Directed paths with random phases

Directed Feynman paths in 1 + 1 dimensions that acquire random phases are examined numerically and analytically. This problem is relevant for the behavior of the conductance in two-dimensional amorphous insulators in the variable-range-hopping regime. Large-scale numerical simulations were performed on a model with short-range correlations. For the scaling of the transverse fluctuations ( t^ν), we obtain ν = 0.68 ± 0.025; and for the r.m.s free-energy fluctuations ( t^ω), we obtain ω = 0.335 ± 0.01. Up to 100 000 random samples were used for times as large as 2000. These results seem to exclude a recent conjecture that ν = 3/4 and ω = 1/2. Two versions of a model with long-range correlations are solved and shown to yield ν = 1/2; a physical explanation is given.     

Frequency and amplitude alterations of sound modes in a space-dependent random mass density field

We investigate the effect of a space-dependent random mass density field on small amplitude acoustic modes that are settled in a semi-infinite medium of a temperature growing linearly with depth. Using a perturbation method, the dispersion relation is derived in the form of Hill's determinant. Numerical solutions of this equation lead to the following conclusions: (a) a weak random field (with σ_eff = 0.05) essentially affects long waves which experience attenuation and a frequency reduction; (b) for a stronger random field (with σ_eff = 0.1), high-order sound modes behave as sound waves as they are attenuated and their frequencies are increased; (c) for a sufficiently strong random field (with σ_eff = 0.2), mode coupling occurs, as a result of which the dispersive curves cross each other, the sound modes loose their identities, and some modes are amplified. Here σ_eff denotes the effective strength of a random field.     

Wave beam tremble within an absorbing random medium with lens properties

The present paper investigates the joint influence of fluctuations of the complex dielectric constant, ε, of a medium and its lens properties on random displacements of a radiation beam. Based on a non-traditional approach, an expression is obtained for the variance of the beam energy centre tremble, σ²_ρ, taking into account the contribution of fluctuations of the real and imaginary parts of ε, as well as that of their correlations. It was shown that the influence of fluctuations of the imaginary part of ε is particularly pronounced in the initial section of the path, as well as in paths of great length. Due to regular refraction, a considerable enhancement of the dependence of σ²_ρ upon the path length occurs, with the greatest contribution being made by fluctuations of the imaginary part of the dielectric constant. A positive correlation of random changes of the real and imaginary parts of ε was shown to result in a partial compensation of the beam tremble.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

Elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media

This paper studies the elastic waves in non-Newtonian (Maxwell) fluid-saturated porous media with the nonzero boundary slip velocity for pore size distribution. The coefficient bF_m(ω) that measures the deviation from Poiseuille flow friction in such media is presented. Based on this coefficient, we investigate the properties of elastic waves by calculating their phase velocities and attenuation coefficients as functions of frequency and the behaviour of the dynamic permeability. The study shows that the pore size distribution removes oscillations in all physical quantities in the non-Newtonian regime. Consideration of the nonzero boundary slip effect in non-Newtonian (Maxwell) fluid-saturated porous media results in (a) an overall increase of the dynamic permeability, (b) an increase of phase velocities of fast Biot waves and shear waves except in the low frequency domain and an overall increase of phase velocity of slow Biot waves and (c) an overall increase of the attenuation of three Biot waves in the intermediate frequency domain except in the deeply non-Newtonian regime. The study also shows that the attenuation coefficient of slow Biot waves is small in the deeply non-Newtonian regime at higher frequency, which encourages us to detect slow Biot waves in oil-saturated porous rock.     

