NASA Astrophysics Data System (ADS)
Borisovich, Andrei; Dymkowska, Jolanta; Szymczak, Czeslaw
2005-07-01
In this paper the von Kármán model for thin, elastic, infinite plate strip resting on a linear elastic foundation of Winkler type is studied. The infinite plate strip is simply-supported and subjected to evenly distributed compressive loads. The critical values of bifurcation parameters and buckling modes for given frequency of longitudinal waves are found on the basis of investigation of linearized problem. The mathematical nonlinear model is reduced to operator equation with Fredholm type operator of index 0 depending on parameters defined in corresponding Hölder spacesE The Lyapunov-Schmidt reduction and the Crandall-Rabinowitz bifurcation theorem (gradient case) are used to examine the postcritical behaviour of the plate. It is proved that there exists maximal frequency of longitudinal waves depending on the compressive load and the stiffness modulus of foundation.
Elastic waves in a semi-infinite body
NASA Astrophysics Data System (ADS)
Apostol, B. F.
2010-04-01
A new method is introduced for studying the propagation of elastic waves in isotropic bodies, based on the Kirchhoff potentials borrowed from electromagnetism. By means of this method we identify and characterize the elastic waves generated in a semi-infinite (half-space) body by the action of an external force localized on, or beneath, the body surface. The method implies coupled integral equations for the wave amplitudes, which we solve for both cases mentioned above. For a force localized on the body surface we identify two transverse waves, corresponding to the two polarizations (normal and parallel to the propagation plane). The longitudinal waves appear as eigenmodes. The waves produced by a force localized beneath the surface are stationary waves along the normal to the surface. We compute the surface displacement in both cases and the force exerted on the surface by a force localized beneath. All these quantities exhibit a characteristic decrease with the distance on the body surface and an oscillatory behaviour. We discuss briefly some possibilities of extending the present method to include the effect of the inhomogeneities on the waves propagation.
Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities
Liu, Y. J.; Song, G.; Yin, H. M.
2015-01-01
The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles. PMID:26345084
NASA Astrophysics Data System (ADS)
Chen, Dai-Heng; Nisitani, Hironobu
This article is concerned with the elastic-plastic analysis of an infinite plate with an elliptic hole or a crack. The method of analysis is the body force method extended to the elastic-plastic problems. In this method, the solutions are obtained by superposing the elastic fields due to the force doublets acting in an infinite plate with an elliptic hole or a crack, so as to satisfy the constitutive equation of plasticity. The elastic-plastic behaviors near a notch root or a crack tip are discussed from the viewpoint of the linear notch mechanics.
The input mobility of an infinite circular cylindrical elastic shell filled with fluid
NASA Technical Reports Server (NTRS)
Fuller, C. R.
1983-01-01
The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.
Three-dimensional elasticity solution of an infinite plate with a circular hole
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1982-01-01
The elasticity problem for a thick plate with a circular hole is formulated in a systematic fashion by using the z-component of the Galerkin vector and that of Muki's harmonic vector function. The problem was originally solved by Alblas. The reasons for reconsidering it are to develop a technique which may be used in solving the elasticity problem for a multilayered plate and to verify and extend the results given by Alblas. The problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Various stress components are tabulated as functions of a/h, z/h, r/a, and nu, a and 2h being the radius of the hole and the plate thickness and nu, the Poisson's ratio. The significant effect of the Poisson's ratio on the behavior and the magnitude of the stresses is discussed.
Dai, Ming; Gao, Cun-Fa; Ru, C. Q.
2015-01-01
Multiple elastic inclusions with uniform internal stress fields in an infinite elastic matrix are constructed under given uniform remote in-plane loadings. The method is based on the sufficient and necessary condition imposed on the boundary value of a holomorphic function that guarantees the existence of the holomorphic function in a multiply connected region. The unknown shape of each of the multiple inclusions is characterized by a conformal mapping. This work focuses on a major large class of multiple inclusions characterized by a simple condition that covers and is much beyond the known related results reported in previous works. Extensive examples of multiple inclusions with or without geometrical symmetry are shown. Our results showed that the inclusion shapes obtained for the uniformity of internal stress fields are independent of the remote loading only when all of the multiple inclusions have the same shear modulus as that of the matrix. Moreover, specific conditions are derived on remote loading, elastic constants of the inclusions and uniform internal stress fields, which guarantee the existence of multiple symmetric inclusions or multiple rotationally symmetrical inclusions with uniform internal stress fields. PMID:27547096
Cumulant solution of the elastic Boltzmann transport equation in an infinite uniform medium
Cai, W.; Lax, M.; Alfano, R. R.
2000-04-01
We consider an analytical solution of the time-dependent elastic Boltzmann transport equation in an infinite uniform isotropic medium with an arbitrary phase function. We obtain (1) the exact distribution in angle, (2) the exact first and second spatial cumulants at any angle, and (3) an approximate combined distribution in position and angle and a spatial distribution whose central position and half-width of spread are always exact. The resulting Gaussian distribution has a center that advances in time, and an ellipsoidal contour that grows and changes shape providing a clear picture of the time evolution of the particle migration from near ballistic, through snakelike and into the final diffusive regime. (c) 2000 The American Physical Society.
Free Oscillations of a Fluid-filled Cavity in an Infinite Elastic Medium
NASA Astrophysics Data System (ADS)
Sakuraba, A.
2016-12-01
Volcanic low-frequency earthquakes and tremor have been widely recognized as a good indicator of hidden activities of volcanoes. It is likely that existence or movement of underground magma and geothermal fluids play a crucial role in their generation mechanisms, but there are still many unknowns. This presentation aims to give a fundamental contribution to understanding and interpreting volcanic low-frequency seismic events. The problem we consider is to compute eigen modes of free oscillations of a fluid-filled cavity surrounded by an infinite linearly elastic medium. A standard boundary element method is used to solve fluid and elastic motion around a cavity of arbitrary shape. Nonlinear advection term is neglected, but viscosity is generally considered in a fluid medium. Of a great importance is to find not only characteristic frequencies but attenuation properties of the oscillations, the latter being determined by both viscous dissipation in the fluid cavity and elastic wave radiation to infinity. One of the simplest cases may be resonance of a fluid-filled crack, which has been studied numerically (Chouet, JGR 1986; Yamamoto and Kawakatsu, GJI 2008) and analytically (Maeda and Kumagai, GRL 2013). In the present study, we generally consider a three-dimensional cavity with emphasis on treating the crack model and other simplest models such as spherical and cylindrical resonators as the extreme cases. In order to reduce computational costs, we assume symmetries about three orthogonal planes and calculate the eigen modes separately for each symmetry. The current status of this project is that the computational code has been checked through comparison to eigen modes of a spherical inviscid cavity (Sakuraba et al., EPS 2002), and another comparison to resonance of a fluid-filled crack is undertook.
Failure of Non-Circular Composite Cylinders
NASA Technical Reports Server (NTRS)
Hyer, M. W.
2004-01-01
In this study, a progressive failure analysis is used to investigate leakage in internally pressurized non-circular composite cylinders. This type of approach accounts for the localized loss of stiffness when material failure occurs at some location in a structure by degrading the local material elastic properties by a certain factor. The manner in which this degradation of material properties takes place depends on the failure modes, which are determined by the application of a failure criterion. The finite-element code STAGS, which has the capability to perform progressive failure analysis using different degradation schemes and failure criteria, is utilized to analyze laboratory scale, graphite-epoxy, elliptical cylinders with quasi-isotropic, circumferentially-stiff, and axially-stiff material orthotropies. The results are divided into two parts. The first part shows that leakage, which is assumed to develop if there is material failure in every layer at some axial and circumferential location within the cylinder, does not occur without failure of fibers. Moreover before fibers begin to fail, only matrix tensile failures, or matrix cracking, takes place, and at least one layer in all three cylinders studied remain uncracked, preventing the formation of a leakage path. That determination is corroborated by the use of different degradation schemes and various failure criteria. Among the degradation schemes investigated are the degradation of different engineering properties, the use of various degradation factors, the recursive or non-recursive degradation of the engineering properties, and the degradation of material properties using different computational approaches. The failure criteria used in the analysis include the noninteractive maximum stress criterion and the interactive Hashin and Tsai-Wu criteria. The second part of the results shows that leakage occurs due to a combination of matrix tensile and compressive, fiber tensile and compressive, and inplane
Rotatable non-circular forebody flow controller
NASA Technical Reports Server (NTRS)
Moskovitz, Cary A. (Inventor)
1991-01-01
The invention is a rotatable, non-circular forebody flow controller. The apparatus comprises a small geometric device located at a nose of a forebody of an aircraft and a non-circular cross-sectional area that extends toward the apex of the aircraft. The device is symmetrical about a reference plane and preferably attaches to an axle which in turn attaches to a rotating motor. The motor rotates the device about an axis of rotation. Preferably, a control unit connected to an aircraft flight control computer signals to the rotating motor the proper rotational positioning of the geometric device.
NASA Astrophysics Data System (ADS)
Honeycutt, Rebecca L.; Johnson, Steven J.
1993-04-01
The sound scattering due to an ambient noise field, approximated by a squared cosine function, is considered for infinite rigid and elastic cylinders and rigid spheres. For the cylinders, it is assumed that the acoustic wave front is parallel to the axis of the cylinder (informally incident). For this assumption, a closed form expression for the scattered sound field-to-incident ambient noise field (signal-to-noise) ratio is obtained not only for the cosine squared directivity, but for any arbitrary directivity which can be expressed in terms of a Fourier series. For the sphere, it is assumed that the noise is circumferentially symmetric which leads to a closed form expression for the signal-to-noise ratio due to a cosine squared directivity.
Combustor with non-circular head end
Kim, Won -Wook; McMahan, Kevin Weston
2015-09-29
The present application provides a combustor for use with a gas turbine engine. The combustor may include a head end with a non-circular configuration, a number of fuel nozzles positioned about the head end, and a transition piece extending downstream of the head end.
NASA Astrophysics Data System (ADS)
Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit
2017-03-01
The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.
NASA Astrophysics Data System (ADS)
Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit
2017-02-01
The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.
NASA Astrophysics Data System (ADS)
Zhang, Sijia; Gu, Bin; Zhang, Hongbin; Pan, Rongying; Alamusi; Feng, Xiqiao
2015-11-01
Research on the propagation of elastic waves in piezoelectric nanostructures is very limited. The frequency dispersion of Love waves in layered piezoelectric nanostructures has not yet been reported when surface effects are taken into account. Based on the surface elasticity theory, the propagation of Love waves with surface effects in a structure consisting of a nanosized piezoelectric film and a semi-infinite elastic substrate is investigated focusing on the frequency dispersion curves of different modes. The results show that under the electrically-open conditions, surface effects give rise to the dependence of Love wave dispersion on the film thickness when the thickness of the piezoelectric film reduces to nanometers. For a given wave frequency, phase velocity of Love waves in all dispersion modes exhibit obvious toward shift as the film thickness decreases or the surface parameters increase. Moreover, there may exist a cut-off frequency in the first mode dispersion below which Love waves will be evanescent in the structure due to surface effects. The cut-off frequency depends on the film thickness, the surface parameters and the bulk material properties.
Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide
NASA Astrophysics Data System (ADS)
Nazarov, Sergey A.; Ruotsalainen, Keijo; Taskinen, Jari
2009-03-01
We describe a periodic homogeneous elastic waveguide of a particular shape of beads connected by ligaments of diameter O(h) such that the essential spectrum contains gaps, the number of which grows unboundedly when h tends to +0. To cite this article: S.A. Nazarov et al., C. R. Mecanique 337 (2009).
Elastic waves in a fluid-loaded, semi-infinite axisymmetric rod.
Ai, Yuhui
2007-04-01
In a fluid-loaded, semi-infinite axisymmetric rod, a free shear stress boundary condition on the circular cross-sectional end introduces complicated, nondispersive waves in the solid. They are composed of a pulse wave, which has the same waveform as the transmitted one and travels at speed c1, and different kinds of pulse trains, each of which travels along the rod at the speed of either c1 or square root of 2c2, where c1 and c2 are the propagating speeds of the longitudinal and transversal bulk waves, respectively. Furthermore, one can conclude from the solutions to the boundary conditions that c1 and square root of 2c2 are the only phase speeds of nondispersive waves. Frequency equations associated with these waves are established, and the solutions are solved and discussed analytically and numerically. The acoustic field in the fluid is also fully discussed, and it is more complicated than a single outgoing Hankel function as described for an infinite rod. The acoustic energy coupling between the solid and the fluid and the end reflection and transmission are quantified as well. In the end, experimental examinations of the echo spectra, using an aluminum rod immersed in the water and air, fully confirm the numerical solutions to the frequency equations.
Shock structure in non-circular jets
NASA Technical Reports Server (NTRS)
Morris, Philip J.; Bhat, Thonse R. S.
1989-01-01
The shock-cell structure of supersonic jets with non-circular exit geometry is modeled using a linearized analysis. The model takes into account the finite thickness of the jet shear layer using realistic velocity and density profiles. The effects of the shear layer turbulence are included by incorporating eddy-viscosity terms. A finite-difference numerical method is used to solve the steady linearized equations of motion. A body-fitted coordinate system is used to describe the shear layer. The variation of the pressure fluctuation with downstream distance is given for circular jets and for an elliptic jet of aspect ratio 2.0. Comparisons with experimental data are made. Difficulties with the numerical technique are also discussed.
