T-stress near the tips of a cruciform crack with unequal arms

The T-stress near the tips of a crack of cross shape embedded in an isotropic elastic solid is analyzed. The integral transform technique is employed to convert the associated boundary value problem to a system of singular integral equations. According to the stress difference method, T-stresses can be expressed as a sum of an integral involving crack opening displacement (COD) and applied loading at infinity. Obtained results indicate that, in addition to applied loading, T-stresses at the horizontal (vertical) crack tips depend on the COD of the vertical (horizontal) crack surface. COD plays a leading role in determining T-stresses, in particular for a cruciform crack of two crack-arm lengths of the same order. Moreover, T-stresses for a single-crack limiting case can be recovered from the present results as the length of one arm approaches zero. For a biaxial tension of the same magnitude, T-stresses are present for a cruciform crack, but absent for a single crack. Finally, for several cases of interest, T-stresses for a cruciform crack are evaluated and compared with those for a single crack, and the influence of the ratio of two crack-arm lengths b/a and the COD on the T-stress of a cruciform crack is examined.     

Magnetic Interaction Force and a Couple on a Superconducting Sphere in an Arbitrary Dipole Field

The calculation of the magnetostatic potential and levitation force due to a point magnetic dipole placed in front of a superconducting sphere in the Meissner state is readdressed. Closed-form analytical expression for the scalar potential function that yields the image system for an arbitrarily oriented magnetic dipole located in the vicinity of a superconducting sphere is given. Analytic expression for the lifting or levitation force acting on the sphere is extracted from the solution for a general dipole. A special case of our expression where the initial magnetic dipole makes an angle with the z-axis is derived. Our expression for the force in this particular case shows that a recently obtained result (J. Supercond. Nov. Magn. 21:93–96, 2008) for an arbitrary dipole is incorrect. A brief discussion of another erroneous result (J. Supercond. Nov. Magn. 15:257–262, 2002) for a transverse/tangential dipole–sphere configuration, corrected elsewhere recently, is reproduced. Correct expressions for the interaction energy with some limiting cases are also provided. The result derived here demonstrates that the value of the levitation force for a dipole that makes an angle with z-axis lies between the values for a radial dipole–sphere and transverse dipole–sphere configurations providing upper and lower bounds. It is found that for a magnetic dipole making an angle with z-axis, there exits a second force component along the negative y-direction, which influences a couple acting on the superconducting sphere. It is also shown that the couple is proportional to the second force component and that both the couple and second force components vanish for a radial dipole–sphere and transverse dipole–sphere configurations, respectively. These results appear to be new and have not had received due attention in the context of superconductivity.     

Longitudinal and transverse waves in anisotropic elastic materials

Summary It is shown that a necessary and sufficient condition for a longitudinal wave to propagate in the direction n in an anisotropic elastic material is that the elastic stiffness C ₁₁ (n) is a stationary value (maximum, minimum or saddle point) at n. Explicit expressions of all n and the corresponding elastic stiffness C ₁₁ (n) for which a longitudinal wave can propagate are presented for orthotropic, tetragonal, trigonal, hexagonal and cubic materials. As to longitudinal waves in triclinic and monoclinic materials, only few explicit expressions are possible. We also present necessary and sufficient conditions for a transverse wave to propagate in the direction n. As an illustration, explicit expressions of all n, the polarization vector a and the wave speed c for which a transverse wave can propagate in cubic and hexagonal materials are given. The search for n in hexagonal materials confirms the known fact that a transverse wave can propagate in any direction. A longitudinal wave is necessarily accompanied by two transverse waves. However, a transverse wave can propagate without being accompanied by a longitudinal wave.     

Der Aufbruch zum „funktionalen Denken“: Geschichte des Mathematikunterrichts im Kaiserreich

  By the end of the 19th century, mathematics teaching underwent a crisis of similar proportion in several European countries. Constrained by the values of classical Antiquity, which dominated in secondary education, mathematics was taught as a formal discipline enhancing elementary geometry and intended as some gymnastics of the mind. Moreover, a specific feature in Germany was that the country was split up into numerous independent states each having a separated educational system of its own. Many of these conferred an only marginal status to mathematics instruction. This complex situation is analyzed for the traditional school system for boys, as well as for the emerging system for girls, and for primary schooling. The study describes the key initiatives by Felix Klein, who forged a dynamic movement of teachers for modernising secondary school teaching. Their culmination in the famous “Meran” reform program is depicted, a program which became the starting point for the first international reform movement in mathematics teaching.

