Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, \(K_{\mathrm{IE},}\) was evaluated numerically as \(K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)\), where \(\upmu \) is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, \(K_{\mathrm{IE,d}}\), was observed to vary as \(K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}\). Consistent with the FEM simulation, experiments conducted using \(12\,\upmu \hbox {m}\) thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of \(\ge \) \(1.85\times 10^{9}\,\hbox {A/m}^{2}\) for \(a/w = 0.5\). Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.     

A comparative study on dielectric behaviours of Au/(Zn-doped PVA)/<Emphasis Type="Italic">n</Emphasis>-4H-SiC (MPS) structures with different interlayer thicknesses using impedance spectroscopy methods

Three different thicknesses (50, 150 and 500 nm) Zn-doped polyvinyl alcohol (PVA) was deposited on n-4H-SiC wafer as interlayer by electrospinning method and so, Au/(Zn-doped PVA)/n-4H-SiC metal–polymer–semiconductor structures were fabricated. The thickness effect of Zn-doped PVA on the dielectric constant (\(\varepsilon ^{\prime }\)), dielectric loss (\(\varepsilon ^{{\prime }{\prime }}\)), loss-tangent (tan \(\delta \)), real and imaginary parts of electric modulus (\(M^{\prime }\) and \(M^{{\prime }{\prime }})\) and ac electrical conductivity \((\sigma _{\mathrm{ac}})\) of them were analysed and compared using experimental capacitance (C) and conductance (\(G/\omega \)) data in the frequency range of 1–500 kHz at room temperature. According to these results, the values of \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) decrease with increasing frequency almost exponentially, \(\sigma _{\mathrm{ac}}\) increases especially, at high frequencies. The \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) values were obtained from the \(\varepsilon ^{\prime }\) and \(\varepsilon ^{{\prime }{\prime }}\) data and the \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) vs. f plots were drawn for these structures. While the values of \(\varepsilon ^{\prime }\), \(\varepsilon ^{{\prime }{\prime }}\) and tan \(\delta \) increase with increasing interlayer thickness, the values of \(M^{\prime }\) and \(M^{{\prime }{\prime }}\) decrease with increasing interlayer thickness. The double logarithmic \(\sigma _{\mathrm{ac}}\) vs. f plots for each structure have two distinct linear regimes with different slopes, which correspond to low and high frequencies, respectively, and it is prominent that there exist two different conduction mechanisms. Obtained results were found as a strong function of frequency and interlayer thickness.     

High-pressure studies of superconductivity in $$\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}$$

\(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\) crystallizes in tetragonal CeOBiS\(_{2}\) structure (S. G. P4/nmm). We have investigated the effect of pressure on magnetization measurements. Our studies suggest improved superconducting properties in polycrystalline samples of \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\). The \(T_{\mathrm{c}}\) in our sample is 5.3 K, at ambient pressure, which is marginal but definite enhancement over \(T_{\mathrm{c}}\) reported earlier (= 5.1 K). The upper critical field \(H_{\mathrm{c}2}\)(0) is greater than 3 T, which is higher than earlier report on this material. As determined from the M–H curve, both \(H_{\mathrm{c}2}\) and \(H_{\mathrm{c}1}\) decrease under external pressure P (0 \(\le P \le \) 1 GPa). We observe a decrease in critical current density and transition temperature on applying pressure in \(\hbox {BiO}_{0.75}\hbox {F}_{0.25}\hbox {BiS}_{2}\).     

Measurement Uncertainty Budget of the PMV Thermal Comfort Equation

Fanger’s predicted mean vote (PMV) equation is the result of the combined quantitative effects of the air temperature, mean radiant temperature, air velocity, humidity activity level and clothing thermal resistance. PMV is a mathematical model of thermal comfort which was developed by Fanger. The uncertainty budget of the PMV equation was developed according to GUM in this study. An example is given for the uncertainty model of PMV in the exemplification section of the study. Sensitivity coefficients were derived from the PMV equation. Uncertainty budgets can be seen in the tables. A mathematical model of the sensitivity coefficients of \(T_{\mathrm{a}}\), \(h_{\mathrm{c}}\), \(T_{\mathrm{mrt}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) is given in this study. And the uncertainty budgets for \(h_{\mathrm{c}}\), \(T_{\mathrm{cl}}\), and \(P_{\mathrm{a}}\) are given in this study.     

