Transient Velocity Research Articles

A dataset of dual calcium and voltage optical mapping in healthy and hypertrophied murine hearts

Pathological hypertrophy underlies sudden cardiac death due to its high incidence of occurrence of ventricular arrhythmias. The alteration of transmural electrophysiological properties in hypertrophic cardiac murine tissue has never been explored previously. In this dataset, we have for the first time conducted high-throughput simultaneous optical imaging of transmembrane potential and calcium transients (CaT) throughout the entire hypertrophic murine hearts at high temporal and spatial resolution. Using ElectroMap, we have conducted multiple parameters analysis including action potential duration/calcium transient duration, conduction velocity, alternans and diastolic interval. Voltage-calcium latency was measured as time difference between action potential and CaT peak. The dataset therefore provides the first high spatial resolution transmural electrophysiological profiling of the murine heart, allowing interrogation of mechanisms driving ventricular arrhythmias associated with pathological hypertrophy. The dataset allows for further reuse and detailed analyses of geometrical, topological and functional analyses and reconstruction of 2-dimensional and 3-dimentional models.

Experimental Research and Numerical Analysis of Pressure Fluctuation Characteristics of Rim Driven Propulsion Pump Outlet

The pressure fluctuation characteristics of a rim driven propulsion pump are studied by an experimental method firstly, and then its unsteady inner flow is studied by numerical simulation to reveal the generating mechanism of the pressure fluctuation. In the experiment, a monitoring point was set in a downstream region with a distance of 1D (D, Diameter of impeller) to the impeller. The monitoring point’s dominant frequencies within a low frequency band are 1APF (APF, Axial Passing Frequency) and 2APF. In the numerical simulation, the main fluctuation near the impeller region appears at 1BPF (BPF, Blade Passing Frequency) and as the monitoring point moves downstream, the amplitude becomes smaller. The 1BPF fluctuation nearly disappears when the distance exceeds 1D, and the main frequency moves to 1APF and 2APF, which is in good agreement with the experimental results in the low frequency band. The transient velocity, pressure and vorticity distribution were studied to reveal the causes of 1BPF, 1APF and 2APF fluctuation. The main cause of 1BPF is the jet from the tail of the blade and the main cause of 2APF is the movement of a large-scale double vortex structure on both sides of the low-pressure zone. The movement of the vortex group near the wall may be the main cause that induces the 1APF fluctuation.

РАЗРАБОТКА И МОДЕЛИРОВАНИЕ МАГНИТООПТИЧЕСКОГО ДАТЧИКА ГРАДИЕНТА МАГНИТНОГО ПОЛЯ С ТОРСИОННЫМ ПОДВЕСОМ ЧУВСТВИТЕЛЬНОГО ЭЛЕМЕНТА

The work has been done to simulate and search for a design solution for a magneto-optical sensor of a magnetic field gradient with a torsion suspension of a sensitive element. A mathematical model has been developed and simulation in the Wolfram Mathematica software environment has been performed. A comparison of air, liquid and magnetic-induction dampers has been made and a selection of the most effective solution has been carried out. The results of the analysis have shown that the most effective solution is the magnetic-induction damper, which allows changing of transition processes duration without direct affection on the sensitive element. Adjustment of the transient process velocity allowed achieving optimal system reaction time. The object of the study is the sensor of the magnetic field gradient with the torsion suspension of the sensitive element. The subject of research is physical processes with a magnetic field gradient sensor with a sensible torsion suspension when changing the external magnetic field. Research objective: development of basic design solutions, modeling, and analysis of the magneto-optical sensor of the magnetic field gradient with the torsion suspension of the sensitive element.

