Softening Instability: Part II—Localization Into Ellipsoidal Regions

1988 ◽  
Vol 55 (3) ◽  
pp. 523-529 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Strain Softening ◽  
Finite Size ◽  
Elastic Solid ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Strain Diagram ◽  
Equilibrium Path ◽  
Special Cases ◽  
Localization Instability

Extending the preceding study of exact solutions for finite-size strain-softening regions in layers and infinite space, exact solution of localization instability is obtained for the localization of strain into an ellipsoidal region in an infinite solid. The solution exploits Eshelby’s theorem for eigenstrains in elliptical inclusions in an infinite elastic solid. The special cases of localization of strain into a spherical region in three dimensions and into a circular region in two dimensions are further solved for finite solids — spheres in 3D and circles in 2D. The solutions show that even if the body is infinite the localization into finite regions of such shapes cannot take place at the start of strain-softening (a state corresponding to the peak of the stress-strain diagram) but at a finite strain-softening slope. If the size of the body relative to the size of the softening region is decreased and the boundary is restrained, homogeneous strain-softening remains stable into a larger strain. The results also can be used as checks for finite element programs for strain-softening. The present solutions determine only stability of equilibration states but not bifurcations of the equilibrium path.

Boundary integrals for oscillating bodies in stratified fluids

2021 ◽  
Vol 927 ◽  
Author(s):  
Bruno Voisin
Keyword(s):  
Single Layer ◽  
Elliptic Cylinder ◽  
Radiation Condition ◽  
Two Dimensions ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Three Dimensions ◽  
Double Layers ◽  
Classical Potential Theory

The theoretical foundations of the boundary integral method are considered for inviscid monochromatic internal waves, and an analytical approach is presented for the solution of the boundary integral equation for oscillating bodies of simple shape: an elliptic cylinder in two dimensions, and a spheroid in three dimensions. The method combines the coordinate stretching introduced by Bryan and Hurley in the frequency range of evanescent waves, with analytic continuation to the range of propagating waves by Lighthill's radiation condition. Not only are the waves obtained for arbitrary oscillations of the body, with application to radial pulsations and rigid vibrations, but also the distribution of singularities equivalent to the body, allowing later inclusion of viscosity in the theory. Both a direct representation of the body as a Kirchhoff–Helmholtz integral involving single and double layers together, and an indirect representation involving a single layer alone, are considered. The indirect representation is seen to require a certain degree of symmetry of the body with respect to the horizontal and the vertical. As the surface of the body is approached the single- and double-layer potentials exhibit the same discontinuities as in classical potential theory.

scholarly journals The flow of viscous liquid past spinning bodies

1933 ◽  
Vol 142 (847) ◽  
pp. 491-508 ◽  
Keyword(s):  
Circular Cylinder ◽  
Viscous Liquid ◽  
Stokes Equations ◽  
Slow Motion ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Stream Velocity ◽  
Flow Past ◽  
Spinning Bodies

The motion produced in a viscous liquid by a spinning sphere has been investigated for small values of the Reynolds’ number, using Stokes’ equations for slow motion, in which the inertia terms are neglected.* By combining the solution for this problem with that given by Stokes for the flow of a stream of viscous liquid past a fixed sphere, we obtain the solution for a stream flowing past a spinning sphere. Oseen introduced a modified system of equations, in which the inertia terms are partly taken into account, and obtained the solution for flow past a fixed sphere using these equations. The problem of the flow of viscous liquid past a fixed circular cylinder has been investigated by Lamb,§ using Oseen’s equations, and the additional solution required if the cylinder is rotating has been given by Oseen.║In the present paper the solution for flow past a spinning sphere is discussed, using Oseen’s equations. The flow of viscous liquid past a spinning body is physically equivalent to motion of the body through the liquid with combined translation and rotation. Now it is well known that in practice when a body moves through a liquid in such a manner, if there is rotation about an axis y perpendicular to the direction of motion x , then ther is a lift on the body in a direction perpendicular to both x and y ¶. In theoretical investigation , if we suppose that the motion is steady, we are restricted in three dimensions to a body rotating about an axis of symmetry, and in two dimensions to the circular cylinder. In these cases it is impossible to obtain a lift if we use Stokes' equations for slow motion. For since that equations are linear, the lift is the sum of the lifts due to the solution for flow past a fixed body and the solution for spin without flow, and these are both zero by symmetry. This argument does not apply to Oseen's equations, since we cannot have a solution for spin alone with no flow, the stream velocity being implied in the equations themselves. In the absence of a method for solving the complete hydrodynamcial equations, it is therefore of interest to investigate the flow of viscous liquid past spinning bodies, using Oseen's equations, and particularly to find whether a lift is obtained.

scholarly journals Cut App&play: um método coreográfico-audiovisual de emergência poética

REPERTÓRIO ◽  
2017 ◽  
pp. 191
Author(s):  
Lali Krotoszynski
Keyword(s):  
Motion Capture ◽  
Test Tube ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Music Video ◽  
Audiovisual Medium ◽  
Dance Training ◽  
Creative Abilities

