Electromagnetic Field Excitation Research Articles

The mutual influence of exciting and induced currents in the circular solenoid – massive conductor system

Problem. The flow of currents in the conductive elements of electrical systems is accompanied by the excitation of electromagnetic fields and the occurrence of induced currents. The excitation of the induced signals, in turn, leads to a change in the parameters of the actual exciting currents. The purpose of the work is to obtain analytical expressions for the quantitative analysis of the results of the mutual influence of the exciting and induced currents and to calculate their ratio depending on the geometric characteristics of the inductor systems. Methodology. The analysis of the processes of mutual influence is carried out on the example of a widespread inductor system, where a flat circular solenoid is placed above the surface of a massive conductor. Analytical expressions for eddy currents excited in a massive conductor and numerical estimates of the effect of induced currents on exciting currents in a solenoid are obtained. Results. It is shown that the influence of the induced current on the current in the solenoid is very significant at small distances between the solenoid and the surface of the massive solenoid. It has been found that an increase in the width of the solenoid winding leads to a significant increase in the influence of the induced current on the excitation current in the solenoid. It is shown that the inductance of the «circular solenoid - massive conductor» system drops with a decrease in the distance between the solenoid and the massive conductor and an increase in the radial dimensions of the solenoid, which requires an increase in the amplitude of the exciting current to maintain a given value of the magnetic flux in the system. Originality. The scientific novelty of this work lies in the proposal of an analytical approach and obtaining numerical estimates of the mutual influence of conductors with exciting and induced currents. Practical value. Estimates of the mutual influence of conductors with currents are of interest for the practice of designing structures of electrical systems for various purposes. Very promising in the direction further research is seen as carrying out experiments with measurements of the quantitative characteristics of the mutual influence of exciting and induced currents in various designs of electrical systems.

Development of a cryogenic passive-scattering-type near-field optical microscopy system.

Passive scattering-type, scanning near-field optical microscopy (s-SNOM) has been employed to study localized, long-wavelength infrared (LWIR) surface waves without external illumination. Here, we develop a cryogenic passive s-SNOM instrument in a vacuum chamber with 4K liquid-helium cooling. Notably, the extremely low-temperature environment inside the chamber enables the realization of passive near-field detection with low background thermal noise. The technique mainly utilizes a highly sensitive LWIR confocal optical system and a tuning fork-based atomic force microscope, and the near-field detection was performed at a wavelength of 10.2 ± 0.9 µm. In this paper, we discuss the cryogenic s-SNOM implementation in detail and report the investigation of thermally excited surface electromagnetic fields on a self-heated NiCr wire deposited on SiO2 at a temperature of 5K. The origin of the surface electromagnetic fields was established to be the thermally excited fluctuating charges of the conduction electrons. The cryogenic s-SNOM method presented herein shows significant promise for application in a variety of spheres, including hot-carrier dissipation in ballistic conductors.

Electromagnetic field excitation during the scattering of an acoustic wave on an inhomogeneity in a poroelastic medium

Elastic wave propagation in porous media containing a movable fluid is frequently accompanied by electromagnetic field generation. Such field can be produced, for instance, by piezoelectric effect or have electrokinetic origin. In the present work, we consider the case of electrolyte-filled pores; thus, the generated electromagnetic field is associated with the electrokinetic effects. In this case, the magnitude of the electric current generated by the elastic wave is proportional to the magnitude of the relative displacement in the fluid and the solid phases. The presence of inhomogeneities in a porous medium can result in appearance of additional fluid flow with respect to the solid phase; thus, an additional electric field is generated. In our work, the magnitude of the electromagnetic field generated during the scattering of an elastic wave on a spherical porous inclusion in a porous matrix is calculated. The inclusion can differ from the matrix by the properties of the fluid in the pores or the properties of the elastic skeleton, such as porosity or permeability. The solution of the dynamic equations of electrokinetics is obtained by using the hypothesis that the inclusion size is much larger than the characteristic size of the pores. We have obtained the dependencies of the amplitude of the generated electromagnetic field on the inclusion parameters and the incident wave frequency. It was shown that the analysis of the additional electromagnetic field generated during the scattering of the elastic wave can provide some useful information about the structure of porous media.

