Normal Reflection Research Articles

Pathwise Differentiability for SDEs in a Smooth Domain with Reflection

In this paper we study a Skorohod SDE in a smooth domain with normal reflection at the boundary, in particular we prove that the solution is pathwise differentiable with respect to the deterministic starting point. The resulting derivatives evolve according to an ordinary differential equation, when the process is in the interior of the domain, and they are projected to the tangent space, when the process hits the boundary.

Ultrasound interferometry for the evaluation of thickness and adhesion of thin layers

A simulation work has been carried out to characterise thin layers by a technique called ultrasound interferometry, which is based on the resonance and anti-resonance of ultrasound waves verified in the presence of some interfaces having different acoustical impedances. Normal incidence ultrasonic reflection measurements have been considered. The reflection coefficients were calculated against frequency, velocity and thickness. A graphical user interface (GUI), developed in Matlab environment was used to simulate the calculation of several coating thicknesses (velocities) over different substrates, like iron and aluminium. The results are based on the representation of reflection or transmission coefficients against frequency, thickness and velocity in the coatings. The developed GUI is a very important tool to predict the behaviour of thin layers embedded between two thicker media, like mechanical properties providing the calculation of its thickness and ultrasonic velocity, in fast and easy way.

Wideband energy reflectance findings in presence of normal tympanogram in children with Down's syndrome

Objectives The prevalence of middle ear disorders in children with Down syndrome is higher than normal children due to the associated craniofacial abnormalities. The goal of this study is to evaluate middle ear function using wideband energy reflectance at ambient pressure in 14 young children with Down syndrome and matched control group (2½–5 years old; N = 19 ears per group) who each have a normal 226 Hz tympanogram. Methods All children underwent otoscopic examination, hearing screening using play audiometry (500–4000 Hz), and middle ear testing using 226 Hz tympanometry and wideband energy reflectance. The chirp signals for the wideband energy reflectance were presented to the child's ear at 65 dB SPL stimulus level and the recording was done over 220–8000 Hz range. The measured energy reflectance represents the ratio of the sound energy reflected from the tympanic membrane to the incident sound energy transmitted to the middle ear at a specific frequency. Paired Samples t-test was computed for the mean, 95th, 75th, 25th, and 5th percentile data of each frequency of the two groups. Results Despite the presence of normal tympanometric findings in both groups, results revealed abnormal wideband energy reflectance findings in 63% of the children with Down syndrome compared to the normal wideband energy reflectance findings in the control group. The mean energy reflectance ratio of the Down syndrome group was abnormally lower than that of the control at 5700–8000 Hz ( p < 0.0005). The 5th and 95th percentile ratios of the Down syndrome group fell outside the 5th and 95th percentile of the control group ( p < 0.0005). Conclusions Abnormally low energy reflectance ratios above 4000 Hz in the presence of normal tympanograms in the Down syndrome group may suggest associated congenital middle ear anomalies in children with DS. The present findings suggest that wideband energy reflectance has the potential to be of more practical value in children with DS than tympanometry. Further research with a larger number of Down syndrome children will illuminate the potential of wideband energy reflectance in diagnosing middle ear disorders in children with Down syndrome.

Quasiparticle current in ballistic F/ScN junctions

The current-voltage (I-V) characteristics of ballistic F/ScN junctions, consisting of a hybrid F/S bilayer of ferromagnetic (F) and superconducting (S) metals and a normal (N) metal, are studied. It is assumed that the size of the constriction, c, is much smaller than the electron mean free path and the superconducting coherence length, and that the transparency is rather high. The amplitudes of Andreev and normal reflection of electrons with specified spin orientations from the constriction are calculated. It is shown that the exchange field (hex) induced in the S metal causes spin splitting of the features of the differential conductivity of the junction. Measurements of the spin splitting of the junction conductivity, which is proportional to hex, can be used to study the induced magnetism of superconductors in hybrid S/F structures with the aid of the measured I-V characteristics of F/ScN junctions.