<p class="p1">Resumo:<span class="Apple-converted-space"> </span></p><p class="p2">Partindo de uma formação eclética em dança e da experiência em <em>performance</em>, interessei-me cada vez mais por explorar a ideia de um pensamento coreográfico aplicado a estruturas audiovisuais interativas, e, nesta direção, realizei projetos em meios, como fotografia, Slow-Scan TV (SSTV), animação, música, vídeo, Motion Capture e Internet. Ao longo dos anos de pesquisa nesse trajeto foi delineando-se uma metodologia que inclui o desenvolvimento de dispositivos computacionais dotados de capacidades criativas, formuladas segundo parâmetros advindos da experiência da dança. Este artigo pretende ilustrar a perspectiva poética da pesquisa que toma o meio audiovisual como um “tubo de ensaio” de criação de movimento na qual articulações entre imagem e som “falam” ao corpo, e “saltam” de duas dimensões para três dimensões, ou seja, da tela para o corpo</p><p class="p3"><span class="s1">Palavras-chave:<span class="Apple-converted-space"> </span></span>Método criativo. Movimento. Coreografia. Audiovisual. Dispositivo computacional interativo.</p><p class="p3"> </p><p class="p3">CUT APP&amp;PLAY: A CHOREOGRAPHIC-AUDIOVISUAL METHOD FOR POETIC EMERGENCE</p><p class="p1"><em>Abstract:<span class="Apple-converted-space"> </span></em></p><p class="p5"><em>Abstract: Departing from an eclectic dance training, and from my experience as performance artist, I have been increasingly drawn to explore the application of choreographic thinking in interactive audiovisual structures and, in this direction, I have developed projects in media such as photography, Slow-Scan TV (SSTV), animation, music, video, Motion Capture and Internet. Throughout the years of research in this path, a methodology utilizing specially developed</em><span class="s2"><em> computational devices endowed with creative abilities, formulated by parameters from dance experience. This article intends to illustrate the poetic perspective of the research that takes the audiovisual medium as a “test tube” for movement creation </em></span><span class="s3"><em>in which articulations between image and sound “speak” to the body, and “jump” from two dimensions to three dimensions, i.e, from the screen to the body.</em></span></p><p class="p6"><span class="s1"><em>Keywords:<span class="Apple-converted-space"> </span></em></span><em>Creative Method. Movement. Choreography. Audiovisual. Interactive Computational Device.</em></p>

Kinematic strategies and sensorimotor transformations in the wiping movements of frogs

1989 ◽  
Vol 62 (3) ◽  
pp. 750-767 ◽  
Author(s):  
S. F. Giszter ◽  
J. McIntyre ◽  
E. Bizzi
Keyword(s):  
Degrees Of Freedom ◽  
Joint Angle ◽  
Video Recording ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Postural Adjustment ◽  
Leopard Frogs ◽  
Motor Commands ◽  
Sensorimotor Transformations

1. Spinal frogs are known to make coordinated and successful wiping movements to almost all places on the body and legs. Such wiping movements involve a sensorimotor transformation. Information from both the spatial locations of stimuli on the skin and the body configuration of the frog is transformed into a set of motor commands that generate body movements adequate to successfully remove the irritant. The spinal cord itself therefore has a limited capacity for sensorimotor transformations. 2. We examined the kinematics of wiping motions in both spinal and intact leopard frogs and bullfrogs. This data was used to assess the flexibility, precision, and strategy of the kinematic sensorimotor transformations used during wiping. The movements involved the use of redundant degrees of freedom in the limbs. Thus many possible movements or solutions could generate successful wiping. This redundancy allows motor-equivalent movements to be used by the frog. 3. Movements were examined in two dimensions by the use of VHS shuttered-video recording and in three dimensions with the use of a WATSMART system of infrared diodes and cameras. The kinematic analysis was applied to those motions in which the limbs did not interact with kinematic constraints, such as the surface of the substrate or body. These unconstrained motions are directly related to motor commands and thus more easily interpreted. 4. Wiping movements to the back were retained in essentially the same form in both spinal and intact frogs. In both cases wiping had four phases with a fifth occasionally present. The phases included flexion, placing, aiming, and whisking, with occasional extension and multiply repeated wipes. However, the aiming phase was often very brief or absent in this data, and flexion was sometimes omitted in multiple wipes. We found that the placing posture was adjusted in a simple way in response to variations in the location of the target stimulus. The rostrocaudal position of the foot tip was strongly and linearly related to the rostrocaudal stimulus location. 5. During the placing posture, joint angles as well as the limb tip in back wipes had linear relationships to the stimulus' rostrocaudal coordinate. The limb configuration used by the frog allowed a strategy of linear (and potentially independent) postural adjustment of joint angle to stimulus position to generate almost linear endpoint adjustments in the placing phase of wiping. This solution to the ill-posed problem of choosing a joint angle for the placing posture in back-wiping may be computationally simple.(ABSTRACT TRUNCATED AT 400 WORDS)

MONTE CARLO STUDIES OF THE THREE-DIMENSIONAL ISING MODEL IN EQUILIBRIUM

2001 ◽  
Vol 12 (07) ◽  
pp. 911-1009 ◽  
Author(s):  
MARTIN HASENBUSCH
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Three Dimensional ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Amplitude Ratios ◽  
Interface Tension ◽  
Monte Carlo Studies

We review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.