Partial permutation decoding for MacDonald codes

We show how to find s-PD-sets of the minimal size \(s+1\) for the \(\left[ \frac{q^n-q^u}{q-1},n,q^{n-1}-q^{u-1}\right] _q \) MacDonald q-ary codes \(C_{n,u}(q)\) where \(n \ge 3\) and \(1 \le u \le n-1\). The construction of [6] can be used and gives s-PD-sets for s up to the bound \(\lfloor \frac{q^{n-u}-1}{(n-u)(q-1)} \rfloor -1\), of effective use for u small; for \(u \ge \lfloor \frac{n}{2} \rfloor \) an alternative construction is given that applies up to a bound that depends on the maximum size of a set of vectors in \(V_u(\mathbb {F}_q)\) with each pair of vectors distance at least 3 apart.     

Critical state behaviors of a coarse granular soil under generalized stress conditions

Critical state line (CSL) is the central concept in soil mechanics. A series of true triaxial compression tests under the constant-\({p}'\) and constant-b loading condition were carried out to investigate the CSL of a coarse granular soil. It was observed that the intermediate principal stress ratio (i.e., the b-value) greatly influenced the CSLs in both \(q{-}{p}'\) and \(e{-}{p}'\) spaces. The CSL slope in the \(q{-}{p}'\) space decreased with an increase in b-value. The intercept and gradient of the CSL in the \(e{-}{p}'\) space decreased with increasing b-value. CSLs incorporating the effects of the b-value in \(q{-}{p}'\) and \(e{-}{p}'\) spaces were extended to three-dimensional critical state surfaces (TCSSs) in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces. Two empirical equations were proposed for the two TCSSs in \(q{-}{p}'{-}b\) and \(e{-}{p}'{-}b\) spaces, respectively. The predictions by the two equations were in good agreement with the corresponding experimental data. The relationship between the excess friction angle (the difference between the peak state and critical state friction angles) and initial state parameter was influenced by the b-value. However, the relationship between the maximum dilatancy and initial state parameter was independent of the b-value.     

Evolution of magnetic structure of Dy(Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>)<Subscript>2</Subscript>B<Subscript>2</Subscript>C

DyNi\(_{2}\)B\(_{2}\)C superconducts at \(T_{c} \approx 6\,{\text{K}}\) and orders antiferromagnetically at \(T_{N}\approx 10\,{\text{K}}.\) Its non-superconducting isomorph DyCo\(_{2}\)B\(_{2}\)C is a ferromagnet with \(T_{C}\approx 6\,{\text{K}}.\) With the aim of mapping out the magnetic properties, in particular magnetic structures, of their solid solutions, we synthesized \(^{11}\)B-enriched Dy(Co\(_{x}\)Ni\(_{1-x}\))\(_{2}\)B\(_{2}\)C (\(x=0.2,0.4,0.6,0.8\)). We investigated the evolution of their magnetic, thermal and transport properties by means of the magnetization, resistivity, specific heat and neutron diffraction techniques. Their crystal structures were confirmed to be ThCr\(_{2}\)-Si\(_{2}\)-type tetragonal (I4/mmm) phase. The magnetic structure was found to be antiferromagnetic with k_0.2 = (0, 0, 1) for x = 0.2; helicoidal with k\(_{0.4}\) = (0, 0, 0.49) and k\(_{0.6}\) = (0, 0, 0.46) for, respectively, x = 0.4 and 0.6 and ferromagnetic with k\(_{0.8}\) = (0, 0, 0) for x = 0.8. We discuss the evolution of such magnetic modes assuming a scenario of an idealized one-dimensional chain of transverse magnetic moments.     