Roles of energy dissipation and asymmetric wettability in spontaneous imbibition dynamics in a nanochannel

HypothesisThe imbibition dynamics is controlled by energy dissipation mechanisms and influenced by asymmetric wettability in a nanochannel. We hypothesize that the imbibition dynamics can be described by a combined model of the Lucas–Washburn equation and the Cox-Voinov law considering velocity-dependent contact angles. MethodsMolecular dynamics simulations are utilized to investigate the imbibition dynamics. A wide range of wetting conditions is achieved via adjusting the liquid–solid interaction parameters, and the spontaneous imbibition processes are quantified and compared. FindingsThe critical condition for the occurrence of spontaneous imbibition is analyzed from a surface energy perspective. The analyses of energy conversion and dissipation indicate that the viscous dissipation is dominant during spontaneous imbibition. The classical Lucas-Washburn equation is modified with the Cox–Voinov law considering the effect of the dynamic contact angle and an effective equilibrium contact angle. We show that the proposed theory well captures the imbibition dynamics embodied in the growth of imbibition length as well as the transient interface shape and velocity for both the symmetric and asymmetric wetting conditions. In nanochannels with asymmetric wettability, the imbibition length difference between the sidewalls and interface oscillations increases with wetting disparity. Our findings deepen the understanding of imbibition dynamics on the nanoscale, and provide a theoretical reference for relevant applications.

Buoyancy-driven instabilities of partially miscible fluids in inclined porous media

This study presents a buoyancy-driven stability analysis in a three-dimensional inclined porous medium with a capillary transition zone that is formed between a non-wetting and an underlying wetting phase. In this two-phase, two-component, partially miscible system, a solute from a non-wetting phase diffuses into a porous layer saturated with a wetting-phase fluid, creating a dense diffusive boundary layer beneath an established capillary transition zone. Transient concentration and gravity-driven velocity fields are derived for the wetting phase while the saturation field remains fixed. Linear stability analysis with the quasi-steady-state approximation is employed to determine the onset of solutal convective instability for buoyancy-dominant, in-transition and capillary-dominant systems. The analysis of the problem leads to a differential eigenvalue problem composed of a system of three complex-valued equations that are numerically solved to determine the critical times, critical wavenumbers and neutral stability curves as a function of inclination angle for different Bond numbers. The layer inclination is shown to play an essential role in the stability of the problem, where the gravity-driven flow removes solute concentrations in the diffusive boundary layer. The results indicate that the horizontal porous layer exhibits the fastest onset of instability, and longitudinal rolls are always more unstable than oblique and transverse rolls. The inclination angle has a more substantial impact on stabilizing the diffusive boundary layer in the buoyancy-dominant than in the capillary-dominant systems. Furthermore, for both buoyancy-dominant and capillary-dominant systems, the critical times and wavenumbers vary exponentially with inclination angle ≤ 60° and follow the Stirling model.

NaV1.5 knockout in iPSCs: a novel approach to study NaV1.5 variants in a human cardiomyocyte environment

Cardiomyocytes derived from patient-specific induced pluripotent stem cells (iPSC-CMs) successfully reproduce the mechanisms of several channelopathies. However, this approach involve cell reprogramming from somatic tissue biopsies or genomic editing in healthy iPSCs for every mutation found and to be investigated. We aim to knockout (KO) NaV1.5, the cardiac sodium channel, in a healthy human iPSC line, characterize the model and then, use it to express variants of NaV1.5. We develop a homozygous NaV1.5 KO iPSC line able to differentiate into cardiomyocytes with CRISPR/Cas9 tool. The NaV1.5 KO iPSC-CMs exhibited an organized contractile apparatus, spontaneous contractile activity, and electrophysiological recordings confirmed the major reduction in total Na+ currents. The action potentials (APs) exhibited a reduction in their amplitude and in their maximal rate of rise. Voltage optical mapping recordings revealed that the conduction velocity Ca2+ transient waves propagation velocities were slow. A wild-type (WT) NaV1.5 channel expressed by transient transfection in the KO iPSC-CMs restored Na+ channel expression and AP properties. The expression of NaV1.5/delQKP, a long QT type 3 (LQT3) variant, in the NaV1.5 KO iPSC-CMs showed that dysfunctional Na+ channels exhibited a persistent Na+ current and caused prolonged AP duration that led to arrhythmic events, characteristics of LQT3.

