Clustering of exponentially separating trajectories

It might be expected that trajectories of a dynamical system which has no negative Lyapunov exponent (implying exponential growth of small separations) will not cluster together. However, clustering can occur such that the density ρ(Δx) of trajectories within distance |Δx| of a reference trajectory has a power-law divergence, so that ρ(Δx) ∼ |Δx| ^−β when |Δx| is sufficiently small, for some 0 < β < 1. We demonstrate this effect using a random map in one dimension. We find no evidence for this effect in the chaotic logistic map, and argue that the effect is harder to observe in deterministic maps.     

On the kinetic theory of energy losses in a randomly heterogeneous medium

The equation describing the distribution of energy losses of a particle propagating in a fractal medium with quenched and dynamic heterogeneities has been derived. It has been shown that in the case of the medium with fractal dimension 2 < D < 3, the losses Δ are characterized by the sublinear anomalous dependence Δ ∼ x ^α with a power-law dependence on the distance x from the surface and exponent α = D − 2.     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Superdiffusion and stable laws

The superdiffusion equation with a fractional Laplacian Δ ^α/2 in _N-dimensional space describes the asymptotic (t→∞) behavior of a generalized Poisson process with the range (discontinuity) distribution density ∼|x|−α−1. The solutions of this equation belong to a class of spherically symmetric stable distributions. The main properties of these solutions are given together with their representations in the form of integrals and series and the results of numerical calculations. It is shown that allowance for the finite velocity of free particle motion for α>1 merely amounts to a reduction in the diffusion coefficient with the form of the distribution remaining stable. For α<1 the situation changes radically: the expansion velocity of the diffusion packet exceeds the velocity of free particle motion and the superdiffusion equation becomes physically meaningless. Zh. éksp. Teor. Fiz. 115, 1411–1425 (April 1999)     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

Small-scale instability of a pulse front traversing a resonant saturable absorber

Wave front of a light pulse is shown to be unstable as it propagates through a resonant saturable absorber, if its frequency is higher than the resonance frequency of the absorber. When ΔωT ₂∼1, a small-scale transverse instability with the dimension of (λl _abs)^1/2 grows rapidly. Its growth-rate is of the order of the small-signal-absorption length of the medium.     

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self-interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one-loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/b ^d)N ^{2 - νd}≥1, where Δ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non-ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength Δ _c ∼ N ^{- γ} where the exponent γ ≈ 0.25 and does not depend from the solvent quality. Received 17 December 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: vilgis@mpip-mainz.mpg.de     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Acoustic probing of two-temperature relaxation initiated by action of ultrashort laser pulse

Ultrashort laser pulse transfers metal into a two-temperature warm dense matter state and triggers a chain of hydrodynamic and kinetic processes—melting, expansion, stretching, creation of tensile stress and transition into metastable state. We study the response of aluminum film deposited on a glass substrate to irradiation by a pump laser pulse transmitted through glass. Several films with thicknesses from 350 to 1200 nm have been investigated. The smallest thickness is of the order of the heating depth d _T∼100 nm in Al. The d _T-layer and the free rear side of the film are coupled through pressure waves propagating between them. Therefore, the processes within d _T-layer affects the time dependent displacement Δ x _rear(t) of the rear surface. We compare simulated and experimental dependencies Δ x _rear(t) obtained by the pump–probe technique. It allows us to define a thickness of molten Al layer and explore the two-temperature processes occurring inside the heated layer.     

Low-lying states of 6He studied via the 6Li(t,3He)6He reaction

We present the recent experimental results on the ⁶He structure studied by the ⁶Li(t, ³He)⁶He reaction at 336 MeV. Above the conspicuous peaks for ground and first excited states for ⁶He, we have observed a broad structures at E _x∼ 5 MeV, and E _x∼ 15 MeV. The angular distribution of this structure exhibits the dominance of a ΔL = 1 transition, indicating the existence of intruder dipole states at low excitation energies in ⁶He. A slight admixture of positive-parity states in this structure has been indicated as well. Received: 1 May 2001 / Accepted: 4 December 2001     