Pulsed Electromagnetic Sounding of the Bazhenov Formation: High-Performance Computing to Justify a New Geophysical Technology

Abstract —The work is devoted to the theoretical substantiation of a new geophysical technology for studying a unique geological object with unconventional hard-to-recover hydrocarbon reserves. The technology is based on transient electromagnetic sounding from a spatially distributed system of highly deviated wells drilled in target objects near the Bazhenov Formation. The results of computer modeling predetermine a new direction for geological exploration of unconventional hydrocarbon deposits. We consider a numerical solution to the 3D direct problem of pulsed electromagnetic sounding and, on its basis, develop a computational scheme and computer program. A mathematical model is built that describes the sensing process through a pulsed source for electromagnetic field excitation. The Fourier transform is used for time discretization, and the vector finite element method for spatial discretization. This approach makes it possible to obtain many independent 3D problems and effectively solve them in parallel by applying the modern multiprocessor technology. Using the KNL and Broadwell computing nodes of the Siberian Supercomputer Center SB RAS, we performed calculations of electromagnetic signals, which showed a high efficiency of the devised computing scheme and a high performance of the implemented algorithm. Despite the fact that the total peak performance of the KNL nodes is 2.5 times higher than that of the Broadwell nodes, their practical application for performing large-scale 3D modeling on the cluster shows a high efficiency of the latter. When choosing the most suitable computing architecture for the implementation of mass calculations, one should not rely on their formal characteristics only; significant performance is achieved taking into account the peculiarities of the computational methods employed for solving a specific problem. The implemented more efficient ways of performing parallel matrix-vector operations did not significantly increase the performance for this computational scheme. The created computational tools form the basis for further design of the configuration of a pulsed electromagnetic sounding system, and for identifying the capabilities of the new geophysical technology for examining complex geological media.

Graphene Nanopore Arrays for Electron Focusing and Antifocusing

We have shown, via numerical simulations, that a symmetric array of nanopores with appropriately designed shapes and sizes arranged along an arc of a circle in a graphene nanoribbon can focus or antifocus an incident ballistic electron wavefunction. The position of the focal/antifocal region depends on the electron energy. This effect, which takes place in the energy interval of one-transverse-mode propagation in the nanoribbon, highlights the similarities with plasmonic focusing by an array of holes in a metallic sheet, while emphasizing the differences between the propagation and excitation of electrons and electromagnetic fields. In particular, the electronic antilens has no counterpart in classical optics.

Infrared Light-Emitting Devices from Antenna-Coupled Luttinger Liquid Plasmons In Carbon Nanotubes.

Electrically driven light-emitting devices provide highly energy-efficient lighting at visible wavelengths, and they have transformed photonic and electronic lighting applications. Efficient infrared light-emitting devices, however, have been challenging because band gap emission from semiconductors becomes inefficient in the mid-infrared to far-infrared spectral range. Here we investigate infrared light-emitting devices (IRLEDs) based on Luttinger liquid (LL) plasmons in one-dimensional (1D) metallic carbon nanotubes. Elementary excitations in LL are characterized by collective charge and spin excitations, i.e., plasmons and spinons. Consequently, electrons injected into the nanotubes transform efficiently into LL plasmons, a hybrid excitation of electromagnetic fields and electrons. We design nanoantennas coupled to the carbon nanotube to radiate LL plasmons into the far field. LL-based IRLEDs can be designed to selectively emit at wavelengths across the far- and mid-infrared spectra. An electrical-to-optical power conversion efficiency up to 3.2% may be achieved. Such efficient and narrowband LL-based IRLEDs can enable novel infrared nanophotonic applications.

Generation of double-frequency radiation in monotron with three-gap cavity

Purpose of this work is to study modes and conditions that make it possible to excite the highest type of microwave oscillations, the frequency of which is a multiple of the frequency of the main type, in a monotron with a three-band resonator. Method of the investigation is a numerical 3D modeling, used to calculate the dimensions and electrodynamic parameters of the resonator (characteristic impedance, coupling coefficient, relative electronic conductivity); operation modes of the monotron are considered, which are characterized by excitation of oscillations in the highest type oscillations. Result. In the resonator under consideration, it is possible to achieve a multiple (equal to three) ratio between the frequency of the 25th highest type of oscillations and the frequency of the π/2-type. It was shown that in such resonator simultaneous excitation of electromagnetic field on those frequencies can be made. The maximum of an output power achieved at 100.22 GHz is 15.4 W with an accelerating voltage of 7825 V and an electronic beam microperveance 0.36 µA/V3/2 . The maximal efficiency on a third harmonic is 0.83% while the total efficiency (generating electromagnetic waves of the first and the third harmonics) is up to 17%. Conclusion. It was set that the described method of generation of terahertz range radiation is promising for further investigation, as it solves problem that orthodox microwave devices meet in the millimeter wavelength range, such as small linear dimensions of the components and critical current density of the electronic beam.