A New Spectrophotometer System for Measuring Hemispherical Reflectance and Normal Emittance of Real Surfaces Simultaneously

A new spectrophotometer system is developed for the study of thermal radiation characteristics of real surfaces in thermal engineering environments. The system measures spectra of normal incidence hemispherical reflectance RNH and normal emittance \({\varepsilon _{\rm N}}\) in the near-ultraviolet through infrared region of wavelength of 0.30 μm to 11 μm simultaneously and repeatedly with a cycle time of 4 s. The system enables evaluation of the normal incidence absorptance AN in this wide spectral region. Transitions of spectra of specular-finished and rough-finished nickel surfaces in a high-temperature air-oxidation process are measured to demonstrate the performance of the system. Clear interference behaviors are found even in the spectra of hemispherical reflectance RNH and emittance \({\varepsilon _{\rm N}}\) of a rough-finished surface.

Optical property and thermal stability of Mo/Mo–SiO2/SiO2 solar‐selective coating prepared by magnetron sputtering

AbstractMo/Mo–SiO2/SiO2 solar‐selective coating for high‐temperature solar thermal application is prepared on quartz glass by direct‐current (DC) and radio‐frequency (RF) co‐sputtering. The normal solar absorptance αn = 0.95 and thermal emittance εn = 0.097 (353 K) are obtained through process optimization. The normal reflectance Rn(λ) before and after 1073 K vacuum annealing, are measured by ultraviolet–visible–infrared (UV–VIS–IR) and Fourier transform infrared (FT‐IR) spectroscopy. There is only a slight increase in Rn(λ) in IR region after annealing, which results in a lower εn = 0.075 (353 K). The crystallized grain of Mo in the coating, obtained from XRD pattern, increased from 23 to 60 nm after vacuum annealing. These phenomena are mainly caused by the change of crystal state and reflectance of Mo IR layer according to the comparison of Rn(λ) and XRD patterns of Mo/SiO2 and Mo–SiO2/SiO2 tandem films.magnified image The near‐normal reflectance of Mo/Mo–SiO2/SiO2 solar‐selective coating before and after 1073 K vacuum annealing.

Resonant tunneling through superconducting double barrier structures in graphene

We study resonant tunneling through a superconducting double barrier structure in graphene as a function of the system parameters. At each barrier, due to the proximity effect, an incident electron can either reflect as an electron or a hole (specular as well as retro Andreev reflection in graphene). Similarly, transport across the barriers can occur via electrons as well as via the crossed (specular and/or retro) Andreev channel, where a hole is transmitted nonlocally to the other lead. In this geometry, in the subgap regime, we find resonant suppression of Andreev reflection at certain energies, due to the formation of Andreev bound levels between the two superconducting barriers, where the transmission probability T for electrons incident on the double barrier structure becomes unity. The evolution of the transport through the superconducting double barrier geometry as a function of the incident energy for various angles of incidence shows the damping of the resonance as normal reflection between the barriers increases.

Signatures of d-wave symmetry on thermal Dirac fermions in graphene-based F|I|d junctions

We study theoretically behavior of thermal massless Dirac fermions inside graphene-based Ferromagnetic |Insulator| d-wave/s-wave superconductor (F|I|d and F|I|S) junctions in the ballistic regime. We employ Dirac–Bogoliubov–de Genne formalism and use Dirac–BdG wave functions within the ferromagnetic, normal, and superconducting regions and appropriate boundary conditions, to derive Andreev and normal reflection coefficients. By employing the obtained Andreev and normal reflection coefficients, thin barrier approximation and also appropriate values of parameters, we investigate characteristics of heat current through the F|I|d and F|I|S junctions. We find that for s-wave superconductors, thermal conductance (Γ) oscillates sinusoidally versus strength of barrier in the thin barrier approximation. The finding persists for all values of α, orientation of d-wave superconductor crystal in the k-space, for values of α very close to π/4, magnitude of the oscillations suppress completely. By increasing temperature, the thermal conductance increases exponentially for small values of α and for larger values of superconductor crystal orientation angle the thermal conductance modifies and interestingly for α=π/4 exhibits linear behavior, i.e., Γ∝T which is similar to Wiedemann–Franz law for metals in low temperatures. While increasing the temperature move minimum value of the thermal conductance with respect to strength of magnetization texture h/Δ0 towards smaller values of h/Δ0, increasing the superconductor crystal orientation angle, α from 0 to π/4 enhances whole values of the thermal conductance and consequently the minimum value move towards up. At last we suggest an experimental setup for verifying these findings.

