Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997     

Moving nonlinear localized vibrational modes for a one-dimensional homogenous lattice with quartic anharmonicity

Moving nonlinear localized vibrational modes (i.e. discrete breathers) for the one-dimensional homogenous lattice with quartic anharmonicity are obtained analytically by means of a semidiscrete approximation plus an integration. In addition to the pulse-envelope type of moving modes which have been found previously both analytically and numerically, we find that a kink-envelope type of moving mode which has not been reported before can also exist for such a lattice system. The two types of modes in both right- and left-moving form can occur with different carrier wavevectors and frequencies in separate parts of the plane. Numerical simulations are performed and their results are in good agreement with the analytical predictions. Received 13 October 1999 and Received in final form 15 May 2000     

Pseudogap effects on the c-axis charge dynamics in copper oxide materials

The c-axis charge dynamics of copper oxide materials in the underdoped and optimally doped regimes has been studied by considering the incoherent interlayer hopping. It is shown that the c-axis charge dynamics for the chain copper oxide materials is mainly governed by the scattering from the in-plane fluctuation, and the c-axis charge dynamics for the no-chain copper oxide materials is dominated by the scattering from the in-plane fluctuation incorporating with the interlayer disorder, which would be suppressed when the holon pseudogap opens at low temperatures and lower doping levels, leading to the crossovers to the semiconducting-like range in the c-axis resistivity and the temperature linear to the nonlinear range in the in-plane resistivity. Received 29 July 1999 and Received in final form 24 January 2000     

The effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system

We investigate the effects of nonlinear couplings and external magnetic field on the thermal entanglement in a two-spin-qutrit system by applying the concept of negativity. It is found that the nonlinear couplings favor the thermal entanglement creating. Only when the nonlinear couplings ∣K∣ are larger than a certain critical value does the entanglement exist. The dependence of the thermal entanglement in this system on the magnetic field and temperature is also presented. The critical magnetic field increases with the increasing nonlinear couplings constant ∣K∣. And for a fixed nonlinear couplings constant, the critical temperature is independent of the magnetic field B.     

Distributions of time- and distance-headways in the Nagel-Schreckenberg model of vehicular traffic: effects of hindrances

In the Nagel-Schreckenberg model of vehicular traffic on single-lane highways vehicles are modelled as particles which hop forward from one site to another on a one dimensional lattice and the inter-particle interactions mimic the manner in which the real vehicles influence each other's motion. In this model the number of empty lattice sites in front of a particle is taken to be a measure of the corresponding distance-headway (DH). The time-headway (TH) is defined as the time interval between the departures (or arrivals) of two successive particles recorded by a detector placed at a fixed position on the model highway. We investigate the effects of spatial inhomogeneities of the highway (static hindrances) on the DH and TH distributions in the steady-state of this model. Received: 2 March 1988 / Revised: 13 April 1998 / Accepted: 17 April 1998     

Collision of a 1-D column of beads with a wall

An experimental study of the collision of a column of N beads () with a fixed wall is presented. For a fixed height of fall and a rigid wall, we show that the maximum force felt by the wall is independent of the number of beads N. The duration of impact, the velocity of the deformation wave in the column and an effective restitution coefficient of the column are also measured as a function of N. For a soft wall, we show that the maximum force depends on N. A non-dissipative numerical model, based on a nonlinear interaction law between nearest neighbours, gives results in agreement with the experimental data. Moreover, we show that, after the compression phase, the beads of the top of the column separate one after the other from the column with a velocity greater than the initial one. The beads at the bottom then bounce upwards in block, with a velocity smaller than the initial one. We emphasize that this detachment effect results from the energy redistribution within the whole system during the collision and not from any dissipative effect. Received: 6 February 1998 / Revised and accepted: 26 May 1998     

X-ray dichroism in biaxial gyrotropic media: Differential absorption and fluorescence excitation spectra

