected.     

Fast decay of high vibronic S1 states in gas-phase benzene

Lifetimes of different vibronic levels at high excess energies in the S₁ state of isolated benzene molecules are measured using for the first time a two-photon ionization pump–probe technique with UV femtosecond pulses. For the 6¹1³ state (3290 cm^-1 excess energy) at the onset of the ‘channel three’ a biexponential decay is found with a fast (τ_f=20 ps) and a slow (τ_s>500 ps) component. The values are in line with previous sub-Doppler high-resolution measurements of this band in our laboratory. We explain the measured faster decay (τ_f=900 fs, τ_s=100 ps) of the 7¹ state at a lower excess energy of 3077 cm^-1 by a simultaneous excitation of the adjacent 6¹ ₀1³ ₀16¹ ₁ hot band leading to a vibronic state of higher excess energy and faster decay. The vibronic levels 6¹1⁴ and 7¹1¹ at a higher excess energy of ≳4000 cm^-1 show a biexponential decay of τ_f=550 fs, τ_s=30 ps and τ_f≲300 fs, τ_s=20 ps, respectively. The experimental results point to dynamic processes within the vibronic level manifold of the S₁ state and a fast nonradiative electronic relaxation process. Received: 3 November 1999 / Published online: 5 July 2000     

Existence of many ergodic absolutely continuous invariant measures for piecewise-expandingC 2 chaotic transformations in ℝ2 on a fixed number of partitions

Let Ω be a region in ℝⁿ and letp = P_i ) _i ^1m , be a partition ofΩ into a finite number of closed subsets having piecewise C² boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C² onP where, τ_i = τ|p_i is aC ² diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτ_i ^-1 ‖ < α^-1, where Dτ_i ^-1 is the derivative matrixτ _i ^- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C² transformation on a fixed partition with a finite number of elements in ℝ², but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures     

Spontaneous-emission spectrum in a cavity: Doublet or triplet?

Summary The Green’s functions formalism together with the new algorithm in operating with ζ-functions has been used to obtain the three-peaked spectrum of spontaneous emission of an atom in a weakly damped cavity. The single-peaked spectrum and exponential decay law with the short (τ_s ~ 1/Γ _c) and long (τ₁ ~Γ _c/g ²) decay times have been shown to exist in the strongly damped cavity with its passive linewidthΓ _c.     

Determination of the saturation parameter of electronic transition in a uranium-neon hollow-cathode discharge by optogalvanic spectroscopy

Summary The optogalvanic signal (OGS) induced in a uranium-neon hollow-cathode discharge was measured as a function of the laser power density for the 0→16900 cm⁻¹ (591.5 nm) uranium transition. Theoretical relations derived by solving a two-level system rate equations showed the OGS dependence on the laser photon flux, for a modulated c.w. light and for stimulated transitions starting from the ground state. A fitting of the theoretical relations to the experimental measurements allowed the determination of the σ₀ τ product, that is, the saturation parameter of the transition. The results showed good agreement between the σ₀ τ values obtained by the optogalvanic and the usual optical absorption processes.     

Universal crossover of liquid dynamics in supercritical region

We demonstrate that all liquids in supercritical region may exist in two qualitatively different states: solid-like and gas-like. Solid-like to gas-like crossover corresponds to the condition τ ≈ τ₀, where τ is liquid relaxation time and τ₀ is the minimum period of transverse waves. This condition corresponds to the loss of shear stiffness of a liquid at all frequencies and defines a new narrow crossover zone on the phase diagram. We show that the intersection of this zone corresponds to the disappearance of high-frequency sound, qualitative changes of diffusion and viscous flow, increase in particle thermal speed to half of the speed of sound and reduction of the specific heat at constant volume to 2k _B per particle. The new crossover is universal: it separates two liquid states at arbitrarily high pressure and temperature, and even exists in systems where liquid-gas transition and the critical point are absent overall.