Real-time measurement of oxidation dynamics of sub-stoichiometric tungsten oxide films by pulsed laser deposition

In this study WO _x films were deposited by laser ablation of ultra-pure (5N) tungsten trioxide targets onto SiO₂ or silicon substrates at 250°C temperature, 100 mTorr oxygen partial pressure and 1×10⁻⁵ Torr vacuum. Surface chemical states and compositions of the deposits were determined by X-ray photoelectron spectroscopy. The results showed that deposits in oxygen partial pressure contain W⁶⁺ with x∼3.1, while vacuum-deposited films have different W states with various percentage distributions as W⁴⁺>W⁵⁺>W⁶⁺>W⁰, and x∼1. We used fast electrical resistance measurement as a probe to study the deposition process. Film resistance as a function of deposition time in vacuum revealed some microsecond fluctuations modulated on the time variation curve of electrical resistance. We attribute these data to surface absorption and desorption of oxygen during layer deposition. Finally, the effect of the laser beam on the target’s structure, surface morphology and chemical state was studied. Our results revealed that in spite of structural variation by laser irradiation, the O/W ratio remained about 3.     

Preparation, magnetoresistance and magnetocaloric effect of two-layered perovskite La 2.5- x K 0.5+ x Mn 2 O 7+δ

Polycrystalline two-layered perovskite La_2.5-xK_0.5+xMn₂O _{7 + δ} (0 < x < 0.5) samples have been prepared by a modified sol-gel method and their magnetoresistance and magnetocaloric effects have been studied. A large deviation between the metal-insulator (MI) transition temperature (T _ρ ) and the magnetic transition temperature (T_C) is observed. Large magnetoresistance (MR) effects with Δρ/ρ of ∼40% at 12 kOe are obtained in wide temperature ranges. The maximum of the magnetic entropy change peaks at its Curie temperature (T_C), far above its MI transition temperature (T _ρ ). The large magnetic entropy change (∼1.4 J/kg.K) is obtained in the sample La_2.5-xK_0.5+xMn₂O _{7 + δ} (x = 0.35) upon 10 kOe applied magnetic field. Received 2 May 2002 / Received in final form 1st October 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: wzhong@ufp.nju.edu.cn     

Ellipsometric in situ control of quantum nanostructures with gradient layers

Methodical aspects of ellipsometric control of growing quantum nanostructures with a gradient distribution of compositions are considered. It is shown that the sensitivity of ellipsometric measurements can be noticeably improved using information on derivatives dΨ/dΔ obtained during the growth of the structures for interpreting the data. With such an approach, structures with different values of composition gradients can be distinguished. The curves plotted in the parameter Δ vs. derivative dΨ/dΔ coordinates have characteristic kinks at points with a composition gradient jump. The accuracy of this approach is estimated for LEF ellipsometers; it is shown that the gradient for structures with a large gradient (δx/d ∼ 0.5 nm⁻¹) can be measured at the very beginning of the growth, when the gradient layer thickness does not exceed 1 nm.     

Electronic structure of thin film iron-tetracyanoethylene: Fe(TCNE)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

Thin film iron-tetracyanoethylene Fe(TCNE) _x , x∼2, as determined by photoelectron spectroscopy, was grown in situ under ultra-high vacuum conditions using a recently developed physical vapor deposition-based technique for fabrication of oxygen- and precursor-free organic-based molecular magnets. Photoelectron spectroscopy results show no spurious trace elements in the films, and the iron is of Fe²⁺ valency. The highest occupied molecular orbital of Fe(TCNE) _x is located at ∼1.7 eV vs. Fermi level and is derived mainly from the TCNE⁻ singly occupied molecular orbital according to photoelectron spectroscopy and resonant photoelectron spectroscopy results. The Fe(3d)-derived states appear at higher binding energy, ∼4.5 eV, which is in contrast to V(TCNE)₂ where the highest occupied molecular orbital is mainly derived from V(3d) states. Fitting ligand field multiplet and charge transfer multiplet calculations to the Fe L-edge near edge X-ray absorption fine structure spectrum yields a high-spin Fe²⁺ (3d⁶) configuration with a crystal field parameter 10Dq∼0.6 eV for the Fe(TCNE) _x system. We propose that the significantly weaker Fe-TCNE ligand interaction as compared to the room temperature magnet V(TCNE)₂ (10Dq∼2.3 eV) is a strongly contributing factor to the substantially lower magnetic ordering temperature (T _C ) seen for Fe(TCNE) _x -type magnets.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Dielectric properties of perovskite ceramics of (1–x)BiFeO3 ? x(KBi)1/2TiO3 (0.40 < x < 0.85) solid solutions from impedance spectroscopy data

