Fluctuation Approximation Research Articles

Angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor

We use time-dependent Ginzburg–Landau theory in a three-dimensional model, including thermal noise, to analyze angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor. The Hall resistivity and longitudinal resistivity are calculated as functions of temperature, magnetic field and the angle θ between the magnetic field and the ab-plane in the vortex-liquid regime. Our theoretical calculations within a self-consistent fluctuation approximation for MgB2 and HgBa2CaCu2O6 materials are in good agreements with the experimental findings for both below and above the critical temperature Tc. We observe that when the field angle decreases, the transition temperature increases and the magnitude of longitudinal resistivity decreases, which is qualitatively comparable to decrease of the perpendicular field component. However, when the magnetic field direction approaches the layer surface, it shows a clear different effect from that of a perpendicular field with the same normal component.

In Ukrainian

Brownian motors belong to the class of nanoscale devices that use the thermal noise of the environment as one of the necessary components in the mechanism of their operation. Today, there are a lot of practical implementations of such nanomachines, both inorganic, fairly simple mechanisms produced artificially, and more complex ones created from separate biological components available at the cellular level. One of the options for implementing the mechanism of straightening the chaotic thermal noise of the environment into unidirectional motion is the presence of a motor particle in the field of action of an asymmetric periodic stationary potential, which undergoes certain small disturbances (fluctuations) periodically over time. To describe such asymmetric one-dimensional structures (for example, dipole chains or fibers of the cytoskeleton) in the theory of Brownian motors, two model potentials are most often used: piecewise linear sawtooth and double sinusoidal. In this work, within the framework of the approximation of small fluctuations, a model of a pulsating Brownian motor with a stationary double sinusoidal potential and a disturbing small harmonic signal is considered. A new method of parametrization of such a problem is proposed, which allows to separate the contributions from various factors affecting the operation of the ratchet, and the numerical procedure for calculating the average speed of the directional movement of nanoparticles for the selected type of model potentials is specified. A number of numerical dependences of the average speed on the main parameters of the system were obtained. Peculiarities of the behavior of the motor as dependent on the parameter responsible for asymmetry and the number of potential wells on the spatial period of the stationary potential have been investigated. It is shown that the direction of the generated flux of nanoparticles depends not only on the phase shift between the stationary and fluctuating components of the potential, but also on the temperature of the system and the frequency of fluctuations, i.e., a possibility of temperature-frequency control of the direction of movement in the considered model has been found. Diagrams have been constructed that allow you to choose the ratio between the parameters of the nanomotor to create a flux of particles in the desired direction.

The Study of Internal Gravity Waves in the Earth’s Atmosphere by Radio Occultations: A Review

Internal gravity waves (IGWs) in the middle atmosphere are the main source of mesoscale fluctuations of wind and temperature. The parameterization of IGWs and study of their climatology is necessary for the development of global atmospheric circulation models. In this review, we focus on the application of Radio Occultation (RO) observations for the retrieval of IGW parameters. (1) The simplest approach employs the retrieved temperature profiles. It is based on the fact that IGWs are highly anisotropic structures and can be accurately retrieved by RO. The basic assumption is that all the temperature fluctuations are caused by IGWs. The smoothed background temperature profile defines the the Brunt–Väisälä frequency, which, together with the temperature fluctuations, defines the IGW specific potential energy. Many studies have derived the distribution and climatology of potential energy, which is one of the most important characteristics of IGWs. (2) More detailed analysis of the temperature profiles is based on the derivation of the temperature fluctuation spectra. For saturated IGWs, the spectra must obey the power law with an exponent of −3. Such spectra are obtained by using Wave Optical (WO) processing. (3) More advanced analysis employs space–frequency analysis. It is based on phase-sensitive techniques like cross S- or wavelet transforms in order to identify propagating IGWs. (4) Another direction is the IGW parameter estimate from separate temperature profiles applying the stability condition in terms of the Richardson number. In this framework, a necessary condition is formulated that defines whether or not the temperature fluctuations can be related to IGW events. The temperature profile retrieval involves integral transforms and filtering that constitute the observation filter. (5) A simpler filter is implemented by the analysis of the RO amplitude fluctuation spectra, based on the diffraction theory in the framework of the phase screen and weak fluctuation approximations. The two spectral parameters, the external scale and the structural characteristic, define the specific potential energy. This approach allows the derivation of the spacial and seasonal distributions of IGW activity. We conclude that the success of IGW study by RO is stimulated by a large number of RO observations and advanced techniques based on Fourier and space–time analysis, physical equations describing IGWs, and diffraction theory.

