Nonstationary Theory Research Articles

An extreme value analysis of UK drought and projections of change in the future

Extreme value analysis of drought indices was used to assess the likelihood of drought over the UK during the 20th century and potential future changes due to increased atmospheric greenhouse gasses. Precipitation indices were derived using 3, 6, 12 and 18 month accumulations, normalised by the 1961–1990 mean and standardized by the corresponding standard deviation. A soil moisture index, similarly standardized, was calculated from monthly soil moisture data. Output from an 11-member perturbed physics ensemble of the Hadley Centre regional climate model (HadRM3), forced at the boundaries by equivalent versions of the Hadley Centre global climate model (HadCM3), was evaluated against available observational-based reference data. Soil moisture reference data were derived from a distributed land surface scheme driven by meteorological reanalysis. Whilst the model ensemble underestimates the variability of the precipitation climatology in the reference data, it accurately replicates the extreme characteristics of dry months for the majority of the ensemble members. Differences in land surface characteristics and the representation of sub-grid scale heterogeneity means that there are significant differences in the representation of soil moisture between model and reference data. However, when HadRM3 is forced at the boundaries by ERA-40 reanalysis data the extreme characteristics of low soil moisture are replicated by the model ensemble indicating that using the regional climate model ensemble to downscale from the coarse resolution of HadCM3 is appropriate. Projections of drought for the 21st century were estimated by applying non-stationary extreme value theory to these monthly drought indices. All drought indices show an overall increase in drought in the future. However, the spread of values is considerable ranging from little change or a slight decrease to a significant increase depending on ensemble member and, to a smaller extent, location. The impact of these projections are put in the context of the notorious UK drought of the summer of 1976. This work provides preliminary steps towards a probabilistic assessment of changes in future drought.

On the neutron diffraction in crystals in the field of a standing sound wave

The diffraction of neutrons is considered in crystals under the influence of a standing sound wave. The scattering probability is calculated for the elastic neutron–crystal interaction, whereas the neutron-standing sound wave interaction can be either elastic and inelastic. The possibility of short-wave (high-energy) neutrons diffraction is illustrated. It is shown that the Debye–Waller factor can be changed and tuned. The analysis of conservation laws are adduced both for thermal and short-wave neutrons. The formation of a “sublattice” is shown in the process of neutrons elastic diffraction with respect to standing sound wave. The analogous to the Kapitza–Dirac effect is considered for neutrons. The problem is solved within the frame of non-stationary S-matrix theory, where the neutron–phonon interaction is described by the Fermi pseudopotential, which is considered as a perturbation.

Equations of two-fluid hydrodynamics in the Hubbard model

A set of equations is obtained using stationary and nonstationary superconductivity theories in terms of the Hubbard model. The equations near Tc and for a weak magnetic field have the general form of superconductivity equations with a strongly anisotropic Fermi surface. Calculations are performed using a kinetic equation for quasiparticles. The low-temperature collective excitations in a superconductor are studied. An explicit relationship for the temperature dependence of second sound is obtained.

The applicability of TD-DFT methods to calculations of the electronic absorption spectrum of hexaamminoruthenium(II) in aqueous solution

The nonstationary density functional theory method (time-dependent DFT, TD-DFT) was used to theoretically estimate the frequencies and intensities of absorption bands of the complex hexaamminoruthenium(II) ion in aqueous solution. The spectrum simultaneously contained both valence (ligand-field, LF) transitions and an intense band of charge transfer to the solvent (CTTS). A comparison of the quality of the results obtained with the use of various exchange-correlation functionals was performed. The closest agreement with the experimental absorption spectrum was obtained with the use of the LC-BLYP hybrid functional with exchange potential corrections at large distances.

Electron Self-Injection and Trapping into an Evolving Plasma Bubble

The blowout (or bubble) regime of laser wakefield acceleration is promising for generating monochromatic high-energy electron beams out of low-density plasmas. It is shown analytically and by particle-in-cell simulations that self-injection of the background plasma electrons into the quasistatic plasma bubble can be caused by slow temporal expansion of the bubble. Sufficient criteria for the electron trapping and bubble's expansion rate are derived using a semianalytic nonstationary Hamiltonian theory. It is further shown that the combination of bubble's expansion and contraction results in monoenergetic electron beams.

Approximate critical conditions in thermal explosion theory for a two-step kinetic model

Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (Ψ cr ) and critical temperature (θ cr ) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ cr ) and the critical temperature (θ cr ) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.

Nonstationary Nonlinear Discrete Model of a Coupled-Cavity Traveling-Wave-Tube Amplifier

A nonstationary nonlinear model for numerical simulation of a coupled-cavity traveling-wave tube is described. The model is based on the nonstationary discrete theory of excitation of a periodic waveguide structure, when it is supposed that the beam-wave interaction takes place only inside the cavity gaps separated by drift spaces. Such an approach allows one to consider properly the dispersion of the slow-wave structure (SWS) and to simulate processes at any point inside the SWS passband, including interaction near cutoff and even beyond the passband. Results of numerical simulations of amplification in small-signal and large-signal regimes are presented. Self-excitation processes near cutoff frequency are studied. In particular, drive-induced self-excitation that takes place only in the presence of a sufficiently strong driving signal is discussed.

