Mean Free Path Length Research Articles

Investigation of physicochemical characteristics of Dy3+ modified ZnO nanoparticles

In this report, pristine and Dy3+ modified ZnO nanoparticles [Zn(1-x)DyxO NPs, where x = 0, 0.05, and 0.10] were synthesized using the sol–gel route, and their physicochemical characteristics were investigated. x-ray diffractograms of all the compositions possess P63mc space group depicting hexagonal crystallinity with wurtzite-type crystal structure with no signature of impurities as confirmed using the Rietveld refinement technique. The granular microstructure displayed grain growth with Dy3+ incorporation in the ZnO crystal framework and an increment in average grain size was found to be 22.83 nm for x = 0 to 36.34 nm. The optical energy band gap also increased from 3.35 eV to 3.88 eV with Dy3+ doping in the host ZnO. Dy3+ substitution inhibits the conduction in ZnO and improves the resistivity (36 Ωcm–79 Ωcm) as carrier concentration diminishes from 7.36 × 1016 cm−3 to 4.23 × 1016 cm−3. Similarly, the mean free path length for ZnO and Dy3+ doped ZnO NPs declines from 0.0301 nm to 0.0198 nm. Dielectric properties of all the compositions were investigated using an LCR impedance analyzer and it was observed that Dy3+ substitution enhances the value of the dielectric constant from 32 to 91 with a low tangent loss at 50 Hz.

Wide-field illumination diffuse optical tomography within a framework of single-pixel time-domain spatial frequency domain imaging.

We present a wide-field illumination time-domain (TD) diffusion optical tomography (DOT) for three-dimensional (3-D) reconstruction within a shallow region under the illuminated surface of the turbid medium. The methodological foundation is laid on the single-pixel spatial frequency domain (SFD) imaging that facilitates the adoption of the well-established time-correlated single-photon counting (TCSPC)-based TD detection and generalized pulse spectrum techniques (GPST)-based reconstruction. To ameliorate the defects of the conventional diffusion equation (DE) in the forward modeling of TD-SFD-DOT, mainly the low accuracy in the near-field region and in profiling early-photon migration, we propose a modified model employing the time-dependent δ-P1 approximation and verify its improved accuracy in comparison with both the Monte Carlo and DE-based ones. For a simplified inversion process, a modified GPST approach is extended to TD-SFD-DOT that enables the effective separation of the absorption and scattering coefficients using a steady-state equivalent strategy. Furthermore, we set up a single-pixel TD-SFD-DOT system that employs the TCSPC-based TD detection in the SFD imaging framework. For assessments of the reconstruction approach and the system performance, phantom experiments are performed for a series of scenarios. The results show the effectiveness of the proposed methodology for rapid 3-D reconstruction of the absorption and scattering coefficients within a depth range of about 5 mean free pathlengths.

New Polarimetric Data for the Galilean Satellites: Io and Ganymede Observations and Modeling

New high-precision disk-integrated measurements of the polarization of Io and Ganymede in the UBVRI bands are presented. The observations were obtained using polarimeters mounted on the Crimean Astrophysical Observatory and the Peak Terskol Observatory in 2019–2023. For Io, the negative polarization branch (NPB) reaches a minimum of P min ≈ −0.25 ± 0.02% in the V band at a phase angle of α min = 2.°1 ± 0.°5. The inversion angle is α inv = 26° ± 6° in the V and R bands. The NPB for Ganymede is an asymmetric curve, with P min = −0.34 ± 0.01% at α min = 0.°52 ± 0.°06 and α inv = 8.°5 ± 0.°2 in the V band. Although Io and Europa have similar geometric albedos (0.63 and 0.67, respectively), their NPB shapes differ. The NPB of Ganymede (albedo of 0.43) is morphologically similar to that of Europa, although it is described by different parameter values (P min, α min, and α inv). This discrepancy is likely due to the compositions of their surfaces: Europa’s with H2O ice, Io’s with sulfuric/silicate composition, and Ganymede’s with H2O ice and silicates. Numerical computations using the radiative transfer coherent backscattering method demonstrated a match to the polarimetric observations and to the geometric albedos for Ganymede with the single-scattering albedo ≈ 0.943 and mean free path length kl = 2πl/λ eff ≈ 150, where λ eff is the wavelength. For Io’s regolith, the single-scattering albedo was found to be ≈ 0.979 and kl ≈ 40.

