Determination Of Mass Density Research Articles

Simultaneous determination of mass density and flexural rigidity of the damped Euler–Bernoulli beam from two boundary measured outputs

Abstract In this paper, we study the inverse coefficient problem of identifying both the mass density ρ ⁢ ( x ) > 0 \rho(x)>0 and flexural rigidity r ⁢ ( x ) > 0 r(x)>0 of a damped Euler–Bernoulli (cantilever) beam governed by the equation ρ ⁢ ( x ) ⁢ u t ⁢ t + μ ⁢ ( x ) ⁢ u t + ( r ⁢ ( x ) ⁢ u x ⁢ x ) x ⁢ x = 0 \rho(x)u_{tt}+\mu(x)u_{t}+(r(x)u_{xx})_{xx}=0 , ( x , t ) ∈ ( 0 , ℓ ) × ( 0 , T ) (x,t)\in(0,\ell)\times(0,T) , subject to boundary conditions u ⁢ ( 0 , t ) = u x ⁢ ( 0 , t ) = 0 u(0,t)=u_{x}(0,t)=0 , u x ⁢ x ⁢ ( ℓ , t ) = 0 u_{xx}(\ell,t)=0 , - ( r ⁢ ( x ) ⁢ u x ⁢ x ⁢ ( x , t ) ) x | x = ℓ = g ⁢ ( t ) -(r(x)u_{xx}(x,t))_{x}|_{x=\ell}=g(t) , from the available measured boundary deflection ν ⁢ ( t ) := u ⁢ ( ℓ , t ) \nu(t):=u(\ell,t) and rotation θ ⁢ ( t ) := u x ⁢ ( ℓ , t ) \theta(t):=u_{x}(\ell,t) at the free end of the beam. The distinctive feature of the considered inverse coefficient problem is that not one, but two Neumann-to-Dirichlet operators have to be formally defined. The inverse problem is hence formulated as a system of nonlinear Neumann-to-Dirichlet operator equations with the right-hand sides consisting of the measured outputs. As a natural consequence of this approach, a vector-form Tikhonov functional is introduced whose components are squares of the L 2 L^{2} -norm differences between predicted and measured outputs. We then prove existence of a quasi-solution of the inverse problem and derive explicit gradient formulae for the Fréchet derivatives of both components of the Tikhonov functional. These results are instrumental to any gradient based algorithms for reconstructing the two unknown coefficients of the considered damped Euler–Bernoulli beam.

Quartz tuning fork mass change sensing for FIB/SEM technology

In this paper we present a metrological method for determination of mass density of focused ion beam induced deposition (FIBID) materials using quartz tuning fork (QTF) mass change sensors. Dimension and density determination of FIBID deposited nanostructures is necessary to develop and reliable and repeatable microfabribrication technology of the highest versatility. The proposed metrological methodology allows to determine mass change with 5 pg resolution and accuracy below 5 % if density is considered. The described method is suitable for precise FIBID precursor parameters determination conducted during the deposition as actuation and signal read-out of the applied QTF can be performed electrically. High accuracy, resolution and stability are ensured due to excellent properties of quartz forming the sensor structure.

Densities and interfacial tensions for fatty acid methyl esters (from methyl formate to methyl heptanoate) + water demixed mixtures at atmospheric pressure conditions

Experimental determination of mass densities and interfacial tensions (IFT) at liquid-liquid equilibrium (LLE) for methyl ester (FAME) demixed aqueous family (from methyl formate to methyl heptanoate) are reported as a function of temperature at atmospheric pressure (101.3 kPa). Mass density determinations are carried out in a vibrating tube densimeter, whereas a spinning drop tensiometer is used for performing IFT measurements. Furthermore, the IFT data have been correlated by using a simplified version of the Square Gradient Theory (SSGT) as applied to the Non-Random Two Liquids (NRTL) activity coefficient model. Based on the experimental results, the mass densities of both aqueous and methyl ester bulk phase decrease with temperature, whereas the IFT increases with the temperature and reaches a maximum value, which is related to the maximum tie line in the LLE. For higher temperatures, IFT starts to decrease with temperature. The correlation approach of IFT (SSGT + NRTL) was found to be suitable for correlating the IFT of the mixtures as a function of temperature and also provides a route to explore other interfacial properties, such as interfacial concentration profiles, which are difficult to measure. Considering the results from the calculated interfacial profiles along the interfacial region, the components (FAMEs and water) neither exhibit surface activity nor adsorption activity and the interfacial width decreases with temperature, as it was expected.