Experimental investigation of fuel temperature effects on transient needle motion and injection velocity of solenoid type diesel injector

Real driving emission (RDE) test conducted in sub-zero temperature conditions has been acting as a severe emission regulation over the existing test methods for diesel engines. In order to cope with this tightened regulation, many studies have been conducted to interpret the factors causing the deteriorated diesel engine combustion in cold operation conditions. The deteriorated fuel injection performance has been regarded as one of the key contributing factors but the governing mechanisms are not thoroughly understood so far. This study aims to provide a comprehensive understanding of the effects of fuel temperature including sub-zero conditions on fuel injection performance by measuring the transient needle motion and injection velocity of a diesel injector using synchrotron X-ray imaging techniques. The factors causing the deteriorated injector performance and their contributions are discussed thoroughly based on the results. The results showed that the injection duration was shortened as the fuel temperature decreased as a result of decreased needle opening speed and increased needle closing speed. The increase of fuel viscosity and bulk modulus was discussed as the main factors associated with these results. The total injection mass was reduced by lowering the fuel temperature not only by the shortened injection duration but also by the decreased injection velocity. These factors exerted near equivalent contribution to the reduced injection mass at low fuel temperatures.

Verification and Validation of a Methodology to Numerically Generate Waves Using Transient Discrete Data as Prescribed Velocity Boundary Condition

This work presents a two-dimensional numerical analysis of a wave channel and a oscillating water column (OWC) device. The main goal is to validate a methodology which uses transient velocity data as a means to impose velocity boundary condition for the generation of numerical waves. To achieve this, a numerical wave channel was simulated using regular waves with the same parameters as those used in a laboratory experiment. First, these waves were imposed as prescribed velocity boundary condition and compared with the analytical solution; then, the OWC device was inserted into the computational domain, aiming to validate this methodology. For the numerical analysis, computational fluid dynamics ANSYS Fluent software was employed, and to tackle with water–air interaction, the nonlinear multiphase model volume of fluid (VOF) was applied. Although the results obtained through the use of discrete data as velocity boundary condition presented a little disparity; in general, they showed a good agreement with laboratory experiment results. Since many studies use regular waves, there is a lack of analysis with ocean waves realistic data; thus, the proposed methodology stands out for its capacity of using realistic sea state data in numerical simulations regarding wave energy converters (WECs).

Transient rotation of a spherical particle in a concentric cavity with slip surfaces

The start-up of slow rotation of a spherical particle due to the sudden application of a constant torque about a diameter in a viscous fluid inside a concentric spherical cavity with slip surfaces is studied. The unsteady Stokes equations governing the fluid velocity are solved by means of the Laplace transform, and an analytical formula for the dimensionless transient angular velocity of the particle is obtained as a function of the relevant dimensionless parameters. The influence of the confining slip cavity on the starting rotation of the slip sphere is significant and interesting. The angular velocity develops continuously with the elapsed time from zero at the beginning to its terminal value and the angular acceleration decreases monotonically with the time. The transient angular velocity increases with an increase in the particle-to-cavity radius ratio as the cavity is sufficiently slippery to enhance the particle rotation, decreases with an increase in this radius ratio as the cavity is sufficiently sticky to retard the rotation, and is not a sensitive function of the radius ratio as the slippage or stickiness of the cavity wall is in between. A particle with a higher relative density, smaller radius ratio, or less stickiness (or stickiness of the cavity) trails behind the reference particle in the development of the angular velocity with respect to individual terminal values, even if the transient angular velocity increases with a decrease in the stickiness of the particle or cavity.

Vibration level induced by the friction of two rough surfaces weakly loaded

This paper presents an experiment to measure the vibration level generated when a light solid slides over a dry and rough surface. The experimental set-up is based on linear constant motion with speed range from 1 to 1000 mm/sec. The aim is to study the evolution of the vibration level as a function of the sliding speed and the friction area. Measurements show that the vibration level is a logarithmic increasing function of the sliding speed with a transient velocity. It is also observed that two regimes exist for the evolution of vibration level versus apparent contact area. On the one hand the vibration level is proportional to the friction area, but on the other hand this level is constant.