Stability of the Supercon ducting d-Wave Pairing Towar d the Intersite Coulomb Repulsion in $$\hbox {CuO}_2$$ Plane

Taking into account the real crystalline structure of the \(\hbox {CuO}_2\) plane and the strong spin-fermion coupling, we study the influence of the intersite Coulomb repulsion between holes on the Cooper instability of the spin-polaron quasiparticles in cuprate superconductors. The analysis shows that only the superconducting d-wave pairing is implemented in the whole region of doping, whereas the solutions of the self-consistent equations for the s-wave pairing are absent. It is shown that intersite Coulomb interaction \(V_1\) between the holes located at the nearest oxygen ions does not affect the d-wave pairing, because its Fourier transform \(V_q\) vanishes in the kernel of the corresponding integral equation. The intersite Coulomb interaction \(V_2\) of quasiparticles located at the next-nearest oxygen ions does not vanish in the integral equations, however, but it is also shown that the d-wave pairing is robust toward this interaction for physically reasonable values of \(V_2\).     

Further Estimates of $$(T-T_{90})$$ Close to the Triple Point of Water

Recent advances in primary acoustic gas thermometry (AGT) have revealed significant differences between temperature measurements using the International Temperature Scale of 1990, \(T_{90}\), and thermodynamic temperature, T. In 2015, we published estimates of the differences \((T-T_{90})\) from 118 K to 303 K, which showed interesting behavior in the region around the triple point of water, \(T_\mathrm{TPW}=273.16\) K. In that work, the \(T_{90}\) measurements below \(T_\mathrm{TPW}\) used a different ensemble of capsule standard platinum resistance thermometers (SPRTs) than the \(T_{90}\) measurements above \(T_\mathrm{TPW}\). In this work, we extend our earlier measurements using the same ensemble of SPRTs above and below \(T_\mathrm{TPW}\), enabling a deeper analysis of the slope \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) around \(T_\mathrm{TPW}\). In this article, we present the results of seven AGT isotherms in the temperature range 258 K to 323 K. The derived values of \((T-T_{90})\) have exceptionally low uncertainties and are in good agreement with our previous data and other AGT results. We present the values \((T-T_{90})\) alongside our previous estimates, with the resistance ratios W(T) from two SPRTs which have been used across the full range 118 K to 323 K. Additionally, our measurements show discontinuities in \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\) which are consistent with the slope discontinuity in the SPRT deviation functions. Since this discontinuity is by definition non-unique, and can take a range of values including zero, we suggest that mathematical representations of \((T-T_{90})\), such as those in the mise en pratique for the kelvin (Fellmuth et al. in Philos Trans R Soc A 374:20150037, 2016. doi: 10.1098/rsta.2015.0037), should have continuity of \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\).     

Effect of Aging on the Spectral Radiative Properties of Plastic Film-Covered Greenhouse under Arid Conditions

Plastic films are widely used to cover greenhouses in arid regions. Unlike predicting the total radiative properties of films, predicting the deterioration behavior of the spectral radiative properties is quite difficult during the service life of the films. These properties should be of great interest for crop morphogenesis studies. This study was to investigate the degradation behavior of spectral transmittance, \( \tau_{\lambda } \), and reflectance, \( \rho_{\lambda } \) (in the solar spectrum range), of a 200 µm thick, LDPE film-covered greenhouse model that was exposed for 1 year to an arid climate. Every 30 days, \( \tau_{\lambda } \) and \( \rho_{\lambda } \) were measured for six samples taken from the six surfaces of the greenhouse cover and averaged to obtain the cover properties. Based on the collected data, nonlinear correlations (each as a function of the wavelength, λ, and the exposure time, t) were obtained to predict \( \tau_{\lambda } \) and \( \rho_{\lambda } \) at any time during the service life of the cover under such climatic conditions. Results showed that 1 year exposure drastically reduced the spectral and total transmittance of the cover film to global and PAR solar radiation by about 32 % and increased the spectral and total reflectance by about 19 % compared to new film. Degradation of the radiative properties of the film did not affect the light quality or the transmission ratios of light into the greenhouse. The transmitted PAR was reduced from 115 W·m^?2 to 27 W·m^?2 after 1 year exposure.     