Yairi, Motoki; Sakagami, Kimihiro; Nishibara, Kosuke; Okuzono, Takeshi
2016-07-01
Although sound radiation from sound-induced vibration and from force-excited vibration of solid structures are similar phenomena in terms of radiating from vibrating structures, the general relationship between them has not been explicitly studied to date. In particular, airborne sound transmission through walls and sound radiation from structurally vibrating surfaces in buildings are treated as different issues in architectural acoustics. In this paper, a fundamental relationship is elucidated through the use of a simple model. The transmission coefficient for random-incidence sound and the radiated sound power under point force excitation of an infinite elastic plate are both analyzed. Exact and approximate solutions are derived for the two problems, and the relationship between them is theoretically discussed. A conversion function that relates the transmission coefficient and radiated sound power is obtained in a simple closed form through the approximate solutions. The exact solutions are also related by the same conversion function. It is composed of the specific impedance and the wavenumber, and is independent of any elastic plate parameters. The sound radiation due to random-incidence sound and point force excitation are similar phenomena, and the only difference is the gradient of those characteristics with respect to the frequency.
Response of a semi-infinite elastic solid to an arbitrary line load along the axis.
NASA Technical Reports Server (NTRS)
Agrawal, G. L.; Gottenberg, W. G.
1971-01-01
The axisymmetric problem of a line load acting along the axis of a semiinfinite elastic solid is solved using Hankel transforms. In this solution the line load is interpreted as a body force loading and by assuming the line load to be of the form of a Dirac delta function the solution of Mindlin's problem of a point load within the interior of the half space is obtained. Solutions of this problem presented in the literature have been obtained using semiinverse techniques whereas the solution given here is obtained in a systematic step-by-step manner.
NASA Astrophysics Data System (ADS)
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2015-01-01
A common goal when using Finite Element (FE) modelling in time domain wave scattering problems is to minimise model size by only considering a region immediately surrounding a scatterer or feature of interest. The model boundaries must simulate infinite space by minimising the reflection of incident waves. This is a significant and long-standing challenge that has only achieved partial success. Industrial companies wishing to perform such modelling are keen to use established commercial FE packages that offer a thorough history of validation and testing. Unfortunately, this limits the flexibility available to modellers preventing the use of popular research tools such as Perfectly Matched Layers (PML). Unlike PML, Absorbing Layers by Increasing Damping (ALID) have proven successful offering practical implementation into any solver that has representation of material damping. Despite good performance further improvements are desirable. Here, a Stiffness Reduction Method (SRM) has been developed and optimised to operate within a significantly reduced spatial domain. The technique is applied by altering damping and stiffness matrices, inducing decay of incident waves. Variables are expressed as a function of known model constants, easing implementation for generic problems. Analytical and numerical solutions have shown that SRM out performs ALID, with results approaching those of PML.
Sound radiation from an infinite elastic cylinder with dual-wave propagation-intensity distributions
NASA Technical Reports Server (NTRS)
Fuller, C. R.
1988-01-01
The radiation of sound from an elastic cylindrical shell filled with fluid and supporting multiwave propagation is studied analytically. Combinations of supersonic and subsonic shell waves are considered. The radiated field is mapped by using acoustic intensity vectors evaluated at various locations. Both time averaged and instantaneous intensity are investigated. The acoustic intensity is seen to vary markedly with axial distance down the cylinder. The effect is shown to be associated with cross terms in the intensity relations, and its magnitude and location to depend upon the relative phase and amplitudes of individual waves. Subsonic shell waves are demonstrated to interact strongly with supersonic shell waves to cause a large modification in the radiated intensity distributions near the shell surface.
Development of laser finishing for non-circular profiles
Liu, K.W.; Sheng, P.S.
1995-03-01
A laser-based technique for finishing of non-circular cylindrical parts is presented. In this process, the frequency characteristics of a desired non-circular shape is extracted from a CAD through a Fast Fourier Transform algorithm and implemented through a CO{sub 2} laser machining system. A galvanometer-based scanner is used in the process to achieve programmable beam trajectories and high-speed finishing. An error estimation scheme can be developed to determine the final dimensional error of the non-circular profile. This process can be selected as both a batch production tool and a rapid prototyping tool based on the designated processing rate and precision. Initial experimental results include the production of two- and three-lobed profiles, as well as definition of part feature using higher-order harmonics, in polymethylmethacrylate (PMMA) with corresponding R{sub a} values of less than 1 {mu}m. The machine tool elements and general procedure for non-circular laser finishing are also presented.
Structural Concepts Study of Non-circular Fuselage Configurations
NASA Technical Reports Server (NTRS)
Mukhopadhyay, Vivel
1996-01-01
A preliminary study of structural concepts for noncircular fuselage configurations is presented. For an unconventional flying-wing type aircraft, in which the fuselage is inside the wing, multiple fuselage bays with non-circular sections need to be considered. In a conventional circular fuselage section, internal pressure is carried efficiently by a thin skin via hoop tension. If the section is non-circular, internal pressure loads also induce large bending stresses. The structure must also withstand additional bending and compression loads from aerodynamic and gravitational forces. Flat and vaulted shell structural configurations for such an unconventional, non-circular pressurized fuselage of a large flying-wing were studied. A deep honeycomb sandwich-shell and a ribbed double-wall shell construction were considered. Combinations of these structural concepts were analyzed using both analytical and simple finite element models of isolated sections for a comparative conceptual study. Weight, stress, and deflection results were compared to identify a suitable configuration for detailed analyses. The flat sandwich-shell concept was found preferable to the vaulted shell concept due to its superior buckling stiffness. Vaulted double-skin ribbed shell configurations were found to be superior due to their weight savings, load diffusion, and fail-safe features. The vaulted double-skin ribbed shell structure concept was also analyzed for an integrated wing-fuselage finite element model. Additional problem areas such as wing-fuselage junction and pressure-bearing spar were identified.
EFFECTS OF NON-CIRCULAR MOTIONS ON AZIMUTHAL COLOR GRADIENTS
Martinez-Garcia, Eric E.; Gonzalez-Lopezlira, Rosa A.; Gomez, Gilberto C. E-mail: r.gonzalez@crya.unam.m
2009-12-20
Assuming that density waves trigger star formation, and that young stars preserve the velocity components of the molecular gas where they are born, we analyze the effects that non-circular gas orbits have on color gradients across spiral arms. We try two approaches, one involving semianalytical solutions for spiral shocks, and another with magnetohydrodynamic (MHD) numerical simulation data. We find that, if non-circular motions are ignored, the comparison between observed color gradients and stellar population synthesis models would in principle yield pattern speed values that are systematically too high for regions inside corotation, with the difference between the real and the measured pattern speeds increasing with decreasing radius. On the other hand, image processing and pixel averaging result in systematically lower measured spiral pattern speed values, regardless of the kinematics of stellar orbits. The net effect is that roughly the correct pattern speeds are recovered, although the trend of higher measured OMEGA{sub p} at lower radii (as expected when non-circular motions exist but are neglected) should still be observed. We examine the MartInez-GarcIa et al. photometric data and confirm that this is indeed the case. The comparison of the size of the systematic pattern speed offset in the data with the predictions of the semianalytical and MHD models corroborates that spirals are more likely to end at outer Lindblad resonance, as these authors had already found.
DOE R&D Accomplishments Database
Nambu, Y.
1967-01-01
The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.
Effects of a Non-Circular Chainring on Sprint Performance During a Cycle Ergometer Test.
Hintzy, Frédérique; Grappe, Frédéric; Belli, Alain
2016-06-01
Non-circular chainrings have been reported to alter the crank angular velocity profile over a pedal revolution so that more time is spent in the effective power phase. The purpose of this study was to determine whether sprint cycling performance could be improved using a non-circular chainring (Osymetric: ellipticity 1.25 and crank lever mounted nearly perpendicular to the major axis), in comparison with a circular chainring. Twenty sprint cyclists performed an 8 s sprint on a cycle ergometer against a 0.5 N/kg(-1) friction force in four crossing conditions (non-circular or circular chainring with or without clipless pedal). Instantaneous force, velocity and power were continuously measured during each sprint. Three main characteristic pedal downstrokes were selected: maximal force (in the beginning of the sprint), maximal power (towards the middle), and maximal velocity (at the end of the sprint). Both average and instantaneous force, velocity and power were calculated during the three selected pedal downstrokes. The important finding of this study was that the maximal power output was significantly higher (+ 4.3%, p < 0.05) when using the non-circular chainring independent from the shoe-pedal linkage condition. This improvement is mainly explained by a significantly higher instantaneous external force that occurs during the downstroke. Non-circular chainring can have potential benefits on sprint cycling performance. Key pointsThe Osymetric non-circular chainring significantly maximized crank power by 4.3% during sprint cycling, in comparison with a circular chainring.This maximal power output improvement was due to significant higher force developed when the crank was in the effective power phase.This maximal power output improvement was independent from the shoe-pedal linkage condition.Present benefits provided by the non-circular chainring on pedalling kinetics occurred only at high cadences.
Effects of a Non-Circular Chainring on Sprint Performance During a Cycle Ergometer Test
Hintzy, Frédérique; Grappe, Frédéric; Belli, Alain
2016-01-01
Non-circular chainrings have been reported to alter the crank angular velocity profile over a pedal revolution so that more time is spent in the effective power phase. The purpose of this study was to determine whether sprint cycling performance could be improved using a non-circular chainring (Osymetric: ellipticity 1.25 and crank lever mounted nearly perpendicular to the major axis), in comparison with a circular chainring. Twenty sprint cyclists performed an 8 s sprint on a cycle ergometer against a 0.5 N/kg-1 friction force in four crossing conditions (non-circular or circular chainring with or without clipless pedal). Instantaneous force, velocity and power were continuously measured during each sprint. Three main characteristic pedal downstrokes were selected: maximal force (in the beginning of the sprint), maximal power (towards the middle), and maximal velocity (at the end of the sprint). Both average and instantaneous force, velocity and power were calculated during the three selected pedal downstrokes. The important finding of this study was that the maximal power output was significantly higher (+ 4.3%, p < 0.05) when using the non-circular chainring independent from the shoe-pedal linkage condition. This improvement is mainly explained by a significantly higher instantaneous external force that occurs during the downstroke. Non-circular chainring can have potential benefits on sprint cycling performance. Key points The Osymetric non-circular chainring significantly maximized crank power by 4.3% during sprint cycling, in comparison with a circular chainring. This maximal power output improvement was due to significant higher force developed when the crank was in the effective power phase. This maximal power output improvement was independent from the shoe-pedal linkage condition. Present benefits provided by the non-circular chainring on pedalling kinetics occurred only at high cadences. PMID:27274658
Flow in tubes of non-circular cross-sections
NASA Astrophysics Data System (ADS)
Quadir, Raushan Ara
Laminar, viscous, incompressible flow in tubes of noncircular cross sections is investigated. The specific aims of the investigation are (1) to look at the problems of both developing flow and fully developed flow, (2) to consider noncircular cross sections in a more systematic manner than has been done in the past, and (3) to develop a relatively simple finite element technique for producing accurate numerical solutions of flow in tubes of fairly arbitrary cross sections. Fully developed flow in tubes is governed by a Poisson type equation for the mainstream velocity. Both analytical and numerical solutions are considered. The cross sections studied include elliptic and rectangular cross sections of different aspect ratios, some triangular cross sections, and a series of crescent-shaped cross sections. The physical characteristics of the flow are examined in a systematic manner in order to determine how these characteristics are affected by certain geometrical features of the cross section. Solutions fall into three basic categories depending on the shape of the cross section. In the first category, which includes circular and elliptic cross sections, solutions are possible in closed form. In the second, including rectangular and some triangular cross sections, solutions are in the form of infinite series. In the third, including cross sections of more complicated or irregular shapes, only numerical solutions are possible. Results of calculations of velocity profiles, flow rate, pumping power, and friction factor are presented in a way which can be useful for engineering applications. In numerical studies of both developing and fully developed flow finite element techniques are used. Results are obtained for tubes of rectangular and elliptic cross sections of different aspect ratios, for tubes of crescent-shaped cross sections, and a tube whose cross section is an oval of Cassini. For fully developed flow, results are compared with the corresponding exact
Analyzing Non-circular Motions in Spiral Galaxies Through 3D Spectroscopy
NASA Astrophysics Data System (ADS)
Fuentes-Carrera, I.; Rosado, M.; Amram, P.
3D spectroscopic techniques allow the assessment of different types of motions in extended objects. In the case of spiral galaxies, thes type of techniques allow us to trace not only the (almost) circular motion of the ionized gas, but also the motions arising from the presence of structure such as bars, spiral arms and tidal features. We present an analysis of non-circular motions in spiral galaxies in interacting pairs using scanning Fabry-Perot interferometry of emission lines. We show how this analysis can be helpful to differentiate circular from non-circular motions in the kinematical analysis of this type of galaxies.
A numerical algorithm of tooth profile of non-circular cylindrical gear
NASA Astrophysics Data System (ADS)
Wang, Xuan
2017-08-01
Non-circular cylindrical gear (NCCG) is a common form of non-circular gear. Different from the circular gear, the tooth profile equation of NCCG cannot be obtained. So it is necessary to use a numerical algorithm to calculate the tooth profile of NCCG. For this reason, this paper presents a simple and highly efficient numerical algorithm to obtain the tooth profile of NCCG. Firstly, the mathematical model of tooth profile envelope of NCCG is established based on the principle of gear shaping, and the tooth profile envelope of NCCG is obtained. Secondly, the polar radius and polar angle of shaper cutter tooth profile are chosen as the criterions, by which the points of NCCG tooth cogging can be screened out. Finally, the boundary of tooth cogging points is extracted by a distance criterion and correspondingly the tooth profile of NCCG is obtained.