Simulation and experimental study on droplet breakup modes and redrawing of their phase diagram

Dimensionless numbers are often used to characterize the various modes of droplet breakup processes. However, the current methods of calculating these dimensionless numbers are not uniform—consequently, the calculation results are different, resulting in different phase diagrams of droplet separation. This paper first summarizes the methods of calculating the Weber number. The maximum transient velocity at the center of a nozzle is then used as the characteristic velocity for calculating the Weber number, and this formulation is used to solve certain scenarios in which the traditional Weber number cannot be applied, such as the strange phenomenon of the upward flight of separated droplets. A mathematical model is established to simulate the various separation forms of droplets, and the experimental study is also carried out. This upward flight of droplets is found to be the result of competition between the liquid inertial force, surface tension force, and suction effect of the nozzle mouth. The final velocity of the droplets depends on the existence of a stagnation surface and the corresponding sweep effect. Finally, the phase diagram of different droplet separation modes is drawn in the Ohnesorge–Weber number space.

Discovery of Dynamic Two-Phase Flow in Porous Media Using Two-Dimensional Multiphase Lattice Boltzmann Simulation

The dynamic two-phase flow in porous media was theoretically developed based on mass, momentum conservation, and fundamental constitutive relationships for simulating immiscible fluid-fluid retention behavior and seepage in the natural geomaterial. The simulation of transient two-phase flow seepage is, therefore, dependent on both the hydraulic boundaries applied and the immiscible fluid-fluid retention behavior experimentally measured. Many previous studies manifested the velocity-dependent capillary pressure–saturation relationship (Pc-S) and relative permeability (Kr-S). However, those works were experimentally conducted on a continuum scale. To discover the dynamic effects from the microscale, the Computational Fluid Dynamic (CFD) is usually adopted as a novel method. Compared to the conventional CFD methods solving Naiver–Stokes (NS) equations incorporated with the fluid phase separation schemes, the two-phase Lattice Boltzmann Method (LBM) can generate the immiscible fluid-fluid interface using the fluid-fluid/solid interactions at a microscale. Therefore, the Shan–Chen multiphase multicomponent LBM was conducted in this study to simulate the transient two-phase flow in porous media. The simulation outputs demonstrate a preferential flow path in porous media after the non-wetting phase fluid is injected until, finally, the void space is fully occupied by the non-wetting phase fluid. In addition, the inter-relationships for each pair of continuum state variables for a Representative Elementary Volume (REV) of porous media were analyzed for further exploring the dynamic nonequilibrium effects. On one hand, the simulating outcomes reconfirmed previous findings that the dynamic effects are dependent on both the transient seepage velocity and interfacial area dynamics. Nevertheless, in comparison to many previous experimental studies showing the various distances between the parallelly dynamic and static Pc-S relationships by applying various constant flux boundary conditions, this study is the first contribution showing the Pc-S striking into the nonequilibrium condition to yield dynamic nonequilibrium effects and finally returning to the equilibrium static Pc-S by applying various pressure boundary conditions. On the other hand, the flow regimes and relative permeability were discussed with this simulating results in regards to the appropriateness of neglecting inertial effects (both accelerating and convective) in multiphase hydrodynamics for a highly pervious porous media. Based on those research findings, the two-phase LBM can be demonstrated to be a powerful tool for investigating dynamic nonequilibrium effects for transient multiphase flow in porous media from the microscale to the REV scale. Finally, future investigations were proposed with discussions on the limitations of this numerical modeling method.

Transient electrophoresis of a conducting spherical particle embedded in an electrolyte-saturated Brinkman medium.

In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.

Exact solutions of Stokes' second problem for hybrid nanofluid flow with a heat source

In this study, Stokes' second problem for Cu-Al2O3/water hybrid nanofluid is considered along with the effects of buoyancy force and a heat source. Using Laplace transforms, transient velocity, skin friction coefficient, and local Nusselt number are established in closed forms involving exponentials and error functions. The exact solutions have been compared with the numerical solutions as well as with available exact solutions, which show excellent agreement. It is found that the temperature, skin friction coefficient, and local Nusselt number are strongly affected and increased owing to the increase in the volume fractions of copper and alumina nanoparticles and heat source parameter. On the other hand, the mixed convection parameter noticeably enhances the flow velocity. When the heat source is absent, the skin friction coefficients are oscillating and the heat transfer approaches an asymptotic value. However, for a higher heat source parameter, when time increases, the amplitude of oscillation of the skin friction coefficients gradually increases and the magnitude of heat transfer exponentially increases. Both eventually go to infinity after a long period of time.

