Exponential fitting using integral equations

The fitting of a function y =\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} to experimental data is considered. Integral equations are developed which have the functions \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} as their solutions for n = 1, 2, 3, These integral equations are used to find the frequencies λ_i. Examples are worked out to illustrate the method. The method is shown to be capable of extension to other functions.     

Numerical integration of structural dynamics equations including natural damping and periodic forcing terms

This paper shows that it is comparatively simple to analyse algorithms for the numerical integration of the Space discretized equations from structural dynamics when applied to \documentclass{article}\pagestyle{empty}\begin{document}$\ddot x + \mu \dot x\omega ^2 x = p{\rm e}^{ist} $\end{document}, instead of the usual \documentclass{article}\pagestyle{empty}\begin{document}$ \ddot x + \omega ^2 x = 0 $\end{document}, and suggests that this should be done in order to gain some insight into the effect with natural damping and/or a periodic forcing term. The method is illustrated on some three- and four-time-level schemes.     

Lebensdauer- und Dauerfestigkeitsabschätzung von zugdruckwechsel- und zugschwellbeanspruchtem Stahl mittels Temperaturmessung

Estimation of the Endurance and the Fatigue Limit of Steel by Measuring Specimens′ Temperatures. Microplastic deformation processes are pre-requisites for fatigue crack formation within metallic materials. If the testing frequency of a specimen, cyclically stressed by a progressively-increasing load test, is not too low it is no great metrological problem to ascertain that special stress amplitude, σ_f,th (f ? fatigue limit, th ? thermometrical), at which specimen's temperature begins to rise due to the start of ‘remarkable’ microplastic deformations. Investigations of this kind, recently carried out by rotating bending showed a very good correspondence between σ_f,th and a statistically ascertained estimate of the fatigue limit, \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma _{({\rm P} \simeq {\rm 0}\%{\rm)}} $\end{document} (P ? Probability of fracture), derived from comparatively performed Wöhler-tests. The purpose of this paper is to investigate the relationship between σ_f,th and \documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma _{({\rm P} \simeq {\rm 0}\%{\rm)}} $\end{document} for some carbon steels when cyclically stressed by push-pull and pulsating tensile loading, respectively. Both, unnotched and notched specimes were tested. Moreover, thermometrically monitored Wöhler-tests revealed that temperature measurements can provide a short-cut prediction of specimens′ lives. Above all it has to be mentioned that a reliable clue is gettable at a very early experimental stadium whether the cyclic stressed specimen will later become a ‘break’ or – normally much later – a ‘run-out’.     

Probleme der zerstörenden Prüfung von Proben mit sehr geringer Verformung

Problems of Destructive Testing of Samples with Very Low Deformation In the case of materials with very low deformation at break, for example ceramics and graphite, the stiffness of the testing machine has to fulfill requirements which must be clearly defined and capable of being checked, in order to avoid errors in the test result. Besides sensitive test factors there are also some which remain constant regardless of the spring stiffness of the testing apparatus. The effect on the commonly used loading methods (v_o = constant; \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm F}\limits^. = {\rm constant} $\end{document}) is investigated. Possibilities for corrections are discussed an appropriate algorithms are given.     

The Influence of Oxygen/Argon Ratio on the Structure and Surface Morphology of GaBa2Cu3O7?δ Films Deposited by RF Magnetic Sputtering

$\mathrm{GaBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7\mbox{-}\delta}$ thin films have been grown on CeO₂ cap layer by RF magnetic sputtering with different oxygen/argon partial pressure ratio from 2:1 to 1:5. The CeO₂ cap layers were fabricated by pulse laser deposition (PLD) on YSZ/CeO₂/Ni-5%W alloy substrate and had good properties in structure and surface morphology. We study the relationship between oxygen/argon ratio and the performance of the $\mathrm{GaBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7\mbox{-}\delta}$ film in order to find out the optimized deposition condition. The structure and surface morphology of the $\mathrm{GaBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7\mbox{-}\delta}$ thin films were measured by X-ray diffraction (XRD), Field emission scanning electron microscope (FE-SEM), Atomic force microscopy (AFM). It was found that the texture and surface performance of $\mathrm{GaBa}_{2}\mathrm{Cu}_{3}\mathrm{O}_{7\mbox{-}\delta}$ film, such as growth orientation, grain roughness, grain size and surface morphology, are deeply affected by the oxygen/argon ratio. And the film??s performance was the best when the oxygen/argon partial pressure ratio is 1:1.     

