scholarly journals Drawdown patterns for two-well systems as applied to straight-line-boundary conditions

1955 ◽  
Author(s):  
S.M. Lang
Keyword(s):  
Boundary Conditions ◽  
Straight Line

scholarly journals The effect of surface plastic hardening technology, residual stresses and boundary conditions on the buckling of a beam

2020 ◽  
pp. 87-98
Author(s):  
V P Radchenko ◽  
O S Afanaseva ◽  
V E Glebov
Keyword(s):  
Residual Stresses ◽  
Boundary Conditions ◽  
Hardened Layer ◽  
Surface Plastic ◽  
Straight Line ◽  
Calculated Profile ◽  
Inhomogeneous Temperature ◽  
Inhomogeneous Temperature Field ◽  
Plastic Hardening ◽  
Initial Strains

The complex influence of the surface plastic hardening technology, residual stresses, and boundary conditions on the bending of a hardened beam of EP742 alloy was performed. A phenomenological method of restoring the fields of residual stress and plastic deformations performed by its experimental verification in the particular case of ultrasonic hardening is given. The correspondence of the calculated and experimental data for the residual stresses is observed. For assess the influence of the formed residual stresses on convex cylinders, the calculation methods are used for initial strains based on using analogies between the initial (residual) plastic strains and temperature strains in an inhomogeneous temperature field. This allowed us to reduce the consideration of the problem to the problem of thermoelasticity, which was further solved by numerical methods. The effect of four types of boundary conditions for fixing the ends of the beams (rigid fastening and articulation of the ends and ribs in various combinations, cantilever) on the shape and size of the bending of the beam 10×10×100 mm after ultrasonic hardening is studied in detail. It was found that the minimum deflection is observed with a hard seal of both ends of the beam. The effect of the thickness of the beam, which varied from 2 to 10 mm, on their buckling under the same distribution of residual stresses in the hardened layer was studied, and the nonlinear nature of the increase in the deflection boom with decreasing thickness for all types of boundary conditions was established. It is shown that under all boundary conditions, the curvature along the length of the beam practically does not change, therefore it can be considered constant. The consequence of this is the preservation of the hypothesis of flat sections after the hardening procedure, which is confirmed by the calculated profile of the beam section in plane symmetry, close to a straight line. The influence of the anisotropy of surface plastic hardening on the buckling of the beam was found to be significant, which can serve as the basis for choosing the optimal hardening procedure. The performed parametric analysis of the task is presented in the form of graphical and tabular information on the results of the calculations.

scholarly journals On the abundance of supersymmetric strings in AdS 3 x S 3 x S 3 x S 1 describing BPS line operators

2021 ◽  
Author(s):  
Diego H Correa ◽  
Victor I Giraldo-Rivera ◽  
Martín Lagares
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Open String ◽  
Neumann Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Open Strings ◽  
Straight Line ◽  
Fermionic Fields

Abstract We study supersymmetric open strings in type IIB $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of $AdS_3$, which can be interpreted as line operators in a dual CFT$_2$. We study both classical configurations and quadratic fluctuations around them. We find that strings sitting at a fixed point in $S^3 \times S^3 \times S^1$, i.e. satisfying Dirichlet boundary conditions, are 1/2 BPS. We also show that strings sitting at different points of certain submanifolds of $S^3 \times S^3 \times S^1$ can still share some fraction of the supersymmetry. This allows to define supersymmetric smeared configurations by the superposition of them, which range from 1/2 BPS to 1/8 BPS. In addition to the smeared configurations, there are as well 1/4 BPS and 1/8 BPS strings satisfying Neumann boundary conditions. All these supersymmetric strings are shown to be connected by a network of interpolating BPS boundary conditions. Our study reveals the existence of a rich moduli of supersymmetric open string configurations, for which the appearance of massless fermionic fields in the spectrum of quadratic fluctuations is crucial.

