Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable

<正>To further identify the dynamics of the period-adding bifurcation scenarios observed in both biological experiment and simulations with the differential Chay model,this paper fits a discontinuous map of a slow control variable of the Chay model based on simulation results.The procedure of period adding bifurcation scenario from period k to period k + 1 bursting(k = 1,2,3,4) involved in the period-adding cascades and the stochastic effect of noise near each bifurcation point is also reproduced in the discontinuous map.Moreover,dynamics of the border-collision bifurcation are identified in the discontinuous map,which is employed to understand the experimentally observed period increment sequence.The simple discontinuous map is of practical importance in the modeling of collective behaviours of neural populations like synchronization in large neural circuits.     

Recombination of nonequilibrium current carriers in n-InAs1−x−ySbxPy

The stationary photoconductivity, the photomagnetic effect, and the relaxation kinetics of photoconductivity in n-InAs_1–x–ySb_xP_y crystals (x=0.06, y=0.11) with n₀ = 8·10¹⁵ and 3·10¹⁶ cm^–3 were measured and the lifetimes of nonequilibrium current carriers in the temperature interval T=78–295 K were determined. The possible mechanisms of recombination, which limit the lifetimes (radiative _R, Auger recombination _A, and recombination through centers with E_f=0.13 eV), which, as is demonstrated, are determined by interband recombination processes with _RA = _RA/(_R + _A), are calculated theoretically. The contribution of the 0.13 eV recombination centers can be significant when n₀10¹⁴ cm^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–54, April, 1991.     

Normal-metal hot-electron bolometer with Andreev reflection from superconductor boundaries

This paper describes the design and experimental testing of a high-sensitivity hot-electron bolometer based a film of normal metal, exploiting the Andreev reflection from superconductor boundaries, and cooled with the help of a superconductor-insulator-normal metal junction. At the measured thermal conductivity, G≈6×10⁻¹² W/K, and a time constant of τ=0.2 μs, and a temperature of 300 mK, the estimated noise-equivalent power NEP=5×10⁻¹⁸ W/Hz^1/2, assuming that temperature fluctuations are the major source of noise. At a temperature of 100 mK, the thermal conductivity drops to G≈7×10⁻¹⁴ W/K, which yields NEP=2×10⁻¹⁹ W/Hz^1/2 at a time constant of τ=5 μs. The microbolometer has been designed to serve as a detector of millimeter and FIR waves in space-based radio telescopes. Zh. éksp. Teor. Fiz. 115, 1085–1092 (March 1999)     

Investigation of the parameters of a high-power picosecond feedback controlled chirp pulsed amplified Nd: glass laser with injection seeding

We describe experimental studies to investigate the parameters of a compact high-power Nd: glass laser. The laser consists of a mode-locked oscillator with negative feedback (=1.4ps), a Q-switched pre-amplifier with an amplification factor of 5×10⁸, and multiple stage amplifiers using a chirped pulse amplification compression technique.     

一类可变禁区的不连续系统的加周期分岔

研究了一类可变禁区不连续系统的加周期分岔行为, 发现由可变禁区导致不同类型的加周期分岔. 研究表明, 系统的迭代轨道和禁区的上下两个边界均可发生边界碰撞, 从而产生加周期分岔. 基于边界碰撞分岔理论, 定义基本的迭代单元, 解析推导出了相应的分岔曲线, 在全参数空间中给出了不同加周期所出现的范围. 与数值模拟结果比较, 理论分析结果与数值结果高度一致.     

Study of the dielectric properties of water in the frequency range 75–120 GHz

We study experimentally the frequency dependences of the refractive index n and the absorption coefficient k of distilled, sea, and river water. The measurements were performed using a quasioptical device with a backward-wave oscillator as the radiation source and OAP-7 optical-acoustic receivers at a water temperature of 27°C in the cell. The quantities n and k were determined from the measured transmission and reflection coefficients of the cell with water by means of joint numerical solution of the equations for these quantities. For distilled water in the frequency range f = 75–120 GHz, we obtained n = 6.142–3.926 · 10–2f[GHz] + 1.307 · 10–4(f[GHz])² and k = 3.607–2.101 · 10⁻² f[GHz] + 5.252 · 10–5(f[GHz])². On the whole, these data are in good agreement with the measurement results obtained by other authors at several frequencies of the indicated range and coincide with the calculation data based on the models by Meissner and Wentz and by Liebe et al. within the limits of the rms determination errors 0.05 and 0.02 for the parameters n and k, respectively. The values of n and k for different seawater samples and river water containing insoluble admixtures coincide with the values of these quantities for distilled water within the limits of the experimental measurement errors 3–5% and 1–2%, respectively. The dependences n(f) and k(f) obtained experimentally for seawater are compared with those calculated on the basis of the developed models. Measurements of the transmission spectrum of a cell with double distilled water were performed for low power density of radiation (less than μW/cm²) to reproduce the effect of water resonant transparency reported many times in the literature. Our measurements did not reveal any resonant features in the spectral behavior of the refractive index n and the absorption coefficient k of water and gave the same result as for a power density exceeding the threshold of appearance of this effect. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 489–501, June 2006.     