The Experimental Study of Temperature Dependence of Binary Diffusion Coefficients of Gases at Different Pressures

An experimental study of the temperature dependence of the binary diffusion coefficients (BDCs) was conducted for five binary mixtures of gases: $\mathrm{H}_{2}{-}\mathrm{N}_{2}, \mathrm{H}_{2}{-}\mathrm{CO}, \mathrm{H}_{2}{-}\mathrm{CH}_{4}, \mathrm{H}_{2}{-}\mathrm{C}_{2}\mathrm{H}_{6}$ , and $\mathrm{H}_{2}{-}\mathrm{C}_{3}\mathrm{H}_{8}$ . Measurements were carried out with the use of a steady-flow method in the temperature range from 250 K to 900 K and the pressure range from 0.1 MPa to 15 MPa. The determination of the BDCs is based on analysis of the volume fraction of the diffusing gas in the gas flow. The experimental data were compared with the results of calculations by the proposed formula evaluated within the framework of the elementary kinetic theory. The obtained results exhibit considerably good agreement with the experimental data within the experimental error. The results of investigations of the temperature dependence of the BDCs show that this dependence can be fitted with a power law only at atmospheric pressure.     

Effect of Previous Milling of Precursors on Magnetoelectric Effect in Multiferroic {\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}} Ceramic

$\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 magnetoelectric (ME) ceramics have been synthesized and investigated. The ME effect can be described as an induced electric polarization under an external magnetic field or an induced magnetization under an external electric field. The materials in the ME effect are called ME materials, and they are considered to be a kind of new promising materials for sensors, processors, actuators, and memory systems. Multiferroics, the materials in which both ferromagnetism and ferroelectricity can coexist, are the prospective candidates which can potentially host the gigantic ME effect. $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 , an Aurivillius compound, was synthesized by sintering a mixture of $\mathrm{Bi}_{2}\mathrm{O}_{3}, \mathrm{Fe}_{2}\mathrm{O}_{3}$ Bi 2 O 3 , Fe 2 O 3 , and $\mathrm{TiO}_{2}$ TiO 2 oxides. The precursor materials were prepared in a high-energy attritorial mill for (1, 5, and 10) h. The orthorhombic $\mathrm{Bi}_{5}\mathrm{Ti}_{3}\mathrm{FeO}_{15}$ Bi 5 Ti 3 FeO 15 ceramics were obtained by a solid-state reaction process at 1313 K. The ME voltage coefficient ( $\alpha _\mathrm{ME}$ α ME ) was measured using the dynamic lock-in method. The highest ME voltage coefficient ( $\alpha _\mathrm{ME} = 8.28\,\text{ mV }{\cdot }\text{ cm }^{-1}{\cdot }\text{ Oe }^{-1})$ α ME = 8.28 mV · cm ? 1 · Oe ? 1 ) is obtained for the sample milled for 1 h at $H_\mathrm{DC }= 4$ H DC = 4  Oe (1 Oe = 79.58  $\text{ A }{\cdot }\text{ m }^{-1})$ A · m ? 1 ) .     