Origin of Terahertz Soft-Mode Nonlinearities in Ferroelectric Perovskites

Soft modes are intimately linked to structural instabilities and are key for the understanding of phase transitions. The soft modes in ferroelectrics, for example, map directly the polar order parameter of a crystal lattice. Driving these modes into the nonlinear, frequency-changing regime with intense terahertz (THz) light fields is an efficient way to alter the lattice and, with it, the physical properties. However, recent studies show that the THz electric-field amplitudes triggering a nonlinear soft-mode response are surprisingly low, which raises the question on the microscopic picture behind the origin of this nonlinear response. Here, we use linear and two-dimensional terahertz (2D THz) spectroscopy to unravel the origin of the soft-mode nonlinearities in a strain-engineered epitaxial ferroelectric SrTiO3 thin film. We find that the linear dielectric function of this mode is quantitatively incompatible with pure ionic or pure electronic motions. Instead, 2D THz spectroscopy reveals a pronounced coupling of electronic and ionic-displacement dipoles. Hence, the soft mode is a hybrid mode of lattice (ionic) motions and electronic interband transitions. We confirm this conclusion with model calculations based on a simplified pseudopotential concept of the electronic band structure. It reveals that the entire THz nonlinearity is caused by the off-resonant nonlinear response of the electronic interband transitions of the lattice-electronic hybrid mode. With this work, we provide fundamental insights into the microscopic processes that govern the softness that any material assumes near a ferroic phase transition. This knowledge will allow us to gain an efficient all-optical control over the associated large nonlinear effects.Received 14 September 2020Revised 20 January 2021Accepted 12 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.021023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDielectric propertiesElectric polarizationElectronic excitation & ionizationElectronic transitionsFerroelectricityLight-matter interactionNonlinear opticsPhononsStrong electromagnetic field effectsUltrafast phenomenaTechniquesTerahertz time-domain spectroscopyUltrafast pump-probe spectroscopyCondensed Matter, Materials & Applied PhysicsNonlinear DynamicsAtomic, Molecular & Optical

Quasi-Stationary Approximation in the Problem of Excitation of Low-Frequency Electromagnetic Fields in Lithosphere

Excitation of electromagnetic field at ultralow, extremely low, and lower frequencies by a horizontal grounded antenna in a two-layer medium is considered. Approximate analytical formulas are derived to describe field evolution in the low-frequency range. Accuracy of the quasi-stationary approximation is analyzed. Substitution of the impedance of a plane wave that is normally incident on the interface for a real surface impedance is estimated. Frequency limits of the approximate approach in the estimation of the Earth conductivity are determined for several experiments performed on the Kola Peninsula in the framework of the FENIСS-2014 and FENICS-2019 International Projects.

Synthesis of a Scalar Automatic Control System of a Valve Engine with Field Control for a Rowing Electric Installation with an Azipod Propulsion and Steering System

The article deals with the main trends in the development of marine automatic AC electric drive systems. A variant of the implementation of an electric drive using an electromechanical converter of a synchronous machine with electromagnetic field excitation is presented. A promising electric drive system with a valve engine for the icebreaker's with the Azipod propulsion and steering system is proposed. The aim of the work is to eliminate the structural complexity and expand the functional capabilities of the electric drive by using a scalar automatic control system of the frequency of rotation in the two-zone control of the valve motor of the EPS. The novelty lies in the use of the approach and representation of the control object-a valve motor as an analog of a DC collector motor controlled by an armature and by a field. The analysis of control processes is directly related to the processes of electromechanical energy conversion occurring in a synchronous machine.