The power spectra of non-circular motions in disk galaxies
NASA Astrophysics Data System (ADS)
Westfall, Kyle; Laws, Anna S. E.; MaNGA Team
2016-01-01
Using data from the first year of the SDSS-IV/MaNGA survey, we present a preliminary study of the amplitude of non-circular motions in a sample of disk galaxies. We select galaxies that have either a visual classification as a spiral galaxy by the Galaxy Zoo project (Lintott et al. 2011) and/or a measured Sersic index of less than 2.5 from the NASA-Sloan Atlas (nsatlas.org). We also remove high-inclination systems by selecting galaxies with isophotal ellipticity measurements of less than 0.6, implying an inclination of less than 65 degrees. For each galaxy, we fit a tilted-disk model to the observed line-of-sight velocities (Andersen & Bershady 2013). The geometric projection of the circularly rotating disk is simultaneously fit to both the ionized-gas (H-alpha) and stellar kinematics, whereas the rotation curves of the two dynamical tracers are allowed to be independent. We deproject the residuals of the velocity-field fit to the disk-plane polar coordinates and select a radial region that is fully covered in aziumuth, yet not undersampled by the on-sky spaxel. Similar to the approach taken by Bovy et al. (2015) for the Milky Way, we then compute the two-dimensional power spectrum of this velocity-residual map, which provides the amplitude of non-circular motions at all modes probed by the data. Our preliminary analysis reveals disk-plane non-circular motions in both the stars and ionized-gas with typical peak amplitudes of approximately 20 km/s. Additionally, our initial findings appear to demonstrate that non-circular motions in barred galaxies are stronger in the ionized gas than in the stars, a trend not seen in unbarred galaxies.
Performance limits of ion extraction systems with non-circular apertures
NASA Astrophysics Data System (ADS)
Shagayda, A.; Madeev, S.
2016-04-01
A three-dimensional computer simulation is used to determine the perveance limitations of ion extraction systems with non-circular apertures. The objective of the study is to analyze the possibilities to improve mechanical strength of the ion optics made of carbon-carbon composite materials. Non-circular grid apertures are better suited to the physical structure of carbon-carbon composite materials, than conventionally used circular holes in a hexagonal pattern, because they allow a fewer number of cut fibers. However, the slit-type accelerating systems, usually regarded as the main alternative to the conventional ion optics, have an intolerably narrow range of operating perveance values at which there is no direct ion impingement on the acceleration grid. This paper presents results of comparative analysis of a number of different ion optical systems with non-circular apertures and conventional ion optical systems with circular apertures. It has been revealed that a relatively wide perveance range without direct ion impingement may be obtained with apertures shaped as a square with rounded corners. Numerical simulations show that this geometry may have equivalent perveance range as the traditional geometry with circular apertures while being more mechanically robust. In addition, such important characteristics, as the effective transparency for both the ions and the neutral atoms, the height of the potential barrier reflecting the downstream plasma electrons and the angular divergence of the beamlet also can be very close to these parameters for the optics with circular apertures.
Does a Non-Circular Chainring Improve Performance in the Bicycle Motocross Cycling Start Sprint?
Mateo-March, Manuel; Fernández-Peña, Eneko; Blasco-Lafarga, Cristina; Morente-Sánchez, Jaime; Zabala, Mikel
2014-01-01
Maximising power output during the initial acceleration phase of a bicycle motocross (BMX) race increases the chance to lead the group for the rest of the race. The purpose of this study was to investigate the effect of non-circular chainrings (Q-ring) on performance during the initial acceleration phase of a BMX race. Sixteen male cyclists (Spanish National BMX team) performed two counterbalanced and randomized initial sprints (3.95s), using Q- ring vs. circular chainring, on a BMX track. The sample was divided into two different groups according to their performance (Elite; n = 8 vs. Cadet; n = 8). Elite group covered a greater distance using Q-ring (+0.26 m, p = 0.02; D = 0.23), whilst the improvement for the Cadet (+0.04 m) was not significant (p = 0.87; D = -0.02). Also, there was no significant difference in power output for the Elite group, while the Cadet group revealed larger peak power with the circular chainring. Neither lactate level, nor heart rate showed significant differences due to the different chainring used. The non-circular chainring improved the initial acceleration capacity only in the Elite riders. Key Points This work provides novel results demonstrating very significant improvements in the sprint performance of BMX cycling discipline using a non-circular chainring system. This study seeks a practical application from scientific analysis All data are obtained in a real context of high competition using a sample comprised by the National Spanish Team. Some variables influencing performance as subjects’ physical fitness are discussed. Technical equipment approved by International Cycling Union is studied to check its potentially beneficial influence on performance. PMID:24570612
Does a non-circular chainring improve performance in the bicycle motocross cycling start sprint?
Mateo-March, Manuel; Fernández-Peña, Eneko; Blasco-Lafarga, Cristina; Morente-Sánchez, Jaime; Zabala, Mikel
2014-01-01
Maximising power output during the initial acceleration phase of a bicycle motocross (BMX) race increases the chance to lead the group for the rest of the race. The purpose of this study was to investigate the effect of non-circular chainrings (Q-ring) on performance during the initial acceleration phase of a BMX race. Sixteen male cyclists (Spanish National BMX team) performed two counterbalanced and randomized initial sprints (3.95s), using Q- ring vs. circular chainring, on a BMX track. The sample was divided into two different groups according to their performance (Elite; n = 8 vs. Cadet; n = 8). Elite group covered a greater distance using Q-ring (+0.26 m, p = 0.02; D = 0.23), whilst the improvement for the Cadet (+0.04 m) was not significant (p = 0.87; D = -0.02). Also, there was no significant difference in power output for the Elite group, while the Cadet group revealed larger peak power with the circular chainring. Neither lactate level, nor heart rate showed significant differences due to the different chainring used. The non-circular chainring improved the initial acceleration capacity only in the Elite riders. Key PointsThis work provides novel results demonstrating very significant improvements in the sprint performance of BMX cycling discipline using a non-circular chainring system.This study seeks a practical application from scientific analysisAll data are obtained in a real context of high competition using a sample comprised by the National Spanish Team.Some variables influencing performance as subjects' physical fitness are discussed.Technical equipment approved by International Cycling Union is studied to check its potentially beneficial influence on performance.
Statistical isotropy violation in WMAP CMB maps resulting from non-circular beams
NASA Astrophysics Data System (ADS)
Das, Santanu; Mitra, Sanjit; Rotti, Aditya; Pant, Nidhi; Souradeep, Tarun
2016-06-01
Statistical isotropy (SI) of cosmic microwave background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. The WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients and . Here we present the first explicit reproduction of the measurements reported in WMAP-7, confirming that beam systematics alone can completely account for the measured SI violation. The possibility of such a systematic origin was alluded to in WMAP-7 paper itself and other authors but not as explicitly so as to account for it accurately. We simulate CMB maps using the actual WMAP non-circular beams and scanning strategy. Our estimated BipoSH spectra from these maps match the WMAP-7 results very well. It is also evident that only a very careful and adequately detailed modelling, as carried out here, can conclusively establish that the entire signal arises from non-circular beam effect. This is important since cosmic SI violation signals are expected to be subtle and dismissing a large SI violation signal as observational artefact based on simplistic plausibility arguments run the serious risk of "throwing the baby out with the bathwater".
Exploring the GalMer database: bar properties and non-circular motions
NASA Astrophysics Data System (ADS)
Randriamampandry, T. H.; Deg, N.; Carignan, C.; Combes, F.; Spekkens, K.
2016-10-01
Context. We use Tree-SPH simulations from the GalMer database to characterize and quantify the non-circular motions induced by the presence of bar-like structures on the observed rotation curve of barred galaxies derived from empirical models of their line-of-sight velocity maps. The GalMer database consists of SPH simulations of galaxies spanning a wide range of morphological types and sizes. Aims: The aim is to compare the intrinsic velocities and bar properties from the simulations with those derived from pseudo-observations. This allows us to estimate the amount of non-circularity and to test the various methods used to derive the bar properties and rotation curves. Methods: The intrinsic velocities in the simulations are calculated from the gravitational forces whereas the observed rotation velocities are derived by applying the ROTCUR and DiskFit algorithms to well-resolved observations of intermediate-inclination, strongly barred galaxies. Results: Our results confirm that the tilted ring method implemented in ROTCUR systematically underestimates or overestimates the rotational velocities by up to 40 percent in the inner part of the galaxy when the bar is aligned with one of the symmetry axes for all the models. For the DiskFit analysis, we find that it produces unrealistic values for all the models used in this work when the bar is within approximately ten degrees of the major or minor axis.
Experiments in dilution jet mixing effects of multiple rows and non-circular orifices
NASA Technical Reports Server (NTRS)
Holdeman, J. D.; Srinivasan, R.; Coleman, E. B.; Meyers, G. D.; White, C. D.
1985-01-01
Experimental and empirical model results are presented that extend previous studies of the mixing of single-sided and opposed rows of jets in a confined duct flow to include effects of non-circular orifices and double rows of jets. Analysis of the mean temperature data obtained in this investigation showed that the effects of orifice shape and double rows are significant only in the region close to the injection plane, provided that the orifices are symmetric with respect to the main flow direction. The penetration and mixing of jets from 45-degree slanted slots is slightly less than that from equivalent-area symmetric orifices. The penetration from 2-dimensional slots is similar to that from equivalent-area closely-spaced rows of holes, but the mixing is slower for the 2-D slots. Calculated mean temperature profiles downstream of jets from non-circular and double rows of orifices, made using an extension developed for a previous empirical model, are shown to be in good agreement with the measured distributions.
Kim, Kwang Hoon; Song, Jinyoung; Kang, I-Seok; Chang, Sung-A; Huh, June; Park, Seung Woo
2013-10-01
The aim of this study was to investigate the balloon occlusive diameter (BOD) of non-circular defects in the transcatheter closure of atrial septal defect (ASD). A total of 67 patients who had undergone transcatheter closure of an ASD were reviewed retrospectively. A non-circular defect was defined as the ratio of the short diameter to the long diameter of the defect on the en-face image less than 0.75. The BOD was compared with the long diameter of the defect and then compared between the two groups. There were 22 patients with circular defects and 45 patients with non-circular defects. The difference in BOD measuring from the long diameter of the defect was quite different between the two groups and significantly smaller in non-circular morphology (0.1±4.0 vs. 2.3±2.1, p=0.006). The difference in BOD measurement from the long diameter of ASD showed a positive correlation with the ratio of the short diameter to the long diameter of ASD (b/a) (r(2)=0.102, p=0.008). In the non-circular morphology of ASD, the difference in BOD measured from the long diameter had a significant negative correlation with the long diameter of ASD (r(2)=0.230, p=0.001), whereas in circular ASD, no significant correlation was found between the difference in BOD and the long diameter of ASD (p=0.201). The BOD compared with the long diameter measured from three-dimensional transesophageal echocardiography was smaller in non-circular ASD than in circular ASD. This difference was much smaller in non-circular ASD with a large long diameter.
Experimental procedure for the study of liquid bridges between non-circular disks
NASA Astrophysics Data System (ADS)
Cabezas, M. G.; Herrera, J. M.; Montanero, J. M.
A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting solids. Apart from its intrinsic basic science interest, the study of liquid bridges has an undoubted technological relevance. Indeed, this fluid configuration has traditionally been seen as an idealization of that appearing in the crystal growth technique known as floating-zone melting, which is used in fabricating ultrapure semiconductor crystals. This has conferred to the analysis of liquid bridges great interest not only in fluid mechanics but also in the material engineering field. As far as the static problem is concerned, studies have focused on the calculation of both the liquid bridge equilibrium interface shape and the stability limits. Most of these studies deal with liquid bridges held between two circular disks, though a few theoretical works with non-circular disks have been published recently. In experiments with liquid bridges, the neutral buoyancy technique has frequently been used to simulate microgravity conditions. In this technique, the liquid bridge is surrounded by an outer liquid with similar density to compensate partially for the effect of the hydrostatic pressure over the interface. Here, a crucial aspect is the accurate knowledge of the surface tension value associated to the interface. In the present contribution, an experimental procedure for analysing the behaviour of liquid bridges between non circular disks is presented. The experiments are performed using the buoyancy technique with a cell designed specifically for this purpose. Two liquid bridges are formed inside the cell. The first one is supported by two circular disks and it is used to measure the surface tension associated to the interface between the fluids involved. To this end, a digital image of the liquid bridge is taken using the ideal conditions (gravity and the axis of the liquid bridge are perpendicular to each other, and the view is frontal
Tang, Keqi; Shvartsburg, Alexandre A.; Smith, Richard D.
2008-03-04
The invention discloses a new interface with non-circular conductance limit aperture(s) useful for effective transmission of non-circular ion beams between stages with different gas pressure. In particular, the invention provides an improved coupling of field asymmetric waveform ion mobility spectrometry (FAIMS) analyzers of planar or side-to-side geometry to downstream stages such as mass spectrometry or ion mobility spectrometry. In this case, the non-circular aperture is rectangular; other geometries may be optimum in other applications. In the preferred embodiment, the non-circular aperture interface is followed by an electrodynamic ion funnel that may focus wide ion beams of any shape into tight circular beams with virtually no losses. The jet disrupter element of the funnel may also have a non-circular geometry, matching the shape of arriving ion beam. The improved sensitivity of planar FAIMS/MS has been demonstrated in experiments using a non-contiguous elongated aperture but other embodiments (e.g., with a contiguous slit aperture) may be preferable, especially in conjunction with an ion funnel operated at high pressures.
Collisionless kinetic-fluid simulation of zonal flows in non-circular tokamaks
Yamagishi, Osamu; Sugama, Hideo
2012-09-15
Fluid simulation of linear zonal flow damping is done with a closure model based on the collisionless gyrokinetics [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. Simulation results of residual zonal flow for low radial wavenumbers are compared with theoretical formulas for circular and non-circular tokamaks. The effects of the elongation and the triangularity are shown to be properly treated in the closure model. Effects of initial parallel flows on zonal flow evolution are also clarified. An appropriate choice of the initial parallel flow gives a much higher residual level than the conventional result with no initial parallel flow. Besides, the zonal flow simulations are done with the E Multiplication-Sign B nonlinearity as initial sources, which is evaluated from linear gyrokinetic microinstabilities such as ion temperature gradient modes, trapped electron modes, and electron temperature gradient modes, in order to estimate efficiency of zonal flow generation by the source instabilities.