Vortex Shedding from an Object Moving in Superfluid $$^4\hbox {He}$$ at mK Temperatures and in a Bose–Einstein Condensate

Vortex shedding from a microsphere oscillating in superfluid \(^4\hbox {He}\) at mK temperatures is compared with that from a laser beam moving in a Bose–Einstein condensate as observed by other authors. In particular, in either case a linear dependence of the shedding frequency \(f_v\) on \(\varDelta v = v - v_c\) is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above a critical velocity \(v_c\) for the onset of turbulent flow: \(f_v = a \,\varDelta v\), where the coefficient a is proportional to the oscillation frequency \( \omega \) above some characteristic frequency \(\omega _k\) and assumes a finite value for steady motion \(\omega \rightarrow 0\).     

Cyclic codes over $${\mathbb {F}}_{2^m}[u]/\langle u^k\rangle $$ of oddly even length

Let \({\mathbb {F}}_{2^m}\) be a finite field of characteristic 2 and \(R={\mathbb {F}}_{2^m}[u]/\langle u^k\rangle ={\mathbb {F}}_{2^m} +u{\mathbb {F}}_{2^m}+\ldots +u^{k-1}{\mathbb {F}}_{2^m}\) (\(u^k=0\)) where \(k\in {\mathbb {Z}}^{+}\) satisfies \(k\ge 2\). For any odd positive integer n, it is known that cyclic codes over R of length 2n are identified with ideals of the ring \(R[x]/\langle x^{2n}-1\rangle \). In this paper, an explicit representation for each cyclic code over R of length 2n is provided and a formula to count the number of codewords in each code is given. Then a formula to calculate the number of cyclic codes over R of length 2n is obtained. Moreover, the dual code of each cyclic code and self-dual cyclic codes over R of length 2n are investigated.     

Aggregate packing and -void saturation in mortar and concrete proportioning

Proportioning was studied by measuring aggregate packing (C) and filling of aggregate void space (1?C) with varying volumes of cement paste (\(V_{\rm p}\)) or matrix (\(V_{\rm matrix}\)), i.e., all material <0.125 mm. Eleven widely different normal density aggregates with C = 0.57 to 0.71, i.e., aggregate void content (1?C) = 0.29 to 0.43, were used at constant w/c = 0.38 and flowing consistency and varying dosage of water reducer and paste- and matrix volume. Analysing plots of four excess phase volumes (paste with/without air, matrix with/without air) versus aggregate void space showed constant aggregate void saturation ratios. Both paste- and matrix-aggregate void saturation ratio can be used with the best estimate (\(V_{\rm p}-V_{\rm air})/{(1-C)}=1.15\) per \(\hbox{m}^{3}\). Including air voids in paste- or matrix volume improved correlation so air void content must be included in the normalized paste aggregate void saturation ratio (\(k=V_{\rm p}\)/[(1?C) \(V_{\rm tot}\)]). Simple measurements of aggregate packing are thus very useful. Cost per unit material, per unit fresh (slump, flow diameter) or hardened (compressive strength) property were used to show the cost efficiency of the mixes. The ranking of cost/MPa strength and cost/mm consistency is similar to ranking of total concrete cost for the 11 aggregates with a certain scatter though.     

Testing of multivariate repeated measures data with block exchangeable covariance structure

A new hypothesis testing of equality of mean vectors in two populations using \(D^2\) statistic for multivariate repeated measures data on q response variables at p sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only \(q +1\), unlike \(pq +1\) in Hotelling’s \(T^2\) test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the \(pq \times pq\) dimensional unknown unstructured variance–covariance matrix. Some simulation studies are performed to compare the power of the new \(D^2\) test and the existing \(BT^2\) test. The performance of the proposed \(D^2\) test is demonstrated with the two medical data sets.     

