Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

Stress analysis of a debonding and a crack around a circular rigid inclusion

A model of a debonding and a crack occurring from a circular rigid inclusion in an infinite plate is analyzed as a mixed boundary value problem under uniform tension. A mapping function represented in the form of a sum of fractional expressions and complex stress functions are used. The stress distribution, stress intensity factors at the tip of a crack, and stress singular values at a debonded tip are presented. By using these stress singular values, the intensity of the debonded tip is also considered.

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Résumé On analyse un modèle de décollement et de fissuration au départ d'une inclusion rigide circulaire dans une tôle infinie, en le considérant comme un problème mixte de valeurs aux limites sous une tension uniforme. On utilise des fonctions complexes de la contrainte et une représentation sous forme d'une somme d'expressions fractionnelles. La distribution des contraintes, des facteurs d'intensité de contraintes à l'extrémité de la fissure, et les valeurs des contraintes singulières à l'extrémité de la zone décollée, sont présentées. En utilisant ces valeurs de contraintes singulières, on prend également en compte l'étendue de cette zone décollée.

     

Discovering a junction tree behind a Markov network by a greedy algorithm

In our paper (Annals of Operations Research, 193:71–90, 2012) we introduced a special kind of k?1-width junction tree, called k-th order cherry tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback–Leibler divergence between the true joint probability distribution and the approximating one is minimal. Finding the best approximating k?1-width junction tree probability distribution is NP-complete if 2<k<d?1, where d is the dimension of the joint probability distribution (see Karger and Srebro in 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2001, Malvestuto in Kybernetika 48:825–844, 2012). In Broad Research in Artificial Intelligence and Neuroscience (BRAIN), special issue on complexity in sciences and artificial intelligence, pp. 40–45, 2010 we also proved that the best approximating k?1-width junction tree probability distribution can be embedded into a k-th order cherry tree probability distribution. We introduce here a greedy algorithm resulting very good approximations in reasonable computing time. We prove then that if the Markov network which encodes the conditional independences of the multivariate probability distribution fulfills some requirements then our greedy algorithm is able to find the true probability distribution. Our algorithm uses just the k-th order marginal probability distributions as input. We compare the results of the greedy algorithm proposed in this paper with the greedy algorithm proposed by Malvestuto (IEEE Trans. Syst. Man Cybern. 21:1287–1294, 1991).     

Analysis of a crack emanating from a circular hole in a loaded plane

The problem of a linear elastic loaded plane containing a circular hole with an arbitrary positioned edge crack is considered. The formulation is based on consideration of the dislocational pile-up in order to represent the crack, and on a fictious dislocation in the hole in order to satisfy single valued displacement requirement for the resulting stress potentials.The results are given in terms of the stress intensity factors at the crack tip for a variety of geometries. As the results indicate, at certain geometries there exists a critical crack length such that, below that value, the crack experiences an intensive growth, and, above this value, retardation of growth or crack arrest will take place.

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Résumé On considère le problème d'une plaque plane linéaire élastique, mise en charge, et comportant un trou circulaire avec une fissure de bord placée de manière arbitraire. Pour la formulation, on se base sur une représentation de la fissure par un empilement de dislocations et, pour satisfaire à l'exigence de déplacement unitaire associé aux potentiels de contrainte résultants, on suppose l'existence d'une dislocation fictive dans le trou.On présente les résultats sous forme de facteurs d'intensité de contraintes correspondant à diverses géométries. Comme l'indiquent les résultats, il existe pour certaines configurations une longueur critique de fissure telle que la fissure passe par une phase de croissance intensive lorsque sa longueur en est inférieure, ou au contraire se ralentit, voire s'arrête, lorsque sa longueur est supérieure à cette longueur critique.

     

Bifurcation of a transonic ideal-gas flow around a symmetric airfoil with a concavity

A transonic flow around a symmetric airfoil with a concavity in its central part has been numerically investigated. The dependences of the lift coefficient on the Mach number of the incident flow M_∞ and on the angle of attack α were determined. It is shown that, depending on M_∞, in the flow past the upper part of the indicated airfoil there can arise one or two supersonic-flow regions. It has been established that, at fairly large angles of attack, the coalescence and separation of supersonic-flow regions are realized in a discrete way. For these angles of attack, singular Mach numbers M_s, in the neighborhood of which the structure of the flow is transformed, were determined and the physical processes occurring in this case were analyzed. It was found that the flow being considered is characterized by a large hysteresis in M_∞. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 4, pp. 63–68, July–August, 2007.     