Analysis of Sound Field Distribution in Architecturally Diverse Temples

The results of the research, which aimed to analyze the acoustic properties of selected sacred buildings located in the city of Czestochowa, Poland are presented in the paper. Three architecturally unusual and completely different from each other churches were selected for the study. The churches differed in shape of their buildings, cubic volume, years of construction, interior furnishings, etc. Nine different objective parameters were used to describe the physical properties of acoustical field in the studied churches. Various factors characterizing the acoustic properties of each building were determined, such as the distribution of sound pressure level (SPL), reverberation time T30, definition D50. Next, they were thoroughly analyzed, so as to ultimately obtain distributions of individual acoustic parameters in the space of the tested building. It allowed to evaluate the quality of the received verbal or musical message depending on the place where the listener was. Further research on speech intelligibility and the musical quality of churches was performed by determining the averaged values of next four objective acoustic parameters: centre time Ts, speech clarity C50, music clarity C80, and speech transmission index (STI). A new approach to analyzing the objective physical parameters describing the sound field was presented in Sec. 4. Mean free path length and critical distance were determined for the investigated acoustic fields in each church and they were associated with a general geometric factor characterizing the complexity of the room shape. The final part of the work presents a comparative analysis of the obtained results of acoustic quality tests of the temples, and thus their usefulness in terms achieving a maximum intelligibility of speech and music. The interesting similarities were found in the spatial distribution of individual acoustic parameters characterizing the distribution of the acoustic field in temples with completely different architecture.

Information transport and limits of optical imaging in the highly diffusive regime

Noninvasive imaging through the human body or dense fog at optical wavelengths requires the collection of highly scattered photons, which corrupt imaging information and restrict most diffuse imaging techniques to $<$ 10 transport mean free path (TMFP) lengths. An information theoretical analysis of numerical simulations including practical considerations shows imaging information exists at the single-photon detection limit beyond 200 TMFP lengths. Information can be enhanced through increasing the collection of light, optimizing detector placement, and resolving measurements in the space-time domain.

Research on propagation characteristic of Laguerre–Gaussian vortex beams with Far-field scattering Electric Monte Carlo method

A Far-field Scattering Electric field Monte Carlo (FSEMC) method is proposed to investigate the propagation and imaging characteristics of Laguerre–Gaussian Beams (LGB) with different Orbital Angular Momentum (OAM) in long-distance (relative to wavelength) scattering environment. As an extension of the Electric field Monte Carlo (EMC) method, the electric field transport mode is simulated to properly analyze the fading effect of scattering. The mean free path and total transmission length in the simulation are equivalent to the environment parameters of experiment. The beam transmission modes, intensity attenuation and effects on imaging quality through different turbidity media are analyzed. It is observed that vortex beams with different topological charges play a subtle role in transmission through turbid media, showing strong correlations with total transmission intensity, retention of ballistic light, and penetration depth. The experimental results fitting well with the FSEMC simulation results, validating the proposed method for far-field propagation characteristic of vortex beams in turbid media.