Non-circular motion estimation of the grand-design spiral galaxy NGC 628
NASA Astrophysics Data System (ADS)
Colombo, D.
2013-09-01
I present a harmonic decomposition analysis of the grand-design spiral galaxy NGC 628 using the H I data from The H I Nearby Galaxy Survey (THINGS), Walter et al., Astron. J. 136, 2563 (2008). The harmonic decomposition analysis allows the estimation of the peculiar motion magnitude of the galaxy not counted in the rotation of the disk. The rotation curve is obtained through a tilted ring analysis and reaches a maximum velocity not higher than 200 km s-1. The residual from the velocity field shows a morphology shift from a m = 1 to a m = 3 feature at R = 120", typical of two spiral arms perturbation of the potential. The non-circular motion have a magnitude of ~10 km s-1, in agreement with previous studies of similar Hubble type galaxies.
WE-G-BRF-07: Non-Circular Scanning Trajectories with Varian Developer Mode
Davis, A; Pearson, E; Pan, X; Pelizzari, C
2014-06-15
Purpose: Cone-beam CT (CBCT) in image-guide radiation therapy (IGRT) typicallyacquires scan data via the circular trajectory of the linearaccelerator's (linac) gantry rotation. Though this lends itself toanalytic reconstruction algorithms like FDK, iterative reconstructionalgorithms allow for a broader range of scanning trajectories. Weimplemented a non-circular scanning trajectory with Varian's TrueBeamDeveloper Mode and performed some preliminary reconstructions toverify the geometry. Methods: We used TrueBeam Developer Mode to program a new scanning trajectorythat increases the field of view (FOV) along the gantry rotation axiswithout moving the patient. This trajectory consisted of moving thegantry in a circle, then translating the source and detector along theaxial direction before acquiring another circular scan 19 cm away fromthe first. The linear portion of the trajectory includes an additional4.5 cm above and below the axial planes of the source's circularrotation. We scanned a calibration phantom consisting of a lucite tubewith a spiral pattern of CT spots and used the maximum-likelihoodalgorithm to iteratively reconstruct the CBCT volume. Results: With the TrueBeam trajectory definition, we acquired projection dataof the calibration phantom using the previously described trajectory.We obtained a scan of the treatment couch for log normalization byscanning with the same trajectory but without the phantom present.Using the nominal geometric parameters reported in the projectionheaders with our iterative reconstruction algorithm, we obtained acorrect reconstruction of the calibration phantom. Conclusion: The ability to implement new scanning trajectories with the TrueBeamDeveloper Mode enables us access to a new parameter space for imagingwith CBCT for IGRT. Previous simulations and simple dual circle scanshave shown iterative reconstruction with non-circular trajectories canincrease the axial FOV with CBCT. Use of Developer Mode allowsexperimentally
Beam quality M 2 factor matrix for non-circular symmetric laser beams
NASA Astrophysics Data System (ADS)
Du, Yongzhao; Fu, Yuqing; Zheng, Chaoying
2017-02-01
It is standard to use Mx2 and My2 to characterize the beam quality of a non-circular symmetrical beam on its x-axis and y-axis orientation. However, we knew that the values of Mx2 and My2 are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this, a new beam quality characterization method, the M 2 factor matrix, is developed. It not only contains the beam quality terms, Mx2 and My2 , to characterize the beam quality along x-axis and y-axis orientation for the non-symmetric beam, but also introduces two additional cross terms, M xy and M yx , which are used to characterize the location relationship between the principal axis of the test beam and coordinate system in experiment. Moreover, M 2 factor matrix can be measured with a similar procedure to the traditional M 2 factor whose measurement instructions are described in ISO11146 by adding some additional image and signal processing procedure. The measurement principle and method is present and the experiment system for beam quality M 2 factor matrix is built to demonstrate the performance of M 2 factor matrix with real experiments.
Residual stress characteristics in a non-circular drawing sequence of pearlitic steel wire
NASA Astrophysics Data System (ADS)
Baek, Hyun Moo; Hwang, Sun Kwang; Son, Il-Heon; Im, Yong-Taek
2016-11-01
In this paper, characteristics of residual stress in pearlitic steel wire drawn by a non-circular drawing (NCD) sequence with two processing routes, NCDA and NCDB, were experimentally and numerically investigated up to the 12th pass in comparison with conventional wire drawing (WD). For experimental investigation of the axial residual stress at the surface of the drawn wire, destructive (deflection) and non-destructive methods were employed. According to the experimental results, axial surface residual stress of the drawn wire by the NCD sequence was lower and more homogeneous compared to the conventional WD. Based on the elasto-plastic numerical simulation results from the surface to the center of the drawn wire using a commercial DEFORM-3D, an empirical relationship between residual stress and reduction of area was determined to predict the residual stress evolution in the multi-pass WD, NCDA, and NCDB, in that order. From the results of this investigation, it can be construed that the NCD sequence, especially the NCDB, might be helpful in improving the residual stress characteristics of pearlitic steel wire to improve its mechanical behavior and service life.
Unification and Infinite Series
ERIC Educational Resources Information Center
Leyendekkers, J. V.; Shannon, A. G.
2008-01-01
Some infinite series are analysed on the basis of the hypergeometric function and integer structure and modular rings. The resulting generalized functions are compared with differentiation of the "mother" series. (Contains 1 table.)
SU-E-I-02: Characterizing Low-Contrast Resolution for Non-Circular CBCT Trajectories
Davis, A; Pan, X; Pelizzari, C; Pearson, E
2015-06-15
Purpose: The use of non-circular scanning trajectories with optimization-basedreconstruction algorithms can be used in conjunction with non-planaracquisition geometries for axial field-of-view (FOV) extension incone-beam CT (CBCT). To evaluate the utility of these trajectories,quantitative image quality metrics should be evaluated. Low-contrastresolution (LCR) and CT number accuracy are significant challenges forCBCT. With unprecedented axial coverage provided by thesetrajectories, measuring such metrics throughout the axial range iscritical. There are currently no phantoms designed to measurelow-contrast resolution over such an extended volume. Methods: The CATPHAN (The Phantom Laboratory, Salem NY) is the current standardfor image quality evaluation. While providing several useful modulesfor different evaluation metrics, each module was designed to beevaluated in a single slice and not for comparison across axialpositions. To characterize the LCR and HU accuracy over an extendedaxial length, we have designed and built a phantom with evaluationmodules at multiple and adjustable axial positions. Results: The modules were made from a cast polyurethane resin. Holes rangingfrom 1/8 to 5/8 inch were added at a constant radius from the modulecenter into which rods of two different plastic materials were pressedto provide two nominal levels of contrast (1.0% and 0.5%). Largerholes were bored to accept various RMI plugs with known electrondensities for HU accuracy evaluation. The modules can be inserted intoan acrylic tube long enough to cover the entire axial FOV and theirpositions adjusted to desired evaluation points. Conclusion: This phantom allows us to measure the LCR and HU accuracy across theaxial coverage within a single acquisition. These metrics can be usedto characterize the impact different trajectories and reconstructionparameters have on clinically relevant image quality performancemetrics. Funding was provided in part by Varian Medical Systems and NIH R01
NASA Astrophysics Data System (ADS)
Van Noten, Koen; Lecocq, Thomas; Hinzen, Klaus-G.; Sira, Christophe; Camelbeeck, Thierry
2016-04-01
Macroseismic data acquisition recently received a strong increase in interest due to public crowdsourcing through internet-based inquiries and real-time smartphone applications. Macroseismic analysis of felt earthquakes is important as the perception of people can be used to detect local/regional site effects in areas without instrumentation. We will demonstrate how post-processing macroseismic data improves the quality of real-time intensity evaluation of new events. Instead of using the classic DYFI representation in which internet intensities are averaged per community, we, first, geocoded all individual responses and structure the model area into 100 km2grid cells. Second, the average intensity of all answers within a grid cell is calculated. The resulting macroseismic grid cell distribution shows a less subjective and more homogeneous intensity distribution than the classical irregular community distribution and helps to improve the calculation of intensity attenuation functions. In this presentation, the 'Did You Feel It' (DYFI) macroseismic data of several >M4, e.g. the 2002 ML 4.9 Alsdorf and 2011 ML 4.3 Goch (Germany) and the 2015 ML 4.1 Ramsgate (UK), earthquakes felt in Belgium, Germany, The Netherlands, France, Luxemburg and UK are analysed. Integration of transfrontier DYFI data of the ROB-BNS, KNMI, BCSF and BGS networks results in a particular non-circular, distribution of the macroseismic data in which the felt area for all these examples extends significantly more in E-W than N-S direction. This intensity distribution cannot be explained by geometrical amplitude attenuation alone, but rather illustrates a low-pass filtering effect due to the south-to-north increasing thickness of cover sediments above the London-Brabant Massif. For the studied M4 to M5 earthquakes, the thick sediments attenuate seismic energy at higher frequencies and consequently less people feel the vibrations at the surface. This example of successful macroseismic data exchange
Infinite dimensional matrix algebras
NASA Astrophysics Data System (ADS)
Bordemann, M.; Hoppe, J.; Schaller, P.
1989-11-01
To each (finite dimensional) Lie algebra g we associate a class L λ(g) of infinite dimensional Lie algebras, induced by representations D λ(g). We show that in the case of sl(2, C) one obtains a series of pairwise non-isomorphic infinite dimensional Lie algebras depending continuously on a complex parameter λ. We connect this method with previous results on the relation between Diff AS 2 and su( N), and comment on a recent conjecture concerning higher spin algebras, and (2 + 1)-dimensional gravity.
Infinite systems in problems for a stiffened rectangular plate
NASA Astrophysics Data System (ADS)
Baburchenkov, M. F.; Borodachev, N. M.
2016-07-01
A method is proposed for obtaining analytic solutions of a set of infinite systems of linear algebraic equations arising in problems of elasticity for stiffened rectangular plates with stiffening ribs. The method is based on a transformation of a set of infinite systems to a single system and on determining a majorant of the function generating the system series with regard to the order of the unknowns. It is proved that the constructed solution satisfies the infinite system for large indices of the unknowns. The amount of computations is decreased, and the reliability of the results increases. Some realization examples are given.
NASA Astrophysics Data System (ADS)
Baccetti, Valentina; Visser, Matt
2013-04-01
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context.
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2009-01-01
This article provides a historical context for the debate between Georg Cantor and Leopold Kronecker regarding the cardinality of different infinities and incorporates the short story "Welcome to the Hotel Infinity," which uses the analogy of a hotel with an infinite number of rooms to help explain this concept. Wanko makes use of this history and…
NASA Astrophysics Data System (ADS)
Vassiliev, Dmitri
2017-04-01
We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833
NASA Astrophysics Data System (ADS)
Jacobson, M. W.; Ketcha, M.; Uneri, A.; Goerres, J.; De Silva, T.; Reaungamornrat, S.; Vogt, S.; Kleinszig, G.; Siewerdsen, J. H.
2017-03-01
Purpose: Traditional BB-based geometric calibration methods for cone-beam CT (CBCT) rely strongly on foreknowledge of the scan trajectory shape. This is a hindrance to the implementation of variable trajectory CBCT systems, normally requiring a dedicated calibration phantom or software algorithm for every scan orbit of interest. A more flexible method of calibration is proposed here that accommodates multiple orbit types - including strongly noncircular trajectories - with a single phantom and software routine. Methods: The proposed method uses a calibration phantom consisting of multiple line-shaped wire segments. Geometric models relating the 3D line equations of the wires to the 2D line equations of their projections are used as the basis for system geometry estimation. This method was tested using a mobile C-arm CT system and comparisons were made to standard BB-based calibrations. Simulation studies were also conducted using a sinusoid-on-sphere orbit. Calibration performance was quantified in terms of Point Spread Function (PSF) width and back projection error. Visual image quality was assessed with respect to spatial resolution in trabecular bone in an anthropomorphic head phantom. Results: The wire-based calibration method performed equal to or better than BB-based calibrations in all evaluated metrics. For the sinusoidal scans, the method provided reliable calibration, validating its application to non-circular trajectories. Furthermore, the ability to improve image quality using non-circular orbits in conjunction with this calibration method was demonstrated. Conclusion: The proposed method has been shown feasible for conventional circular CBCT scans and offers a promising tool for non-circular scan orbits that can improve image quality, reduce dose, and extend field of view.
Zheng, Zhen; Chang, Long; Nekrashevich, Ivan; Ruchhoeft, Paul; Khizroev, Sakhrat; Litvinov, Dmitri
2013-01-01
We describe a low-energy glow-discharge process using reactive ion etching system that enables non-circular device patterns, such as squares or hexagons, to be formed from a precursor array of uniform circular openings in polymethyl methacrylate, PMMA, defined by electron beam lithography. This technique is of a particular interest for bit-patterned magnetic recording medium fabrication, where close packed square magnetic bits may improve its recording performance. The process and results of generating close packed square patterns by self-limiting low-energy glow-discharge are investigated. Dense magnetic arrays formed by electrochemical deposition of nickel over self-limiting formed molds are demonstrated.
NASA Astrophysics Data System (ADS)
Szűgyi, Zalán; Góbi, Attila
2013-10-01
Self-referencing data is widely-used in lazy functional languages. This technique enables us to express infinite data with a finite structure. Since C++ is a multiparadigm language, it is possible to utilize the advantages of these functional methods in C++ programs. In this paper besides we describe the basic concept of stream-oriented programming in C++ we mainly focus on integration to the Standard Template Library (STL).