Nonlinear nonstationary theory of light propagation through a resonance medium taking into account optical pumping of atoms

The general nonstationary theory of propagation of an elliptically polarized pulse resonantly interacting with the 1/2–1/2 transition is presented. The theory that takes into account relaxation processes is developed in terms of irreducible tensor operator representation allowing diagonalization of the relaxation matrix and introduction of effective decay times governing relaxation of both population and coherence between magnetic sublevels of the resonant system. It is shown that interference of magnetic sublevels in the field of polarized radiation that optically pumps the atoms can result in inversionless amplification of radiation.

Gravitational radiation of the Lemaître primordial atom

A non-traditional secondary quantizing of a strong gravitational field is realized. Using an earlier developed gravitational analog of the non-stationary perturbation theory it is shown that the Lemaitre primordial atom can generate hard gravitational radiation under spontaneous transitions of an effective Planckian particle in its discrete energy spectrum. Thus, the Lemaitre atom can be considered as a regular Big Bang model.

Electrical stress effect on Josephson tunneling through ultrathin AlOx barrier in Nb/Al/AlOx/Nb junctions

The effect of dc electrical stress and breakdown on Josephson and quasiparticle tunneling in Nb/Al/AlOx/Nb junctions with ultrathin AlOx barriers typical for applications in superconductor digital electronics has been investigated. The junctions’ conductance at room temperature and current-voltage (I-V) characteristics at 4.2 K have been measured after the consecutive stressing of the tunnel barrier at room temperature. Electrical stress was applied using current ramps with increasing amplitude ranging from 0 to ∼1000Ic corresponding to voltages across the barrier up to ∼0.65 V, where Ic is the Josephson critical current. A very soft breakdown has been observed with polarity-dependent breakdown current (voltage). As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and a gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. The observed changes in superconducting tunneling suggest a model in which a progressively increasing number of defects and associated additional conduction channels [superconducting quantum point contacts (SQPCs)] are induced by electric field in the tunnel barrier. By comparing the I-V characteristics of these conduction channels with the nonstationary theory of current transport in SQPCs based on multiple Andreev reflections by Averin and Bardas, the typical transparency D of the induced SQPCs was estimated as D∼0.7. The number of induced SQPCs was found to grow with voltage across the barrier as sinh(V/V0) with V0=0.045 V, in good agreement with the proposed model of defect formation by ion electromigration. The observed polarity dependence of the breakdown current (voltage) is also consistent with the model. Based on the observed magnitude of breakdown currents, electric breakdown of AlOx barrier during plasma processing was considered to be an unlikely cause of fabrication-induced, circuit pattern-dependent nonuniformities of Josephson junctions’ critical currents in superconductor integrated circuits.

Prediction of corrugation in rails using a non-stationary wheel-rail contact model

Most of the models used for simulating the conditions existing in the wheel-rail contact are based on stationary theories. In such theories, the parameters associated with the wheel-rail contact are independent on the conditions applied on it previously. This supposition is a simplification of the real phenomenon, whose validity lies in the rapid convergence of the contact parameters to their stationary values. However, the conditions simulated by means of non-stationary theories may differ from those obtained by using stationary theories when external conditions vary rapidly. Certain types of rail corrugation may be related to high-frequency normal or tangential forces transmitted through the contact, which may determine the effect of the temporal history on the contact parameters, and consequently on the rail wear. In order to investigate the influence of the contact process on the results of models of corrugation calculation, a methodology for estimating the rail wear depth due to a wheel running on a stretch of rail is developed. The method implements an improved contact model where non-stationary hypotheses and an exact elastic model are taken into account. The results show the influence of the more realistic hypotheses adopted in the proposed method.

Analysis of Alongwind Tall Building Response to Transient Nonstationary Winds

Transient nonstationary extreme winds such as thunderstorm downbursts are responsible for significant structural damage and failures. This study deals with the frequency domain analysis of alongwind tall building response to transient nonstationary winds based on nonstationary random vibration theory. The transient wind fluctuations and associated wind loads are modeled as the sum of deterministic time varying mean and evolutionary random fluctuating components. The alongwind loads on buildings are determined through the approaching winds by using strip theory and taking into account the unsteady force characteristics in terms of aerodynamic admittance and joint acceptance functions. An analysis framework is developed to quantify the time varying mean, evolutionary spectrum, and time varying root-mean-square values of building response. The traditional analysis framework concerning stationary boundary layer winds serves as a special case of this novel framework. Applications of this general framework are addressed to the cases where the mean wind speed is characterized by a time-invariant vertical profile and a single time varying function that also serves as the modulation function for the wind fluctuations. The influence of time varying mean wind speed, mean wind speed vertical profile, and spatial correlation of wind fluctuations on building response is discussed using tall building examples.

Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses

Dissipative multi-pulse three-wave coupled states, appearing with collinear Bragg light scattering in a two-mode square-law nonlinear medium with linear non-optical losses, are revealed. Both the localization conditions and the spatio-temporal distributions of their optical components are studied theoretically in quasi-stationary and non-stationary regimes. Then, dissipative multi-pulse three-wave coupled states have been observed within the acousto-optical experiments in a calcium molybdate crystalline collinear cell. The obtained experimental results are in rather good agreement with the non-stationary theory developed.