A practical approach to modelling railway vehicle interior acoustics

The aim of the current work is to propose a practical approach for modelling the interior acoustics of railway vehicles by investigating the spatial decay of sound within the vehicle and its relation to the reverberation time and absorption. Measurements are presented of the longitudinal distribution of sound level inside five railway vehicles as well as the corresponding reverberation times. Both quantities are determined using an omnidirectional sound source located near one end of the vehicle. The measured sound pressure level follows a roughly linear dependence with longitudinal distance and the rate of decay is found to follow a consistent trend over all five datasets when plotted against reverberation time. To interpret these results, three different modelling approaches are considered: ray tracing, Statistical Energy Analysis, and an analytical corridor model. Ray tracing models with a simple geometry resembling the interior of a railway carriage are used to explore the dependence of the spatial decay and reverberation time on the absorption and scattering coefficients of the surfaces. For high values of scattering coefficient, the reverberation time approaches the Sabine estimate but for low values of scattering coefficient it can be up to a factor of 2.5 greater than this estimate. This implies difficulties in deducing the average absorption coefficients from the measured reverberation times. The spatial decay rates obtained from the ray tracing model do not have the same consistent dependence on reverberation time as the measured results, although the results for low values of scattering coefficient are closer to the measured trend than those for higher values. Investigation of the Statistical Energy Analysis approach shows that it predicts a spatial decay rate that depends explicitly on length of the subsystems used in the model; consequently, the results do not converge as the model is refined. It is possible to use modified coupling loss factors based on an analytical corridor model to give a better approximation to the spatial decay. This corridor model is shown to give results that are consistent with the measurements if the average absorption is obtained from the reverberation time using a modified formula for the mean free path length, and if the cross-section area is reduced to allow for the blocking effect of the seats. This provides a practical way forward for using SEA for the interior sound in railway vehicles.

Finite-difference diffusion-equation modeling of reverberation chambers in time-domain

Conventional chamber-based methods of random incidence absorbing coefficients overlook the non-diffused sound field in the room acoustics, which decreases accuracy and may even lead to conflicting results. This work applies the diffusion equation model to room-acoustic simulations of standardized reverberation chambers. The simulations can more efficiently capture the chamber's non-diffuse sound field and energy flows than wave-based simulation models. The diffusion equation represents the governing equation of reverberant sound energy densities within the reverberation chamber which is solved using the finite-difference time-domain method. Its computational efficiency of diffusion equation-based modeling lies in a highly sparse domain meshing condition dictated by the mean-free path length rather than wavelengths and still derives a wideband simulation result. This work also dedicates the effort to reexamine the meshing condition, particularly for standardized finite sizes of sound absorbers for measurements of random incidence absorption coefficients. By comparing the outcomes of simulations with measurement data, an a posteriori absorption coefficient is inversely estimated involving Bayesian parameter estimation.

Superballistic boundary conductance and hydrodynamic transport in microstructures

It is shown that the ideal boundary between a perfectly conducting electrode and electron liquid state acts as a contact whose conductance per unit area is higher than the fundamental Sharvin conductance by a numerical coefficient $2\ensuremath{\alpha}$, where $\ensuremath{\alpha}$ is slightly smaller than unity and depends on the dimensionality of the system. If the boundary has a finite curvature, an additional correction to the boundary conductance appears, which is parametrically small as a product of the curvature by the electron-electron mean free path length. The relation of the normal current density to the voltage between the electrode and electron liquid represents itself a hydrodynamic boundary condition for current-penetrable boundary. Calculations of the conductance and potential distribution in microstructures by means of numerical solution of the Boltzmann equation show that the concept of boundary conductance works very good when the hydrodynamic transport regime is reached. The superballistic transport, when the device conductance is higher than the Sharvin conductance, can be realized in Corbino disk devices not only in the hydrodynamic regime, although requires that the electron-electron scattering rate must be higher than the momentum-relaxing scattering rate. The theoretical results for Corbino disks are consistent with recent experimental findings.

Combined Raman Spectroscopy and Magneto-Transport Measurements in Disordered Graphene: Correlating Raman D Band and Weak Localization Features

Although previous studies have reported the Raman and weak localization properties of graphene separately, very few studies have examined the correlation between the Raman and weak localization characterizations of graphene. Here, we report a Raman spectroscopy and low-magnetic-field electronic transport study of graphene devices with a controlled amount of defects introduced into the graphene by exposure to electron-beam irradiation and oxygen plasma etching. The relationship between the defect correlation length (LD), calculated from the Raman “D” peak, and the characteristic scattering lengths, Lϕ, Li and L*, computed from the weak localization effects measured in magneto-transport was investigated. Furthermore, the effect on the mean free path length due to the increasing amounts of irradiation incident on the graphene device was examined. Both parameters—including LD and Lϕ—decreased with the increase of irradiation, which was shown to be related to the increase of disorder through the concomitant decrease in the mean free path length, l. Although these are similar trends that have been observed separately in previous reports, this work revealed a novel nonlinear relationship between LD and Lϕ, particularly at lower levels of disorder. These findings are valuable for understanding the correlation between disorder in graphene and the phase coherence and scattering lengths of its charge carriers.