The differential absorption and the differential change in the polarization state of an X-ray beam propagating inside a gyrotropic crystal are described using a Müller matrix, the 16 elements of which are related to the anisotropic components of the multipolar polarizability tensors at the absorbing site. Analytical expressions are given up to third order for X-ray linear and circular dichroism, X-ray optical rotation and X-ray circular polarimetry in transmission. The same formalism is extended to discuss Fluorescence detected dichroism spectra with or without polarization analysis of the fluorescence. Fluorescence detected dichroism is strictly proportional to dichroism measured in the transmission geometry only for uniaxial crystals. In biaxial crystals, the tiny effects of X-ray gyrotropy are swamped by large linear dichroism signals due to the imperfect polarization transfer function of Bragg monochromators. Second order effects should also be taken into consideration. Our general formulation of linear and circular dichroism includes terms of odd parity with respect to the action of the time reversal operator: such terms cannot contribute to natural dichroism but can be activated by a magnetic field. The terms responsible for X-ray magnetic circular dichroism are well known but non-reciprocal X-ray gyrotropy effects are also predicted in magnetic crystals of appropriate symmetry. Received 3 March 1999     

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and “active” emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections. Received: 26 February 1998 / Revised: 13 March 1998 / Accepted: 15 March 1998     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Low-density band-filling in strained InAs quantum wells

We study the low-temperature photoluminescence (PL) of strained InAs single quantum wells (SQWs) embedded in a Ga_0.47In_0.53As matrix grown on InP substrates by modified solid-source molecular beam epitaxy. The spectra are interpreted in the frame of a two-level rate equation model describing the carrier dynamics in the structures. We show that band-filling occurs in these QWs for an excitation power as low as 30 Wcm^–2. Moreover, the spectra reveal that the band-filling results from the rapid population of the hole subband. This observation highlights the low in-plane heavy-hole mass in the compressively strained film. Our results therefore demonstrate the high potential of InAs/Ga_0.47In_0.53As QW nonlinear optical devices operating in the mid-IR wavelength range.     

Magnetic tunneling told to ignorants by two ignorants

Magnetic tunneling of a large spin subject to the Hamiltonian is investigated by elementary methods for weak fields H. In zero field (H=0) the tunnel frequency in the ground state is found to be equal to [0pt] multiplied by a quantity whose variation with s is slower than exponential. This result coincides with that of path integral methods [#!schi!#]. For the values of the longitudinal field which allow tunneling, the tunnel frequency is shown to vanish when H _y =0 for certain “diabolic" values of [0pt] , in qualitative agreement with experiments by Wernsdorfer and Sessoli. The particular case H _z =0 was already obtained by Garg by means of path integrals. The diabolic values of are in agreement with numerical results but, as already noticed by Wernsdorfer and Sessoli, they disagree with the experimental ones. This may be an effect of higher order anisotropy terms, which is briefly addressed in the conclusion. Received 17 May 2000     

Local environment and electron correlation effects on the magnetic properties of clusters

The electronic and magnetic properties of clusters are investigated in the framework of the Hubbard model by treating electron correlations effects in a saddle-point slave-boson approximation. The size dependent single-particle spectrum is calculated using a third moment real-space expansion of the local density of states. Results for the magnetic moments, magnetic order, average number of double occupations and hopping renormalizations are given as a function of the local coordination number z, for different representative values of the Coulomb interaction strength U/t and band filling n. Several transitions between paramagnetic, ferromagnetic and antiferromagnetic behaviors are obtained as a function of z. The environment dependence of the magnetic behavior and of the degree of electron delocalization is analyzed. Advantages and limitations of the present approach are discussed. Received: 8 January 1998 / Revised: 22 June 1998 / Accepted: 6 August 1998     

Spatio-temporal patterns in the thermoconvection of a planar nematic layer: I. Weakly nonlinear models

We study theoretically the formation of convection patterns in a laterally extended planar nematic layer heated from below, in the linear and weakly nonlinear regimes. By reformulating the viscous coupling terms of the basic nematohydrodynamic equations, a simple interpretation of the flow effects on the director dynamics can be proposed. A detailed linear analysis of the problem is presented. A systematic method to investigate nonlinear mechanisms is developed, and exemplified by the study of the nonlinear saturation in rolls. The extension of the roll amplitude equation with the envelope formalism is used to characterize the dynamics of the roll modulations near threshold. Coupled envelope equations are shown to describe the structure of the point defects in zig-zags observed experimentally. Finally the bifurcation to the bimodal varicose is studied. The secondary wavevector in the bimodal appears to be selected by a rotation of the director in the horizontal plane. Quantitative predictions concerning the amplitude of this rotation are given. Received: 1st December 1997 / Revised: 25 May 1998 / Accepted: 2 June 1998     