Evaluation of Power Heat Losses in Multidomain Iron Particles Under the Influence of AC Magnetic Field in RF Range

The magnetic properties and hyperthermia effect were studied in a magnetorheological fluid (MRF) containing iron particles of $1 \upmu \mathrm{m}\, \text{ to}\, 5 \,\upmu \mathrm{m}$ in diameter. The measurements showed that the magnetization in the saturation state reaches a value of 171 $\text{ A}\cdot \text{ m}^{2}\cdot \mathrm{kg}^{-1}$ with very small values of coercivity and remanence. They also showed the ferromagnetic behavior in the system together with a value of the magnetic susceptibility of 1.7. Theoretical and experimental results of the calorimetric effect investigation under a changeable magnetic field of high frequency ( $f = 504$ kHz) in an MRF will be presented in the article. The sample was subjected to an alternating magnetic field of different strengths ( $H = 0$ to 4 $\text{ kA}\cdot \text{ m}^{-1})$ . It results from a theoretical analysis that the heat power density (released in the MRF sample) referenced to the eddy current is proportional to the square of frequency, the magnetic field amplitude, and the iron grain diameter. Experimental results indicate that there are some reasons for the released heat energy such as: energy losses from magnetic hysteresis and eddy currents induced in the iron grains. If the magnetic field intensity amplitude grows, the participation of losses connected with magnetic hysteresis is increased. From the calorimetric measurements, the conclusion is as follows: for a magnetic field $H<1946\,\text{ A}\cdot \mathrm{m}^{-1}$ , the eddy current processes dominate in the heat generation mechanism, whereas hysteresis processes for the total release of thermal energy dominate for higher magnetic fields. Both mechanisms take equal parts in heating the tested sample at a magnetic field intensity amplitude $H= 1946\,\text{ A}\cdot \mathrm{m}^{-1}$ . The specific absorption rate referenced to the mass unit of the MRF sample at the amplitude of the magnetic field strength 4 $\text{ kA}\cdot \mathrm{m}^{-1}$ equals 24.94 $\text{ W} \cdot \mathrm{kg}^{-1}$ at a frequency $f$ = 504 kHz.     

Magnetic Properties of Nanocrystalline Nickel–Cobalt Ferrites (\mathrm{Ni}_{1/2}{\mathrm{{Co}}}_{1/2}{\mathrm{{Fe}}}_{2}{\mathrm{O}}_{4})

In this study, the nanocrystalline nickel–cobalt ferrites $(\mathrm{Ni}_{1/2}\mathrm{Co}_{1/2}\mathrm{Fe}_{2}\mathrm{O}_{4})$ were prepared via the citrate route method at $27\,^{\circ }\mathrm{C}$ . The samples were calcined at $300\,^{\circ }\mathrm{C}$ for 3 h. The crystalline structure and the single-phase formations were confirmed by X-ray diffraction (XRD) measurements. Prepared materials showed the cubic spinel structure with m3m symmetry and Fd3m space group. The analyses of XRD patterns were carried out using POWD software. It gave an estimation of lattice constant “ $a$ ” of 8.3584 Å, which was in good agreement with the results reported in JCPDS file no. 742081. The crystal size of the prepared materials calculated by Scherer’s formula was 27.6 nm and the electrical conductivity was around $10^{-5}~\mathrm{S}\,\cdot \, \mathrm{m}^{-1}$ . The permeability component variations with frequency were realized. The magnetic properties of the prepared materials were analyzed by a vibrating sample magnetometer (VSM). It showed a saturation magnetization of $27.26\,\mathrm{emu} \cdot \mathrm{m}^{-1}$ and the behavior of a hard magnet.     

Thermal-Conductivity Studies of Macro-porous Polymer-Derived SiOC Ceramics

A three-dimensional reticular macro-porous SiOC ceramics structure, made of spherical agglomerates, has been thermally characterized using a freestanding sensor-based $3\omega $ method. The effective thermal conductivity of the macro-porous SiOC ceramics, including the effects of voids, is found to be $0.041\,\hbox { W}\cdot \hbox { m}^{-1}\cdot \hbox { K}^{-1}$ to $0.078\,\hbox { W}\cdot \hbox { m}^{-1}\cdot \hbox { K}^{-1}$ at room temperature, comparable with that of alumina aerogel or carbon aerogel. These results suggest that SiOC ceramics hold great promise as a thermal insulation material for use at high temperatures. The measured results further reveal that the effective thermal conductivity is limited by the low solid-phase volume fraction for the SiOC series processed at the same conditions. For SiOC ceramics processed under different pyrolysis temperatures, the contact condition between neighboring particles in the SiOC networks is another key factor influencing the effective thermal conductivity.     