NASA Astrophysics Data System (ADS)
Li, Jiaxiong; Du, Jiangbing; Ma, Lin; Li, Ming-Jun; Jiang, Shoulin; Xu, Xiao; He, Zuyuan
2017-01-01
We study the coupling between two identical weakly-coupled few-mode fibers based on coupled-mode theory. The coupling behavior of non-circular-symmetric modes, such as LP11 and LP21, is investigated analytically and numerically. By carefully choosing the fiber core separation and coupler length, we can design orientation-insensitive fiber couplers for non-circular-symmetric modes at arbitrary coupling ratios. Based on the design method, we propose an orientation-insensitive two-mode fiber coupler at 850 nm working as a mode multiplexer/demultiplexer for two-mode transmission using standard single-mode fiber. Within the band from 845 to 855 nm, the insertion losses of LP01 and LP11 modes are less than 0.03 dB and 0.24 dB, respectively. When the two-mode fiber coupler is used as mode demultiplexer, the LP01/LP11 and LP11/LP01 extinction ratios in the separated branches are respectively above 12.6 dB and 21.2 dB. Our design method can be extended to two-mode communication or sensing systems at other wavelengths.
NASA Astrophysics Data System (ADS)
Islam, M. A.; Hossain, M. A.
2012-11-01
We present a highly nonlinear non-circular core photonic crystal fiber (HNL-NCPCF) with all normal group velocity dispersion (GVD) to design a supercontinuum (SC) light source for optical coherence tomography (OCT) system. Nonlinear coefficient γ is increased as large as 66 W-1 km-1 at 1.31 μm by reducing the effective mode area and core is made non-circular to increase birefringence by putting the square lattice of air-holes inside the silica host. About 85 nm 10 dB spectral bandwidths for 2.5 ps input optical pulse and 140 nm 10 dB spectral bandwidths for 1.0 ps input optical pulse have been observed using the same fiber length of 200 m and input optical power of 15 W. Coherent lengths of the generated supercontinuum light sources are found 8.91 μm for 2.5 ps input optical pulse and 5.41 μm for 1.0 ps input optical pulse. Therefore, the highest longitudinal resolution for dental OCT at 1.31 μm is found about 3.28 μm for tooth enamel.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Jaunky, Navin
1999-01-01
The goal of this research project is to develop modelling and analysis strategy for the penetration of aluminium plates impacted by titanium impactors. Finite element analysis is used to study the penetration of aluminium plates impacted by titanium impactors in order to study the effect of such uncontained engine debris impacts on aircraft-like skin panels. LS-DYNA3D) is used in the simulations to model the impactor, test fixture frame and target barrier plate. The effects of mesh refinement, contact modeling, and impactor initial velocity and orientation were studied. The research project also includes development of a design tool for optimum design of grid-stiffened non-circular shells or panels subjected to buckling.
NASA Astrophysics Data System (ADS)
Hanke, U.; Modler, K.-H.; Neumann, R.; Fischer, C.
The objective of this paper is to simplify a very complex guidance mechanism, currently used for lid separating issues in a packaging-machine. The task of this machine is to pick up a lid from a magazine file, rotate it around 180° and place it on tins. The developed mechanism works successfully but with a very complex construction. It consists of a planetary cam mechanism, combined with a toothed gear (with a constant transmission ratio) and a guiding mechanism with a toothed belt and circular pulleys. Such complex constructions are very common in industrial solutions. The idea of the authors is to show a much simpler design in solving the same problem. They developed a guidance mechanism realizing the same function, consisting only of a toothed belt with non-circular pulleys. The used parts are common trade articles.
Students' Conception of Infinite Series
ERIC Educational Resources Information Center
Martinez-Planell, Rafael; Gonzalez, Ana Carmen; DiCristina, Gladys; Acevedo, Vanessa
2012-01-01
This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…
Infinitely Large New Dimensions
Arkani-Hamed, Nima; Dimopoulos, Savas; Dvali, Gia; Kaloper, Nemanja
1999-07-29
We construct intersecting brane configurations in Anti-de-Sitter space localizing gravity to the intersection region, with any number n of extra dimensions. This allows us to construct two kinds of theories with infinitely large new dimensions, TeV scale quantum gravity and sub-millimeter deviations from Newton's Law. The effective 4D Planck scale M{sub Pl} is determined in terms of the fundamental Planck scale M{sub *} and the AdS radius of curvature L via the familiar relation M{sub Pl}{sup 2} {approx} M{sub *}{sup 2+n} L{sup n}; L acts as an effective radius of compactification for gravity on the intersection. Taking M{sub *} {approx} TeV and L {approx} sub-mm reproduces the phenomenology of theories with large extra dimensions. Alternately, taking M{sub *} {approx} L{sup -1} {approx} M{sub Pl}, and placing our 3-brane a distance {approx} 100M{sub Pl}{sup -1} away from the intersection gives us a theory with an exponential determination of the Weak/Planck hierarchy.
Infinitely variable steering transmission
Reed, B.O.
1989-04-04
A steering transmission is described comprising: first and second drive units each driven at a substantially constant speed for producing respective first and second unidirectional, continuous outputs infinitely variable between a minimum speed and a maximum speed; a first output planetary gear drivingly connected to a first transmission output; a second output planetary gear set drivingly connected to a second transmission output; an input gear set; means interconnecting the first and second output planetary gear sets; means connecting the first drive unit to the first output planetary gear set; means applying the second drive unit output to the second output planetary gear set; means applying a substantially constant speed input to the input gear set; means for selectively conditioning the input gear set to drive the one output planetary gear set at a speed having a first predetermined fixed ratio to the constant speed input, whereby to operate the transmission in one speed range; and means for selectively applying the first drive unit output to second output planetary gear set, whereby to operate the transmission in another speed range different from the one speed range.
Pant, Nidhi; Das, Santanu; Mitra, Sanjit; Souradeep, Tarun; Rotti, Aditya E-mail: santanud@iucaa.ernet.in E-mail: sanjit@iucaa.in
2016-03-01
Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper, we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations.
Infinite swapping in curved spaces
NASA Astrophysics Data System (ADS)
Curotto, E.; Mella, Massimo
2014-01-01
We develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys. 135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.
Infinite swapping in curved spaces.
Curotto, E; Mella, Massimo
2014-01-07
We develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys. 135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.
Rigid rod anchored to infinite membrane.
Guo, Kunkun; Qiu, Feng; Zhang, Hongdong; Yang, Yuliang
2005-08-15
We investigate the shape deformation of an infinite membrane anchored by a rigid rod. The density profile of the rod is calculated by the self-consistent-field theory and the shape of the membrane is predicted by the Helfrich membrane elasticity theory [W. Helfrich, Z. Naturforsch. 28c, 693 (1973)]. It is found that the membrane bends away from the rigid rod when the interaction between the rod and the membrane is repulsive or weakly attractive (adsorption). However, the pulled height of the membrane at first increases and then decreases with the increase of the adsorption strength. Compared to a Gaussian chain with the same length, the rigid rod covers much larger area of the membrane, whereas exerts less local entropic pressure on the membrane. An evident gap is found between the membrane and the rigid rod because the membrane's curvature has to be continuous. These behaviors are compared with that of the flexible-polymer-anchored membranes studied by previous Monte Carlo simulations and theoretical analysis. It is straightforward to extend this method to more complicated and real biological systems, such as infinite membrane/multiple chains, protein inclusion, or systems with phase separation.
Online Program Capacity: Limited, Static, Elastic, or Infinite?
ERIC Educational Resources Information Center
Meyer, Katrina A.
2008-01-01
What is the capacity of online programs? Can these types of programs enroll more students than their face-to-face counterparts or not? This article looks at research on achieving cost-efficiencies through online learning, identifies the parts of an online program that can be changed to increase enrollments, and discusses whether a program's…
Online Program Capacity: Limited, Static, Elastic, or Infinite?
ERIC Educational Resources Information Center
Meyer, Katrina A.
2008-01-01
What is the capacity of online programs? Can these types of programs enroll more students than their face-to-face counterparts or not? This article looks at research on achieving cost-efficiencies through online learning, identifies the parts of an online program that can be changed to increase enrollments, and discusses whether a program's…
Javidi, Soroush; Mandic, Danilo P; Took, Clive Cheong; Cichocki, Andrzej
2011-01-01
A new class of complex domain blind source extraction algorithms suitable for the extraction of both circular and non-circular complex signals is proposed. This is achieved through sequential extraction based on the degree of kurtosis and in the presence of non-circular measurement noise. The existence and uniqueness analysis of the solution is followed by a study of fast converging variants of the algorithm. The performance is first assessed through simulations on well understood benchmark signals, followed by a case study on real-time artifact removal from EEG signals, verified using both qualitative and quantitative metrics. The results illustrate the power of the proposed approach in real-time blind extraction of general complex-valued sources.
Decoherence in infinite quantum systems
Blanchard, Philippe; Hellmich, Mario
2012-09-01
We review and discuss a notion of decoherence formulated in the algebraic framework of quantum physics. Besides presenting some sufficient conditions for the appearance of decoherence in the case of Markovian time evolutions we provide an overview over possible decoherence scenarios. The framework for decoherence we establish is sufficiently general to accommodate quantum systems with infinitely many degrees of freedom.
Stress and strain concentration at a circular hole in an infinite plate
NASA Technical Reports Server (NTRS)
Stowell, Elbridge Z
1950-01-01
The theory of elasticity shows that the maximum stress at a circular hole in an infinite plate in tension is three times the applied stress when the material remains elastic. The effect of plasticity of the material is to lower this ratio. This paper considers the theoretical problem of the stress distribution in an infinitely large sheet with a circular hole for the general case where the material may have any stress-strain curve. The plate is assumed to be under uniform tension at a large distance from the hole. The material is taken to be isotropic and incompressible. (author)
An Infinite Restricted Boltzmann Machine.
Côté, Marc-Alexandre; Larochelle, Hugo
2016-07-01
We present a mathematical construction for the restricted Boltzmann machine (RBM) that does not require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, with a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behavior of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size.
Duraiswamy, Nandini; Weaver, Jason D; Ekrami, Yasamin; Retta, Stephen M; Wu, Changfu
2016-06-01
Although generally manufactured as circular devices with symmetric leaflets, transcatheter heart valves can become non-circular post-implantation, the impact of which on the long-term durability of the device is unclear. We investigated the effects of five non-circular (EllipMajor, EllipMinor, D-Shape, TriVertex, TriSides) annular configurations on valve leaflet stresses and valve leaflet deformations through finite element analysis. The highest in-plane principal stresses and strains were observed under an elliptical configuration with an aspect ratio of 1.25 where one of the commissures was on the minor axis of the ellipse. In this elliptical configuration (EllipMinor), the maximum principal stress increased 218% and the maximum principal strain increased 80% as compared with those in the circular configuration, and occurred along the free edge of the leaflet whose commissures were not on the minor axis (i.e., the "stretched" leaflet). The D-Shape configuration was similar to this elliptical configuration, with the degree to which the leaflets were stretched or sagging being less than the EllipMinor configuration. The TriVertex and TriSides configurations had similar leaflet deformation patterns in all three leaflets and similar to the Circular configuration. In the D-Shape, TriVertex, and TriSides configurations, the maximum principal stress was located near the commissures similar to the Circular configuration. In the EllipMinor and EllipMajor configurations, the maximum principal stress occurred near the center of the free edge of the "stretched" leaflets. These results further affirm recommendations by the International Standards Organization (ISO) that pre-clinical testing should consider non-circular configurations for transcatheter valve durability testing.
Teleportation schemes in infinite dimensional Hilbert spaces
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-10-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples.
One-dimensional gravity in infinite point distributions.
Gabrielli, A; Joyce, M; Sicard, F
2009-10-01
The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties of the evolution (notably its "self-similarity") like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.
Counting Multiplicity over Infinite Alphabets
NASA Astrophysics Data System (ADS)
Manuel, Amaldev; Ramanujam, R.
In the theory of automata over infinite alphabets, a central difficulty is that of finding a suitable compromise between expressiveness and algorithmic complexity. We propose an automaton model where we count the multiplicity of data values on an input word. This is particularly useful when such languages represent behaviour of systems with unboundedly many processes, where system states carry such counts as summaries. A typical recognizable language is: “every process does at most k actions labelled a”. We show that emptiness is elementarily decidable, by reduction to the covering problem on Petri nets.
Elastic properties of spherically anisotropic piezoelectric composites
NASA Astrophysics Data System (ADS)
Wei, En-Bo; Gu, Guo-Qing; Poon, Ying-Ming
2010-09-01
Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezoelectric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.
On Forced Vibration in the Linear Theory of Micropolar Elasticity.
The present work is concerned with the problem of determining the dynamic response of a finite micropolar elastic body subject to time-dependent...properties of the general theory of micropolar elasticity. As a specific example of this theory, the forced thickness-shear vibrations of an infinite plate
Squashed entanglement in infinite dimensions
Shirokov, M. E.
2016-03-15
We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. It is also shown that the second definition gives an adequate lower semicontinuous extension of this measure to all states of the infinite-dimensional bipartite system. A general condition relating continuity of the squashed entanglement to continuity of the quantum mutual information is proved and its corollaries are considered. Continuity bound for the squashed entanglement under the energy constraint on one subsystem is obtained by using the tight continuity bound for quantum conditional mutual information (proved in the Appendix by using Winter’s technique). It is shown that the same continuity bound is valid for the entanglement of formation. As a result the asymptotic continuity of the both entanglement measures under the energy constraint on one subsystem is proved.
Sparse Bayesian infinite factor models
Bhattacharya, A.; Dunson, D. B.