Data on the impact of increasing the W amount on the mass density and compressive properties of Ni-W alloys processed by spark plasma sintering.

Bulk Ni–W alloys having composite-like microstructures are processed by spark plasma sintering (SPS) route of Ni and W powder blends as reported in a recent study of Sadat et al. (2016) (DOI of original article: doi:10.1016/j.matdes.2015.10.083) [1]. The present dataset deals with determination of mass density and evaluation of room temperature compressive mechanical properties as function of the amount of W (%wt. basis). The presented data concern: (i) measurement of the mass of each investigated Ni–W alloy which is subsequently used to compute the mass density of the alloy and (ii) the raw (stress (MPa) and strain ()) data, which can be subsequently used for stress/ strain plots.

Atmospheric densities and interfacial tensions for 1-alkanol (1-butanol to 1-octanol) + water and ether (MTBE, ETBE, DIPE, TAME and THP) + water demixed mixtures

Experimental mass densities and interfacial tensions (IFT) at liquid–liquid equilibrium (LLE) for two binary demixed aqueous families: 1-alkanol (from 1-butanol to 1-octanol)+water and ether (MTBE, ETBE, DIPE, TAME and THP)+water are reported as a function of temperature at atmospheric pressure. Mass density determinations are carried out in a vibrating tube densimeter, whereas a spinning drop tensiometer is used for performing IFT measurements. Additionally, the IFT data have been correlated by using a simplified version of the square gradient theory (SSGT) as applied to the non-random two liquids (NRTL) activity coefficient model.According to the experimental results, the mass densities of both aqueous and organic (1-alkanols or ethers) bulk phase decreases with temperature, whereas the IFT for 1-alkanol+water mixtures increases with the temperature and reaches a maximum value, which is related to the maximum tie line in the LLE. For higher temperatures, IFT starts to decrease with temperature. For the case of ether+water mixtures, the IFT increases as the temperature increases without reach a maximum in the experimental temperature range.The SSGT+NRTL approach was found to be suitable for correlating the IFT of the mixtures and to provide a route to explore other interfacial properties, such as interfacial profiles, which are difficult to measure. Based on the calculated interfacial profiles along the interfacial region, the components (1-alkanols, ethers, and water) neither exhibit surface activity nor adsorption activity and the interfacial width decreases with temperature as it is expected.

Quantitative X-ray phase contrast waveguide imaging of bacterial endospores.

Quantitative waveguide-based X-ray phase contrast imaging has been carried out on the level of single, unstained, unsliced and freeze-dried bacterial cells of Bacillus thuringiensis and Bacillus subtilis using hard X-rays of 7.9 keV photon energy. The cells have been prepared in the metabolically dormant state of an endospore. The quantitative phase maps obtained by iterative phase retrieval using a modified hybrid input-output algorithm allow for mass and mass density determinations on the level of single individual endospores but include also large field of view investigations. Additionally, a direct reconstruction based on the contrast transfer function is investigated, and the two approaches are compared. Depending on the field of view and method, a resolution down to 65 nm was achieved at a maximum applied dose of below 5 × 105 Gy. Masses in the range of about ∼110-190 (20) fg for isolated endospores have been obtained.

The measuring of the cortical bone thickness in L4 vertebra and comparison with bone mass density

The aim of this work is to identify the cortical bone thickness in L4 vertebra, through a digital methodology using computed tomography and an experimental methodology with the rapid prototyping, and to compare with the body mass density for each vertebra in analysis. The study presents clinic results of 16 women from the Northwest of Portugal, with age between 52 and 83 years, collected from May to June 2011. The patients underwent a dual energy X-ray densitometry scan system (Lunar, DPX Pro, daily calibrated) at L4 vertebra for body mass density determination, and simultaneous a lumbar spine computed tomography scan (Lightspeed Plus, GE Medical System) was performed. All clinical data were obtained in a Medical Imaging Centre of Radiology. Discussions of results regarding the measuring of the cortical bone thickness and the relation with body mass density in L4 vertebra are presented in this work. The L4 vertebra is one of the most common spinal sites that lead to chronic lower back pain. The goal of this study is to acquire accurate values, concerning cortical bone thickness, which could improve the prediction of vertebral fractures.