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Renate Tobies zum 60. Geburtstag gewidmet.     

Evaluation of VOC recovery strategies

Many manufactured items receive surface coatings for decoration and/or protection against damage. In a number of places along the production line emissions of (VOC) Volatile Organic Compounds can occur. Because VOC are a major contributor to photochemical smog, control of VOC emissions is a major concern for the industries' commitment to the environment. Approaches for process optimisation have a long tradition within chemical and process engineering for the systematic identification of cost- and resource-efficient production options. The challenge in the context of supply chain management is the optimal recovery and reuse of materials not only for single substances or energy flows in large chemical installations, but also for smaller production processes and various mass and energy flows within and between enterprises. Based on a case study from the industrial coating of bicycle frames, an approach for Multi Objective Pinch Analysis (MOPA) for the evaluation of overall recovery potentials for energy, water and VOC is presented. Moreover, a metric for resource efficiency is introduced as a measure for the possible savings potential and for the savings ultimately realised. This integrated approach requires a tight coupling of mass, energy, economic and environmental assessment methods and demands a highly interdisciplinary approach.

On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J₂-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms.     

A comparative study on chitosan nanoparticle synthesis methodologies for application in aquaculture through toxicity studies

Chitosan nanoparticles (CSNPs) have been recently used for various applications in aquaculture, especially as drug carriers. The aim of this study was to synthesise and investigate a superlative method of CSNP synthesis for application in aquaculture through aquaculture‐based toxicology screening methods. Two different methods were analysed: the first a direct ionic gelation method (A) and the other involving a low‐molecular‐weight chitosan microparticle intermediate method (B). Dynamic light scattering characterisation revealed that the CSNP particle sizes were 192.7 ± 11.8 and 22.9 nm from methods A and B, respectively. The LC₅₀ values for brine shrimp toxicity were found to be 1.51 and 0.02 ppt in 24 h for methods A and B, respectively. Acute toxicity studies in Litopenaeus vannamei rendered LC₅₀ values of 3235.94 and 2884.03 ppt in 24 h for methods A and B, respectively. Zebrafish toxicity studies revealed mortality rates of 21.67% and 55% at 20 mg/L concentration for methods A and B, respectively, with an increased expression of intracellular reactive oxygen species in method B. From these findings, it can be concluded that a comparatively reduced toxicity of CSNPs derived from ionic gelation method makes it more appropriate for application in aquaculture.     

A Critical Evaluation of Interlaboratory Data on Total,Elemental, and Isotopic Carbon in the Carbonaceous Particle Reference Material,NIST SRM 1649a

Because of increased interest in the marine and atmospheric sciences in elemental carbon (EC), or black carbon (BC) or soot carbon (SC), and because of the difficulties in analyzing or even defining this pervasive component of particulate carbon, it has become quite important to have appropriate reference materials for intercomparison and quality control. The NIST “urban dust” Standard Reference Material^® SRM 1649a is useful in this respect, in part because it comprises a considerable array of inorganic and organic species, and because it exhibits a large degree of (¹⁴C) isotopic heterogeneity, with biomass carbon source contributions ranging from about 2 % (essentially fossil aliphatic fraction) to about 32 % (polar fraction).A primary purpose of this report is to provide documentation for the new isotopic and chemical particulate carbon data for the most recent (31 Jan. 2001) SRM 1649a Certificate of Analysis. Supporting this is a critical review of underlying international intercomparison data and methodologies, provided by 18 teams of analytical experts from 11 institutions. Key results of the intercomparison are: (1) a new, Certified Value for total carbon (TC) in SRM 1649a; (2) ¹⁴C Reference Values for total carbon and a number of organic species, including for the first time 8 individual PAHs; and (3) elemental carbon (EC) Information Values derived from 13 analytical methods applied to this component. Results for elemental carbon, which comprised a special focus of the intercomparison, were quite diverse, reflecting the confounding of methodological-matrix artifacts, and methods that tended to probe more or less refractory regions of this universal, but ill-defined product of incomplete combustion. Availability of both chemical and ¹⁴C speciation data for SRM 1649a holds great promise for improved analytical insight through comparative analysis (e.g., fossil/biomass partition in EC compared to PAH), and through application of the principle of isotopic mass balance.     

