Higher order approximation for local behaviour of two dimensional flows at the confluence of free streamlines and analytic solid boundaries

Summary The problem considered is a steady, two-dimensional, and irrotational flow of an incompressible and inviscid fluid under the action of gravity. The boundary of the flow domain consists of a free boundary part “C _f ” and an analytic solid boundary part “C _s ” and they meet in a common endpoint “0”. The flow is determined by the inverse velocity potential functionz=f(w) and the conjugate flow velocity is given by the reciprocal derivative . Following the method suggested by Carter, we will be able to expressz(w) andu(w) as an infinite asymptotic expansion near the origin in powers ofw ^1/2 andw ^1/2 lnw. Upon imposing the flow conditions on these expansions we will obtain the expansion of the conjugate velocityu to terms of orderw ^3/2 as well as the shape of free streamline. The importance of the results of this problem is that it gives simple, and more accurate, qualitative features of the local flow behaviour. Numerical examples have been considered and the results are given in quantitative diagrams to show the progress of the obtained higher approximation. With 5 Figures     

Evolution of a Network of Vortex Loops in the Turbulent Superfluid Helium; Derivation of the Vinen Equation

The evolution a network of vortex loops due to the fusion and breakdown in the turbulent superfluid helium is studied. We perform investigation on the base of the “rate equation” for the distribution function n(l) of number of loops in space of their length l. There are two mechanisms for change of quantity n(l). Firstly, the function changes due to deterministic process of mutual friction, when the length grows or decreases depending on orientation. Secondly, the change of n(l) occurs due to random events when the loop crosses itself breaking down into two daughter or two loops collide merging into one larger loop. Accordingly the “rate equation” includes the “collision” term collecting random processes of fusion and breakdown and the deterministic term. Assuming, further, that processes of random colliding are fastest we are in position to study more slow processes related to deterministic term. In this way we study the evolution of full length of vortex loops per unit volume—so-called vortex line density ℒ(t). It is shown this evolution to obey the famous Vinen equation. In conclusion we discuss properties of the Vinen equation from the point of view of the developed approach.     

Theoretical and numerical results of a deterministic two-dimensional vortex method

The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the corespreading model. The aim of the second part is to confirm the results of the previous analysis and to estimate the accuracy of these methods numerically. In the present paper, the model problem of a transient flow past an impulsively started circular cylinder is studied by several numerical methods. The numerical results show that (1) the Gaussian core-spreading methods are comparable with the random walk vortex method, (2) the numerical fluctuation of the deterministic methods is small, and (3) the number of panels is smaller than those in the random walk vortex method to obtain the flow with almost the same accuracy. The theoretical results in § 2–4 of the present paper are summarized from “Core-spreading vortex methods in two-dimensional viscous flows”,Computer methods in applied mechanics and engineering (in press), by Kida and Nakajima, with permission from Elsevier Science, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. The experimental picture is transferred from “The early stage of development of the wake behind an impulsively started cylinder for 40<Re<⁴”, by R Bouard and M Coutanceau,J. Fluid Mech. (1980) 101: 583–607.     

On some helical flows of Oldroyd-B fluids

Summary In this study the velocity fields and the associated tangential stresses corresponding to some helical flows of Oldroyd-B fluids between two infinite coaxial circular cylinders and within an infinite circular cylinder are determined in forms of series in terms of Bessel functions. At time t = 0 the fluid is at rest and the motion is produced by the combined action of rotating and sliding cylinders. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. For λ _r = 0, λ = 0 or λ _r = λ = 0 they reduce to the similar solutions for a Maxwell, second grade or Newtonian fluid, respectively. Finally, for comparison, the velocity profiles corresponding to the four models are plotted for different values of t.     