Features of Electromagnetic Field Excitation in a Capacitive HF Discharge. II. Symmetric Discharge Completely Filling Vacuum Chamber under Symmetric and Asymmetric Excitation

Electrodynamic characteristics of a low pressure (electron collision frequency much lower than the field frequency) capacitive high frequency (HF) discharge maintained by electromagnetic field with a frequency between 10 and 1000 MHz are studied analytically and numerically. The discharge is assumed to fill completely a cylindrical metallic discharge chamber that contains a large area active electrode and a substrate holder connected to HF generators. The discharge is sustained by surface waves propagating along the plasma–space-charge sheath–metal interface. General analytical expressions governing impedance of the discharge are derived treating it as a two-point network. It is demonstrated that excitation of higher-order field modes substantially modifies position of current and voltage resonances related to propagation of surface waves along the three-layer structure as functions of electron density. Regimes of field excitation by symmetric and antisymmetric fields are analyzed within the framework of the matrix sheath model. Contribution of sheath formed near the sidewall of the vacuum chamber to the impedance must be taken into account in the case of excitation by an antisymmetric field. Obtained results qualitatively agree with numerical calculation of the impedance and field space distribution in the discharge carried out by using the COMSOL Multiphysics® software package.

Nanoscale probing of thermally excited evanescent fields in an electrically biased graphene by near-field optical microscopy

This paper demonstrates nanoscale infrared thermal imaging in electrically biased bilayer graphene (BLG) by using a scattering-type scanning near-field optical microscope (s-SNOM). s-SNOM provides a noncontact technique to detect the thermally excited electromagnetic evanescent fields (∼21 THz) generated on the surface of a Joule-heated BLG. With increasing bias current, a strong near-field signal appears mainly in the sub-micrometer-sized constricted region. The temperature mapping of the graphene film can be derived from the infrared near-field signals, and shows good agreement with the finite-element simulation. Hence, we prove that s-SNOM is a potential infrared nano-thermography for the graphene device.

BBU instability in rectangular dielectric resonator

Studies were made into the arise and an evolution of the beam breakup (BBU) instability in a rectangular dielectric resonator under excitation by a sequence of relativistic electron bunches. The dielectric resonator is a section of a rectangular waveguide loaded by the two dielectric slabs (located along the wide side) and closed by the metal grids. A material of the slabs is teflon. A thickness of the slabs is 8.2 mm, a wide size and a length of the slabs are equal to the resonator wide size and length respectively. The metal grids are transparent for the charged particles and nontransparent for the excited electromagnetic fields. The wavelength of the LSM2,1,12 (Longitudinal Section Magnetic) operating mode is 53.2 mm. The electron energy of bunches is 4.5 MeV , the charge of each bunch is 6.4 nC, the bunch repetition period is equal to twice the wavelength of the LSM2,1,12 mode. By the use of numerical PIC simulations, the charge losses of electron bunches on the dielectric plates were investigated as the bunches were displaced relative to the cavity axis. It is found that the charge losses on the dielectric slabs due to the BBU instability do not exceed 5%. When the bunch repetition period is changed to a multiple of another eigenfrequency (e.g., the LSM1,1,12 mode), the charge losses of drive bunches do not change appreciably.

Wide-Band Electromagnetic Wave Propagation and Resonance in Long Cobalt Nanoprisms