Particle sizing in non-dilute dispersions using diffusing wave spectroscopy with multiple optical path lengths

Non-dilute dispersed phase systems, such as foams, emulsions, and suspensions, are an important class of final formulations and chemical process intermediates in a variety of industries. The utility of these systems hinges on their stability over the lifetime of use, and therefore an accurate assessment of chemical and physical dynamics, asformulated, is required. We describe a unified treatment of diffusing wave spectroscopy (DWS) data using a range of optical path length with a goniometric instrument. DWS correlation data from multiple angles and robust Monte Carlo simulations are used to determine accurate values of the photon transport mean free path length. The variance on each correlation function is used to determine the physical time range that the mean squared displacement can be analyzed. Using standard solid particle suspensions of polystyrene and SiO2, we determine the average particle size with accuracy comparable to dynamic light scattering.

New Polarimetric Data for the Galilean Satellites: Europa Observations and Modeling

This paper is dedicated to a long-standing problem of the shape of the negative branch of polarization (NBP) for Jupiter's moon Europa, determination of which is crucial for the characterization of the icy regolith on this satellite and similar objects, as well as for further progress in understanding light scattering by particulate surfaces. To establish the shape of Europa's NBP, in 2018–2021 we accomplished high-precision disk-integrated polarimetry of Europa in the UBVR I bands using the identical two-channel photoelectric polarimeters mounted on the 2.6 m Shajn reflector of the Crimean Astrophysical Observatory and the 2 m telescope of the Peak Terskol Observatory. We found that the polarization dependence on the phase angle in each filter is an asymmetric curve with a sharp polarization minimum at phase angle , after which the polarization degree gradually increases to positive values, passing the inversion angle at α inv ≈ 6° − 7°. Within the error limits, the parameters P min, , and α inv of the NPB are independent of the wavelength in the visible spectrum. The polarization curve clearly demonstrates the so-called polarization opposition effect (POE). Our analysis of the previous and new polarimetric observations of Europa allows us to conclude that the POE is caused by coherent backscattering of sunlight on microscopic icy grains covering Europa’s surface. Computer modeling with the numerical radiative transfer coherent backscattering method demonstrates that the best fit to the polarimetric observations and geometric albedo of Europa is provided by a regolith layer of elementary single-scattering albedo ∼0.985 and extinction mean free path length 2π l/λ eff ≈ 150, λ eff representing the effective wavelength in the UBVR I spectral bands.

Phonon scattering and vibrational localization in 2D embedded nanoparticle composites

The frequency domain perfectly matched layer (FDPML) approach is used to study phonon transport in a series of large 2D domains with randomly embedded nanoparticles over a wide range of nanoparticle loadings and wavelengths. The effect of nanoparticle packing density on the mean free path and localization length is characterized. We observe that, in the Mie scattering regime, the independent scattering approximation is valid up to volume fractions exceeding 10% and often higher depending on scattering parameter, indicating that the mean free path can usually be calculated much less expensively using the number density and the scattering cross section of a single scatterer. We also study localization lengths and their dependence on particle loading. For heavy nanoparticles embedded in a lighter material, using the FDPML approach, we only observe localization at volume fractions >30% and only for short wavelength modes where vibrational frequencies exceed those available in the embedded nanoparticles. Using modal analysis, we show that localization in nanoparticle laden materials is primarily due to energetic confinement rather than Anderson localization. We then show that, by using light particles in a heavy matrix, the fraction of confined modes can be substantially increased.

