Role of field losses on the Risken–Nummedal–Graham–Haken laser instability: application to erbium-doped fibre lasers

We analyse the effect of both distributed and localised losses in a laser cavity on the Risken–Nummedal–Graham–Haken multimode instability. For two-level lasers, distributed losses are found to have a negligible influence on the instability conditions as long as they remain below 10 dB, a value hardly ever exceeded under common experimental conditions. If one keeps raising the distributed loss above that value, finally the uniform-field-limit results are recovered: localised loss becomes less and less important, and in the limit does not enter at all. In contrast, for three-level lasers – in particular for erbium-doped fibre lasers – distributed losses are found to have a profound quantitative influence on the instability threshold.     

A Gribov equation for the photon Green’s function

We present a derivation of the Gribov equation for the gluon/photon Green’s function D(q). Our derivation is based on the second derivative of the gauge-invariant quantity Trln?D(q), which we interpret as the gauge-boson ‘self-loop’. By considering the higher-order corrections to this quantity, we are able to obtain a Gribov equation which sums the logarithmically enhanced corrections. By solving this equation, we obtain the non-perturbative running coupling in both QCD and QED. In the case of QCD, α _S has a singularity in the space-like region corresponding to super-criticality, which is argued to be resolved in Gribov’s light-quark confinement scenario. For the QED coupling in the UV limit, we obtain a ∝ Q ² behavior for space-like Q ²=?q ². This implies the decoupling of the photon and an NJLVL-type effective theory in the UV limit.     

Study on the response characteristics of adaptive focusing system for flying optics

The ABCD law of parameter q for fundamental-mode Gaussian beam is deduced in this paper. The result shows that the changes of focal length and focal depth are not related to the orders of the Gaussian beam modes when focus lens moves along optical axis in a large range, indicating that the ABCD law of parameter q can be used for any order modes. A laser focusing setup is designed, and the response characteristics of oil pressure system therein are also studied.     

A comparison of the reproducibility of the parameters of the ¹³C-aminopyrine breath test for the assessment of hepatic function

This study determined the within-subject and between-subject variability of different ways of expressing the results of the (13)C-aminopyrine breath test ((13)C-ABT) and the effect of shortening the test duration. The (13)C-ABT was conducted on three separate occasions in 10 healthy volunteers and on a single occasion in 22 patients with established liver cirrhosis. The within-subject variability of cumulative percentage dose recovered (cPDR), using measured CO(2) production rate (VCO(2)), in the reference group over three trials was 15% over 120 min. Higher within-subject variability in cPDR would have been evident if the test was terminated at either 30 or 60 min. Substitution of predicted VCO(2) to calculate cPDR yielded comparable values at all time points. Significant differences between cirrhotics and reference group were evident after just 10 min using PDR/h, cPDR or enrichment (all P<0.05). The ABT demonstrates clinically acceptable reproducibility. Shortening of the duration may make the test more acceptable clinically, but it is associated with increasing imprecision.     

Dependence of the lidar signal depolarization on the receiver’s field of view in the sounding of fog and clouds

We report an experimental study of the lidar signal depolarization as a function of the relative contribution of the multiple scattering in case of optically dense objects in the atmospheric planetary boundary layer. Results of the observation of fog and stratus clouds are presented, as well as those obtained by sounding of stratocumulus clouds during a snowfall. The lidar data point to a rise of the depolarization coefficient as the influence of the multiple scattering increases in consequence of both viewing angle enlargement and penetration into the object sounded. The variations of the depolarization coefficient are studied as a function of the field of view. In the case of fog, this dependence is approximated by a three-parameter exponential law; it is found that the depolarization increases steeply when the viewing angle is increased from 9 mrad to 12.5 mrad. The relationships between the approximation parameters and the microphysical characteristics of the scattering medium are considered. The experimentally determined size of the area where multiple scattering occurs is in good agreement with that calculated according to the diffusion model. The results obtained on the multiple scattering effect on the depolarization can also be employed in determining the extinction coefficient profiles in optically dense objects, as well as in evaluating the characteristic size of the scattering particles. Received: 6 September 1999 / Revised version: 7 February 2000 / Published online: 6 September 2000     

Reconstructing the energy spectra of backscattered electrons with allowance for the spectrometer’s response function

The inverse problem of reconstructing the true spectrum of electrons backscattered from massive and layered targets with allowance for the spread function of the toroidal sector energy analyzer and for the response function of the spectrometer??s electron detector is solved. We present the results from studying the energy spectra of a number of homogeneous samples and film-on-substrate systems obtained at different energies of the irradiating electron beam at normal incidence of the electrons on the surface, and at a 45° angle of backscattered electron detection.     

Nanoscale device modeling: the Green’s function method

The non-equilibrium Green’s function (NEGF) formalism provides a sound conceptual basis for the devlopment of atomic-level quantum mechanical simulators that will be needed for nanoscale devices of the future. However, this formalism is based on concepts that are unfamiliar to most device physicists and chemists and as such remains relatively obscure. In this paper we try to achieve two objectives: (1) explain the central concepts that define the ‘language’ of quantum transport, and (2) illustrate the NEGF formalism with simple examples that interested readers can easily duplicate on their PCs. These examples all involve a short n ^+  + – n ⁺ – n ^+  + resistor whose physics is easily understood. However, the basic formulation is quite general and can even be applied to something as different as a nanotube or a molecular wire, once a suitable Hamiltonian has been identified. These examples also underscore the importance of performing self-consistent calculations that include the Poisson equation. The I–V characteristics of nanoscale structures is determined by an interesting interplay between twentieth century physics (quantum transport) and nineteenth century physics (electrostatics) and there is a tendency to emphasize one or the other depending on one’s background. However, it is important to do justice to both aspects in order to derive real insights.     