2011-01-01
We focus on sparse modelling of high-dimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameter-expanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs sampler that scales well as data dimensionality increases. The gain in efficiency is achieved by the joint conjugacy property of the proposed prior, which allows block updating of the loadings matrix. We propose an adaptive Gibbs sampler for automatically truncating the infinite loading matrix through selection of the number of important factors. Theoretical results are provided on the support of the prior and truncation approximation bounds. A fast algorithm is proposed to produce approximate Bayes estimates. Latent factor regression methods are developed for prediction and variable selection in applications with high-dimensional correlated predictors. Operating characteristics are assessed through simulation studies, and the approach is applied to predict survival times from gene expression data. PMID:23049129
Energy in elastic fiber embedded in elastic matrix containing incident SH wave
NASA Technical Reports Server (NTRS)
Williams, James H., Jr.; Nagem, Raymond J.
1989-01-01
A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.
Gao, Lianghui; Golubović, Leonardo
2003-02-01
In this paper, we first elucidate the classical problem of the elastic free energy of a semi-infinite smectic-A liquid crystals, that fills the semispace above an interface (a boundary smectic layer) of a given shape. For the free energy of this interface, we obtain an effective interface Hamiltonian that takes into account the system discreteness introduced by the layered character of smectic-A liquid crystals. It is thus applicable to both short and long wavelength fluctuations of the interface shape. Next, we use our interface Hamiltonian to develop an efficient approach to the statistical mechanics of stacks of N semiflexible manifolds, such as two-dimensional smectic phases of long semiflexible polymers and three-dimensional lamellar fluid membrane phases. Within our approach, doing the practically interesting thermodynamic limit N--> infinity is reduced to considering a small stack, with just a few interacting manifolds, representing a subsystem of an infinite smectic. This dramatic reduction in the number of degrees of freedom is achieved by treating the first (the last) manifold of the small stack as an interface with the semi-infinite smectic medium below (above) the small stack. We illustrate our approach by considering in detail two-dimensional sterically stabilized smectic liquid crystals of long semiflexible polymers with hard-core repulsion. Smectic bulk (N= infinity ) equation of state and the universal constant characterizing entropic repulsion in these phases are obtained with a high accuracy from numerical simulations of small subsystems with just a few semiflexible polymers.
Asymptotic properties of infinite Leslie matrices.
Gosselin, Frédéric; Lebreton, Jean-Dominique
2009-01-21
The stable population theory is classically applicable to populations in which there is a maximum age after which individuals die. Demetrius [1972. On an infinite population matrix. Math. Biosci. 13, 133-137] extended this theory to infinite Leslie matrices, in which the longevity of individuals is potentially infinite. However, Demetrius had to assume that the survival probability per time step tends to 0 with age. We generalise here the conditions of application of the stable population theory to infinite Leslie matrix models and apply these results to two examples, including or not senescence.
Improving the Instruction of Infinite Series
ERIC Educational Resources Information Center
Lindaman, Brian; Gay, A. Susan
2012-01-01
Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…
Understanding the Behaviour of Infinite Ladder Circuits
ERIC Educational Resources Information Center
Ucak, C.; Yegin, K.
2008-01-01
Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…
Envisioning the Infinite by Projecting Finite Properties
ERIC Educational Resources Information Center
Ely, Robert
2011-01-01
We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…
Understanding the Behaviour of Infinite Ladder Circuits
ERIC Educational Resources Information Center
Ucak, C.; Yegin, K.
2008-01-01
Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Envisioning the Infinite by Projecting Finite Properties
ERIC Educational Resources Information Center
Ely, Robert
2011-01-01
We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…
Boundary Conditions for Infinite Conservation Laws
NASA Astrophysics Data System (ADS)
Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.
2016-12-01
Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.
Subdivisions with infinitely supported mask
NASA Astrophysics Data System (ADS)
Li, Song; Pan, Yali
2008-04-01
In this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formwhere the vector of functions [phi]=([phi]1,E..,[phi]r)T is in and is polynomially decay sequence of rxr matrices called refinement mask. Associated with the mask a is a linear operator on given byBy using same methods in [B. Han, R. Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, manuscript]; [BE Han, Refinable functions and cascade algorithms in weighted spaces with infinitely supported masks, manuscript]; [R.Q. Jia, Q.T. Jiang, Z.W. Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001) 415-427]; [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, in: Advances in Wavelet, Hong Kong,1997, Springer, Singapore, 1998, pp. 199-227], a characterization of convergence of the sequences in the L2-norm is given, which extends the main results in [R.Q. Jia, S.D. Riemenschneider, D.X. Zhou, Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533-1563] on convergence of the subdivision schemes associated with a finitely supported mask to the case in which mask a is polynomially decay sequence. As an application, we also obtain a characterization of smoothness of solutions of the refinement equation mentioned above for the case r=1.
Infinite sets and double binds.
Arden, M
1984-01-01
There have been many attempts to bring psychoanalytical theory up to date. This paper approaches the problem by discussing the work of Gregory Bateson and Ignacio Matte-Blanco, with particular reference to the use made by these authors of Russell's theory of logical types. Bateson's theory of the double bind and Matte-Blanco's bilogic are both based on concepts of logical typing. It is argued that the two theories can be linked by the idea that neurotic symptoms are based on category errors in thinking. Clinical material is presented from the analysis of a middle-aged woman. The intention is to demonstrate that the process of making interpretations can be thought of as revealing errors in thinking. Changes in the patient's inner world are then seen to be the result of clarifying childhood experiences based on category errors. Matte-Blanco's theory of bilogic and infinite experiences is a re-evaluation of the place of the primary process in mental life. It is suggested that a combination of bilogic and double bind theory provides a possibility of reformulating psychoanalytical theory.
Lyapunov exponents for infinite dimensional dynamical systems
NASA Technical Reports Server (NTRS)
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
Entropy exchange for infinite-dimensional systems
Duan, Zhoubo; Hou, Jinchuan
2017-01-01
In this paper the entropy exchange for channels and states in infinite-dimensional systems are defined and studied. It is shown that, this entropy exchange depends only on the given channel and the state. An explicit expression of the entropy exchange in terms of the state and the channel is proposed. The generalized Klein’s inequality, the subadditivity and the triangle inequality about the entropy including infinite entropy for the infinite-dimensional systems are established, and then, applied to compare the entropy exchange with the entropy change. PMID:28164995
Boundary control for a flexible manipulator based on infinite dimensional disturbance observer
NASA Astrophysics Data System (ADS)
Jiang, Tingting; Liu, Jinkun; He, Wei
2015-07-01
This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.
Semi-infinite cohomology and string theory
Frenkel, I. B.; Garland, H.; Zuckerman, G. J.
1986-01-01
We develop the theory of semi-infinite cohomology of graded Lie algebras first introduced by Feigin. We show that the relative semi-infinite cohomology has a structure analogous to that of the de Rham cohomology in Kähler geometry. We prove a vanishing theorem for a special class of modules, and we apply our results to the case of the Virasoro algebra and the Fock module. In this case the zero cohomology is identified as the physical subspace of the Fock module and the no-ghost theorem follows. We reveal the profound relation of semi-infinite cohomology theory to the gauge-invariant free string theory constructed by Banks and Peskin. We then indicate the connection between gauge-invariant interacting string theories and the geometric realizations of the infinite-dimensional Lie algebras. PMID:16578792
Infinite order decompositions of C*-algebras.
Nematjonovich, Arzikulov Farhodjon
2016-01-01
The present paper is devoted to infinite order decompositions of C*-algebras. It is proved that an infinite order decomposition (IOD) of a C*-algebra forms the complexification of an order unit space, and, if the C*-algebra is monotone complete (not necessarily weakly closed) then its IOD is also monotone complete ordered vector space. Also it is established that an IOD of a C*-algebra is a C*-algebra if and only if this C*-algebra is a von Neumann algebra. As a summary we obtain that the norm of an infinite dimensional matrix is equal to the supremum of norms of all finite dimensional main diagonal submatrices of this matrix and an infinite dimensional matrix is positive if and only if all finite dimensional main diagonal submatrices of this matrix are positive.
The Basic Infinitive: A Reply to Langston.
ERIC Educational Resources Information Center
Hoeing, Robert G.
1990-01-01
Argues that the traditional method for learning German verbs by their infinitives is a more practical and communicative approach to German language instruction than a recent pedagogically harmful suggestion that verbs be introduced by their stems. (Author/CB)
NASA Astrophysics Data System (ADS)
Kochemasov, G. G.
2011-10-01
Recently obtained images of Hartley 2 and Tempe l 1 co mets ( NASA's EPOXI and NEXT missions) reveal unprecedented details of the comets shaping and structurizat ion helping understand making them forces. The wave planetology [1-6 & others ] long ago s tated that "orbits make s tructures '. This as s ertion was bas ed on recognition of ine rtiagravity forces aroused in any cosmic body because of its movement in non-circular keplerian orbit. Such an orbit implies periodically changing accelerations causing inertia-gravity forces absorbed by a cosmic body by its warping, undulations. These standing wave warpings in rotating bodies have four interfering ortho- and diagonal direct ions producing uplifted (+), subsided (-) and neutral compensated (0) tectonic blocks. The blocks sizes depend on warping wavelengths the longest and most amplitudinal of which is the fundamental wave 1 long 2πR. Thes e waves produce inevitable tectonic dichotomy - a body division in two opposite segments -hemispheres: one uplifted, another subsided (an example is Earth with its uplifted continental and subsided oceanic hemispheres). In small bodies with a weak gravity one often observes oblong convexoconcave shapes so typical for the Main Belt asteroids.
Guided wave propagation in single and double layer hollow cylinders embedded in infinite media.
Jia, Hua; Jing, Mu; Joseph, L Rose
2011-02-01
Millions of miles of pipes are being used for the transportation, distribution, and local use of petroleum products, gas, water, and chemicals. Most of the pipes are buried in soil, leading to the significance of the study on the subject of guided wave propagation in pipes with soil influence. Previous investigations of ultrasonic guided wave propagation in an elastic hollow cylinder and in an elastic hollow cylinder coated with a viscoelastic material have led to the development of inspection techniques for bare and coated pipes. However, the lack of investigation on guided wave propagation in hollow cylinders embedded in infinite media like soil has hindered the development of pipe inspection methods. Therefore the influence of infinite media on wave propagation is explored in this paper. Dispersion curves and wave structures of both axisymmetric and nonaxisymmetric wave modes are developed. Due to the importance of the convergence of numerical calculations, the requirements of thickness and element number of the finite soil layer between hollow cylinder and infinite element layer are discussed, and an optimal combination is obtained in this paper. Wave structures are used for the mode identification in the non-monotonic region caused by the viscoelastic properties of coating and infinite media.
NASA Astrophysics Data System (ADS)
Cruz, Philip Christopher S.; Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.
2017-04-01
We calculate the energy levels of a quantum particle on a cylindrical surface with non-circular cross-section in uniform electric and magnetic fields. Using separation of variables method and a change of independent variable, we show that the problem can be reduced to a one-dimensional Schrödinger equation for a periodic potential. The effects of varying the shape of the cross-section while keeping the same perimeter and the strengths of the electric and magnetic fields are investigated for elliptical, corrugated, and nearly-rectangular tubes with radial dimensions of the order of a nanometer. The geometric potential has minima at the angular positions where there is a significant amount of curvature. For the elliptical and corrugated tubes, it is shown that as the tube departs from the circular shape of cross-section the double-degeneracy between the energy levels is lifted. For the nearly-rectangular tube, it is shown that energy level crossings occur as the horizontal dimension of the tube is varied while keeping the same perimeter and radius of circular corners. The interplay between the curvature and the strength of the electric and magnetic fields determines the overall behavior of the energy levels. As the strength of the electric field increases, the overall potential gets skewed creating a potential well on the side corresponding to the more negative electric potential. The energy levels of the first few excited states approach more positive values while the ground state energy level approaches a more negative value. For large electric fields, all bound state energy levels tend to more negative values. The contribution of weak magnetic fields to the overall potential behaves in the same way as the electric field contribution but with its sign depending on the direction of the component of the momentum parallel to the cylindrical axis. Large magnetic fields lead to pairing of energy levels reminiscent of 2D Landau levels for the elliptical and nearly
NASA Astrophysics Data System (ADS)
Spagnolie, Saverio E.; Lauga, Eric
2010-03-01
Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (nonsmooth). Physically, biological organisms (or engineered microswimmers) must expend internal energy in order to produce the waves of deformation responsible for the motion. Here we propose a physically motivated derivation of the optimal flagellum shape. We determine analytically and numerically the shape of the flagellar wave which leads to the fastest swimming for a given appropriately defined energetic expenditure. Our novel approach is to define an energy which includes not only the work against the surrounding fluid, but also (1) the energy stored elastically in the bending of the flagellum, (2) the energy stored elastically in the internal sliding of the polymeric filaments which are responsible for the generation of the bending waves (microtubules), and (3) the viscous dissipation due to the presence of an internal fluid. This approach regularizes the optimal sawtooth shape for two-dimensional deformation at the expense of a small loss in hydrodynamic efficiency. The optimal waveforms of finite-size flagella are shown to depend on a competition between rotational motions and bending costs, and we observe a surprising bias toward half-integer wave numbers. Their final hydrodynamic efficiencies are above 6%, significantly larger than those of swimming cells, therefore indicating available room for further biological tuning.
Elastic Fluctuations and Rubber Elasticity
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Goldbart, Paul; Rradzihovsky, Leo
2006-03-01
A coarse-grained phenomenological model is constructed to describe both phonon fluctuations and elastic heterogeneities in rubbery materials. It is a nonlocal, spatially heterogeneous generalization of the classical model of rubber elasticity, and with a tunable repulsion interaction. This model can also be derived from the Vulcanization theory. The residual stress and the non-affine deformation field, as well as their correlations, are calculated perturbatively, to the leading order of quenched randomness. It is explicitly shown that the interplay between the repulsive interaction and quenched randomness induces non- affine deformation. The spatial correlations of the non- affine deformation field and residual stress exhibit power-law scaling, with no characteristic length scale. We also calculate the contributions to the elastic free energy from both thermal and quenched fluctuations for arbitrary deformation. We find that they naturally explain the universal features in the Mooney-Rivlin plot of the stress-strain curve for rubbery materials. The (disorder averaged) thermal fluctuation of monomers is shown to depend on deformation, and becomes anisotropic upon shear deformation, as long as the repulsive interaction is finite.