Modeling of reverberation chambers for sound absorption measurements using a diffusion equation

The sound field in reverberation chambers used for measuring sound absorption coefficients is usually non-diffuse, leading to inaccuracies and disagreements in the results. In this paper, a diffusion equation model is applied to simulating reverberation chambers in order to obtain reverberant energy distributions and sound energy flows of the chamber under investigation in a more efficient way than wave-based simulation models. The computational efficiency of the diffusion equation lies in the fact that the meshing condition of the simulation domain is dictated by the room's mean-free path length (MFPL). Further investigation shows one-twelfth of MFPL as the meshing condition is considered practically sufficient for obtaining random incidence absorption coefficient of standardized sample sizes. With the computational efficiency given by a meshing of up to twelfth MFPL, an inversion calculation of random incident absorption coefficients of highly absorptive materials is possible with a mixed boundary condition [Jing and Xiang, JASA 123, pp. 145–153 (2008)]. Based on analysis of both chamber-based measurements and simulated data, ways to scrutinize measurement results of absorptive materials are investigated.

An approach to implement a heat flux limit in a model for fusion relevant plasmas

An approach to implement a heat flux limit (HFL) in a plasma model is proposed. The HFL arises if the mean free path length of the heat carrying electrons, λh, significantly exceeds the characteristic length of the temperature variation, LT. For λh≫LT, the heat flux becomes nearly independent of the temperature gradient, in contrast to the case of λh≪LT where it is gradient dependent. As a result, by going from λh≪LT to λh≫LT, the order of the heat balance equation changes and the method proposed allows a reliable integration of this equation in these limits, as well as for λh∼LT. By solving a set of one-dimensional fluid equations for particle, momentum, and heat balance numerically, the importance of the HFL for fusion relevant conditions is demonstrated for plasma parameter profiles at the edge of the heliotron Large Helical Device and detachment conditions in helium plasmas of the linear device NAGDIS-II.

Terahertz-infrared spectroscopy of wafer-scale films of single-walled carbon nanotubes treated by plasma

We investigated terahertz-infrared electrodynamic properties of wafer-scale films composed of plasma-treated single-walled carbon nanotubes (SWCNTs) and films comprising SWCNTs grown with different lengths. The spectra of complex conductance of the films were measured at frequencies 5–20 000 cm−1 and in the temperature interval 5–300 K. Terahertz spectral response of films of pristine SWCNTs is well described with the Drude conductivity model and a plasmon resonance located at ≈100 cm−1. Stepwise treatment of the films with oxygen plasma led to a gradual suppression of the Drude spectral weight from the low-frequency side. For films with the nanotubes shorter than 1 μm, i.e., close to electrons mean free path and localization length, scattering of charge carriers at the nanotubes edges is shown to additionally contribute to the carriers scattering rate and to the damping of plasmon resonance. The temperature coefficient of ac resistance (ac TCR) in both kinds of films is found to strongly increase in amplitude during cooling and frequency decrease. The values of ac TCR increase in films with longer time of plasma treatment and nanotubes with shorter length but reach saturation in films with exposure time longer than ≈100 s or composed from SWCNTs shorter than 1 μm.

The influence of the GM tube insulation parameters on the GM counter characteristics

The paper presents the results of testing the Geiger-Muller chamber cathode radii on the GM counters characteristics. The influence of the cathode radius is tested on: 1 - the GM counter characteristic; 2 - the length and plateau slope; and 3 - the GM counter chamber lifetime. The influence of small amounts of electronegative gas in the GM chamber working gas on the observed characteristics was also analyzed. The obtained results differ drastically from the results of similar tests presented in previously published papers on similar topics. This result is explained by the fact that the law of similarity for gas emissions was taken into consideration when making the tested tubes (i.e., the mean free path length of the electron was treated as a geometric parameter). In that way, the relevant results for the application of GM counters in practice were obtained. The result obtained with a small percentage of electronegative gas in the three-component mixture of gases noble gas + quenching gas + electronegative gas confirms the positive synergistic effect of the electronegative gas addition. This result contradicts the general view that GM chamber working gas must not contain electronegative gas.