Possible Nature of Field-Induced Antiferromagnetic Ordering in SC Cuprates

In the present work, the results of recent neutron scattering, STM, and NMR experiments concerning the structure of the vortex core in resistive state of the cuprates are discussed. It is demonstrated that “field-induced” antiferromagnetic (SDW) ordering observed in the SC state is the same as “temperature-induced” one arising above T _c in the pseudogap (SDW) state. It is pointed out that in resistivity measurements, due to short mobile charge carrier relaxation time, a magnetic structure is sampled on much shorter time scale as compared with other techniques such as neutron scattering, Mossbauer effect, etc. It is noted that existing theoretical models mainly consider the SDW order only as competing to the SC one rather than stimulating the SC to appear at higher temperature.     

Evaporation of NH3 in NH3/H2 atmosphere by 25 bar for neutral gas absorption refrigeration units

The present work considers the evaporation process ofNH ₃ inNH ₃/H₂ atmosphere, that takes place in neutral gas absorption refrigeration units. The data obtained are used to calculate the “psychrometric problem” and the evaporation process within an insulated tube. The “psychrometric problem” deals with the determination of the mass fraction of theNH ₃/H ₂ gas mixture from known “dry” and “wet bulb” temperatures for Lewis numbers not equal to one. The results are in good agreement with some existing experimental data.     

Bactericidal action of the plasma of high-frequency capacitive and barrier discharges on microorganisms

The bactericidal action of the plasma of a high-frequency discharge excited at a frequency f = 5.28 MHz and a low pressure in air on different test-strains of microorganisms has been investigated. The high-efficiency plasma inactivation of strains of E. coli, B. subtilis, C. albicans, and S. aureus at an initial contamination N ₀ ≤ 10³ CFU / ml was detected. It was established that the most probable sterilization agents of the plasma generated are the “hot” and “cold” OH radicals, the excited electrically neutral N₂ and O₂ molecules, and the UV plasma radiation.     

Time dependent behavior of elements combining ultra-high performance fiber reinforced concretes (UHPFRC) and reinforced concrete

Structural elements combining Ultra-High Performance Fiber Reinforced Concretes (UHPFRC) and concrete offer a high potential in view of rehabilitation and modification of existing structures. The investigation of the time-dependent behavior of composite “UHPFRC-concrete” elements is a fundamental step in the determination of durability and serviceability. For this, an experimental program was conducted on large composite “UHPFRC-concrete” beams and a numerical model was validated with the test results. The experimental results and a parametric study performed with the numerical model showed that UHPFRC and normal strength reinforced concrete are compatible in the long-term and that the critical period of composite “UHPFRC-concrete” elements are the first 90 days after the casting of the UHPFRC layer. Thus, the high potential of such composite elements can be exploited also in the long term.     

Crystallization of Mg-containing phases in β′-Si-Al-O-N ceramics

The microstructures ofβ′-Si-Al-O-N ceramics of base composition Si₄Al₂O₂N₆ with large MgO additive (6 to 7 wt %) have been compared in the hot-pressed and sintered conditions. In both ceramics Mg shows only a small solubility inβ′ crystals and is mainly segregated in a “matrix” phase. In hot-pressed materials this is an Mg-Al-silicate glass whereas in sintered materials, inhomogeneities in composition and internal cavities are believed to catalyse its crystallization as the spinel phase (MgAl₂O₄ with partial Si substitution). A minor phase in sintered ceramics is the 15R “polytype” of the AlN structure.     

The Kramers-Kronig relations for permittivity, “True” screening radius,and critical point of a coulomb system

A correlation between the peculiarities of the electric permittivity (EP) ɛ(q, ω) of a homogenous and isotropic Coulomb system (CS) in the limit of ω → 0, q → 0 and q → 0, ω → 0 is established on the basis of exact limiting relations; general expression for static EP ɛ(q, 0) of a CS is obtained in the region of small wave vectors q. The concepts of a “true” dielectric and “ideal” conductor are introduced. The definition of a “true” screening radius is considered. A critical point of two-component CS is shown to correspond to either the “true” dielectric state or the “ideal” conductor one.     