The Elastic Properties, Generalized Stacking Fault Energy and Dissociated Dislocations in MgB2 Under Different Pressure

The $\langle11\overline{2}0\rangle$ perfect dislocation in MgB₂ is suggested to dissociate into two partial dislocations in an energy favorable way $\langle11\overline{2}0\rangle\rightarrow\frac{1}{2}\langle11\overline{2}0\rangle +\mathrm{SF}+\frac{1}{2}\langle11\overline{2}0\rangle$ . This dissociation style is a correction of the previous dissociation $\langle1000\rangle\rightarrow\frac{1}{3}\langle1\overline{1}00\rangle+\mathrm{SF}+\frac{1}{3}\langle2100\rangle$ proposed by Zhu et al. to model the partial dislocations and stacking fault observed by transmission electron microscopy. The latter dissociation results in a maximal stacking fault energy rather than a minimal one according to the generalized stacking fault energy calculated from first-principles methods. Furthermore, the elastic constants and anisotropy of MgB₂ under different pressure are investigated. The core structures and mobilities of the $\langle11\overline{2}0\rangle$ dissociated dislocations are studied within the modified Peierls–Nabarro (P–N) dislocation theory. The variational method is used to solve the modified P–N dislocation equation and the Peierls stress is also determined under different pressure. High pressure effects on elastic anisotropy, core structure and Peierls stress are also presented.     

A Novel Vibrating Finger Viscometer for High-Temperature Measurements in Liquid Metals and Alloys

A novel vibrating finger viscometer for high-temperature measurement in liquid metals and alloys up to 1823 K was constructed. The dynamic viscosity (\(\eta \)) of the liquid fluid is measured as a product of \((\rho \cdot \eta )^{0.5}\) and the relative change of the field coil input for a constant amplitude recording at the resonant frequency of the oscillator. The viscometer was calibrated at 298 K using reference silicon oils with varying kinematic viscosities (\(\nu \)), \((0.79\hbox { to } 200)\times 10^{-6}\hbox { m}^{2}\cdot \hbox {s}^{-1}\). In the present study, the viscosity of liquid gold (\(99.99\,\%\) Au), silver (\(99.9\, \%\) Ag), and tin (\(99.9\,\%\) Sn) was measured. The viscosities expressed as an Arrhenius function of temperature are:

$$\begin{aligned} \hbox {for Au:}\quad \quad \hbox {ln }\eta= & {} -0.1990+\frac{2669}{T}\\ \hbox {for Ag:} \quad \quad \hbox {ln }\eta= & {} -0.4631+\frac{2089}{T}\\ \hbox {for Sn:} \quad \quad \hbox {ln }\eta= & {} -0.5472+\frac{671}{T} \end{aligned}$$

The viscosity values are consistent within the range of available literature data.

     

Hypersensitive Transition of Nd(III) Complexes in Liquids Detected by Pulsed-Laser-Induced Photoacoustic Spectroscopy