Post-Hartree-Fock methods and dynamic correlation in atoms and molecules

The methods of calculation of the matrix of the exchange-correlation interaction are considered within the framework of one post-Hartree-Fock one-electron method of investigation of the properties of many-electron systems. Such post-Hartree-Fock methods are based on two-step variational self-consistent calculations of the spin orbitals and superposition coefficients of configurations in the multiconfiguration approximation. The post-Hartree-Fock method used involves an approach related to the extended Koopmans’ theorem, which, in turn, proves to be a high-energy approximation for quantum Green’s functions. Obvious application areas of the calculations of the exchange-correlation interaction within the framework of the method proposed are the multiparticle perturbation theory, the parameterization of the energy representation as a functional of the single-particle density matrix, and the theory of Green’s functions in the multiconfiguration approximation. A relativistic generalization of the method with the aim of calculating the radiative corrections for many-electron atoms and for problems of interaction with an external field in the nonstationary Floquet theory is possible.

Analytical results for state-to-state transition probabilities in the multistate Landau-Zener model by nonstationary perturbation theory

Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. New expressions for some state-to-state transition probabilities are derived in degenerate cases.

CLUSTER ANALYSIS FOR NON-GAUSSIAN LOCALLY STATIONARY PROCESSES

Time series analysis under stationary assumption has been well established. However, stationary time series models are not plausible to describe the real world. Indeed, relatively long stretches of time series data should contain either slow or rapid changes in the spectra. To develop a general non-stationary theory, we have to pay careful attention to constituting a suitable model, otherwise the observations obtained in the future give no information about the present structure. Dahlhaus [1–4] has introduced an important class of non-stationary processes, called locally stationary processes which have the time varying spectral densities. In this paper, for a clustering problem of stock returns in Tokyo Stock Exchanges, we propose nonparametric approach based on generalized integral functional measures of the time varying spectral densities. The generalized measures include Gaussian Kullback–Leibler information and Chernoff information measures. The clustering results well extract the features of the relationship among the companies.

Nonstationary theory for short-pulse near-threshold photoionization of inner atomic shells

A theoretical description of near-threshold ionization of inner atomic shells by short electromagnetic pulses is developed. It is based on a nonstationary approach to the Fano-Feshbach problem of photoexcitation with simultaneous Auger decay of the produced vacancy. We suggest a method of solving the system of time-dependent Schr\odinger equations describing a resonant state embedded into continuum. The method gives a nonstationary description of the post-collision interaction in near-threshold photoionization including the recapture of the slow photoelectron in high Rydberg states. As an example, $1s$ photoionization in Ne with the following $\mathit{KLL}$ Auger decay is considered. The influence of the duration of the pulse on the recapture probability and shape of the emitted electron peak is studied.

Duration of nucleation process in supercooled halide melts

We present a model allowing to estimate the so-called time lag of nucleating halide melts using electrical conductivity measurements. Due to the complex-forming nature of molten halide salts we suppose two basic types of charge carriers in the melt: complexes (playing the role of monomers-building units) and clusters of a newly forming solid phase. Within context of the nonstationary nucleation theory we determined a formula expressing the time dependency of electrical conductivity of such a system and compared this result with the experimental data obtained for the melts of PbBr2, PbCl2, and KPb2Cl5. In terms of this formula the time lag of nucleation may be estimated. This important quantity characterizing the moment from which the nucleated clusters only grow to the macroscopic sizes has been found to be approximately 75% of the total duration of the nucleation process itself.

A study of photoelectron recapture due to post-collision interaction in Ne at the 1s photoionization threshold

Electron spectra from radiationless decay of a Ne 1s vacancy are measured with excitation energies immediately at the 1s ionization threshold. Special attention is given to the excess energy region where Γ is the lifetime width of the 1s vacancy. Spectra are dominated by recapture of photoelectrons into Rydberg states of Ne+ above the threshold, and by a smooth transition into the spectator resonant Auger spectrum below the threshold. High resolution of the present experiment allowed us to clearly observe Rydberg states up to n = 8 and to determine the individual probabilities for populating of these states by photoelectron recapture. Results are compared with calculations based on the semiclassical theory of post-collision interaction extended to high Rydberg excitations of the primary photoexcited electron, as well as with a non-stationary quantum mechanical theory of near-threshold photoionization with subsequent Auger decay.

Permittivity of plasma and nonstationary theory of nonlocal transport

A regular procedure is proposed for finding the solution to a linearized kinetic equation for charged particles with the Landau collision integral in a plasma with large Z. The expression for longitudinal permittivity of a collisional plasma, which is obtained using this procedure for the entire range of frequencies and wavenumbers, as well as the collision parameter, is transformed to the known expressions in the corresponding asymptotic limits. The nonlocal transport equations for small perturbations are also formulated for arbitrary relations between the characteristic space and time scales of the plasma; these relations considerably extend the limits of applicability for previously developed theories.