Accelerated microwave curing of concrete: A design and performance-related experiments

Microwave (MW)-accelerated curing has emerged as an innovative and popular curing method for concrete materials. This paper reports the results of a study to model the horn antenna used for the MW irradiation of a workpiece with a mobile MW-accelerated concrete curing unit, based on a coupled thermal and electromagnetic analysis. The mathematical models were useful for evaluating the heat generation within a horn antenna and as a basis for constructing a mobile MW-accelerated curing unit with an operating frequency of 2.45 GHz and a MW power level of 800 W. Further, the early-age compressive strength development and volume stability of MW-cured concrete were investigated in terms of its shrinkage and compared to the properties of autoclave-cured concrete. The design results showed that under the concept of the allowable maximum temperature for the concrete workpiece, which was controlled to less than 80 °C, a horn antenna that was 216.70 mm wide, 333.68 mm long, and 273.0 mm high produced a uniform thermal distribution in a concrete workpiece. Moreover, experimental investigations showed that the application period for curing using a mobile MW-curing unit was considerably shorter than that in autoclave curing methods. The appropriate delay time (time after concrete mixing) was 30 min, and MW irradiation for 45 min could improve the maximum 8-h early-age compressive strength of MW-cured concrete, whereas an application time of 15 min produced the 28-day compressive strength. When a concrete workpiece was cured at high temperature using MW energy for more than 15 min at a temperature greater than 80 °C, the effect was a continuous increase in the early-age compressive strength, which was greater than that achieved by autoclave curing. In terms of volumetric stability, MW-curing for 30 and 45 min increased the ultimate shrinkage to a greater extent than that by autoclave curing and vice versa in the case of a MW application time of 15 min.     

Waiting times,probabilities and the Q factor of fluorescent photons

Photons in resonance fluorescence from a single atom are correlated, and this affects the photon detection statistics. We consider the time dependence of the variance for the number of counts in a time interval [0,?T], and we show that there exist Poisson points for certain values of the atomic parameters. At these points, the variance equals the average, like for a Poisson process. We also show that the conditional probability density for the detection of the nth photon after a detection of a photon at time zero can be obtained from the conditional probability density for the first photon, and we illustrate this by computing several conditional probability densities for a special case of interest. The unconditional probability density for the detection of the nth photon can be obtained from the conditional probability densities and the probability for detecting n photons in [0,?T] can subsequently be found from the unconditional probability densities.     

An algorithm for interpolating a finite-spectrum function truncated on a semiopen interval with a redundant digitization frequency

A new method is proposed for interpolating an initial function by the use of a condition for redundancy in the sampling frequency for a function with a finite spectrum over a restricted interval (by comparison with a condition in Kotel’nikov’s theorem). __________ Translated from Izmeritel’naya Tekhnika, No. 11, pp. 9–12, November, 2007.     

Measurement of Speed of Sound with a Spherical Resonator: HCFC-22, HFC-152a, HFC-143a, and Propane

A spherical resonator and acoustic signal measurement apparatus have been designed and developed for measuring the speed of sound in the gaseous phase. The inner radius of the spherical resonator, being about 6.177 cm, was determined by measuring the speed of sound in gaseous argon at temperatures between 293 and 323 K and at pressures up to 200 kPa. Measurements of the speed of sound in four halogenated hydrocarbons are presented, the compounds are chlorodifluoromethane (CHClF₂ or HCFC-22), 1,1-difluoroethane (CH₃CHF₂ or HFC-152a), 1,1,1-trifluoroethane (CH₃CF₃ or HFC-143a), and propane (CH₃CH₂CH₃ or HC-290). Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the present data. The results were compared with those from other studies. In this work, the experimental uncertainties in temperature, pressure, and speed of sound are estimated to be less than ±14 mK, ±2.0 kPa, and ±0.0037%, respectively. In addition, equations for the ideal-gas isobaric specific heat capacity for HFC-152a, HFC-143a, and propane are proposed, which are applicable in temperature ranges 240 to 400 K for HFC-152a, 250 to 400 K for HFC-143a, 225 to 375 K for propane. The purities for each of the samples of HCFC-22, HFC-152a, HFC-143a, and propane are better than 99.95 mass%.     