Laser-induced photoacoustic (PA) spectroscopy for the spectral measurements of extremely weak absorption such as a forbidden transition of lanthanide ions in liquids has been established. In spectroscopy, a pulsed Nd:YAG laser connected with a MOPO series optical parametric oscillator which emits a broad spectrum covering UV and visible regions is used as the excitation source, and the induced PA signals are detected by an optimized PA piezoelectric transducer. The absorption spectra of trivalent lanthanide ions ( $\text{ Pr}^{3+}, \text{ Ho}^{3+}$ , and $\text{ Nd}^{3+})$ in aqueous solutions have been obtained by the detection system with a detection-limit absorbance of $1.3\times 10^{-5}\,\text{ cm}^{-1}$ at room temperature. In addition, the effects of different binding environments on the band shapes and oscillator strengths of the hypersensitive transitions of $\text{ Nd}^{3+}$ ions, i.e., $\text{ Nd}(\text{ CH}_{3}\text{ COO})_{3}$ $\cdot $ $\text{ H}_{2}\text{ O}$ dissolved in $0.1\,{\text{ mol}} \cdot \text{ l}^{-1}$ acetic acid and $\text{ Nd(3-butanedione)}_{3}{\cdot } 2\text{ H}_{2} \text{ O}$ dissolved in triglycol compared with $\text{ NdCl}_{3}$ in $0.1\,{\text{ mol}}\cdot \text{ l}^{-1}$ hydrochloric acid, are observed. The results show that the chemical environment around the lanthanide ions has great impact on 4f–4f transitions, which is rationalized as the impact in terms of ligand (or solvent) special structures and coordination properties.     

Dislocation structure at a \{ {\overline{1} 2\overline{1} 0} \}/ {\langle} 10\overline{1} 0 {\rangle} low-angle tilt grain boundary in LiNbO3

LiNbO₃ is a ferroelectric material with a rhombohedral R3c structure at room temperature. A LiNbO₃ bicrystal with a $ \{ {\overline{1} 2\overline{1} 0} \}/ {\langle}10\overline{1} 0{\rangle}$ 1° low-angle tilt grain boundary was successfully fabricated by diffusion bonding. The resultant boundary was then investigated using high-resolution TEM. The boundary composed a periodic array of dislocations with $ b = { 1}/ 3{\langle} \overline{1} 2\overline{1} 0{\rangle} $ . They dissociated into two partial dislocations by climb. A crystallographic consideration suggests that the Burgers vectors of the partial dislocations should be $ 1/ 3{\langle}01\overline{1} 0{\rangle} $ and $ 1/ 3{\langle}\overline{1} 100{\rangle} $ , and a stacking fault on $ \{ {\overline{1} 2\overline{1} 0} \} $ is formed between the two partial dislocations. From the separation distance of a partial dislocation pair, a stacking fault energy on $ \{ {\overline{1} 2\overline{1} 0} \} $ was estimated to be 0.25?J/m² on the basis of isotropic elasticity theory.     

Surface Recombination Velocity Dependence on Morphological Properties of CdTe Thin Films Prepared by Close-Spaced Sublimation

Cadmium telluride (CdTe) thin films were prepared on glass substrates by employing the close-spaced sublimation technique. Different source ( $T_\mathrm{sou}$ ) and substrate temperatures ( $T_\mathrm{sub}$ ) were used in order to change the structural properties of layers. The ranges chosen were: $550\,^{\circ }\hbox {C} \le T_\mathrm{sou} \le 650\,^{\circ }\hbox {C}$ and $400\,^{\circ }\hbox {C} \le T_\mathrm{sub} \le 600\,^{\circ }\hbox {C}$ . The environment in the growing chamber was also changed with the purpose to study its influence on the crystalline properties of the surface and volume of the material. Three different surroundings were used: vacuum, high-purity argon, and high-purity oxygen. The surface recombination velocity (SRV) was calculated from photoacoustic (PA) measurements by employing the open PA cell configuration. The behavior of the experimental results was analyzed as a function of the structural characteristics of the films: texture and grain size. Scanning electron microscopy, optical absorption, X-ray diffraction, and dark resistivity measurements were also employed to analyze the properties of the CdTe films. The minimum value for the SRV was found for $T_\mathrm{sou} = 650\,^{\circ }\hbox {C},\, T_\mathrm{sub} = 600\,^{\circ }\hbox {C}$ in an oxygen ambient.     