Tunneling conductance in a gapped graphene-based normal metal–insulator–d-wave superconductor junction: Case of massive Dirac electrons

Using the extended Blonder–Tinkham–Klapwijk formalism, the normal conductance spectra in a normal/insulator/d-wave superconductor gapped graphene junction, considering effect of asymmetric pairing potential (anisotropic d-wave) is investigated in the limit of a thin barrier. The charged Dirac carriers in this structure are treated as massive relativistic particles. The exact solutions of Dirac–Bogoliubov–de Gennes Hamiltonain for three normal gapped graphene, insulator and superconductor region of junction and related normal and Andreev reflection coefficients are obtained. In this work, we focus to study in detail the effect of rotated angle α caused by d-wave order parameter of superconductor in tunneling conductance behavior in our system. In particular, the conductance spectra in terms of the bias voltage eV, the d-wave superconducting orientation angular α and also the electrostatic potentials U 0 and V 0 is plotted. It is shown that by increasing rotated angle α in that case of U 0 → ∞ and mv 2 F / E F =0.99, the maximum of resonant peak of normal conductance decreases and also the position of peak shifts from eV / Δ = 1 to progressively lower values. We also observe an oscillatory behavior of conductance versus insulator potential V 0.

Structural, electronic, and optical properties of ITO thin films prepared at room temperature by pulsed laser deposition

In this work, indium tin oxide (ITO) thin films have been prepared by pulsed laser deposition (PLD) on quartz and silicon substrates at room temperature, starting from an ITO target with a Sn/In concentration ratio of 0.18. Structural, optical, and electronic properties of these films have been analyzed by means of X-ray photoemission and optical spectroscopy. By the analysis of the X-ray photoemission spectroscopy spectra in the In 3d5/2, Sn 3d5/2, and O 1s binding energy regions, carried out both for films and target, evidence of structural changes after the ablation process was found. It was deduced that the deposited films have an Sn/In ratio equal to 0.10, and are characterized by a predominantly amorphous structure. The optical properties in the visible and the near ultraviolet regions have been deduced by near normal incidence optical reflectivity and absorption measurements. A value of 3.7 eV for the optical band gap and an average refraction index of about 3.0 in the visible photon energy range have been obtained, in agreement with the results of other authors.

Tunneling conductance in gapped graphene-based normal metal–insulator–superconductor junctions: Case of massive Dirac electrons

We study the quantum transport property in a gapped graphene-based normal metal–insulator–superconductor junctions ( NG/ IG/ SG), in the limit of a thin barrier. The charged fermions in NG/ IG/ SG structure are treated as massive relativistic particles. Based on Andreev and normal reflections in normal-superconductor graphene-based junction and BTK formalism, the tunneling conductance’s in terms of some different electrostatic superconductor, U 0 and barrier, V 0 potential are obtained. Using the experimental based values of the Fermi energy in the NG and SG ( E FN and E FN + U 0, respectively), energy gap in graphene 2 mv F 2 and superconducting order parameter, Δ, it is shown that the conductance spectra of such system represent a new behavior, i.e. if we take | E FN - mv F 2 | → 0 , it becomes as a step function of V 0. This behavior of charge transportation can be considered as a nano switch.

Multi-gap superconductivity in a BaFe1.84Co0.16As2 film from optical measurements at terahertz frequencies

We measured the THz reflectance properties of a high quality epitaxial thin film of the Fe-based superconductor BaFe$_{1.84}$Co$_{0.16}$As$_2$ with T$_c$=22.5 K. The film was grown by pulsed laser deposition on a DyScO$_3$ substrate with an epitaxial SrTiO$_3$ intermediate layer. The measured $R_S/R_N$ spectrum, i.e. the reflectivity ratio between the superconducting and normal state reflectance, provides clear evidence of a superconducting gap $\Delta_A$ close to 15 cm$^{-1}$. A detailed data analysis shows that a two-band, two-gap model is absolutely necessary to obtain a good description of the measured $R_S/R_N$ spectrum. The low-energy $\Delta_A$ gap results to be well determined ($\Delta_A$=15.5$\pm$0.5 cm$^{-1}$), while the value of the high-energy gap $\Delta_B$ is more uncertain ($\Delta_B$=55$\pm$7 cm$^{-1}$). Our results provide evidence of a nodeless isotropic double-gap scenario, with the presence of two optical gaps corresponding to 2$\Delta/kT_c$ values close to 2 and 7.