Electromagnetic wave interaction with confined metallic magnetic structures is complex due to the excitation of nonuniform electromagnetic fields and magnetic precession and spin-wave modes over length scales that are dependent on the geometric, electromagnetic, and micromagnetic properties of the magnetic structures. Here, we solve the coupled system of Maxwell's equations and the Landau-Lifshitz-Gilbert equation using a stable algorithm based on the finite-difference time-domain method to study the transient wide-band electromagnetic propagation and resonance in infinitely long cobalt nanoprisms with a square cross section of side lengths 50--1000 nm. In particular, we identify the resonance mechanisms through studying the local transient and spectral distributions of magnetization in the prisms. The nanoprisms are excited by an axially polarized plane wave at normal incidence with a 70 GHz Gaussian pulse profile. For this incident wave condition, the simulations confirm that resonance in the cobalt prisms is excited mainly by the current-induced magnetic fields and indicate a magnetization curling resonance mode for prism side lengths less than 100 nm. The eigenfrequencies for the curling mode are confirmed theoretically using a model for an equivalent long circular cylinder with radial spin-wave modes. For prism side lengths longer than 100 nm (but less than the nonmagnetic skin depth), the magnetic response is confined to thin regions along the prism edges due to resonance-induced skin effects. The simulations indicate predominately uniform magnetization precession in the confined edge regions with increased pinning in the corners. The uniform resonance mode in the central part of the edge regions increases in intensity with prism size, with frequency described using Kittel's ferromagnetic resonance frequency of a thin planar structure. A higher-frequency size-independent uniform resonance mode is observed in the corner regions with frequency determined by the local demagnetizing factors. Local and integrated power absorption spectra are calculated using the simulated transient magnetization and fields, and confirm the resonance modes and frequencies in the cobalt prisms and their size dependence. The profile of the local power absorption spectra is also used to estimate the thickness of the confined edge regions or magnetic skin depth in the cobalt prisms at the fundamental resonance mode and is found to be approximately 50 nm. The outcomes of this work would benefit the design and engineering of lightweight and compact materials and devices incorporating metallic magnetic nanostructures. This work also provides a foundation for further modeling and understanding of electromagnetic transmission and propagation in more complex metallic ferromagnetic structures and composites excited by different electromagnetic wave conditions.

The controlled fabrication of upconverting hollow structures, enhanced effect on photoluminescence and applications

Lanthanide-doped upconverting photoluminescence nanomaterials which exhibit excellent photostability, long luminescent lifetimes, large anti-Stokes shifts and sharp-band emissions have attracted considerable attention in various research domains, including lasing, displays, anti-counterfeiting, biological systems. Hollow structures possess attractive physicochemical characteristics such as low density, high loading capacity. More importantly, they also possess multiple adjustable shells numbers, shell thickness and inter-shell spaces. Hollow structures can also generate multiple reflection and scattering of incident light by the adjustable inner structures, which is beneficial to the enhancement of light harvesting efficiency and modulation of electric field density. Therefore, it is of great importance to do intense research on developing lanthanide-doped photoluminescence hollow structures (LPHS). Hollow structures with various morphologies and compositions have been fabricated by many approach, such as hard-template method, soft-template strategy, self-template tactics and other techniques. However, the controllabl esynthesis of hollow structures remained a great challenge by using soft-template strategy, which impede the synthesis of hollow structures. With the good repeatability and generality, carbonaceous spheres hard-template method has been demonstrated a straightforward and versatile technique to prepare uniform LPHS. By using carbonaceous spheres hard-template method, the diversity of LPHS has been flourished in both geometrical morphology and composition. Benefiting from the enrichment of synthetic method, various LPHS have been prepared and employed in many domains. However, enhanced effect on photoluminescence remained indistinct, which impede the design of excellent LPHS. Herein, we focus on efforts on synthesis, enhanced effect on photoluminescence and application of LPHS. We first review efforts in geometrical and compositional manipulation based on carbonaceous spheres hard templates approach. After reviewing the compositional and geometrical manipulation, we consider that how hollow structures influence upconversion emission and review recent developments on modulating upconversion emission. Finally, we systematically discuss the typical examples to highlight applications in various areas, especially for imaging, drug delivery and therapy. Due to the preeminent characteristic, lanthanide-doped upconverting nanomaterials with hollow multi-shelled structures (LUHoMSs) demonstrate excellent upconversion emissions. Upconversion emission spectra states that with the increase of shell numbers, LUHoMSs show improved luminous intensities and tunable green/red ratio. This enhanced upconverting luminescence might be attributed to the enhanced NIR excitation light harvesting efficiency. Lanthanide-doped 1D upconverting microrod comprising isolated holes can modulate the upconverted emission intensity because of the intensified electric field density, which originated from NIR excitation light reflection and scattering by inner walls. As the understanding of light reflection and scattering and plasmonic effect on upconversion process has improved, hollow structures have been testified available for boosting upconversion emission. In the plasmonic system, emission enhancement of LUHoMSs indicates that it mainly derived from the combined effects of surface plasmon with excitation electromagnetic field. Considering the unique features of LUHoMSs, they are extremely suitable for applications in multimodal bioimaging, drug delivering and phototherapy. LUHoMSs with large drug loading can boost local drug concentrations and promote drug efficiency. LUHoMSs with high signal/noise ratio and excellent imaging function, which includes magnetic resonance imaging and X-ray computed tomography, can achieve precise diagnosis and benign therapeutic effect. By making use of the combination of phototherapy with drug release can achieve the enhancement of synergistic disease diagnosis and therapy. We believe that with in-depth understandings of enhanced effect on photoluminescence, hollow structures can play important role in guiding the fabrication of LPHS, light conversion and further improve the application performance.