Open Photoacoustic Cell Configuration Applied to the Thermal Characterization of Liquid CdS Nanocomposites

CdS nanofluids were prepared by the gamma-radiation method at different radiation doses. The samples were characterized by UV–Vis spectroscopy and transmission electron microscopy. The open cell photoacoustic technique was used to measure the thermal effusivity of the CdS nanocomposites. In this technique a He–Ne laser was used as the excitation source and was operated at 632.8 nm with an output power of 70 mW. The precision and accuracy of this technique were initially established by measuring the thermal effusivity of distilled water and ethylene glycol. The thermal-effusivity values of these two samples were found to be close to the values reported in the literature. The thermal effusivity of CdS nanofluids decreased from (0.453 to 0.268) $\mathrm {W}\cdot \mathrm {S}^{1/2}\cdot \mathrm {cm}^{-2}\cdot \mathrm {K}^{-1}$ with increased dosage of gamma radiation.     

Photopyroelectric Calorimetry of \hbox {Fe}_{3}\hbox {O}_{4} Magnetic Nanofluids: Effect of Type of Surfactant and Magnetic Field

Five types of magnetic nanofluids, based on \(\hbox {Fe}_{3}\hbox {O}_{4}\) nanoparticles with water as the carrier liquid, were investigated by using the two photopyroelectric (PPE) detection configurations (back (BPPE) and front (FPPE)), together with the thermal-wave resonator cavity (TWRC) technique as the scanning procedure. The difference between the nanofluids was the type of surfactant: double layers of lauric (LA–LA), oleic (OA–OA), and miristic (MA–MA) acids and also double layers of lauric–miristic (LA–MA) and palmitic-oleic (PA–OA) fatty acids were used. In both detection configurations, the information was contained in the phase of the PPE signal. The thermal diffusivity of nanofluids was obtained in the BPPE configuration, from the scan of the phase of the signal as a function of the liquid’s thickness. Using the same scanning procedure in the FPPE configuration, the thermal effusivity was directly measured. The influence of a 0.12 kG magnetic field on the thermal effusivity and thermal diffusivity was also investigated. Because of different surfactants, the thermal effusivity of the investigated nanofluids ranges from \(1530\,\hbox {W}\cdot \hbox {s}^{1/2} \cdot \hbox { m}^{-2}\cdot \hbox { K}^{-1}\) to \(1790\,\hbox { W}\cdot \hbox {s}^{1/2}\cdot \hbox { m}^{-2}\cdot \hbox { K}^{-1}\) , and the thermal diffusivity, from \(14.54~\times ~10^{-8}\,\hbox { m}^{2}\cdot \hbox { s}^{-1}\) to \(14.79~\times ~10^{-8}\,\hbox { m}^{2}\cdot \hbox { s}^{-1}\) . The magnetic field has practically no influence on the thermal effusivity, and produces a maximum increase of the thermal diffusivity (LA–LA surfactant) of about 4 %.     

Anomalous roughness of fracture surfaces in 2D fuse models

We study anomalous scaling and multiscaling of two-dimensional crack profiles in the random fuse model using both periodic and open boundary conditions. Our large scale and extensively sampled numerical results reveal the importance of crack branching and coalescence of microcracks, which induce jumps in the solid-on-solid crack profiles. Removal of overhangs (jumps) in the crack profiles eliminates the multiscaling observed in earlier studies and reduces anomalous scaling. We find that the probability density distribution ${p(\Delta h(\ell))}$ of the height differences ${\Delta h(\ell) = [h(x+\ell) - h(x)]}$ of the crack profile obtained after removing the jumps in the profiles has the scaling form ${p(\Delta h(\ell)) = \langle\Delta h^2(\ell)\rangle^{-1/2} ~f\left(\frac{\Delta h(\ell)}{\langle\Delta h^2(\ell)\rangle^{1/2}}\right)}$ , and follows a Gaussian distribution even for small bin sizes ?. The anomalous scaling can be summarized with the scaling relation ${\left[\frac{\langle\Delta h^2(\ell)\rangle^{1/2}}{\langle\Delta h^2(L/2)\rangle^{1/2}}\right]^{1/\zeta_{loc}} + \frac{(\ell-L/2)^2}{(L/2)^2} = 1}$ , where ${\langle\Delta h^2(L/2)\rangle^{1/2}\sim L^{\zeta}}$ and L is the system size.