Design of the Deployable Mechanisms Based on the Cardanic Motion of Planar Four-Bar Linkage

2014 ◽  
Author(s):  
Win-Bin Shieh
Keyword(s):  
Boundary Conditions ◽  
Planar Model ◽  
Building Unit ◽  
The Past ◽  
Straight Line ◽  
Systematic Methodology ◽  
Deployable Mechanism ◽  
Four Bar Linkage

A deployable mechanism is a mechanism that is designed to be repeatedly expanded and contracted without failure. Most deployable mechanisms are over-constrained mechanisms with a mobility of one. Although many deployable mechanisms had been proposed and employed in application in the past decades, few generalized methodologies for the synthesis of both planar and spatial deployable mechanisms are available. In this paper, a systematic methodology, based on the Cardanic motion of planar linkage, for the synthesis of both the spatial and planar deployable mechanisms is presented. By using the characteristics that some of the coupler points of Cardanic linkages are able to move along a straight line, a building unit mechanism that utilizes such a linkage can be extended or retracted as desired. Once the boundary conditions of the building unit mechanisms are obtained, design of an entire deployable mechanism, planar or spatial, can be fulfilled. After the design is achieved, motion of the synthesized mechanism is simulated in Pro/Engineer, and the prototype of a planar model is manufactured for the justification of this method.

scholarly journals Classical solution of the mixed problem in the quarter of the plane for the wave equation

2019 ◽  
Vol 62 (6) ◽  
pp. 647-651
Author(s):  
V. I. Korzyuk ◽  
I. S. Kozlovskaya ◽  
V. Yu. Sokolovich
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Analytical Form ◽  
Partial Solution ◽  
Differentiable Functions ◽  
Straight Line ◽  
Straight Lines

This article presents the classical solution with mixed boundary conditions in the quarter of the plane for the wave equation in the analytical form. The boundary of the region consists of two perpendicular half-straight lines. On one of them, Cauchy’s boundary conditions are assigned. The second half-straight line is divided into two parts. Dirichlet’s condition is assigned on the straight line and Neumann’s conditions – on the half-straight line. The classical solution of the considered problem is defined in the class of double continuous differentiable functions in the quarter of the plane. To build this solution, the partial solution of the initial wave equation is written. For the assigned functions of the problem, the matching conditions are written, which are necessary and enough so that the solution of the problem would be classical and unique.

Periodic Contact and Mixed Problems of the Elasticity Theory (Review)

2021 ◽  
pp. 22-33
Author(s):  
Dmitrii A. Pozharskii
Keyword(s):  
Boundary Conditions ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Contact Problems ◽  
Mixed Problems ◽  
Periodic Problems ◽  
Straight Line ◽  
Periodic Contact ◽  
Space Boundary

Results are reviewed collected in the investigations of periodic contact and mixed problems of the plane, axially symmetric and spatial elasticity theory. Among mixed problems, cut (crack) problems are focused integral equations of which are connected with those for contact problems. The periodic contact problems stimulate research of the discrete contact of rough (wavy) surfaces. Together with classical elastic domains (half-plane, half-space, plane and full space), we consider periodic problems for cylinder, layer, cone and spatial wedge. Most publications including fun-damental ones by Westergaard and Shtaerman deals with plane periodic problems of the elasticity theory. Here, one can mention approaches based on complex variable functions, Fourier series, Green’s functions and potential func-tions. A fracture mechanics approach to the plane periodic contact problem was developed. Methods and approaches are considered which allow us to take friction forces, adhesion and wear into account in the periodic contact. For spatial periodic and doubly periodic contact and properly mixed problems, we describe such methods as the localiza-tion method, the asymptotic methods, the method of nonlinear boundary integral equations, the fast Fourier trans-form. The half-space is the simplest model for elastic solids. But for the simplest straight-line periodic punch system, some three-dimensional contact problems (normal contact or tangential contact for shifted cohesive coatings) turn out to be incorrect because their integral equations contain divergent series. Considering three-dimensional periodic problems, I.G. Goryacheva disposes circular punches in special way (circular orbits, polar coordinated are used for centers of the punches), in this case one can prove convergence of the series in the integral equation (it is important that the punches are circular). For the periodic problems for an elastic layer, V.M. Aleksandrov has shown that the series in integral equations converge but the kernels become more complicated. In the present paper, we demonstrate that for the straight-line periodic punch system of arbitrary form the contact problem for a half-space turns out to be correct in case of more complicated boundary conditions. Namely, it can be sliding support or rigid fixation of a half-plane on the half-space boundary, the half-plane boundary should be parallel to the straight-line (the punch system axis) for arbitrary finite distance between the parallel lines. On this way, for sliding support, the kernel of the period-ic problem integral equation kernel is free of integrals, it consists of single convergent series (normal contact, the kernel is given in two equivalent forms). We consider classical percolation (how neighboring contact domains pene-trate one to another, investigated by K.L. Johnson, V.A. Yastrebov with co-authors) for the three-dimensional periodic contact amplification as well as percolation for the straight-line punch system. A similar approach is suggested for the case of periodic tangential contact (coatings system cohesive with a half-space boundary shifted along its axis or perpendicular to it). Here, one can separate out unique solutions of auxiliary problems because the line of changing boundary conditions on the half-space boundary can provoke non-uniqueness. The method proposed opens possibility to consider more complicated three-dimensional periodic contact problems for straight-line punch systems with changing boundary conditions inside the period.