Some properties of vortices in layered superconducting structures

Some properties of vortices in layered superconductors and superconducting structures with the Josephson interaction between S-layers are studied theoretically. The Josephson vortex lattice is formed in the system if the magnetic fieldH _e is parallel to the layers. Long-wave oscillations of this lattice have a sound-like spectrum; the velocity of “magnetic sound” propagating across the layers is small and diminishes with increase ofH _e . Using an analogy with electron-hole plasma in semiconductors, we investigate also the behaviour of the layered structure in the fieldH _e perpendicular to the layers at temperatures close to the Kosterlitz-Thouless transition temperatureT _KT. The spatial dependence ofH(r) and the impedance of the system are determined atT>T _KT.     

Stripes, non-fermi-liquid behavior, and high-T c superconductivity

The electronic structure of the high-T_c. cuprates is studied in terms of “large-U” and “small-U” orbitals. A striped structure and three types of quasiparticles are obtained, polaron-like “stripons” carrying charge, “svivons” carrying spin, and “quasielectrons” carrying both. The anomalous properties are explained, and specifically the behavior of the resistivity. Hall constant, and thermoelectric power. High-temperature superconductivity results from transitions between pair states of quasielectrons and stripons.     

Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing

Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline–Upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters, which we call “YZβ Shock-Capturing”, are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZβ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code     

A unified model of initiation and growth of fatigue macrocracks. part 3. stage of growth of a macrocrack

From a common viewpoint, fatigue fracture of materials is simulated by the process of initiation of an initial macrorack of lengtha _i =d ^* (d ^* is the constant of the material), which is successively (stepwise) repeated at the stage of its growth. As a result, the diagram “range of local stresses-period of initiation of an initial macrocrack” or ”range of local strains-period of initiation of an initial macrocrack,” which was determined for notched specimens, can be used for the construction of the diagram “growth rate of a macrocrack-range of the stress intensity factor” or “growth rate of a macrocrack-range of local strains,” respectively, if the crack is presented as a sharp notch with effective rounded radius ρ_eff=d ^* of the tip. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 3, pp. 5–14, May–June, 1999.     

On the “local approach” to the brittle fracture of structural materials

We consider the principles and sources of an important scientific direction in fracture mechanics-the so-called “local approach” to the problem of fracture of materials. This approach provides a possibility to describe their crack resistance based on conventional mechanical properties and opens up a direct way to determining the limiting state of structural elements. As the first example of the application of this approach, we present the principal propositions of the two-parameter K _μ-model of fracture, which relates the “global” K _Ic and “local” ρ_c and σ_c parameters via the yield condition on the contour of a small plastic zone near the tip of a crack. For the last decades, this direction was developed substantially and extended to the regions of quasi-brittle and ductile fracture. We also present the basic statements of this approach that were corroborated for the last decades. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 39–44, March–April, 2006.     

Models of thermomechanical behavior of polymeric materials undergoing glass transition

The phenomenological models of the thermomechanical behavior of polymeric materials in a temperature range including the relaxation transition from the highly elastic to the glassy state (vitrification) and the reverse transition (softening) are considered. A model based on the interpretation of the glass transition as a process of gradual increase in intermolecular bonds in the polymer network, “freezing” the current strain with decreasing temperature is developed. A scalar parameter is introduced—the “degree of vitrification,” to establish the quantitative dependence of the relaxation transition completion by temperature. Constitutive relations of thermomechanical behavior of vitrifying polymers in uniaxial and complicated stress states in the “elastic approximation” simplification are obtained. A system of experiments for the identification of the proposed model material functions and constants is formulated and implemented. Analytical model problems are solved, clearly illustrating the mechanism for generation of technological and residual stresses in glass polymers in non-uniform cooling.     