An examination of the Neutral Penetration Model1/ne,pedscaling for its validity of spatially varying neutral sources

The core transport code, JETTO, coupled to the neutral Monte Carlo code, EIRENE, has been used to examine the sensitivity of the JET H-mode pedestal to the neutral flux crossing the separatrix. The Neutral Penetration Model (NPM) [Groebner et. al., Physics of Plasmas 9, 2134 (2002)] predicts the width of the density pedestal along the neutral path to scale with the inverse of its height: 1/ne,ped. By keeping the same physics assumptions in the NPM, and setting the deuterium atoms to cross the separatrix at the same location as the synthetic diagnostic line of sight (i.e. at the outer mid-plane, OMP), we were able to reproduce this scaling in JETTO-EIRENE. However, when the atoms were set to cross the separatrix at the X-point (more consistent with EDGE2D-EIRENE simulations of JET H-modes), the density width at the OMP was found to be much more sensitive to the pedestal height (approximately proportional to 1/ne,ped2). This is attributed to a radial variation in the poloidal flux expansion from OMP to X-point, over the range of ionisation mean free path lengths explored in the scan. Accounting for this variation allowed the expected scaling at the OMP to be recovered. Implications are discussed for experimental comparisons to the NPM and its application to pedestal prediction models.

Monte Carlo simulation of proton- and neutron-induced radiation damage in a tantalum target irradiated by 70 MeV protons

Beams of free neutrons are an important probe to analyze the structure and dynamics of condensed matter and are produced at neutron research reactors, neutron spallation sources or compact accelerator-based neutron sources (CANS). An efficient construction of CANS with a maximized neutron yield and brilliance requires reliable knowledge of the consequences of radiation-induced material damage, the predominating bottleneck of a target’s lifetime. In the framework of the Jülich High-Brilliance neutron Source project, the impact of proton- and neutron-induced material damage of a tantalum target was investigated. The Monte Carlo codes FLUKA and SRIM were utilized to extract the number of displacements per atom resulting from atomic rearrangements. The simulations performed distinctly identify the rear of the neutron target as the most vulnerable area, with the protons as main damage contributors. The minor contribution of neutrons is a material-specific phenomenon due to their high mean free path length in tantalum. Numerical results of the simulations served to calculate average and peak damage rates {R}_{mathrm{d}} (dpa/s), both in turn scaled to annual displacement doses for continuous operation in a full power year (dpa/fpy). Supplemented by the literature, a minimum target lifetime tau _{min } of 2.6 years (33 Ah) is concluded.

Mean Free Path of Photoelectronic Excitations in Hydrogenated Amorphous Silicon and Silicon Germanium Alloy Semiconductors

Hydrogenated amorphous silicon germanium alloy (a‐Si1−x Ge x :H) films are prepared by plasma enhanced chemical vapor deposition (PECVD) and characterized by in situ real time spectroscopic ellipsometry (RTSE). From complex dielectric function spectra extracted, the broadening width energy (Γ) of the primary absorption feature centered near 3.7 eV is quantified using the Cody–Lorentz oscillator model. Mean free path length of photoelectronic excitations is calculated from Γ based on reasonable estimates for speed of electron–hole photoexcitations. A model is applied with excited state lifetime assumed to be limited by scattering from network disorder and provides a relative measure of short‐range order. The simple model applied is an extension of that widely used to characterize broadening of optical transitions in polycrystalline semiconductors. Decreases in mean free path of up to ∼30% occur with germanium. Relative increases in mean free path with increased hydrogen during PECVD a‐Si:H, a‐Si0.73Ge0.27:H, and a‐Si0.60Ge0.40:H occur from ∼5% to ∼8% and with hydrogen plasma treatment of a‐Si:H by ∼6%. Mean free path changes are tracked with thickness to provide short range order evolution and the effect of the underlying material. Mean free path of photoexcitations in electronic quality a‐Si1−x Ge x :H is estimated at ∼3.5 Å, on the same order as interatomic spacing.