The Ideal and Real Gas Heat Capacity of Potassium Atoms at High Temperatures

The ideal gas heat capacity, \(C_{p}\), of potassium atoms is calculated to high temperatures using statistical mechanics. Since there are a large number of electronic energy levels in the partition function (Boltzmann sum) below the first ionization potential, the partition function and \(C_{p}\) will become very large as the temperature increases unless the number of energy levels contributing to the partition function is constrained. Two primary categories of arguments are used to do this. First, at high temperatures, the increased size of the atoms constrains the sum (Bethe method). Second, an argument based on the existence of interacting charged species at higher temperatures is used to constrain the sum (ionization potential lowering method). When potassium atoms are assumed to constitute a real gas that obeys the virial equation of state, the lowest non-ideal contribution to \(C_{p}\) depends on the second derivative of the second virial coefficient, B(T), which depends on the interaction potential energy curves between two potassium atoms. When two ground-state (\(^{2}\hbox {S}\)) atoms interact, they can follow either of the two potential energy curves. When a \(^{2}\hbox {S}\) atom interacts with an atom in the first electronically excited (\(^{2}\hbox {P}\)) state, they can follow any of the eight potential energy curves. The values of B(T) for the ten states are determined, then averaged, and used to calculate the nonideal contribution to \(C_{p}\).     

Experimental modelling of free-surface dry granular flows under a centrifugal acceleration field

We investigate the dynamics of granular flows under the action of a centrifugal acceleration field. The granular flows consist of a monodisperse set of glass beads flowing down an inclined plane. The experiments are performed at variable slope angles \(\zeta \) and equivalent centrifugal accelerations \(a_\text {cf}\equiv Ng\). We study the effect of this parameters on the superficial flow velocity u and flow height h. Two trends are observed, by increasing \(\zeta \) and \(a_\text {cf}\), u increases proportionally, and h decreases asymptotically until a constant height. This relation is analysed in terms of the system potential and kinetic energy, leading to the estimation of equivalent impact forces one order of magnitude larger than those observed in small scale 1g laboratory experiments, with the possibility to reach higher forces by increasing N. Finally, considering the trend of u and h, our results suggest a scaling principle of inertial velocity proportional to \(\sqrt{N}\).     

An illumination problem with tradeoff between coverage of a dataset and aperture angle of a conic light beam

Let \(\{a_i:i\in I\}\) be a finite set in \({\mathbb{R}}^n\). The illumination problem addressed in this work concerns the optimal location and orientation of a conic light beam

$$ R\big (z,y,s\big )= \left\{ x \in {\mathbb{R}}^n : s\,\Vert x-z\Vert - \langle y, x-z\rangle \le 0\right\} .$$

The aperture angle \(\vartheta = 2\arccos s\) of the conic light beam is a decreasing function of the sharpness coefficient \( s\in [0,1]\). The problem at hand is to select an apex z in a prescribed compact region \(Z\subseteq {\mathbb{R}}^n\) and a unit vector \(y\in {\mathbb{R}}^n\) so that the conic light beam R(z, y, s) fulfils two conflicting requirements: it captures as many points \(a_i\) as possible and, at the same time, it has a sharpness coefficient s as large as possible.

     

Nonparametric density and survival function estimation in the multiplicative censoring model

Consider the multiplicative censoring model given by \(Y_i=X_iU_i\), \(i=1, \ldots ,n\) where \((X_i)\) are i.i.d. with unknown density f on \({\mathbb {R}}\), \((U_i)\) are i.i.d. with uniform distribution \({\mathcal {U}}([0,1])\) and \((U_i)\) and \((X_i)\) are independent sequences. Only the sample \((Y_i)\) is observed. We study nonparametric estimators of both the density f and the corresponding survival function \(\bar{F}\). First, kernel estimators are built. Pointwise risk bounds for the quadratic risk are given, and upper and lower bounds for the rates in this setting are provided. Then, in a global setting, a data-driven bandwidth selection procedure is proposed. The resulting estimator has been proved to be adaptive in the sense that its risk automatically realizes the bias-variance compromise. Second, when the \(X_i\)s are nonnegative, using kernels fitted for \({\mathbb {R}}^+\)-supported functions, we propose new estimators of the survival function which are also adaptive. By simulation experiments, we check the good performances of the estimators and compare the two strategies.