Microdensitometer—computer correlation analysis of ultrastructural periodicity

1978 ◽  
Vol 36 (2) ◽  
pp. 32-33
Author(s):  
D.R. Ensor ◽  
C.G. Jensen ◽  
J.A. Fillery ◽  
R.J.K. Baker
Keyword(s):  
Correlation Analysis ◽  
Background Noise ◽  
Computer Control ◽  
Optical Diffraction ◽  
Screw Thread ◽  
Straight Line ◽  
Computer Storage ◽  
Correlation Process ◽  
Electron Microscope Image ◽  
Fixed Beam

Because periodicity is a major indicator of structural organisation numerous methods have been devised to demonstrate periodicity masked by background “noise” in the electron microscope image (e.g. photographic image reinforcement, Markham et al, 1964; optical diffraction techniques, Horne, 1977; McIntosh,1974). Computer correlation analysis of a densitometer tracing provides another means of minimising "noise". The correlation process uncovers periodic information by cancelling random elements. The technique is easily executed, the results are readily interpreted and the computer removes tedium, lends accuracy and assists in impartiality.A scanning densitometer was adapted to allow computer control of the scan and to give direct computer storage of the data. A photographic transparency of the image to be scanned is mounted on a stage coupled directly to an accurate screw thread driven by a stepping motor. The stage is moved so that the fixed beam of the densitometer (which is directed normal to the transparency) traces a straight line along the structure of interest in the image.

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

1970 ◽  
Vol 28 ◽  
pp. 360-361
Author(s):  
John W. Coleman
Keyword(s):  
Boundary Conditions ◽  
High Performance ◽  
Force Fields ◽  
Optical Design ◽  
Direct Conversion ◽  
Design Engineering ◽  
Design Data ◽  
Scalar Potentials ◽  
Geometric Elements ◽  
At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

Human Enamel Replication

1976 ◽  
Vol 34 ◽  
pp. 180-181
Author(s):  
Norman L. Dockum ◽  
John G. Dockum
Keyword(s):  
Organic Matrix ◽  
Human Teeth ◽  
Human Enamel ◽  
Straight Line ◽  
Ultrastructural Characteristics

Ultrastructural characteristics of fractured human enamel and acid-etched enamel were compared using acetate replicas shadowed with platinum and palladium. Shadowed replications of acid-etched surfaces were also obtained by the same method.Enamel from human teeth has a rod structure within which there are crystals of hydroxyapatite contained within a structureless organic matrix composed of keratin. The rods which run at right angles from the dentino-enamel junction are considered to run in a straight line perpendicular to the perimeter of the enamel, however, in many areas these enamel rods overlap, interlacing and intertwining with one another.

A digital vocal tract simulator with boundary conditions at lips and glottis

1981 ◽  
Vol 64 (11) ◽  
pp. 18-26 ◽  
Author(s):  
Tetsuya Nomura ◽  
Nobuhiro Miki ◽  
Nobuo Nagai
Keyword(s):  
Boundary Conditions ◽  
Vocal Tract
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