Investigation of Sub-Grid Scale Turbulence-Radiation Interaction Effects on Turbulence Energy Transport and Varying Thermophysical Properties Using Large Eddy Simulation

Abstract The main objective of this article is to investigate sub-grid scale turbulence–radiation interaction (SGS TRI) effects on SGS turbulence kinetic energy (TKE) fluctuations and varying thermophysical properties in a partially premixed combustion system for a laboratory-piloted methane/air flame. The large eddy simulation approach is employed to simulate the turbulence of the compressible reactive flow. SGS quantities, including turbulent stress and fluxes of enthalpy and species in the sub-grid scale, are computed using the standard Smagorinsky–Lilly model. The radiative transfer equation is modeled by applying the spherical harmonic P1 approximation by considering the radiative heat source related to the SGS TRI contribution. Optically thin fluctuation approximation is utilized to simplify the radiative absorption term. A chemical reaction mechanism comprising 41 steps and 16 species is applied to model methane–air mixture combustion. Diffusion flamelet-generated manifolds are employed to govern the species transport equation. About 87% of TKE is resolved by applying the finest grid consisting of 1,822,580 cells. Impacts of SGS TRI on the spatially filtered density, eddy viscosity, SGS velocity and TKE, overall radiative emission, RMS temperature fluctuations, and nitrogen monoxide (NO) formation are studied. The results reveal that considering SGS TRI in the simulation leads to remarkable discrepancies, particularly in SGS velocity and TKE by 6.70% and 7.40%, respectively. Meanwhile, SGS density and eddy viscosity deviate negligibly in the presence of SGS TRI. Also, the filtered mass fraction of NO reduces up to 17.54% on average by considering TRI.

Thermodynamic Properties of a One-dimensional, Harmonically Trapped Bosonic (87Rb) Gas Mixture Using the Static Fluctuation Approximation

Thermodynamic Properties of a One-dimensional, Harmonically Trapped Bosonic (87Rb) Gas Mixture Using the Static Fluctuation Approximation

Linear approximation to the statistical significance autocovariance matrix in the asymptotic regime

Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel, highly efficient method to estimate the covariance matrix of such a Gaussian field. The method is based on the linear approximation of statistical fluctuations of the signal amplitude. For one-dimensional searches the upper bound on the trials factor can then be calculated directly from the covariance matrix. For higher dimensions, the Gaussian process described by this covariance matrix may be sampled to calculate the trials factor directly. This method also serves as the theoretical basis for a recent study of the trials factor with an empirically constructed set of Asmiov-like background datasets. We illustrate the method with studies of a H → γγ inspired model that was used in the empirical paper.

Investigation of the electronic structure of biphenylene ribbons of the armchair type

The electronic structure of chair-type biphenylene ribbons is studied within the framework of the Hubbard Hamiltonian in the approximation of static fluctuations. An expression is obtained for the Fourier transform of the Green's functions, whose poles determine the spectrum of elementary excitations. The energy spectrum of biphenylene ribbons indicates that nanoribbons with a width of 6, 9, 12, 15, 18 carbon atoms are in the semiconductor state. Densities of state of electrons of biphenylene ribbons of various widths are presented in comparison with the results of experimental measurements of differential conductance of biphenylene ribbons. It is shown that the width of the band gap decreases exponentially with an increase in the width of the biphenylene ribbon. Ribbons with a width of 21 carbon atoms or more are in the metallic state.