Determination of very slow μ+ hop rates in Cu by LLF-μSRhop rates in Cu by LLF-μSR

Muon spin relaxation in low (weak) longitudinal magnetic field (LLF-μSR) provides a means of independently determining the static dipolar width Δ characterizing the μ⁺ lattice site and the correlation time τ_c for μ⁺ hopping, in a manner that is nearly model-independent for τ_c and especially accurate in the near-static limit (τ_c>τ_μ). The advantages of this method are illustrated by its application to muon hopping in Cu near the τ_c maximum around 50 K.     

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     

Metastable states in two-lane traffic flow models with slow-to-start rule

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers (which do not look back before changing lanes) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability p_ch and the number of aggressive drivers present in the circuit. It is found also that the relaxation time τ diverges as the form of a power-law: τ∝p_ch ^-β, β=1. 89.40.+k     

Study of W-boson polarisations and triple gauge boson couplings in the reaction e+e-→W+W- at LEP 2

A determination of the single W spin density matrix (SDM) elements in the reaction e⁺e^-→W⁺W^-→lνqq̄(l=e/μ) is reported at centre-of-mass energies between 189 and 209 GeV. The data sample used corresponds to an integrated luminosity of 520 pb^-1 taken by DELPHI between 1998 and 2000. The single W SDM elements, ρ_ττ’ ^W± (τ,τ’=± 1 or 0), are determined as a function of the W^- production angle with respect to the e^- beam direction and are obtained from measurements of the W decay products by the application of suitable projection operators, Λ_ττ’, which assume the V-A coupling of the W-boson to fermions. The measured SDM elements are used to obtain the fraction of longitudinally polarised Ws, with the result: at a mean energy of 198 GeV. The SDM elements are also used to determine the triple gauge couplings Δg₁ ^Z,Δκ_γ,λ_γ and g₄ ^Z, and . For the CP-violating couplings the results of single parameter fits are: The errors are a combination of statistical and systematic errors. All results are consistent with the Standard Model.     

Lift order problems for ordinary differential equations on manifolds

Fork≥0, let ττ_k:T ^k+1(M)=T(T ^k(M))→T ^k(M) denote the (k+1)th iterated tangent bundle in relation to a base manifoldT ⁰(M)=M. LetV represent a possibly nonstationary vector field overT ^k(M), and letQ be a subset/submanifold inT ^k(M). Sufficient conditions (and, whenV is completely integrable inQ, necessary and sufficient conditions) are established to ensure that all solutionsg toy′=V(t, y) lying entirely inQ have the formG=f ^[k], wheref ^[k] is thekth-order differential lift of a curvef lying inM. The relevance of the issue for higher order dynamical systems (especially in mechanics) is discussed. Higher order involutions and complete vector field lifts are examined from the viewpoint of the differential equations they present. Collateral results on the general solvability of initial value problems are obtained and numerous examples are discussed in detail. To the memory of my teacher and friend M. Kuga (1928–1990).     

Closed timelike smooth curves in the general theory of relativity

For a space-time which admits a closed timelike smooth curve it is estimated that 2 · 10^–24 · l ², where is the real time andl the spatial length associated with the timelike curve, and is the density of material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 33–36, September, 1973.     

Effect of step permeability on step instabilities due to alternation of kinetic coefficients on a growing vicinal face

We study the effect of step permeability on step instabilities on a growing vicinal face. When alternation of kinetic coefficients is taken into account, pairing of steps occurs on the vicinal face. Irrespective of the step permeability, the step pairs are stable for a wandering instability. The bunching of step pairs occurs if the steps are impermeable. The bunch size increases with time as t^β with β=1/2, which does not depend on the form of the repulsive interaction potential between steps. The repulsion influences the relation between the step distance in a bunch and the bunch size. When the repulsive potential ζ with the step distance l is given by ζ∼l^-ν, the average step distance in a bunch decreases as with α=1/(ν+1). The exponents, β and α are the same as those in the bunching induced by the Ehrlich-Schowebel effect in growth.     