The dielectric properties of the ceramics of (1 − x)BiFeO₃ − x(KBi)_1/2TiO₃ (0.40 < x < 0.85) solid solutions with an orthorhombic structure have been studied using impedance spectroscopy in the frequency range 25–10⁶ Hz at different temperatures. It has been shown that these solid solutions undergo a diffuse ferroelectric phase transition. The Curie temperature is found to be in the range 620–640 K. The activation energies of dielectric polarization relaxation (δE _M ) and dc charge carriers (ΔE _dc) are determined. It has been established that, in the vicinity of 460 K, ΔE _dc increases jumpwise as the temperature increases.     

Development of three-dimensional turbulent separation in the neighborhood of incident crossing shock waves

The results are presented for experimental investigation of the peculiarities of the development of three-dimensional turbulent separated flows on a flat surface for the Mach number M_∞ = 4 and the Reynolds number Re₁ ∼ 55·10⁶ m⁻¹ under the conditions of the flow around two identical cylindrical bodies of revolution of diameter D = 50 mm and the body aspect ratio L _b/D = 5 with conical forebodies with semi-apex angles β_c = 30, 20, 15, and 10° located above plate in parallel to one another and to the flow. The typical stages of the three-dimensional separation development are considered under the reducing distance between the axes of the bodies within the range of Z = Δz/D = 1.06–3.0 at their fixed distance from the surface (Y = Δy/D = 0.96). The topology of limiting streamlines and the peculiarities of pressure fields on the surface as well as the gasdynamic structure of separated flows arising at the interaction of crossing bow shocks propagating from the bodies and at the interaction of secondary disturbances with the boundary layer are analysed.     

Structure,transport and field-emission properties of compound nanotubes: CN<Subscript>x</Subscript> vs. BNC<Subscript>x</Subscript> (<Emphasis Type="Italic">x</Emphasis><0.1)

Transport and field-emission properties of as-synthesized CN_x and BNC_x (x<0.1) multi-walled nanotubes were compared in detail. Individual ropes made of these nanotubes and macrofilms of those were tested. Before measurements, the nanotubes were thoroughly characterized using high-resolution and energy-filtered electron microscopy, electron diffraction and electron-energy-loss spectroscopy. Individual ropes composed of dozens of CN_x nanotubes displayed well-defined metallic behavior and low resistivities of ∼10–100 kΩ or less at room temperature, whereas those made of BNC_x nanotubes exhibited semiconducting properties and high resistivities of ∼50–300 MΩ. Both types of ropes revealed good field-emission properties with emitting currents per rope reaching ∼4 μA(CN_x) and ∼2 μA (BNC_x), albeit the latter ropes se- verely deteriorated during the field emission. Macrofilms made of randomly oriented CN_x or BNC_x nanotubes displayed low and similar turn-on fields of ∼2–3 V/μm. 3 mA/cm² (BNC_x) and 5.5 mA/cm² (CN_x) current densities were reached at 5.5 V/μm macroscopic fields. At a current density of 0.2–0.4 mA/cm² both types of compound nanotubes exhibited equally good emission stability over tens of minutes; by contrast, on increasing the current density to 0.2–0.4 A/cm², only CN_x films continued to emit steadily, while the field emission from BNC_x nanotube films was prone to fast degradation within several tens of seconds, likely due to arcing and/or resistive heating. Received: 29 October 2002 / Accepted: 1 November 2002 / Published online: 10 March 2003 RID="*" ID="*"Corresponding author. Fax: +81-298/51-6280, E-mail: golberg.dmitri@nims.go.jp