Calculation of a transient in a two-pole network with a thermistor

An analytical expression is derived which describes the variation of the thermistor temperature during a relay-effect transient process following an instantaneous change in the supply voltage in an R — R_T two-pole network.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 465–472, March, 1980.     

Stretching a stiff polymer in a tube

The present paper investigates the force-extension behavior of a stiff polymer under stretching inside a small tube. We develop a theory and perform Brownian dynamic simulations based on a recently developed generalized bead-rod model (GBR) to show that the force-extension relation of such a strongly confined polymer chain can be described by that of an unconfined polymer subject to an effective force which is derived based on Odijk’s theory of a confined polymer chain.

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Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

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Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

Free convection about a vertical frustum of a cone in a micropolar fluid

The paper studies the problem of free convection about a vertical frustum of a cone in a micropolar fluid. It is assumed that the flow is steady, and the surface temperature of the frustum of the cone is constant. Another assumption is that the angles of the frustum of the cone are large enough so that the transverse curvature effects are negligible. Under these assumptions, the governing boundary layer equations subjected to appropriate boundary conditions are first written in a non-dimensional form. These equations are then transformed into a set of non-similar partial differential equations of parabolic type, which is amenable to a direct numerical solution, using a very efficient method known as Keller-box method. Numerical solutions are obtained for a range values of the micropolar parameter Δ varying between Δ = 0 (Newtonian fluid) to Δ = 2 and Prandtl number Pr is varied from 0.1 to 10. Flow and heat transfer characteristics are determined and are given in tables and also shown on graphs. The obtained results are also compared with those known from the open literature and it is found that they are in excellent agreement.     

Stress intensity factors for a crack in a sheet with a partially debonded stiffener

A model is considered for a crack growing in the main sheet of a panel which has a continuously attached stiffener which is either partially debonded or partially cracked and debonded. The panel is modelled by two uniformly stressed, mutually perpendicular, infinite sheets each containing a crack perpendicular to and bisected by the line of intersection of the sheets; compatibility of displacements is maintained along the line of intersection of the sheets outside the debonded region. The determination of the stress intensity factor is reduced to the solution of a singular integral equation. Results are obtained as a function of relative crack length for various lengths of debonding and various relative stiffnesses.

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Résumé On considère un modèle décrivant la croissance d'une fissure dans la tôle principale d'un panneau comportant un raidisseur fixé de façon continue, qui présente soit un décollement, soit un décollement et une fissuration d'une de ses portions. Le panneau est représenté par deux tôles minces infinies, perpendiculaires l'une à l'autre et uniformément sollicitées. Chacune comporte une fissure perpendiculaire à la ligne d'intersection des tôles, et s'étendant de façon égale de part et d'autre de celle-ci. Les déplacements sont maintenus compatibles le long de la ligne de liaison des tôles et au dehors de la zône de décollement.La détermination du facteur d'intensité des contraintes se réduit à la solution d'une équation d'intégrale singulière. Les résultats sont présentés en fonction de la longueur relative de la fissure, pour diverses longueurs de décollement et diverses raideurs relatives.

     

Fracture conditions of a crack approaching a disturbance

The conditions which drive a crack to propagate in the vicinity of a cylindrical disturbance (cavity, bonded or unbonded inclusion) is expressed by linear fracture mechanics terms. A basic elastic solution with three levels of converging approximations is proposed and compared with finite element solution. The major finding is that a cavity under a given transverse (to cylindrical axis) tensile load attracts a nearby crack and promotes local fracture, whereas a rigid perfectly bonded inclusion repels the crack advancement and arrests local fracture. Unbonded or weakly bonded inclusion fall between those limits. Quantitative values of the relative stress intensity factor are given for large spectrum of geometries and elastic constants. A complementary numerical study is focused on the effect of a thin-layered binder around the inclusion on the stress intensity factor at the crack tip while approaching the binder. The conclusion is that the binder should be as thin as possible and with high shear modulus in order not to neutralize the local toughening effect of the inclusion.