Towards accurate atmospheric mass density determination Using precise positional information of space objects

This paper presents a new method of deriving atmospheric mass densities with a high temporal resolution from precise orbit data of low earth orbiting (LEO) space objects. This method is based on the drag perturbation equation of the semi-major axis of the orbit of LEO space objects which relates the change rate of the semi-major axis to the atmospheric mass density. The effectiveness of the new method is evaluated using the GFZ-ISDC GPS rapid science orbit (RSO) products of the CHAMP satellite over a time period of 3months. The densities derived using this new method and obtained from accelerometer data are compared and good agreements are achieved. An example of using the derived density to generate good orbit prediction for CHAMP is presented.

Determination of mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal

Mass density, dielectric, elastic, and piezoelectric constants of bulk GaN crystal were determined. Mass density was obtained from the measured ratio of mass to volume of a cuboid. The dielectric constants were determined from the measured capacitances of an interdigital transducer (IDT) deposited on a Z-cut plate and from a parallel plate capacitor fabricated from this plate. The elastic and piezoelectric constants were determined by comparing the measured and calculated SAW velocities and electromechanical coupling coefficients on the Z- and X-cut plates. The following new constants were obtained: mass density p = 5986 kg/m(3); relative dielectric constants (at constant strain S) ε(S)(11)/ε(0) = 8.6 and ε(S)(11)/ε(0) = 10.5, where ε(0) is a dielectric constant of free space; elastic constants (at constant electric field E) C(E)(11) = 349.7, C(E)(12) = 128.1, C(E)(13) = 129.4, C(E)(33) = 430.3, and C(E)(44) = 96.5 GPa; and piezoelectric constants e(33) = 0.84, e(31) = -0.47, and e(15) = -0.41 C/m(2).

Following the Kinetics of a Chemical Reaction in Ultrathin Supported Polymer Films by Reliable Mass Density Determination with X-ray Reflectivity

Numerous modern functionalities with ultrathin polymer films involve chemical reactions within the films. X-ray reflectivity can be used to quantitatively follow these chemical reactions by a reliable determination of mass density, which is feasible within certain thickness constraints (e.g., 5-17 nm thickness for common polymer films).

Simultaneous Determination of the Surface Tension and Density of Polystyrene in Supercritical Nitrogen

In this paper we present a simple procedure for calculating the mass density of polymers at high temperature and pressure conditions. The proposed method entails the integration of a pendant drop volume from an axisymmetric drop image profile; this same pendant drop profile can be used to determine the surface tension using axisymmetric drop shape analysis (ADSA). Our approach yields both density and surface tension data simultaneously and is advantageous since it does not require any additional procedure or module to calculate the density of polymers in a fluid. This integration method provides a set of density data for the sample polymer, polystyrene, in supercritical fluid nitrogen, which is similar to the data derived from the empirical Tait equation and the semiempirical Sanchez−Lacombe equation of state when the temperature is above the polymer glass transition point. The results corroborate the use of all three approaches in determining the mass density of polymers at high temperatures. The comparable surface tension data are obtained at temperatures above the glass transition temperature of polymer with the densities generated by the three density determination approaches. We expect that the approach based on ADSA in conjunction with the mass density determination by the current integration method can be applied to the surface tension measurements of many other polymer melts in various fluid environments.

Accuracy in x-ray reflectivity analysis

The influence of Poisson noise on the accuracy of x-ray reflectivity analysis is studied with an aluminium oxide (AlO) layer on silicon. A null hypothesis which argues that other than the exact solution gives the best fitness is examined with a statistical p-value test using a significance level of α = 0.01. Simulations are performed for a fit instead of a measurement since the exact error caused by noise cannot be determined from the measurement. The p-value is studied by comparing trial curves to 1000 ‘measurements’, each of them including synthetic Poisson noise. Confidence limits for the parameters of Parratt's formalism and the Nevot–Croce approximation are determined in (mass density, surface roughness), (thickness, surface roughness) and (thickness, mass density) planes. The most significant result is that the thickness determination accuracy of AlO is approximately ±0.09 nm but the accuracy is better for materials having higher mass density. It is also shown that the accuracy of mass density determination can be significantly improved using a suitably designed fitness measure. Although the power of the presented method is demonstrated only in one case, it can be used in any parameter region for a plethora of single layer systems to find the lower limit of the error made in x-ray reflectivity analysis.