Geophysical model of the lithosphere across the Variscan Belt of SW-Iberia: Multidisciplinary assessment

A multidisciplinary geophysical study along a large seismic transect in the SW-Iberian Peninsula has been carried out. This study integrates the crustal structure, geometry and composition obtained from normal incidence and wide-angle seismic reflection data with other observables (geoid, gravity and topography). The internal architecture of the lithosphere across the Variscan Orogen of SW-Iberia is constrained by the 300 km long high resolution deep normal seismic reflection IBERSEIS Transect. The most prominent feature imaged by the seismic survey is the Iberseis Reflective Body (IRB), a 140 km long high amplitude reflective body located in the middle crust of the northern half of the transect. The seismic velocity (Vp) distribution within the crust and the upper mantle is constrained by two wide-angle seismic transects acquired in the same area. The velocity models show a complex crust, with a specially complex middle crust, which features higher velocities than the average continental crust. Also the wide-angle data revealed that the IRB is characterized by high velocities. This feature was then interpreted as sill-like structure built up by a series of mafic intrusions. Therefore, a key issue is to study if this relatively mafic crust is consistent with other geophysical observables. Based on the velocity models, two lithospheric density models have been derived along the IBERSEIS wide-angle transects. The geoid, gravity and topography response of these models have been calculated using a finite elements code that solves, simultaneously, the geopotential, lithostatic, and heat flow equations. The resulting values are then compared with the measured observables and the crustal and lithospheric mantle geometry and density is modified until the best fit is obtained. The initial density models calculated from the seismic data adjust quite well to the real potential field data. However, minor modifications have been required in order to properly fit the observables. The final density models are consistent with the existence of relatively high density bodies in the mid-crust providing further support to the seismic interpretation. In addition, they place new constraints on the location of the lithosphere–asthenosphere boundary and on the tectonic evolution of SW-Iberia.

Spin-polarized conductance in graphene-based FSF junctions

In this paper, conductance of spin and electron in graphene-based ferromagnet—superconductor (FS) and parallel and antiparallel ferromagnet–superconductor–ferromagnet (FSF) junctions are studied. Using the Dirac–Bogoliubov–de Gennes equations, Andreev and normal reflections are obtained and then using these coefficients, conductance of spin and electrons are calculated at the FS interface(s) analytically. As a result, both the energy dependence of spin and charge differential conductances are investigated and a comparison between electron and spin transport is done in this paper. Effect of exchange energy of ferromagnet h on conductances is studied too.

Moveout approximation for horizontal transversely isotropic and vertical transversely isotropic layered medium. Part I: 1D ray propagation‡

ABSTRACTAnisotropy in subsurface geological models is primarily caused by two factors: sedimentation in shale/sand layers and fractures. The sedimentation factor is mainly modelled by vertical transverse isotropy (VTI), whereas the fractures are modelled by a horizontal transversely isotropic medium (HTI). In this paper we study hyperbolic and non‐hyperbolic normal reflection moveout for a package of HTI/VTI layers, considering arbitrary azimuthal orientation of the symmetry axis at each HTI layer. We consider a local 1D medium, whose properties change vertically, with flat interfaces between the layers. In this case, the horizontal slowness is preserved; thus, the azimuth of the phase velocity is the same for all layers of the package. In general, however, the azimuth of the ray velocity differs from the azimuth of the phase velocity. The ray azimuth depends on the layer properties and may be different for each layer. In this case, the use of the Dix equation requires projection of the moveout velocity of each layer on the phase plane. We derive an accurate equation for hyperbolic and high‐order terms of the normal moveout, relating the traveltime to the surface offset, or alternatively, to the subsurface reflection angle. We relate the azimuth of the surface offset to its magnitude (or to the reflection angle), considering short and long offsets. We compare the derived approximations with analytical ray tracing.