Fast compressional wave attenuation and dispersion due to conversion scattering into slow shear waves in randomly heterogeneous porous media

Within the viscosity-extended Biot framework of wave propagation in porous media, the existence of a slow shear wave mode with non-vanishing velocity is predicted. It is a highly diffusive shear mode wherein the two constituent phases essentially undergo out-of-phase shear motions (slow shear wave). In order to elucidate the interaction of this wave mode with propagating wave fields in an inhomogeneous medium the process of conversion scattering from fast compressional waves into slow shear waves is analyzed using the method of statistical smoothing in randomly heterogeneous poroelastic media. The result is a complex wave number of a coherent plane compressional wave propagating in a dynamic-equivalent homogeneous medium. Analysis of the results shows that the conversion scattering process draws energy from the propagating wave and therefore leads to attenuation and phase velocity dispersion. Attenuation and dispersion characteristics are typical for a relaxation process, in this case shear stress relaxation. The mechanism of conversion scattering into the slow shear wave is associated with the development of viscous boundary layers in the transition from the viscosity-dominated to inertial regime in a macroscopically homogeneous poroelastic solid.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

Ultrasonic measurements on poroelastic slabs: Determination of reflection and transmission coefficients and processing for Biot input parameters

Ultrasonic reflection and transmission measurements on saturated, plane-parallel, poroelastic slabs are presented. A data processing technique is proposed to obtain poroelastic parameters from transmission measurements. A special experimental data acquisition and processing technique is applied to minimize the finite beam effects of the transducers. This technique yields results which can be compared with poroelastic plane-wave theory. Results of normal- and oblique-incidence measurements are presented, and transmission data are processed to yield wave speeds, sample thickness, angle of incidence, tortuosity, and permeability. The results show good agreement with independent measurements, and they are subsequently used as input for a forward modeling of the complete transmitted and reflected waveforms utilizing Biot theory. The agreement between recorded and modeled signals is good, both in time and frequency domain.     

Coupling Biot and Navier–Stokes equations for modelling fluid–poroelastic media interaction

The interaction between a fluid and a poroelastic structure is a complex problem that couples the Navier–Stokes equations with the Biot system. The finite element approximation of this problem is involved due to the fact that both subproblems are indefinite. In this work, we first design residual-based stabilization techniques for the Biot system, motivated by the variational multiscale approach. Then, we state the monolithic Navier–Stokes/Biot system with the appropriate transmission conditions at the interface. For the solution of the coupled system, we adopt both monolithic solvers and heterogeneous domain decomposition strategies. Different domain decomposition methods are considered and their convergence is analyzed for a simplified problem. We compare the efficiency of all the methods on a test problem that exhibits a large added-mass effect, as it happens in hemodynamics applications.     

Unified multiphase modeling for evolving,acoustically coupled systems consisting of acoustic,elastic, poroelastic media and septa

This paper presents a new modeling technique that can represent acoustically coupled systems in a unified manner. The proposed unified multiphase (UMP) modeling technique uses Biot’s equations that are originally derived for poroelastic media to represent not only poroelastic media but also non-poroelastic ones ranging from acoustic and elastic media to septa. To recover the original vibro-acoustic behaviors of non-poroelastic media, material parameters of a base poroelastic medium are adjusted depending on the target media. The real virtue of this UMP technique is that interface coupling conditions between any media can be automatically satisfied, so no medium-dependent interface condition needs to be imposed explicitly. Thereby, the proposed technique can effectively model any acoustically coupled system having locally varying medium phases and evolving interfaces. A typical situation can occur in an iterative design process. Because the proposed UMP modeling technique needs theoretical justifications for further development, this work is mainly focused on how the technique recovers the governing equations of non-poroelastic media and expresses their interface conditions. We also address how to describe various boundary conditions of the media in the technique. Some numerical studies are carried out to demonstrate the validity of the proposed modeling technique.     