Discrete nonlinear Schrödinger breathers in a phonon bath

We study the dynamics of the discrete nonlinear Schr?dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather. Received 21 January 1999 and Received in final form 20 September 1999     

On the competition between magnetic order and local Kondo effect in Kondo lattice

We investigate the competition between magnetic order and local Kondo effect in a Kondo lattice model (i.e. the Coqblin-Schrieffer Hamiltonian extended to a lattice) in a mean-field approximation, taking account of the spin-orbit degeneracy of each localized f level. This leads to the definition of a dependent Kondo temperature. We study the Kondo phase and compare its energy with the energies of magnetic phases, when the number of the conduction band electron per site is near one. We present a phase diagram which shows the occurrence of three phases: Kondo, antiferromagnetic and paramagnetic phases. Our model in the mean-field approximation also shows a somewhat flat Kondo temperature, for large values of , as a function of the exchange coupling J between conduction and localized f electrons. Finally we show some scaling effects between and J and we define a corresponding Kondo temperature. Received 21 September 1998 and Received in final form 8 February 1999     

Light-induced bistability in spin transition solids leading to thermal and optical hysteresis

We investigate the behaviour of photo-excitable, bistable systems, under permanent light irradiation, in presence of relaxation towards the non-excited state. Cooperativity causes bistability of the steady state, leading to light-induced thermal and optical hysteresis (LITH and LIOH). The light-induced instability is expected to induce demixtion, i.e. the coexistence of domains of the two stable steady states. Such effects are evidenced by magnetic and reflectivity measurements on the spin-crossover solid solution: , with x= 0.3, 0.5, 0.85. Experimental data are in quantitative agreement with a simple macroscopic model which includes a non-linear relaxation term in the master equation. Received: 5 June 1997 / Accepted: 17 July 1998     

Polaron formation and hopping conductivity in the Holstein-Hubbard model

On the basis of the Holstein-Hubbard model the formation of polarons at finite densities is investigated by means of a variational approach appropriate for describing squeezing and correlation effects. An effective Hubbard model for the polarons is derived, where the correlations are treated within the slave-boson saddlepoint approximation. For low enough phonon frequencies, with increasing coupling an abrupt self-trapping transition from light to heavy polarons is found. With increasing density the squeezing effect increases, and the transition is shifted to higher couplings. In the case of an effective Coulomb repulsion, the self-trapping transition is shifted to lower couplings with increasing Hubbard interaction, and the effective polaron mass below the transition is enhanced. In the heavy polaron regime, the frequency-dependent polaron hopping conductivity is calculated. There occur qualitative finite-density and correlation effects on the zero-temperature absorption spectrum which are discussed with respect to their possible relevance to the midinfrared absorption in high-T _c superconductors.     

Stochastic diagrams for critical point spectra

A new technique for calculating the time-evolution, correlations and steady state spectra for nonlinear stochastic differential equations is presented. To illustrate the method, we consider examples involving cubic nonlinearities in an N-dimensional phase-space. These serve as a useful paradigm for describing critical point phase transitions in numerous equilibrium and non-equilibrium systems, ranging from chemistry, physics and biology, to engineering, sociology and economics. The technique consists in developing the stochastic variable as a power series in time, and using this to compute the short time expansion for the correlation functions. This is then extrapolated to large times, and Fourier transformed to obtain the spectrum. Stochastic diagrams are developed to facilitate computation of the coefficients of the relevant power series expansion. Two different types of long-time extrapolation technique, involving either simple exponentials or logarithmic rational approximations, are evaluated for third-order diagrams. The analytical results thus obtained are compared with numerical simulations, together with exact results available in special cases. The agreement is found to be excellent up to and including the neighborhood of the critical point. Exponential extrapolation works especially well even above the critical point at large N values, where the dynamics is one of phase-diffusion in the presence of a spontaneously broken symmetry. This method also enables the calculation of the steady state spectra of polynomial functions of the stochastic variables. In these cases, the final correlations can be non-bistable even above threshold. Here logarithmic rational extrapolation has the greater accuracy of the two extrapolation methods. Stochastic diagrams are also applicable to more general problems involving spatial variation, in addition to temporal variation. Received: 12 January 1998     

A remark on the optimal cloning of an N-level quantum system

We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity. We also extend the results to treat the case of M copies from () identical N-level quantum systems. Received 21 September 1999