The commensurate and incommensurate TGBC^* liquid crystal phases

We propose complements to the Renn model of the liquid crystal TGBC^* phase. We argue that the rotation angle per helislab is spontaneously in the radian range, not too small to limit the energy cost of the twist grain boundaries between the helislabs, not too large to preserve the double twisting efficiency. Taking the elastic interactions between the helislabs into account, we show that the structure may undergo two different lock-ins, provided that the uncontrolled interactions at the sample surfaces are small enough. First, for appropriate values of the elastic constants, an angular lock-in may fix the rotation angle per helislab at values exactly commensurate to π. Three characteristic lengths of the TGBC^* phase, the TGB period and the thicknesses of both the smectic blocks and of the helislabs are then commensurate to one another, with moreover, integer ratios at the most efficient commensurabilities. The TGBC^* phase could thus exist in several versions, incommensurate and commensurate, according to the steps of a restricted Devil's staircase. A second elastic lock-in should then arise in the commensurate TGBC^* phases, to set the arrays of disclination lines between the helislabs in simple rectangular lattices, arranged in a helical manner. Being placed right behind one another, the disclination lines then coincide when observed along the TGB axis. This could explain the typical textures with square or hexagonal grids, observed in oriented samples. The commensurability of the TGBC^* phases could be analyzed with X-ray scattering experiments in the same manner as already reported for the TGBC phase. Received 30 November 1999 and Received in final form 5 May 2000     

Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ^-1. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv₀≪ T≪ω is equal to σ(ω,k)=e²/4ħ and independent of the band structure parameters γ and v₀. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.     

Longitudinal field relaxation measurements in monocrystalline DyAl2

Longitudinal μSR measurements were performed on a single crystal sphere of DyAl₂ in the range 4K≤T≤300 K (i.e. both in the ferromagnetic and paramagnetic phases). Contrary to previous reports the dynamic depolarization rate does not diverge near T_C≌65 K. Rather a well defined peak in the depolariation rate is observed around 95 K with 1/T₁ (95 K)∼4 μsec⁻¹. The depolariztion rate above T_C is field independent in the range 0≤B_ext≤2.5 kG. The observed behavior may be accounted for by assuming that the effective correlation time τ is given by τ⁻=τ _4f ⁻¹ +τ _diffusion ⁻¹ . The field independence requires that τ_eff<2·10⁻¹¹. The peak in 1/T₁ could then reflect a slowing down in μ⁺.     

Weak Coupling and Continuous Limits for Repeated Quantum Interactions

We consider a quantum system in contact with a heat bath consisting in an infinite chain of identical sub-systems at thermal equilibrium at inverse temperature β. The time evolution is discrete and such that over each time step of duration τ, the reference system is coupled to one new element of the chain only, by means of an interaction of strength λ. We consider three asymptotic regimes of the parameters λ and τ for which the effective evolution of observables on the small system becomes continuous over suitable macroscopic time scales T and whose generator can be computed: the weak coupling limit regime λ → 0, τ = 1, the regime τ → 0, λ²τ → 0 and the critical case λ²τ = 1, τ → 0. The first two regimes are perturbative in nature and the effective generators they determine is such that a non-trivial invariant sub-algebra of observables naturally emerges. The third asymptotic regime goes beyond the perturbative regime and provides an effective dynamics governed by a general Lindblad generator naturally constructed from the interaction Hamiltonian. Conversely, this result shows that one can attach to any Lindblad generator a repeated quantum interactions model whose asymptotic effective evolution is generated by this Lindblad operator.     

In-vivo study of the nuclear quadrupole interaction of99Mo (β- 99)Tc in nitrogenase of Klebsiella pneumoniaein nitrogenase of Klebsiella pneumoniae

We report on the first TDPAC-measurements of the nuclear quadrupole interaction (NQI) of (NQI) of⁹⁹Mo(β^-)⁹⁹Tc in the nitrogenase of the bacteria Klebsiella pneumoniae. Because nitrogenase is the only Mo-containing enzyme in Klebsiella pneumoniae under the chosen conditions, no further isolation of this enzyme was necessary. The majority of the incorporated⁹⁹Mo is subjected to a well defined NQI with ω=365(7) Mrad/s, η=1 and a reorientational correlation time of τ_coττ≈10nsec and is attributed to the active site of the FeMo cofactor. During sample preparation we noted a pronounced affinity of the bacteria to^99mTc.     

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     

Low temperature thermal magnetoconductance of metals

A low temperature transverse thermal magnetoconductance of metals and semimetals is treated theoretically. It is shown that its high magnetic field behavior is determined by the characteristic time τ_ɛ of jumps from one cyclotron circle to another due to electron-phonon collisions rather than by the transport time τ_tr that determines the conductance. The phonon-electron drag contribution to the magnetoconductance is also discussed.