Wave classification and resonant excitations in lossy metal–dielectric multilayers

Loss-induced optical Bloch waves are investigated in a metal–dielectric semi-infinite multilayer placed over a substrate. In addition to the well-known classification of the electromagnetic waves into forward and backward waves, the electrostatics-based sub-classification elucidates one-level finer details of the wave nature. For this purpose, a hypothetical process is devised by continuously varying the signal velocity. As a result, a given electromagnetic wave turns out to be related to a certain electrostatic state. By this way, the metal's material loss is found to play an essential role in inducing depthwise energy flows, although it has the usual detrimental role in wave attenuation. Depending on the wave direction, normal and inverted reflection peaks on resonant excitations are illustrated.

Characterization of a lossy elastic plate thanks to the relationships between its reflection and transmission coefficients.

The normal reflection and transmission coefficients of a lossy elastic plate are measured and associated according to the outcomes of resonance scattering theory (RST) and S-matrix theory (SMT). The sum and the difference of those coefficients provide valuable tools, the transition terms, we use to characterize the plate. The absorption in the plate can be expressed via different manners recalled in the following. By means of a dimensionless loss factor, the velocities of the longitudinal and transverse waves of the studied aluminum plate are no more real but complex. The width of a resonance is the sum of two parts: the elastic width and the absorption one. In the vicinity of a resonance frequency, the transition terms obey the Breit–Wigner resonant form which makes it possible an easy determination of the two parts of the resonant width. There is a good experiment/theory agreement when an imaginary part is added to the Lamé coefficients of the aluminum plate. The loss factor is of the order 5.10–4. On the whole, the effect of the attenuation rises with frequency and reaches a maximal importance at the vicinity of a resonance frequency.

Spectroscopic study of nanocrystalline V 2O 5·nH 2O films doped with Li ions

Optical properties of nanocrystalline, Li x V 2O 5· nH 2O films (0< x<22 mol%), are explored in the present work. These films have been produced by the sol–gel technique (colloidal route), which was used for the preparation of high purity and homogeneity films. Optical measurements were carried out using a double-beam spectrophotometer. The optical constants such as refractive index n, the extinction coefficient k, absorption coefficient α, and optical band gap of the films material have been evaluated. The optical absorption coefficient was calculated from the measured normal reflectance, R, and transmittance, T, spectra. The optical spectra of all samples exhibited two distinct regions: at high energy, which suggests a direct forbidden transition with optical gap ranging from 1.75 to 2.0 eV and increases with increase in Li-content. On the other hand a second low-energy band suggests a direct allowed transition with optical gap ranging from 0.40 to 0.42 eV. The width of the localized states (band tail) E e was also estimated for all samples. Additional calculations applying the real part of the optical dielectric function led to the evaluation of the charge carrier concentration and their effective mass.

On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints

Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and positivity constraints. We obtain sufficient conditions for existence and uniqueness of stationary distributions for such equations. The results are applied to an example from Internet rate control and a simple biochemical reaction system.

熱ふく射に関するKirchhoffの法則の実験的検証(熱工学,内燃機関,動力など)

This paper discusses the Kirchhoff's law on thermal radiation. The logic of derivation of the law is reconsidered, first. Then, spectra of normal emittance ε_N and normal incidence hemispherical reflectance R_<NH> are measured on surfaces whose microstructure changes in a non-equilibrium experimental system to examine the validity of the complementary relation between ε_N and R_<NH>, which is the suggestion of the Kirchhoff's law. As the results of the examination, it is illustrated experimentally on a variety of surfaces that the complementary relation is valid within an experimental uncertainty. Provided this conclusion is admitted, the followings are suggested. If a surface is designed so that it does not reflect a narrow spectral region of radiation to any direction and reflects the other spectral regions of radiation much over the hemisphere, then the surface can be a new spectrally-functional emitter of radiation. It is also suggested that thermal radiation emitted at a surface is considered as the emission of plane waves at the surface rather than as the emission of spherical waves by electric dipoles.