Leben zwischen ,,Vegetativ“ und ,,Vegetieren“

The modern scientific and ordinary language contains several specific terms which refer to the words “vegetative”or “vegetate” as in “persistent vegetative state” or “human vegetable”.There is a long tradition from ancient times until today to compare specific functions and situations concerning human beings with the state of plants, e.g. in natural philosophy, medicine or ethics. A specific “vegetative terminology” has been established in medicine around 1800 in anatomical, physiological and clinical considerations (e.g. on the autonomous nervous system since Reil).The following paper presents firstly the historical background and some stations in the use of this vegetative terminology within the history of ideas and medicine especially around 1800. The second part presents a bioethical approach to problems of a human vegetative state or “human vegetable” by Hans Jonas.

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Leben zwischen ,,Vegetativ“ und ,,Vegetieren“ Zur historischen und ethischen Bedeutung der vegetativen Terminologie in der Wissenschafts- und Alltagssprache

     

The effect of flaw shape on fracture initiation at a blunt flaw

The author is involved in a wide-ranging research programme, the objective being to extend the fracture mechanics methodology for sharp cracks to blunt flaws, so as to take credit for the blunt flaw geometry. The approach is based on the cohesive process zone representation of the micro-mechanistic processes that are associated with fracture. An earlier paper has derived a blunt flaw fracture initiation relation which gives the critical elastic flaw-tip peak stress σ_pcr (a “signifier” of a critical condition in the process zone) in terms of the process zone material parameters, subject to the proviso that the process zone size s is small compared with the flaw depth (length) and any characteristic dimension other than the flaw root radius ρ. The relation has been derived using a “two-extremes” procedure, whereby the separate σ_pcr solutions for small and large s/ρ are blended together to give an all-embracing relation that is valid for all s/ρ. A key feature of the relation is that σ_pcr essentially depends on only one geometrical parameter: the flaw root radius ρ. Though the relation has evolved from a consideration of the characteristics of one model, i.e. that of an elliptical flaw in an infinite solid that is subjected to an applied tensile stress, it is anticipated that the relation can be applied equally well for a wide range of geometrical configurations involving different flaw shapes. It is against this background that the present paper demonstrates that the relation also applies to the behaviour of an intrusion type flaw in the surface of a semi-infinite solid subjected to an applied tensile stress.     

Vortex Pinning to a Solid Sphere in Helium II

We report here the results of a computer simulation of quantized vortex pinning in He II at 0 K in the simple situation where a single sphere and a rectilinear vortex are considered. Our simulation shows that a vortex nearby a sphere is captured due to a velocity field produced by the sphere, exciting Kelvin waves. The dependence of the “pinning” on temperature is investigated as well. Finally, the possibility of pinning in PIV experiments, which visualize superfluid turbulence, is discussed.     

Modelling of gusts and wind shear for aircraft assessment and certification

Recent research in the UK on the subject of turbulence modelling for aircraft assessment and certification has emphasised the importance of considering ordered structures existing in apparently disordered air motions. A consequence of the existence of such order within disorder is that probability distributions of velocity gradients and associated velocity increments are often strongly non-Gaussian, even in so-called continuous turbulence. This non-Gaussian characteristic of turbulence (which may be related to the phenomenon of “intermittency”) is a source of dissatisfaction with the widely-used power-spectral method for modelling turbulence and is the main incentive for developing an alternative. One approach to the problem has been the development of a statistical discretegust model of turbulence which takes a discrete ramp gust as a basic element from which representative gust patterns may be built up and related to probability of occurrence. On this basis an alternative approach to aircraft certification has been proposed in which the assessment of a particular design (of aircraft, or gust-alleviation system) involves a systematic search over a specified family of equiprobable gust patterns for a “worst case” which produces maximum aircraft response. Such an equiprobable family is a generalisation of the traditional concept of a “design gust.” An important feature of the method is that the “worst case” response may be directly related to the statistical characteristics of response when the input has a random character representative of real turbulence. The technique is illustrated with particular reference to the assessment of autoland systems in severe wind shear and to limit-load criteria (for which a vortex-tube model is proposed to augment the statistical family of discrete ramp gusts).