Stress fields around two pores in an elastic body: exact quadrature domain solutions.
Crowdy, Darren
2015-08-08
Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.
Stress fields around two pores in an elastic body: exact quadrature domain solutions
Crowdy, Darren
2015-01-01
Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky–Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores. PMID:26339198
Extinction properties of infinitely long graphite cylinders
NASA Astrophysics Data System (ADS)
Jazbi, B.; Hoyle, F.; Wickramasinghe, N. C.
1991-12-01
The extinction efficiencies of randomly oriented infinite graphite cylinders, including hollow cylinders are calculated, using the rigorous Kerker-Matijevic formulas. The peak in the mid-UV extinction varies in wavelength with particle radius and cavity size in a way that makes such particles of limited interest as models of interstellar grains.
Infinite Sums of M-Bonacci Numbers
ERIC Educational Resources Information Center
A-iru, Muniru A.
2009-01-01
In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
Infinite Sums of M-Bonacci Numbers
ERIC Educational Resources Information Center
A-iru, Muniru A.
2009-01-01
In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
A Planar Calculus for Infinite Index Subfactors
NASA Astrophysics Data System (ADS)
Penneys, David
2013-05-01
We develop an analog of Jones' planar calculus for II 1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.
Elastic interactions synchronize beating in cardiomyocytes.
Cohen, Ohad; Safran, Samuel A
2016-07-13
Motivated by recent experimental results, we study theoretically the synchronization of the beating phase and frequency of two nearby cardiomyocyte cells. Each cell is represented as an oscillating force dipole in an infinite, viscoelastic medium and the propagation of the elastic signal within the medium is predicted. We examine the steady-state beating of two nearby cells, and show that elastic interactions result in forces that synchronize the phase and frequency of beating in a manner that depends on their mutual orientation. The theory predicts both in-phase and anti-phase steady-state beating depending on the relative cell orientations, as well as how synchronized beating varies with substrate elasticity and the inter-cell distance. These results suggest how mechanics plays a role in cardiac efficiency, and may be relevant for the design of cardiomyocyte based micro devices and other biomedical applications.
History of the Infinitely Small and the Infinitely Large in Calculus.
ERIC Educational Resources Information Center
Kleiner, Israel
2001-01-01
Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)
Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.
Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K
2016-02-01
This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices.
NASA Astrophysics Data System (ADS)
Kim, Jaehwan; Jung, Eunmi; Choi, Seung-Bok
2002-07-01
This paper presents a numerical modeling technique of piezoelectric transducers by taking into account wave radiation and scattering. It is based on the finite element modeling. Coupling problems between piezoelectric and elastic materials as well as fluid and structure systems associated with the modeling of piezoelectric underwater acoustic sensors are formulated. In the finite element modeling of unbounded acoustic fluid, IWEE (Infinite Wave Envelop Element) is adopted to take into account the infinite domain. The IWEE code is added to an in-house finite element program, and commercial pre and post-processor are used for mesh generation and to see the output. The validation of the numerical modeling is proved through an example, and scattering and radiation analysis of Tonpilz transducer is performed. The scattered wave on the sensor is calculated, and the sensor response, so called RVS (Receiving Voltage Sensitivity) is predicted.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Infinitely many singular interactions on noncompact manifolds
Kaynak, Burak Tevfik Turgut, O. Teoman
2015-05-15
We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004). - Highlights: • Schrödinger-operator for infinitely many singular interactions on noncompact manifolds. • Proof of the finiteness of the ground-state energy.
Quark ensembles with the infinite correlation length
Zinov’ev, G. M.; Molodtsov, S. V.
2015-01-15
A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.
Infinite Products of Random Isotropically Distributed Matrices
NASA Astrophysics Data System (ADS)
Il'yn, A. S.; Sirota, V. A.; Zybin, K. P.
2017-01-01
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to calculate easily the Lyapunov spectrum and generalized Lyapunov exponents is developed. This problem is of interest to probability theory, statistical characteristics of matrix T-exponentials are also needed for turbulent transport problems, dynamical chaos and other parts of statistical physics.
Variational Infinite Hidden Conditional Random Fields.
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja; Ghahramani, Zoubin
2015-09-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models which have been shown to successfully learn the hidden structure of a given classification problem. An Infinite hidden conditional random field is a hidden conditional random field with a countably infinite number of hidden states, which rids us not only of the necessity to specify a priori a fixed number of hidden states available but also of the problem of overfitting. Markov chain Monte Carlo (MCMC) sampling algorithms are often employed for inference in such models. However, convergence of such algorithms is rather difficult to verify, and as the complexity of the task at hand increases the computational cost of such algorithms often becomes prohibitive. These limitations can be overcome by variational techniques. In this paper, we present a generalized framework for infinite HCRF models, and a novel variational inference approach on a model based on coupled Dirichlet Process Mixtures, the HCRF-DPM. We show that the variational HCRF-DPM is able to converge to a correct number of represented hidden states, and performs as well as the best parametric HCRFs-chosen via cross-validation-for the difficult tasks of recognizing instances of agreement, disagreement, and pain in audiovisual sequences.
The Bursting of the Dam (Infinite Sets, Countable and Otherwise).
ERIC Educational Resources Information Center
Francis, Richard L.
1992-01-01
Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting…
Elastic field of approaching dislocation loop in isotropic bimaterial
NASA Astrophysics Data System (ADS)
Wu, Wenwang; Xia, Re; Xu, Shucai; Qian, Guian; Zhang, Jinhuan
2015-10-01
A semi-analytical solution is developed for calculating interface traction stress (ITS) fields due to elastic modulus mismatch across the interface plane of isotropic perfectly bounded bimaterial system. Based on the semi-analytical approaches developed, ITS is used to correct the bulk elastic field of dislocation loop within infinite homogenous medium, and to produce continuous displacement and stress fields across the perfectly-bounded interface. Firstly, calculation examples of dislocation loops in Al-Cu bimaterial system are performed to demonstrate the efficiency of the developed semi-analytical approach; Then, the elastic fields of dislocation loops in twinning Cu and Cu-Nb bimaterial are analyzed; Finally, the effect of modulus mismatch across interface plane on the elastic field of bimaterial system is investigated, it is found that modulus mismatch has a drastic impact on the elastic fields of dislocation loops within bimaterial system.
2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations
NASA Astrophysics Data System (ADS)
Yang, Y. B.; Hung, H. H.; Kao, J. C.
2010-05-01
The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.
Spherical Wave Propagation in a Poroelastic Medium with Infinite Permeability: Time Domain Solution
Ozyazicioglu, Mehmet
2014-01-01
Exact time domain solutions for displacement and porepressure are derived for waves emanating from a pressurized spherical cavity, in an infinitely permeable poroelastic medium with a permeable boundary. Cases for blast and exponentially decaying step pulse loadings are considered; letter case, in the limit as decay constant goes to zero, also covers the step (uniform) pressure. Solutions clearly show the propagation of the second (slow) p-wave. Furthermore, Biot modulus Q is shown to have a pronounced influence on wave propagation characteristics in poroelastic media. Results are compared with solutions in classical elasticity theory. PMID:24701190
Continuously-variable series-elastic actuator.
Mooney, Luke; Herr, Hugh
2013-06-01
Actuator efficiency is an important factor in the design of powered leg prostheses, orthoses, exoskeletons, and legged robots. A continuously-variable series-elastic actuator (CV-SEA) is presented as an efficient actuator for legged locomotion. The CV-SEA implements a continuously-variable transmission (CVT) between a motor and series elastic element. The CVT reduces the torque seen at the motor and allows the motor to operate in speed regimes of higher efficiency, while the series-elastic element efficiently stores and releases mechanical energy, reducing motor work requirements for actuator applications where an elastic response is sought. An energy efficient control strategy for the CV-SEA was developed using a Monte-Carlo minimization method that randomly generates transmission profiles and converges on those that minimize the electrical energy consumption of the motor. The CV-SEA is compared to a standard SEA and an infinitely variable series elastic actuator (IV-SEA). Simulations suggest that a CV-SEA will require less energy that an SEA or IV-SEA when used in a knee prosthesis during level-ground walking.
The Great Celestial Numbers - The Infinitely Big and The Infinitely Small
NASA Astrophysics Data System (ADS)
Teodorani, M.
2009-11-01
This book is a travel that brings the reader to penetrate dimensionally the infinitely small and the infinitely large in the Universe, ranging from quarks to galaxies, and to compare these extreme numbers with the numbers that people encounters in normal life here on Earth. Several numerical examples are illustrated all over the text in a sort of scientific orienteering that describes dimensionally the realms of space, time and energy. The last part of the book shows how all spatial and temporal dimensions disappear when the mechanism of quantum entanglement is considered.
Triton,... electron,... cosmon,...: An infinite regression?
Dehmelt, Hans
1989-01-01
I propose an elementary particle model in which the simplest near-Dirac particles triton, proton, and electron are members of the three top layers of a bottomless stack. Each particle is a composite of three particles from the next layer below in an infinite regression approaching Dirac point particles. The cosmon, an immensely heavy lower layer subquark, is the elementary particle. The world-atom, a tightly bound cosmon/anticosmon pair of zero relativistic total mass, arose from the nothing state in a quantum jump. Rapid decay of the pair launched the big bang and created the universe. PMID:16594084
Quantum Machine Learning over Infinite Dimensions.
Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2017-02-24
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that can lead to exponential speedups in situations where classical algorithms scale polynomially. Finally, we also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.
Quantum Machine Learning over Infinite Dimensions
NASA Astrophysics Data System (ADS)
Lau, Hoi-Kwan; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2017-02-01
Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that can lead to exponential speedups in situations where classical algorithms scale polynomially. Finally, we also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.
A billiard-theoretic approach to elementary one-dimensional elastic collisions
NASA Astrophysics Data System (ADS)
Redner, S.
2004-12-01
A simple relation is developed between the elastic collisions of freely moving particles in one dimension and a corresponding billiard system. For two particles with masses m1 and m2 on the half-line x>0 that approach an elastic barrier at x=0, the corresponding billiard system is an infinite wedge. The collision history of the two particles can be easily inferred from the corresponding billiard trajectory. This connection explains the classic demonstrations of the "dime on the superball" and the "baseball on the basketball" that are a staple in elementary physics courses. It also is shown that three elastic particles on an infinite line and three particles on a finite ring correspond, respectively, to the motion of a billiard ball in an infinite wedge and on a triangular billiard table. It is shown how to determine the angles of these two sets in terms of the particle masses.
Thermal convection at infinite Prandtl number
NASA Technical Reports Server (NTRS)
Herring, J. R.
1969-01-01
Numerical solutions are developed for the full scaled three dimensional thermal convection problem, at infinite Prandtl number, and for rigid boundaries. The procedure is designed to give an approximate account of horizontally homogeneous and isotropic flow situations. Results, which included a maximum of 36 horizontal wave number vectors and 20 vertical wave numbers, appear to adequately describe the flow fill up to R = 100,000; beyond this R the results appear to show horizontal wave number truncation error. This error seems to affect the boundary slope of the mean temperature field more than other mean quantities. Despite some numerical uncertainities, certain of the qualitative features of the flow fill are predicted with reasonable confidence.
Algebraic independence properties related to certain infinite products
NASA Astrophysics Data System (ADS)
Tanaka, Taka-aki
2011-09-01
In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.
Dynamics for QCD on an Infinite Lattice
NASA Astrophysics Data System (ADS)
Grundling, Hendrik; Rudolph, Gerd
2017-02-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796-1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.
Shape regulation generates elastic interaction between living cells
NASA Astrophysics Data System (ADS)
Golkov, Roman; Shokef, Yair
2017-06-01
The organization of live cells to tissues is associated with the mechanical interaction between cells, which is mediated through their elastic environment. We model cells as spherical active force dipoles surrounded by an infinite elastic matrix, and analytically evaluate the interaction energy for different scenarios of their regulatory behavior. We obtain attraction for homeostatic (set point) forces and repulsion for homeostatic displacements. When the translational motion of the cells is regulated, the interaction energy decays with distance as 1/{d}4, while when it is not regulated the energy decays as 1/{d}6. This arises from the same reasons as the van der Waals interaction between induced electric dipoles.
Dynamic energy release rate in couple-stress elasticity
NASA Astrophysics Data System (ADS)
Morini, L.; Piccolroaz, A.; Mishuris, G.
2013-07-01
This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated.
Multi/infinite dimensional neural networks, multi/infinite dimensional logic theory.
Murthy, Garimella Rama
2005-06-01
A mathematical model of an arbitrary multi-dimensional neural network is developed and a convergence theorem for an arbitrary multi-dimensional neural network represented by a fully symmetric tensor is stated and proved. The input and output signal states of a multi-dimensional neural network/logic gate are related through an energy function, defined over the fully symmetric tensor (representing the connection structure of a multi-dimensional neural network). The inputs and outputs are related such that the minimum/maximum energy states correspond to the output states of the logic gate/neural network realizing a logic function. Similarly, a logic circuit consisting of the interconnection of logic gates, represented by a block symmetric tensor, is associated with a quadratic/higher degree energy function. Infinite dimensional logic theory is discussed through the utilization of infinite dimension/order tensors.
Scatter of elastic waves by a thin flat elliptical inhomogeneity
NASA Technical Reports Server (NTRS)
Fu, L. S.
1983-01-01
Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.