Collective excitations of a charged Fermi superfluid in the BCS-BEC crossover

We consider collective excitations in the superfluid state of Fermi condensed charged gases. The dispersion and damping of collective excitations at nonzero temperatures are examined, and the coexistence and interaction of different branches of collective excitations: plasma oscillations, pair-breaking Higgs modes, and Carlson–Goldman phonon-like excitations are taken into account. The path integral methods for superfluid Fermi gases and for Coulomb gas are combined into a unified formalism that extends the Gaussian fluctuation approximation to account for plasmonic modes. This approximation of Gaussian pair and density fluctuations is able to describe all branches of collective excitations existing in a charged superfluid. The spectra of collective excitations are determined in two ways: from the spectral functions and from the complex poles of the fluctuation propagator. A resonant avoided crossing of different modes is shown. It is accompanied by resonant enhancement of the response provided by the pair-breaking modes due to their interaction with plasma oscillations. This may facilitate the experimental observation of the pair-breaking modes.

Modulational instability in vector exciton-polariton condensates with photonic spin-orbit coupling

The paper demonstrates the existence of modulational instability (MI) in nonlinear exciton-polariton condensates (EPCs). A set of coupled two-dimensional (2D) driven-dissipative Gross-Pitaevskii equations describing the spin-up and spin-down polaritons, containing the photonic spin-orbit (SO) coupling and the rate equations describing the density of incoherent excitonic reservoir density, is reduced to a system of two coupled 2D complex Ginzburg-Landau (2DCGL) equations, with saturable nonlinearities for complex polariton order parameters, thanks to the adiabatic approximation and small density fluctuations approximation. The analytical approach relies on the linear stability analysis of continuous waves (CWs) to derive an expression for the growth rate and conduct a parametric study of MI. The effect of different parameters on the growth rate spectrum is discussed with an emphasis on the photonic SO coupling and the pumping power. The predictions are verified against a direct simulation of the 2DCGL equations, and excellent agreement is found. The emergence of solitonic clusters manifests the evolution of MI. Phase diagrams on a MI spectrum for the CWs are presented against the magnetic field ($B$) and SO coupling strength ($\ensuremath{\sigma}$), based on which the dynamical behaviors of the emerging structures are debated, along with their response to changing $\ensuremath{\sigma}$ and $B$. The results suggest that the photonic SO coupling and the magnetic field constitute efficient tools for nonlinear mode selection and characterization via the MI process and are equally important in any eventual experimental realization of such a process in the studied EPC system.

Thermodynamic properties and effective mass of a weakly-interacting Bose gas using the static fluctuation approximation

The Static Fluctuation Approximation is used to investigate the thermodynamic properties and the single-particle effective mass of a weakly-interacting Bose gas. These properties include: the transition temperature, condensate fraction, energy spectrum, total energy, and specific heat capacity. The effects of the potential strength, number density, and temperature on these properties are studied. The transition temperature decreases as the potential strength increases, or the number density decreases. Also, the condensate fraction decreases drastically with increasing potential strength or decreasing density number. The total energy and specific heat indicate that the system is in the classical (quantum) regime at temperatures greater (less) than the transition temperature. The specific heat has a peak at the transition temperature. Regarding the effective mass: in higher excited states, it is close to the ‘bare’ mass, regardless of the potential strength and number density; but, in low-lying states, it is tangibly affected by these variables.

Электронное строение и оптические свойства соединений изомеров фуллерена С-=SUB=-90-=/SUB=- с хлором

Within the framework of Hubbard’s model using an approximation of static fluctuations, the electronic structure and optical properties of compounds of C90 fullerene isomers with chlorine atoms are investigated. The energy spectrum of π electron subsystem is shown to be divided into several unbound electronic subsystems when the number of the attached chlorine atoms becomes greater than (or about) 30. Each of subsystems behaves like a separate system in this case. The energy spectra and optical absorption spectra of ten different chlorine compounds C90@Cln have been calculated. Their optical properties are predicted.