Influence of electromagnetic fluctuations on the resonant tunneling of electrons

We have considered the influence of electromagnetic fluctuations on electron tunneling via one non-degenerate resonant level, the problem that is relevant for electron transport through quantum dots in the Coulomb blockade regime. We show that the overall effect of the fluctuations depends on whether the electron bands in external electrodes are empty or filled. In the empty band case, depending on the relation between the tunneling rate Γ and characteristic frequency Ω of the fluctuations, the field either simply shifts the conductance peak (for rapid tunneling, Γ Ω) or broadens it (for Γ Ω). In the latter case, the system can be in three different regimes for different values of the coupling g between electrons and the field. Increasing interaction strength in the region g < 1 leads to gradual suppression of the conductance peak at the bare energy of the resonant level ε₀, while at g 1 it leads to the formation of a new peak of width at the energy ε₀ + E_cis a charging energy. For intermediate values of g the conductance is non-vanishing in the entire energy range from ε₀ to ε₀ + E_c. For filled bands the problem is essentially multi-electron in character. One consequence of this is that, in contrast to the situation with the empty band, the fluctuations of the resonant level do not suppress conductance at resonance for g < 1. At g> 1 a Coulomb gap appears in the position of the resonant level as a function of its bare energy which leads to suppression of conductance.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

Abstract

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.     

On the low-frequency limit of the Schönfeld pulse 1/f law

On the basis of propositions of the common fluctuation theory, peculiarities of small fluctuations in real physical systems with limited sizes are analyzed. It is established that small fluctuations should necessarily be divided into two types of fluctuations: “small” and “very small”. It is shown that the damping process of “small” fluctuations has relaxation character, while the damping process of “very small” fluctuations is of random character, i.e., it represents a random rectangular signal. The probability density of “very small” fluctuations is shown to be Gaussian. The agreement of the obtained results with experimental data acquired from semiconductor-based devices is analyzed. A relation between the generation–recombination noise and phonon number fluctuations in semiconductors is studied. On the basis of this consideration it is shown that the Schönfeld pulse spectrum preserves its well-known 1/f form only in the range of intermediate frequencies; at lower frequencies the spectrum gets saturated. An expression for the low-frequency limit of Schönfeld pulse 1/f law is obtained.     

Determination of optical properties of aluminium including electron reradiation in the Lorentz-Drude model

The effect of electron reradiation was included in the Lorentz-Drude (LD) model and by applying the least-squares fitting method the values of the characteristic parameters (ω_p, Г, τ) of electrons in aluminium were determined. The values of these parameters allowed the determination of optical properties of aluminium for light of wavelengths λ[43.5 nm, 200 μm]. By including the reradiation of electrons the precision of the LD model has been increased in the infra-red region of wavelengths λ[1 μm, 200 μm]. In addition, the reradiation of electrons gives the square frequency dependence for damping frequency [Г′(ω) = Г +τω²], enabling the suitable application of the LD model in the broad range of wavelengths λ[43.5 nm, 200 μm]. It was estimated that the short wave limit at which the LD model can be used for aluminium occurs at about λ_min = 43.5 nm.     

Σ hypernuclear spectra from (K, π) inclusive reactions

We report on DWIA calculations of the pion inclusive spectra related to Σ-formation in (K⁻, π⁺) reactions on nuclei. Realistic distorted waves are used to describe the incoming kaon and outgoing pion. The Σ wave function is calculated in a real Woods-Saxon potential, the depth of which provides information about the underlying Σ N effective interaction. The absorptive effect due to the Σ-Λ conversion process in the nuclear medium is taken into account by effective two-channel coupled equations. Comparisons are made with the available data on ¹²C and ¹⁶O. Using a weak Σ-nucleus potential the overall agreement is satisfactory for the spectrum derived from kaon-in-flight experiments. Concerning the three peaks reported in a stopped kaon experiment on ¹²C, the lowest peak structure can be generated by increasing the depth of the Σ potential in ¹²C. However, the remaining two narrow structures cannot be reproduced as Σ-particle-proton-hole states in our continuum treatment of the Σ spectrum. The difficulties in extracting the strength of the Σ-nucleus spin-orbit potential are also discussed.     