Geometric interpretation of Zhou’s explicit formula for the Witten–Kontsevich tau function

Based on the work of Itzykson and Zuber on Kontsevich’s integrals, we give a geometric interpretation and a simple proof of Zhou’s explicit formula for the Witten–Kontsevich tau function. More precisely, we show that the numbers \(A_{m,n}^\mathrm{Zhou}\) defined by Zhou coincide with the affine coordinates for the point of the Sato Grassmannian corresponding to the Witten–Kontsevich tau function. Generating functions and new recursion relations for \(A_{m,n}^\mathrm{Zhou}\) are derived. Our formulation on matrix-valued affine coordinates and on tau functions remains valid for generic Grassmannian solutions of the KdV hierarchy. A by-product of our study indicates an interesting relation between the matrix-valued affine coordinates for the Witten–Kontsevich tau function and the V-matrices associated with the R-matrix of Witten’s 3-spin structures.     

Influence of external nonuniform magnetic field on the spectral characteristics of a virtual cathode oscillator’s output radiation

The influence of an external non-uniform magnetic field created using a periodic magnetic focusing system on the spectral characteristics of a virtual cathode oscillator’s output radiation is investigated by means of numerical simulation. It is shown that raising the magnetization intensity of a single magnetic ring or the number of magnetic rings leads to an increase in the output microwave radiation power spectrum’s irregularity. As consequence, the output microwave signal exhibits wide-band oscillations with a bandwidth close to one octave.     

Influence of the Investor’s Behavior on the Complexity of the Stock Market

One of the pillars of the finance theory is the efficient-market hypothesis, which is used to analyze the stock market. However, in recent years, this hypothesis has been questioned by a number of studies showing evidence of unusual behaviors in the returns of financial assets (“anomalies”) caused by behavioral aspects of the economic agents. Therefore, it is time to initiate a debate about the efficient-market hypothesis and the “behavioral finances.” We here introduce a cellular automaton model to study the stock market complexity, considering different behaviors of the economical agents. From the analysis of the stationary standard of investment observed in the simulations and the Hurst exponents obtained for the term series of stock index, we draw conclusions concerning the complexity of the model compared to real markets. We also investigate which conditions of the investors are able to influence the efficient market hypothesis statements.     

Dependence of the form of a phase shifter’s phase–temporal characteristics on the parameters of ferrite spinels and the means of their fabrication

On the basis of experimental results, it is shown that the form of a phase shifter’s phase–temporal characteristics when working with waves of linear polarization in the 8 mm range can deviate substantially from linear and be unstable in the range of operating temperatures at the similar parameters of ferrites with critical saturation magnetic moments but certain differences in the manufacturing process.     

On the use of information theory for detecting upper limb motor dysfunction: An application to Parkinson’s disease

Parkinson’s disease (PD) is a chronic neurodegenerative disorder characterized by a selective loss of dopaminergic neurons in the substantia nigra, decreased striatal dopamine levels, and consequent extrapyramidal motor dysfunctions. Several potential early diagnostic markers of PD have been proposed. Since they have not been validated in presymptomatic PD, the diagnosis and monitoring of the disease is based on subjective clinical assessment of cognitive and motor symptoms. In this study, we investigated interjoint coordination synergies in the upper limb of healthy and parkinsonian subjects during the performance of unconstrained linear-periodic movements in a horizontal plane using the mutual information (MI). We found that the MI is a sensitive metric in detecting upper limb motor dysfunction, thus suggesting that this method might be applicable to quantitatively evaluating the effects of the antiparkinsonian medication and to monitor the disease progression.     

A new method for the analysis of transmission property in carbon nanotubes using Green’s function

A new method for the analysis of electron transmission property in single-walled carbon nanotubes (SWCNTs) using Green’s function is presented in this paper for the first time. Using the proposed method, a new relation for the transmission function through a deformed SWCNT is obtained, which depends on the energy variations and the coupling matrices related to the mechanical deformations applied to the structure of CNT. The obtained new relation is explained by the presented results in the literature.     

Effect of the spatial structure of an acoustic field on Bragg’s acoustooptic diffraction under strong acoustic anisotropy conditions

Bragg’s acoustooptic diffraction in an acoustically anisotropic medium is considered taking into account the two-dimensional spatial diffraction structure of the acoustic beam. The conditions are determined under which reverse transfer of optical power from the diffracted to the transmitted beam in the regime of 100% efficiency of diffraction is considerably suppressed. It is shown that this effect is due to diffraction bending of wave fronts of the acoustic beam in the acoustooptic diffraction plane. The problem of optimization of the piezoelectric transducer size and the spatial position of the input light beam is solved using the criterion of the minimal required power of the acoustic field. The results of simulation in a wide range of the acoustooptic interaction parameters for a Gaussian light beam are reported. The correctness of the model is confirmed experimentally. Recommendations for designers of acoustooptic devices are formulated.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Alternative Proof for the Localization of Sinai’s Walk

We give an alternative proof of the localization of Sinais random walk in random environment under weaker hypothesis than the ones used by Sinai. Moreover, we give estimates that are stronger than the one of Sinai on the localization neighborhood and on the probability for the random walk to stay inside this neighborhood.     

Green’s tensor for crystals of the hexagonal system

Expressions for components of the Green’s tensor of the basic equation of the elasticity theory for hexagonal system crystals have been obtained using the Lifshitz-Rozentsveig method. A problem is in principle reduced to finding the roots of a sixth-order algebraic equation. They are either complex or purely imaginary for all known hcp metals. In both cases, the desired components of the Green’s tensor are calculated exactly in contrast to metals of the cubic system. A limiting transition to the isotropic approximation is shown.