A Data-Driven Hybrid Methodology Using Randomized Low-Rank DMD Approximation and Flat-Top FIR Filter for Voltage Fluctuations Monitoring in Grid-Connected Distributed Generation Systems

The voltage fluctuations are caused by variations in renewable energy source outputs, increased usage of nonlinear loads, high reactive power consumption of loads, etc. This results in damage to electric components and enormous economic losses. It is necessary to measure the parameters of voltage fluctuations and flicker levels to achieve a secure supply of power. However, higher-order harmonics and noises in voltage waveform make such assessment a burdensome task. The traditional techniques fail to provide exact monitoring due to the uncharacteristic variations in the input voltage signal. Nowadays, data-driven methods have become a prominent choice for non-stationary, nonlinear signal analysis as it efficiently tackles atypical changes by its capability to identify spatio-temporal information from given data. The present paper proposes a data-driven hybrid methodology for monitoring voltage fluctuations using the low-rank approximation of dynamic mode decomposition (DMD) and flat-top finite impulse response (FIR) filter. The low-rank approximation of DMD enables to identify the spatio-temporal coherent structures from the data by mapping the data into a lower-dimensional space. Adaptive flat-top FIR filter tracks the fundamental dynamic phasor by identifying the instantaneous frequency, magnitude and phase variations. The performance of the proposed hybrid methodology is assessed using different test cases, and is compared with various existing approaches. The promising results suggest that the proposed methodology can be used for accurate parameter identification and monitoring voltage fluctuations in smart grid scenarios. It can also be used as an accurate tool in distribution grids to detect higher-order harmonics.

Nonlinear dynamics of kinetic fluctuations and quasi-linear relaxation in plasma

We propose an approximation of pair correlations for solving the equations of the kinetic theory of long-wave (or large-scale) fluctuations in gaseous media. The basic ones are the general nonlinear equations of the large-scale fluctuations theory at the kinetic stage of system evolution, derived from the first principles of statistical mechanics. We show that based on the equations of the long-wave fluctuations kinetics in the case of weak interaction between particles, in the approximation of pair fluctuations it is possible to reproduce the main results of the quasi-linear theory of plasma. Thus, the well-known quasi-linear theory of plasma is provided with a first-principle justification.

Энергетический спектр и спектр оптического поглощения экзоэдрального фуллерена С-=SUB=-70-=/SUB=-Br-=SUB=-10-=/SUB=- в модели Хаббарда

Energy spectrum exohedral fullerene С70Br10 with the Cs symmetry groups have been obtained within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecule С70Br10 have been determined. On the basis of the energy spectrum of exohedral fullerene С70Br10 is given an interpretation of experimentally observed optical absorption bands molecule С70Br10.

Energy Spectrum and Optical Absorption Spectra of exohedral Fullerene C-=SUB=-70-=/SUB=-Br-=SUB=-10-=/SUB=- within the Hubbard Model

Energy spectrum exohedral fullerene C70Br10 with the Cs symmetry groups have been obtained within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of molecule C70Br10 have been determined. On the basis of the energy spectrum of exohedral fullerene C70Br10 is given an interpretation of experimentally observed optical absorption bands molecule C70Br10. Keywords: Hubbard model, Green's functions, energy spectrum, fullerenes, nanosystems, fullerene C70, exohedral fullerene C70Br10.

Quasilinear theory of general electromagnetic fluctuations including discrete particle effects for magnetized plasmas: General analysis

The general quasilinear Fokker–Planck kinetic equation for the gyrophase-averaged plasma particle distribution functions in magnetized plasmas is derived, making no restrictions on the energy of the particles and on the frequency of the electromagnetic fluctuations and avoiding the often made Coulomb approximation of the electromagnetic interactions. The inclusion of discrete particle effects breaks the dichotomy of nonlinear kinetic plasma theory divided into the test particle and the test fluctuation approximation because it provides expression of both the non-collective and collective electromagnetic fluctuation spectra in terms of the plasma particle distribution functions. Within the validity of the quasilinear approach, the resulting full quasilinear transport equation can be regarded as a determining nonlinear equation for the time evolution of the plasma particle distribution functions.

Investigating thermal properties of Kr Gas for temperatures [120–180] K using static fluctuation approximation

Particular thermal properties of internal energy, entropy, specific heat capacity and pressure are indicated using static fluctuation approximation (SFA) for specified temperatures and densities where the interaction between particles is still valid. This ab initio study starts initially from the most reliable krypton interatomic potential and develops with complementary SFA assumptions that depend mainly on substituting the local field mean value instead of its operator, thus developing a numerical solution of a nonlinear close set equation by iteration technique. The results are matched with the ideal gas and show a considerable sense.