Experimental validation of differential evolution indicators for ultrasonic imaging in unknown backgrounds

The differential evolution indicators, recently introduced Pourahmadian and Haddar (2020) [1] for imaging mechanical evolution in highly scattering solids, is examined in a laboratory setting with the focus on spatiotemporal tracking of an advancing damage zone in an elastic specimen. To this end, a prismatic slab of charcoal granite is quasi-statically fractured in the three-point-bending (3 PB) configuration, while ultrasonic shear waves are periodically generated in the sample at certain time steps tκ,κ=∘,1,2,…,4. The interaction of probing waves with the propagating damage give rise to transient velocity responses measured on the plate’s boundary by a 3D scanning laser Doppler vibrometer. Thus obtained sensory data are then carefully processed to retrieve the associated spectra of scattered displacement fields vκ at every tκ. On deploying consecutive pairs of multifrequency data (vκ,vκ+1), the differential indicators are computed exposing the progress of 3 PB-induced damage in the specimen. Verified with in situ observations, each indicator map successfully reconstructs (a) the support of newborn fractures, and (b) the loci of discontinuities in the process zone that undergo interfacial evolution in the designated timeframe [tκtκ+1]. Further, it is shown that the evolution indicators help better understand the damage mechanism e.g., by shining light on the fragmented nature of induced cracks and their coalescence. For completeness, data inversion via reduced and partial-aperture data is investigated, including the one-sided reconstruction.

History of the Super Dual Auroral Radar Network (SuperDARN)-I: pre-SuperDARN developments in high frequency radar technology for ionospheric research and selected scientific results

Abstract. Part I of this history describes the motivations for developing radars in the high frequency (HF) band to study plasma density irregularities in the F region of the auroral zone and polar cap ionospheres. French and Swedish scientists were the first to use HF frequencies to study the Doppler velocities of HF radar backscatter from F-region plasma density irregularities over northern Sweden. These observations encouraged the author of this paper to pursue similar measurements over northeastern Alaska, and this eventually led to the construction of a large HF-phased-array radar at Goose Bay, Labrador, Canada. This radar utilized frequencies from 8–20 MHz and could be electronically steered over 16 beam directions, covering a 52∘ azimuth sector. Subsequently, similar radars were constructed at Schefferville, Quebec, and Halley Station, Antarctica. Observations with these radars showed that F-region backscatter often exhibited Doppler velocities that were significantly above and below the ion-acoustic velocity. This distinguished HF Doppler measurements from prior measurements of E-region irregularities that were obtained with radars operating at very high frequency (VHF) and ultra-high frequency (UHF). Results obtained with these early HF radars are also presented. They include comparisons of Doppler velocities observed with HF radars and incoherent scatter radars, comparisons of plasma convection patterns observed simultaneously in conjugate hemispheres, and the response of these patterns to changes in the interplanetary magnetic field, transient velocity enhancements in the dayside cusp, preferred frequencies for geomagnetic pulsations, and observations of medium-scale atmospheric gravity waves with HF radars.

Simulations of the Surf Zone Eddy Field and Cross‐Shore Exchange on a Nonidealized Bathymetry

AbstractX‐band radar observations from the 2017 Inner Shelf Dynamics Experiment (ISDE) in central California show multiple persistent and pulsatory rip currents on a relatively straight coastline with alongshore‐varying bathymetry. Although past studies have assessed the characteristics of transient rip currents on alongshore uniform beaches, the relative balance of transient versus steady rip current behavior on nonuniform beaches in realistic wave conditions remains poorly understood. Here, a phase‐resolving Boussinesq‐type wave model (funwaveC) is used to assess the role of alongshore‐varying bathymetry and incident conditions in controlling mean and transient surf zone vorticity and velocity fields and their effect on surf zone exchange. The model simulates wave conditions chosen from the ISDE observations and utilizes both an alongshore‐varying bathymetry estimated from the ISDE radar observations and a uniform bathymetry. Results show that the variable bathymetry significantly increases the alongshore‐ and time‐averaged kinetic energy but that this increase is primarily due to the increase in the standing component resulting from mean circulation patterns, with only small changes in the transient component. A variable bathymetry also increases the spectral energy of surf zone vorticity and time‐averaged vorticity forcing at large spatial scales (>100 m). Wave directional spreading has a large impact on the alongshore‐ and time‐averaged enstrophy and on the spectral energy of surf zone vorticity and vorticity forcing at smaller spatial scales (<100 m). In the presence of a directionally spread wavefield, an alongshore‐varying bathymetry slightly increases the total exchange velocity but has little effect on its transient component.