Vacuum effects of non-nucleonic baryons in nuclear matter

The role of vacuum properties of non-nucleonic baryons in hadronic field theories is discussed. We use an extension of Walecka's σω model treated at the mean-field level. Due to energy considerations the non-nucleonic baryons yield only vacuum effects near normal nuclear matter density. We study the effect of Roper resonance vacuum fluctuations on the nuclear matter equation of state and Coulomb sum. In addition we perform a schematic calculation of the effect of Δ-isobar vacuum fluctuations on the nuclear matter equation of state. Although the Roper resonance produces only a marginal change in the Coulomb sum, the Roper and delta may produce a significant softening of the equation of state. Thus these normally neglected degrees of freedom might serve an important role.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Solvent fluctuations and viscosity-dependent rates of solution reactions in a regime indescribable by the transition state theory

An organic molecule isomerizes in viscous solvents when appropriate cavities are formed around it in the course of slow diffusive thermal fluctuations of solvent molecules. The isomerization occurs when fast twisting (vibrational) fluctuations around a bond get to have large amplitudes in such cavities. This situation can be described by the two-reaction-coordinate model of Sumi and Marcus originally proposed for electron transfer reactions. In fact, the rate constant derived from this model fits nicely to that observed for thermal Z→E isomerization of substituted azobenzenes and N-benzylideneanilines. The rate constant is influenced by slow speeds of diffusive motions of solvent molecules, whose relaxation time τ is usually proportional to the solvent viscosity η. It has a form of k = 1/(k_TST⁻¹+k_f⁻¹), where k_TST, independent of τ, represents the rate constant expected from the transition state theory (TST), while k_f ∝ τ⁻ with 0 < ≤ 1 represents the part controlled by solvent fluctuations. An analytic expression of for the isomerization reactions is given in terms of physical parameters underlying the reaction mechanism with cavity formation.

This rate-constant formula is a general one applicable widely also to other solution reactions, covering from the TST-validated regime for a small τ to the TST-invalidated one for a large τ. In the former, k approaches k_TST since k_f k_TST, while in the latter, k approaches k_f since k_f k_TST, becoming decreasing with a decrease in the typical speed (∝ τ⁻¹) of solvent fluctuations. The dependence of k ≈ k_f ∝ η⁻ in the non-TST regime has often been observed also in biological reactions such as enzymatic ones. In this case, it is not appropriate to say that reactions are controlled by slow speeds of solvent fluctuations, but we should rather say that enzymes utilize this situation, which has been called conformational gating, in the course of solvent-fluctuation-driven conformational fluctuations of proteins. It has important meanings in protein functions.     

Backscattering enhancement analysis for targets in continuous random media based on wave polarization

Owing to the double passage effect, the phenomenon of backscattering enhancement arises in which the radar cross-section (RCS) in a random medium is twice that in free space. In a previous study, it was proved that the enhancement in radar cross-section (ERCS) deviates from two and has large and anomalous fluctuations, sometimes as a result of the wave polarization and other parameters, especially for targets in strong random media. Linear, including horizontal and vertical, polarizations were considered. In this paper, a numerical analysis is presented to show that the fluctuations can be reduced and make ERCS dependent almost only on the double passage effect under certain conditions. Therefore, we will have a better detection technique of targets of large sizes in continuous random media. In doing that, the linear and circular polarizations of incident waves are considered. We assume the case where a directly incident wave is produced by a line source in the far field distributed uniformly along the axis parallel to the conducting cylinder (target) axis.     

Joint moments of the wave beam amplitude and inverse power in an absorbing random medium with lens properties

This paper presents a derivation of a system of closed equations for joint moments of the amplitude and inverse power of a wave beam propagating in a regularly inhomogeneous dissipative random medium. The radiation transfer in the medium is characterized by non-conservation of the total radiation energy flux and by the existence of power fluctuations. The statistics of the wave beam power fluctuations have been studied. Information on the power statistical characteristics is applied to close the system of equations for joint moments. For task parameters which are not very strict (an effective radius of the wave beam should be considerably less than the outer scale of the turbulence) a system of independent equations for arbitrary joint moments has been obtained. The equations for the first two lower joint moments of the beam intensity and inverse power have been solved analytically. With the solutions obtained the effective wave beam parameters were calculated, i.e. the beam mean displacement, effective broadening and tremble variance (the beam wandering variance) for the propagation of radiation in the refractive channel of an absorbing turbulent medium. Radically new characteristics of the behaviour of the effective parameters in random absorbing and transparent media have been revealed.