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Résumé Les conditions qui gouvernent la propagation d'une fissure au voisinage d'une discontinuité cylindrique (cavité, inclusion soudée ou non) peuvent être décrites par la théorie linéaire de la mécanique de rupture. On propose, et on compare à une solution par éléments finis, une solution élastique de base comportant trois niveaux d'approximations convergentes. On trouve essentiellement qu'une cavité sujette à une charge de traction transversalement à son axe cylindrique a pour effet d'attirer une fissure en son voisinage et provoquer une rupture locale. Par contre, une inclusion rigide et parfaitement soudée repousse l'avance de la fissure et provoque un arrêt de la rupture.Des inclusions non soudées ou partiellement soudées ont un effet situé entre ces deux limites. On fournit des valeurs quantitatives du facteur d'intensité des contraintes, pour un large spectre de géométries et de constantes élastiques. Une analyse numérique complémentaire est centrée sur l'effet d'un film de liaison autour de l'inclusion sur le facteur d'intensité des contraintes à l'extrémité de la fissure lorsque celle-ci avoisine cette zône de liaison.On en conclut que le film de liaison devrait être aussi mince que possible et posséder un module de cisaillement élevé, afin de neutraliser l'effet de durcissement local de l'inclusion.

     

Strength analysis of a split sleeve in a pipe containing a defect

We study the decrease in the strength of a pipe containing an artificial defect. On the basis of the analytic and numerical models, we consider the influence of the structural features of a split sleeve on its load-carrying ability. We also analyze the joint operation of a sleeve and a pipe containing an artificially made axial surface defect. The results of the numerical analysis are compared with the experimental data. Translated from Problemy Prochnosti, No. 2, pp. 102–111, March–April, 2009.     

Convective instability of a layer of a ferromagnetic fluid rotating about a vertical axis

Thermal instability in a layer of a ferromagnetic fluid rotating about a vertical axis and permeated by a vertical magnetic field is investigated within the framework of linear theory. Overstability cannot occur if the Prandtl number $\text{P > 1}$. For overstable oscillations, Rayleigh number is plotted as a function of wave number for several values of the magnetization parameter $\text{M}{}_3$. Critical Rayleigh number is found to decrease with increase in $\text{M}{}_3$.     

Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan-Thein-Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient K_i(t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K₁ and K₂(t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K₂(t) depends on the value of Deborah number (De=a measure of the level of elasticity in the fluid) whereas the value of K₁ is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θ_m is investigated in detail.     

Stress concentration around a cylindrical cavity in a bone treated as a poroelastic body

Summary Two-phase poroelastic material is taken as a model of a living bone in the sense that the osseous tissue is treated as a linear isotropic perfectly elastic solid, and the fluid substances filling the pores as a Newtonian viscous fluid. Using Biot equations, derived in his consolidation theory, and assuming a plane state of strain governing equations involving fluid excess pressure and the stress function are derived. Laplace transform technique enables one to find explicit solutions for stresses. It is found that under a constant external load the bone element starts to creep, so that the viscoelastic properties of the adopted bone model seem to be in agreement with the experimental findings ofSedlin.

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Spannungserhöhung am Rande eines zylindrischen Loches in einem als porösen elastischen Körper betrachteten Knochen

Zusammenfassung Ein zweiphasiges poröses elastisches Material wird als Model eimes lebenden Knochens genommen. Das knöcherne Gewebe wird als linearer isotroper und vollkommen elastischer Körper und die die Poren füllende Flüssigkeit als Newtonsche behandelt. Unter Verwendung der vonBiot hergeleiteten Gleichungen und unter der Annahme eines ebenen Verzerrungszustandes werden die den Flüssigkeitsüberdruck und die Spannungsfunktion beinhaltenden Grundgleichungen hergeleitet. Laplace-Transformation ermöglicht das Auffinden explizierter Lösungen für die Spannungen. Es zeigt sich, daß unter konstanter äußerer Belastung das Knochenelement zu kriechen beginnt, so daß die viskoelastischen Eigenschaften dieses Knochenmodells mit den experimentellen Ergebnissen vonSedlin übereinzustimmen scheint.