Scintillation theory of optical waves propagating through moderate to strong compressible turbulence

Compressible turbulence around an aircraft will cause irradiance fluctuations in the optical waves in optical communication between the aircraft and the outside. Turbulence can cause signal fluctuation or even interruption, and the exploration of the issue plays an important role in aero-optics. Based on the extended Rytov theory, we develop theoretical expressions of the scintillation index for plane and spherical waves propagating in moderate to strong compressible fluctuations by a near wall compressible turbulence refractive index spectrum. The numerical results show that the derived scintillation index is in good agreement with weak fluctuation and asymptotic theory approximation. The predicted scintillation index first increases sharply with the path length and reaches a peak, after which it falls back to saturation. During weak fluctuations, the scintillation index of long wavelength waves is smaller than that of short wavelength waves, but in moderate to strong turbulence, the scintillation index of short wavelength waves has an advantage over that of long wavelength waves. Furthermore, we provide physical explanations for the scintillation index trend.

Using a flamelet generated manifold method in transported probability density function modeling of soot formation and thermal radiation

The simple semi-empirical precursor soot model of Brookes and Moss based on the soot number density and soot mass concentration is adopted in a transported probability density function (PDF) method for turbulent diffusion flames. The gas phase chemistry is described by a flamelet generated manifold (FGM) based on the mixture fraction, progress variable and enthalpy loss. The accuracy of the FGM method is validated by using flamelet solutions that are not included in the generating set of the FGM. To account for the radiative heat transfer in the flames, we use a non-gray weighted sum of gray gases model for the gas radiation and a gray soot radiation model. Turbulence–radiation interaction is closed at the level of the optically thin fluctuation approximation and the Reynolds averaged radiative transfer equation is solved by means of a discrete transfer method. The proposed modeling approach is applied in simulations of two turbulent non-premixed methane–air flames at one bar and three bar pressure, respectively. Predictions of the mean temperature and mean soot volume fraction are in good agreement with the measurements in the one bar flame. In the higher pressure flame the mean soot volume fraction is over predicted. For this flame, simulation results using the semi-empirical model of Lindstedt provided better agreement with the measurements. The main difference between the Brookes and Moss model and the Lindstedt model is the nine-times increased soot particle agglomeration rate of the latter. When using the same increased agglomeration rate parameter in the Brookes and Moss model the results become virtually identical. The negligible molecular diffusion of the soot was accounted for by neglecting mean molecular diffusion of the soot variables and by greatly reducing their micro-mixing. The effect of this differential soot diffusion on the mean soot volume fraction is found to be small, but it is significant for the variance of the soot volume fraction.

Local contributions of resolved and subgrid turbulence-radiation interaction in LES/presumed FDF modelling of large-scale methanol pool fires

The present study aims to quantify individual contributions to turbulence-radiation interaction (TRI) in LES of large methanol pool fires with diameters ranging from 1m to 4m. These simulations feature a steady laminar flamelet (SLF)/presumed Filtered Density Function (FDF) combustion model and the Rank Correlated Full Spectrum k-distribution (RC FSK) for spectral gas radiation. This quantification has a fundamental interest to, on the one hand, understand how these contributions affect the radiative heat transfer from the flame to the surroundings that controls fire growth in industrial fires and, on the other hand, to provide guidance for the development of simplified models for TRI. This analysis is accomplished by exercising a well-validated fire model and using a scaling strategy that preserves the relative contributions of resolved-scale and subgrid-scale (SGS) scalar fluctuations. Large-scale non-luminous pool fires feature large optical thicknesses that increase significantly with the pool diameter. As a result, applying the optically-thin fluctuation approximation (OTFA) leads to a noticeable overestimation of the global radiative loss. The fire plume dynamics is governed by the puffing process whose frequency decreases with the pool size, and, in turn, affects the levels of turbulent intensity. As a result, emission TRI increases in the continuous flame and decreases in the high intermittent flame regions. The contribution of SGS emission TRI to global emission TRI becomes progressively dominant as the pool size increases. The largest contributions to both resolved-scale and SGS emission TRI are the temperature self-correlation and the absorption coefficient-temperature cross correlation, although this latter becomes negligible at the subgrid scale for pool diameters larger than 1m. In addition, the SGS absorption-coefficient self-correlation is also found to be negligible.