Mathematical modelling of Transient Free Convection MHD Flow Past a Vertical Plate with Periodic Temperature Using Homotopy Perturbation Method

A mathematical model is used to study the effect of the magnetic field on the temporary free convection flow of the electrically conductive fluid past the vertical plate under periodic temperature. The governing momentum and energy equations are solved analytically using the homotopy perturbation method. An approximate analytical solution using Homotopy perturbation method and Laplace transform is carried out for temperature profile in case of constant plate temperature. The results are obtained the analytical and limiting case results ones, and a good agreement is achieved. The effect of different physical parameters on transient velocity and temperature, such as Grashof number, magnetic parameter, Prandtl number and temperature frequency, is examined. Also, the local Skin-friction and local Nusselt number coefficients are obtained and analyzed.

Exploring Viscosity Space in an Eddy‐Permitting Global Ocean Model: Is Viscosity a Useful Control for Numerical Mixing?

AbstractA generic shortcoming of constant‐depth (or “z‐coordinate”) ocean models such as MOM5 and Nucleus for European Models of the Ocean (NEMO) is a tendency for the advection scheme to produce unphysical numerical diapycnal mixing, which may exceed the explicitly parameterized mixing based on observed physical processes. Megann (2018, https://doi.org/10.1016/j.ocemod.2017.11.001) estimated the effective diapycnal diffusivity in the Global Ocean Version 5.0 (GO5.0) 0.25° global implementation of the NEMO model and showed that this was up to 10 times the explicit diffusivity used in the model's mixing scheme and argued that this was at least partly caused by large transient vertical velocities on length scales comparable to the horizontal grid scale. The current UK global NEMO configuration GO6, as used in the Global Coupled Model version 3.1 (GC3.1) and UK Earth System Model (UKESM1), is integrated in forced mode at 0.25° resolution with a range of viscosity parameterizations. In the present study, the effective diffusivity is evaluated for each integration and compared with the explicit value from the model mixing scheme, as well as with that in the control (using the default viscosity). It is shown that there is a strong correspondence between lower viscosity and enhanced numerical mixing and that larger viscosities lead to a marked reduction in the unrealistic internal temperature drift seen in the control configuration, without incurring excessive damping of the large‐scale circulation, mixed layer depths, or sea ice cover. The results presented here will inform the choices made in global ocean configurations used in climate and Earth System models following the sixth Coupled Model Intercomparison Project (CMIP6).

Laboratory application of sampling approaches to inverse scattering

This study presents an experimental investigation of the recently established generalized linear sampling method (GLSM) (Pourahmadian et al 2017 Inverse Problems 33 055007) for non-destructive evaluation of damage in elastic materials. To this end, ultrasonic shear waves are generated in a prismatic slab of charcoal granite featuring a discontinuity interface induced by the three-point bending (3PB). The interaction of probing waves with the 3PB-induced damage gives rise to transient velocity responses measured on the sample’s boundary by a 3D scanning laser Doppler vibrometer. Thus obtained waveform data are then carefully processed to retrieve the associated spectra of scattered displacement fields. On deploying multifrequency sensory data, the GLSM indicators are computed and their counterparts associated with the classical linear sampling method (LSM) (Cakoni and Colton 2003 Inverse Problems 19 279–95) for comparative analysis. Verified with in situ observations, the GLSM map successfully exposes the support of hidden scatterers in the specimen with a remarkable clarity and resolution compared to its predecessor LSM. It is further shown that the GLSM remains robust for sparse and partial-aperture data inversion, thanks to its rigorous formulation. For completeness, the one-sided reconstruction by both indicators is investigated.