A Three-Dimensional Generalization of Instant Center Method Using Line Geometry

2007 ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Line Geometry ◽  
Screw Axis ◽  
Instantaneous Screw Axis ◽  
Instantaneous Center ◽  
Point Of Intersection ◽  
Instantaneous Screw

For a planar motion of a body, there exists an instantaneous center of zero velocity or what is known as the centrode. In three-dimensions, the same is represented by the instantaneous screw axis. In two dimensions, however, there is a geometric method of construction the instant center by using the velocity vectors of two points of the body. The instant center is the point of intersection of the lines perpendicular to the two velocity vectors. This type of construction, however, did not exist for the instantaneous screw axis. In this paper, we present such a geometric construction for the instantaneous screw axis using line geometry.

LOCALIZATION IN THIN FILMS: CROSS-OVER FROM TWO DIMENSIONS TO THREE DIMENSIONS

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2627-2639 ◽  
Author(s):  
R. K. BROJEN SINGH ◽  
DEEPAK KUMAR
Keyword(s):  
Thin Films ◽  
Finite Thickness ◽  
Localization Length ◽  
Finite Size ◽  
Electronic States ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Weak Disorder ◽  
Weak Scattering ◽  
Present Understanding

We have examined the localization of electronic states in disordered thin films as a function of film thickness. The study is motivated by the following consideration. According to the present understanding, in two-dimensions all electronic states are localized for any strength of disorder, however weak. Whereas in three-dimensions, there is a threshold disorder W3c, only above which all the band states are localized. We consider a film of thickness b, with a disorder strength smaller than W3c. With increasing thickness, one might expect a dimensional cross-over, so that film becomes conducting. We have examined questions that arise in this context by two techniques. The first is a finite size scaling technique due to Pichard and Sarma, in which the localization length is calculated numerically for strips and bars as a function of their lateral dimensions. Using this technique we study the delocalization of states at the band centre, as the thickness of the film is increased for moderate to strong disorders. The second technique involves the incorporation of quantum corrections to conductivity by extending the weak scattering methods to films of finite thickness. The two techniques complement each other, as the first one is more suitable for strong disorder, while the latter for weak disorder.

NUMERICAL STUDY OF THE Q-COLOR PROBLEM ON A LATTICE

1987 ◽  
Vol 01 (01) ◽  
pp. 111-119 ◽  
Author(s):  
XIYAO CHEN ◽  
C.Y. PAN
Keyword(s):  
Numerical Study ◽  
Strong Support ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Zero Temperature ◽  
Color Problem ◽  
Exact Answer ◽  
Hypercubic Lattice ◽  
Good Agreement

By using the finite size extrapolation method and combined with a Monte Carlo simulation we have calculated the zero temperature entropy of the q-state Potts Antiferromagnet in two and three dimensions which is identical to the q-color problem in two and three dimensions. The model is laid on a hypercubic lattice. When q=3 (in two dimensions) the result is in good agreement with Lieb’s exact answer. When q>3 (in two and three dimensions) the results are in strong support of Mattis’ recent conjecture for the q-color problem. This method can also treat the d>3 cases without serious difficulties.

Equilibrium Path Bifurcation Due to Strain-Softening Localization in Ellipsoidal Region

1990 ◽  
Vol 57 (4) ◽  
pp. 810-814 ◽  
Author(s):  
Z. P. Bazˇant
Keyword(s):  
Strain State ◽  
Strain Softening ◽  
Strain Diagram ◽  
Equilibrium Path ◽  
Loss Of Stability ◽  
Infinite Layer ◽  
Neutral Equilibrium ◽  
Homogeneous Strain ◽  
Preceding Study ◽  
Path Bifurcation

A preceding study of the loss of stability of a homogeneous strain state in infinite homogeneous solid due to localization of strain into an ellipsoidal region is complemented by determining the condition of bifurcation of equilibrium path due to ellipsoidal localization mode. The bifurcation occurs when the tangential moduli matrix becomes singular, which coincides with Hill’s classical bifurcation condition for localization into an infinite layer. The bifurcation is normally of Shanley type, occurring in absence of neutral equilibrium while the controlled displacements at infinity increase. During the loading process with displacement increase controlled at infinity, this type of bifurcation precedes the loss of stability of equilibrium due to an ellipsoidal localization mode, except when the tangential moduli change suddenly (which happens, e.g., when the slope of the stress-strain diagram is discontinuous, or when temperature is increased).

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