Influence of Light Polarization on Photoswitching of Fulgimide Monolayers on Surfaces

The photoisomerization characteristic parameters [photostationary states (PSSs), cross section σ, and quantum yield η] of indolyl fulgimide compounds dispersed in solution are quantitatively compared to those of the same compounds covalently immobilized as a monolayer on functionalized Si(111) surfaces (see Adv. Mater. 2013, 25, 416). The photoisomerization kinetics of fulgimide compounds in solution is monitored using UV–vis spectroscopy and that of monolayers is monitored by in situ calibrated Fourier transform infrared spectroscopy. Although the isomeric composition at PSSs is very similar in solution and at surfaces, a strong influence of the incident light polarization is found on photoisomerization cross section σ (σs ≪ σp < σsol). Accounting for the local excitation electromagnetic field indicates that the fulgimide groups adopt a preferential tilt angle with respect to the surface normal and their transition dipole is almost parallel to the surface plane for either C or E/Z isomers. Density functi...

Effect of Ionosphere on the Excitation of Electromagnetic Field at Extremely Low and Lower Frequencies in the Near-Field Zone

Excitation of electromagnetic fields at extremely low and lower frequencies in the near-field zone of the Earth–ionosphere waveguide is considered. Variations in the field amplitude in the lower part of the extremely low frequency (ELF) range and lower frequencies are experimentally determined under different geophysical conditions in the absence of variations in the ultralow frequency (ULF) range. The effects related to such variations are analyzed with the aid of theoretical calculations that show significant effect of ionosphere in the near-field zone at relatively low terrestrial conduction.

Broadband Circuit Model for Wire-Interconnection Structures Based on a MoM-Eigenvalue Approach

A novel highly versatile broadband Foster-type circuit model for arbitrary wire networks with moderate radiation losses is presented in this paper. Based on a quasi-static method-of-moments-eigenvalue problem, a modal multiport circuit is derived with minimal computational effort, offering fast convergence and inherent stability for time-domain simulations with arbitrary active/passive nonlinear loads. The model order can be estimated rigorously from the given frequency range. Incident electromagnetic field excitation is considered by additional modal sources, which are calculated with minimal effort. The proposed model is validated in the frequency and time domain.

Assessment of the human exposure to transient and time-harmonic fields using the enhanced transmission line theory approach

ABSTRACTThe paper deals with the assessment of human exposure to the transient electromagnetic fields and high-frequency (HF) radiation. The formulation of the problem is based on a simplified cylindrical representation of the human body. The analysis is based on the enhanced transmission line (TL) theory. For this purpose, in order to quantify the induced current inside the human body, we solve linear system equations, where the electromagnetic field excitation is represented by two equivalent current and voltage generators. Once the axial current is determined, it is possible to calculate the specific absorption rate (SAR). Some illustrative computational examples are presented in the paper.

Microscopic Origin of Surface-Enhanced Circular Dichroism

Circular dichroism (CD), the difference in absorption of two opposite circularly polarized light sources by chiral molecules, can be significantly enhanced when molecules are adsorbed on the surface of nanostructures. We present a theory based on Poynting’s theorem adapted for chiral media to analyze the surface-enhanced CD of a chiral molecule/nanostructure coupled system. Our theory clarifies the microscopic origin of surface-enhanced CD signals by showing that the enhanced CD has two forms, inherent and induced. The inherent CD is the direct molecular CD that becomes enhanced due to the strongly localized optical helicity density near the nanostructure. The induced CD, previously ignored, derives from asymmetric excitation and absorption of electromagnetic fields inside the nanostructures surrounded by chiral molecules upon the injection of two oppositely circularly polarized light sources. Moreover, it is demonstrated that the induced CD can contribute significantly to the CD signals measured by surfa...