Stiff macro-porous bioactive glass–ceramic scaffold: Fabrication by rapid prototyping template,characterization and in vitro bioactivity

Bioactive glass–ceramic scaffolds with interconnected pore networks suitable for bone regeneration were produced through rapid prototyping techniques by a photosensitive resin mold. The 45S5 Bioglass^® was used in this study with a composition (wt%): 45% SiO₂, 24.5% CaO, 24.5% Na₂O and 6% P₂O₅. All variables in the process were investigated systematically to devise an optimal process. Characterization methods such as XRD, FTIR and FESEM were used for determination of the in vitro bioactivity of the scaffolds after immersion in SBF. The results show that hydroxycarbonate apatite crystals formed and to be a layer in 14 days. The compressive strength of the scaffolds was approximately 12.37 ± 1.25 MPa for the well-defined interconnected pores with a mean diameter of 900 μm, which is thought to be a suitable porous network for vascularized bone regeneration. This scaffold has the potential to bond to bone for application in bone repair and regeneration.     

Isolation of Highly Reactive Cobalt Phthalocyanine via Electrochemical Activation for Enhanced CO2 Reduction Reaction

Electrochemical CO₂-to-CO conversion offers an attractive and efficient route to recycle CO₂ greenhouse gas. Molecular catalysts, like CoPc, are proved to be possible replacement for precious metal-based catalysts. These molecules, a combination of metal center and organic ligand molecule, may evolve into single atom structure for enhanced performance; besides, the manipulation of molecules’ behavior also plays an important role in mechanism research. Here, in this work, the structure evolution of CoPc molecules is investigated via electrochemical-induced activation process. After numbers of cyclic voltammetry scanning, CoPc molecular crystals become cracked and crumbled, meanwhile the released CoPc molecules migrate to the conductive substrate. Atomic-scale HAADF-STEM proves the migration of CoPc molecules, which is the main reason for the enhancement in CO₂-to-CO performance. The as-activated CoPc exhibits a maximum FE_CO of 99% in an H-type cell and affords a long-term durability at 100 mA cm⁻² for 29.3 h in a membrane electrode assembly reactor. Density-functional theory (DFT) calculation also demonstrates a favorable CO₂ activation energy with such an activated CoPc structure. This work provides a different perspective for understanding molecular catalysts as well as a reliable and universal method for practical utilization.     

Renewal type bootstrap for Markov chains

In this paper we treat a renewal type of bootstrap for atomic Markov chains under minimal moment conditions on renewal times, i.e.Er ²<∞. Three main results are: a) if a Markov chain satisfies the CLT for the mean then it also satisfies a bootstrap CLT; b) if a Markov chain satisfies a uniform CLT over classes of functions then, it also satisfies bootstrap uniform CLT with minimal condition on envelope functionF; c) we establish second order correctness for this procedure. All results are for “in probability” bootstrap and constitute the final word in this setting.     

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. To find solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N^2?×^?N². When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a 15-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.     

Peristaltic pumping of a micropolar fluid in a tube

Summary.  Peristaltic transport of a micropolar fluid in a circular tube is studied under low Reynolds number and long wavelength approximations. The closed form solutions are obtained for velocity, microrotation components, as well as the stream function and they contain new additional parameters namely, N the coupling number and m the micropolar parameter. In the case of free pumping (pressure difference Δp=0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Δp>0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena are presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Δp are discussed. Received June 20, 2002; revised October 23, 2002 Published online: April 17, 2003 The authors thank the referees for pointing out some mistakes in the governing equations and for the suggestions to improve the presentation of the paper.     

A mixed mode fracture specimen for mode II dominant deformation

Several theories have been proposed for the failure of metals, as well as for the angle of crack propagation in mixed mode loading. In order to demonstrate the validity of these theories, the majority of tests have been carried out with an oblique crack placed in a uniaxial stress field. Better testing conditions may be achieved by placing a crack in a uniform bidimensional stress field. A specimen which was recently developed for $\text{K}{}_{\mathrm{IIC}}$ measurement may be readily adapted to achieve a bidimensional stress field and be used for mixed mode testing for the case in which shear deformation is dominant. The main aims of this study are to examine both the cracked and uncracked specimen by means of photoelasticity and finite elements in order to analyze the capabilities and limitations of this specimen for mixed mode testing. It will be demonstrated that there exists a nearly uniform biaxial field in the uncracked specimen. Moreover, calibration formulas will be presented for $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$.     

Prediction of welded joint thinning by the method of polarization resistance

The equivalent electric circuits for determiningR _p in electrolytic cells with two dissimilar electrodes are investigated. For welded joints, we suggest a relation for estimating the corrosion rate in terms ofR _p and describe the design of a solion for determining this rate in a local zone of a welded joint.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 5, pp. 94–96, September–October, 1993.