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With 3 Figures

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Research supported by a grant of the National Science Foundation.     

Temperature jump across a plane interface for a phase transition in a pure liquid

We develop a theoretical model of the development of a temperature jump across the boundary between phases during a phase transition in pure liquids.Notation G₁ mass flux of molecules of the liquid into the liquid - G₂ mass flux of molecules of the liquid into the vapor - G_v mass flux of vapor molecules - T₁ vapor temperature near the liquid surface - T₂ temperature of the liquid - T_v vapor temperature - R universal gas constant - c_p, c_v specific heats - r heat of vaporization - q heat flux density - K ratio c_p/c_v - parameter of the phase transition - F₀ area of the interface - P₁ pressure of the liquid - P₂ phase transition pressure - P_v vapor pressure Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 793–797, May, 1988.     

Estimation of a crater volume formed by impact of a projectile on a metallic target

The crater volume has been an important factor in ballistics and has many influences such as material strength, initial projectile velocity, angle of incidence, and nose shape. The goal of this research is to predict the resulting crater volume of a long rod penetration based on the initial projectile velocity and mass. Mooney’s (Bull Seism Soc Am 64(2):473, 1974) displacement equations were used to calculate the elastic crater volume for a given impulse force, P, varying as a delta function in time on the surface of an isotropic, semi-infinite solid. This estimated elastic volume, V_elastic is linearly related to the experimental ballistic volume, V_experimental by an “energy dissipation factor”, k. V_elastic = kV_experimental. The energy dissipation factor “lumps” together elastic and plastic deformation mechanisms. Terminal ballistic data for a steel long-rod projectile into “semiinfinite” steel or aluminum target will be compared to the crater volume calculated through the use of k.     

Generation of a homogeneous plasma in a glow discharge with a hollow anode and a wide-aperture hollow cathode

The principles for designing electrode systems for sources of ion beams of large cross section on the basis of a glow discharge are considered, and a system with combined magnetic and electrostatic confinement of the fast electrons in a wide-aperture hollow cathode and the generation of an ion-emitting plasma in the anode cavity is proposed. It is shown that the system investigated generates a plasma with a nearly homogeneous distribution of the ion emission current density at low gas pressures and can be effectively used to obtain ion beams over a broad range of energies. Pis’ma Zh. Tekh. Fiz. 25, 83–88 (June 26, 1999)     

Calculation of a three-dimensional flow of a viscous incompressible liquid in the neighborhood of a shallow well on a flat surface

A three-dimensional flow in the neighborhood of a shallow well on a plane was simulated numerically on the basis of a solution of the Reynolds equations written in curvilinear nonorthogonal coordinates and closed by a two-parametric dissipative model of turbulence.The work has been financed by the Russian Basic Research Foundation (Grant No. 94-02-04092 a).Civil Aviation Academy, St. Petersburg, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 67, Nos. 5–6, pp. 373–378, November–December, 1994.     

Prototype of a microwave generator with a high-temperature superconductor disk resonator in a feedback circuit with a low phase-noise level

Phase noise of a prototype of microwave generator with a disk resonator based on high-temperature superconductor (HTSC) Y₁Ba₂Cu₃O_{7 ? δ} films in the feedback circuit has been measured for the first time. The disk resonator was cooled to a temperature of 77 K, while the other generator components remained at room temperature. The generator carrier frequency was 7.5 GHz. Phase noises have been measured for different offsets from the carrier frequency. For example, the minimum measured phase-noise level was found to be 136.2 dB/Hz for a 10-kHz offset from the carrier frequency. It is shown that the results obtained correspond to the classical Leeson formula with flicker noise neglected. Thus, a disk resonator based on Y₁Ba₂Cu₃O_{7 ? δ} films does not introduce additional noise (in comparison with the amplifier noise) at small offsets and, correspondingly, is promising for microwave generators with extremely low phase noise. The possibility of further decrease in the phase-noise level by increasing the Q factor of the HTSC disk resonator and optimizing its housing design is discussed.