Mass density determination of thin organosilicon films by X-ray reflectometry

The mass density of thin organosilicon films deposited by chemical vapour deposition on silicon (0 0 1) surfaces has been determined by X-ray reflectometry. This method does not give a unique mass density value, but instead a bandwidth of possible values and compositions that are compatible with the experimental data if the layer thickness is not larger than about 350 nm. For thicker films thickness values obtained from ellipsometry data are used. The possible composition ranges are compared with data obtained by X-ray photo electron spectroscopy.

Assembled tau filaments differ from native paired helical filaments as determined by scanning transmission electron microscopy (STEM)

Paired helical filaments (PHF) are abnormal, approximately 20–25-nm wide periodically twisted filaments, which accumulate in Alzheimer's disease (AD) brain and other neurodegenerative disorders, including corticobasal degeneration (CBD). PHF are primarily composed of highly phosphorylated tau protein. However, both phosphorylated and non-phosphorylated forms of tau are able to assemble in vitro into filaments similar in the ultrastructural appearance to PHF. In the present study, filaments were assembled in vitro from unmodified recombinant human tau and the physical mass per unit length of filaments and the mass density were determined using scanning transmission electron microscopy (STEM). Two general types of filaments were observed. One type was composed of 11.4 nm-wide, 10–75 nm long, frequently twisted and PHF-like filaments, with a mass per unit length (44 kDa/nm) approximately one third of that observed in isolated AD filaments. The other were straight filaments, approximately 6.8-nm wide and 0.2–2 μm long, which often formed parallel clusters of two or more filaments. Triple clusters were 19.2-nm wide and had a mass per unit length (70 kDa/nm) approximately two thirds of that seen in isolated AD filaments. Despite different morphology, both twisted and straight filaments had mass densities between 0.48–0.55 kDa/nm 3. These values are significantly higher than those reported for PHF found either in AD (0.40 kDa/nm 3) or CBD (0.33 kDa/nm 3). These results suggest that the packing of tau differs in vivo from that observed in vitro and that specific tau isoform content, elongation of tau molecules by phosphorylation or other factors may be required to reproduce pathological assembly. Therefore mass density determinations appear to be an important criterion in comparing various filaments.

Modeling of transmittance, reflectance and scattering of rough polycrystalline CVD diamond layers in application to the determination of optical constants

The optical constants of CVD diamond layers on silicon substrates have been determined from spectrophotometric measurements. The rough surface of polycrystalline diamond layers causes scatter losses, which reduce the specular transmittance and reflectance of the layers. A model is derived to consider the effects of surface roughness in terms of surface scattering and coherence disturbance. Both effects can be described by means of a single parameter — the root mean square (rms) roughness. The model has proved useful to fit the experimental spectra. The optical and geometrical parameters obtained from the fit are in good agreement with the results of additional measurements, such as SEM, mass density determination. Raman spectroscopy and direct measurements of the position of the band gap of the samples.

Determination of local areal densities of heterogeneous biological samples by elastically backscattered protons in pixe microanalysis

It is shown that by using elastically backscattered protons as a measure of the areal mass density of the sample, a quantitative determination of element concentrations in biological material by PIXE can be achieved. To improve the accuracy in the local areal mass density determination, the backscattering yield is calibrated for different matrix compositions and a correction for changes in scattering cross sections is suggested.

Alfven wave resonances in a realistic magnetospheric magnetic field geometry

The notion of magnetic field line resonance has been very effective in explaining many features of long‐period geomagnetic pulsations. To date the decoupled transverse wave equations have been solved in a magnetic dipole field, whereas only WKB approximate solutions have been used in more general geometries. We have developed a solution of the decoupled equations that includes both a general magnetic field geometry and the effects of density and mass composition. The aim of this paper is to isolate and examine the effect on eigenfrequencies of only the field geometry by keeping density constant along all field lines. We review the diurnal variations in wave period predicted on the ground and in space by using the recent Olson‐Pfitzer magnetospheric magnetic field model in our solution. For example, on the ground at 67° magnetic latitude the diurnal variation in period caused by field geometry is larger than a factor of 2. At 6.6 RE, where the dipole field line from 67° crosses the magnetospheric equator, there is negligible diurnal variation in period. Significant diurnal variations in period (≳10%) at fixed radial distance in the equatorial plane in space occur only at distances ≳10 RE. Knowledge of the field geometry is shown to be important for the determination of mass density in space from ground pulsation observations. We discuss the impact of our results in interpretation of experimental data.