Pang, Yu; Liu, Yu-Shan; Liu, Jin-Xi; Feng, Wen-Jie
2016-04-01
In this paper, SH bulk/surface waves propagating in the corresponding infinite/semi-infinite piezoelectric (PE)/piezomagnetic (PM) and PM/PE periodically layered composites are investigated by two methods, the stiffness matrix method and the transfer matrix method. For a semi-infinite PE/PM or PM/PE medium, the free surface is parallel to the layer interface. Both PE and PM materials are assumed to be transversely isotropic solids. Dispersion equations are derived by the stiffness/transfer matrix methods, respectively. The effects of electric-magnetic (ME) boundary conditions at the free surface and the layer thickness ratios on dispersion curves are considered in detail. Numerical examples show that the results calculated by the two methods are the same. The dispersion curves of SH surface waves are below the bulk bands or inside the frequency gaps. The ratio of the layer thickness has an important effect not only on the bulk bands but also on the dispersion curves of SH surface waves. Electric and magnetic boundary conditions, respectively, determine the dispersion curves of SH surface waves for the PE/PM and PM/PE semi-infinite structures. The band structures of SH bulk waves are consistent for the PE/PM and PM/PE structures, however, the dispersive behaviors of SH surface waves are indeed different for the two composites. The realization of the above-mentioned characteristics of SH waves will make it possible to design PE/PM acoustic wave devices with periodical structures and achieve the better performance.
Frictional contact of two rotating elastic disks
NASA Astrophysics Data System (ADS)
Ostrik, V. I.; Ulitko, A. F.
2007-10-01
We study the problem of constrained uniform rotation of two precompressed elastic disks made of different materials with friction forces in the contact region taken into account. The exact solution of the problem is obtained by the Wiener-Hopf method. An important stage in the study of rolling of elastic bodies is the Hertz theory [1] of contact interaction of elastic bodies with smoothly varying curvature in the contact region under normal compression. Friction in the contact region is assumed to be negligible. If there are tangential forces and the friction in the contact region is taken into account, then the picture of contact interaction of elastic bodies changes significantly. Although the normal contact stress distribution strictly follows the Hertz theory for bodies with identical elastic properties and apparently slightly differs from the Hertz diagram for bodies made of different materials, the presence of tangential stresses results in the splitting of the contact region into the adhesion region and the slip region. This phenomenon was first established by Reynolds [2], who experimentally discovered slip regions near points of material entry in and exit from the contact region under constrained rolling of an aluminum cylinder on a rubber base. The theoretical justification of the partial slip phenomenon in the contact region, discovered by Reynolds [2], can be found in Carter [3] and Fromm [4]. Moreover, Fromm presents a complete solution of the problem of constrained uniform rotation of two identical disks. Apparently, Fromm was the first to consider the so-called "clamped" strain and postulated that slip is absent at the point at which the disk materials enter the contact region. Ishlinskii [5, 6] gave an engineering solution of the problem on slip in the contact region under rolling friction. Considering the problem on a rigid disk rolling on an elastic half-plane, we model this problem by an infinite set of elastic vertical rods using Winkler
Commuting Flows and Infinite-Dimensional Tori: Sine-Gordon
NASA Astrophysics Data System (ADS)
Schwarz, Martin
2017-02-01
The present work concerns the periodic sine-Gordon equation. We explain why the complete set of conserved functionals for sine-Gordon is an infinite-dimensional torus; the periodic sine-Gordon solution is almost periodic in time on an infinite-dimensional torus.
Solenoid magnetic fields calculated from superposed semi-infinite solenoids
NASA Technical Reports Server (NTRS)
Brown, G. V.; Flax, L.
1966-01-01
Calculation of a thick solenoid coils magnetic field components is made by a superposition of the fields produced by four solenoids of infinite length and zero inner radius. The field produced by this semi-infinite solenoid is dependent on only two variables, the radial and axial field point coordinates.
Infinite statistics condensate as a model of dark matter
Ebadi, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein E-mail: b.mirza@cc.iut.ac.ir
2013-11-01
In some models, dark matter is considered as a condensate bosonic system. In this paper, we prove that condensation is also possible for particles that obey infinite statistics and derive the critical condensation temperature. We argue that a condensed state of a gas of very weakly interacting particles obeying infinite statistics could be considered as a consistent model of dark matter.
Use of Physical Analogs to Evaluate Infinite Series.
ERIC Educational Resources Information Center
Epstein, D. J.; Smith, A. C.
1979-01-01
Discusses the paradoxes that can result when physical examples lead to infinite series. Two examples are presented: the Madelung energy of a one-dimensional array of alternating positive and negative charges, and a point charge between infinite parallel plates. (BB)
The Infinite Challenge: Levels of Conceiving the Endlessness of Numbers
ERIC Educational Resources Information Center
Falk, Ruma
2010-01-01
To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three…
Nonanalyticities of entropy functions of finite and infinite systems.
Casetti, Lapo; Kastner, Michael
2006-09-08
In contrast to the canonical ensemble where thermodynamic functions are smooth for all finite system sizes, the microcanonical entropy can show nonanalytic points also for finite systems. The relation between finite and infinite system nonanalyticities is illustrated by means of a simple classical spinlike model which is exactly solvable for both finite and infinite system sizes, showing a phase transition in the latter case. The microcanonical entropy is found to have exactly one nonanalytic point in the interior of its domain. For all finite system sizes, this point is located at the same fixed energy value epsilon(c)(finite), jumping discontinuously to a different value epsilon(c)(infinite) in the thermodynamic limit. Remarkably, epsilon(c)(finite) equals the average potential energy of the infinite system at the phase transition point. The result indicates that care is required when trying to infer infinite system properties from finite system nonanalyticities.
Hearing and Infinite-Period Bifurcations
NASA Astrophysics Data System (ADS)
Ji, Seung; Bozovic, Dolores; Bruinsma, Robijn
2011-03-01
Auditory and vestibular systems present us with biological sensors that can achieve sub-nanometer sensitivity orders of magnitude in the dynamic range, while operating in a fluid-immersed, room-temperature environment. While the mechanisms behind this extreme sensitivity and robustness of the inner ear have not been fully explained, nonlinear response has been shown to be crucial to its proper function. Recent experiments have recorded innate motility of hair cells of the bullfrog sacculus, under varying degrees of steady-state offset. The bundle deflection was shown to suppress or enhance spontaneous oscillations, and affect the sensitivity of the mechanical response. We will present a theoretical model based on cubic nonlinearity and show that in different parameter regimes, the system can be induced to cross a supercritical Hopf bifurcation, an infinite-period bifurcation, or a multi-critical point. Comparing the numerical simulation to the experiment, we will present evidence that the multi-critical point corresponds most closely to the dynamic state of saccular hair cells. Further, we will discuss the crossing of the bifurcation, and the sensitivity of the phase-locked response in various frequency regimes.
Many-body localization in infinite chains
NASA Astrophysics Data System (ADS)
Enss, T.; Andraschko, F.; Sirker, J.
2017-01-01
We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin-1 /2 Heisenberg chains with binary disorder. Starting from the Néel state, we analyze the decay of antiferromagnetic order ms(t ) and the growth of entanglement entropy Sent(t ) during unitary time evolution. Near the phase transition we find that ms(t ) decays exponentially to its asymptotic value ms(∞ ) ≠0 in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, ms(∞ ) shows an exponential sensitivity on disorder with a critical exponent ν ˜0.9 . The entanglement entropy in the ergodic phase grows subballistically, Sent(t ) ˜tα , α ≤1 , with α varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.
Nonlinear dynamos at infinite magnetic Prandtl number.
Alexakis, Alexandros
2011-03-01
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.
Numerical solution of acoustic scattering by finite perforated elastic plates.
Cavalieri, A V G; Wolf, W R; Jaworski, J W
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.
Numerical solution of acoustic scattering by finite perforated elastic plates
2016-01-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates. PMID:27274685
Numerical solution of acoustic scattering by finite perforated elastic plates
NASA Astrophysics Data System (ADS)
Cavalieri, A. V. G.; Wolf, W. R.; Jaworski, J. W.
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.
Contact problem for an elastic reinforcement bonded to an elastic plate
NASA Technical Reports Server (NTRS)
Erdogan, F.; Civelek, M. B.
1973-01-01
The stiffening layer is treated as an elastic membrane and the base plate is assumed to be an elastic continuum. The bonding between the two materials is assumed to be either one of direct adhesion ro through a thin adhesive layer which is treated as a shear spring. The solution for the simple case in which both the stiffener and the base plate are treated as membranes is also given. The contact stress is obtained for a series of numerical examples. In the direct adhesion case the contact stress becomes infinite at the stiffener ends with a typical square root singularity for the continuum model, and behaving as a delta function for the membrane model. In the case of bonding through an adhesive layer the contact stress becomes finite and continuous along the entire contact area.
Elastically Decoupling Dark Matter.
Kuflik, Eric; Perelstein, Maxim; Lorier, Nicolas Rey-Le; Tsai, Yu-Dai
2016-06-03
We present a novel dark matter candidate, an elastically decoupling relic, which is a cold thermal relic whose present abundance is determined by the cross section of its elastic scattering on standard model particles. The dark matter candidate is predicted to have a mass ranging from a few to a few hundred MeV, and an elastic scattering cross section with electrons, photons and/or neutrinos in the 10^{-3}-1 fb range.
Tight Lower Bound for Percolation Threshold on an Infinite Graph
NASA Astrophysics Data System (ADS)
Hamilton, Kathleen E.; Pryadko, Leonid P.
2014-11-01
We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.
Inequality for the infinite-cluster density in Bernoulli percolation
Chayes, J.T.; Chayes, L.
1986-04-21
Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, P/sub infinity/(p), in Bernoulli percolation. The principal implication of this result is that if P/sub infinity/(p) vanishes with critical exponent ..beta.., then ..beta.. obeys the mean-field bound ..beta..< or =1. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density.
Parabosons, parafermions, and explicit representations of infinite-dimensional algebras
Stoilova, N. I.; Van der Jeugt, J.
2010-03-15
The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so({infinity}) and of the Lie superalgebra osp(1 vertical bar {infinity}). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.
Infinitely Challenging: Pitowsky's Subjective Interpretation and the Physics of Infinite Systems
NASA Astrophysics Data System (ADS)
Ruetsche, Laura; Earman, John
On Itamar Pitowsky's subjective interpretation of quantum mechanics, "the Hilbert space formalism of quantum mechanics [QM] is just a new kind of probability theory" (2006, 213), one whose probabilities correspond to odds rational agents would accept on the outcomes of gambles concerning quantum event structures. Our aim here is to ask whether Pitowsky's approach can be extended from its original context, of quantum theories for systems with an finite number of degrees of freedom, to systems with an infinite number of degrees of freedom, such as quantum field theory and quantum statistical mechanics in the thermodynamic limit. An impediment to generalization is that Pitowsky adopts the framework of event structures encoded by atomic algebras, whereas the algebras typical of QM for infinitely many degrees of freedom are usually non-atomic. We describe challenges to Pitowsky's approach deriving from this impediment, and sketch and assess strategies Pitowsky might use to meet those challenges. Although we offer no final verdict about the eventual success of those strategies, a testament to the worth of Pitowsky's approach is that attempting to extend it engages us in provocative foundational issues.
Elastic internal flywheel gimbal
Rabenhorst, D.W.
1981-01-13
An elastic joint mounting and rotatably coupling a rotary inertial energy storage device or flywheel, to a shaft, the present gimbal structure reduces vibration and shock while allowing precession of the flywheel without the need for external gimbal mounts. The present elastic joint usually takes the form of an annular elastic member either integrally formed into the flywheel as a centermost segment thereof or attached to the flywheel or flywheel hub member at the center thereof, the rotary shaft then being mounted centrally to the elastic member.
Speed of sound in periodic elastic composites
NASA Astrophysics Data System (ADS)
Krokhin, Arkady; Arriaga, Jesús; Gumen, Ludmila
2003-03-01
Using the method of homogenization^1 we calculate the effective speed of sound in periodic elastic structures (phononic crystals) in the low-frequency limit. We proof that in this limit a periodic medium behaves like a homogeneous one and derive analytical formulas for the speed of longitudinal sound in 3D mixtures of liquids and gases and for the speed of transversal waves in 2D phononic crystals. In the latter case the structure consists of infinite parallel rods arranged periodically in solid elastic medium. Our formulas are valid for arbitrary Bravais lattice, and form of inclusions. Unlike the phenomenological Wood's law for the elastic modulus of composites, our exact formula involves all the details of the microstructure of the periodic medium. We show that a periodic medium exhibits in general anisotropic acoustic properties, i.e. the speed of sound depends on the direction of propagation. We consider a particular case of air bubbles in water and calculate the speed of sound as a function of air fraction. The famous effect of the drop of speed of sound in mixtures is clearly seen and our data are in a good agreement with the data obtained in the coherent potential approximation.^2 ^1A.A. Krokhin, et al., Phys. Rev. B 65, 115208 (2002). ^2M. Kafesaki, et al., Phys. Rev. Lett. 84, 6050 (2000).
Some Properties of the Transverse Elastic Waves in Quasiperiodic Structures
NASA Astrophysics Data System (ADS)
Tutor, J.; Velasco, V. R.
We have studied the integrated density of states and fractal dimension of the transverse elastic waves spectrum in quasiperiodic systems following the Fibonacci, Thue-Morse and Rudin-Shapiro sequences. Due to the finiteness of the quasiperiodic generations, in spite of the high number of materials included, we have studied the possible influence of the boundary conditions, infinite periodic or finite systems, together with that of the different ways to generate the constituent blocks of the quasiperiodic systems, on the transverse elastic waves spectra. No relevant differences have been found for the different boundary conditions, but the different ways of generating the building blocks produce appreciable consequences in the properties of the transverse elastic waves spectra of the quasiperiodic systems studied here.
Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces
Benatti, Fabio; Oskouei, Samad Khabbazi Deh Abad, Ahmad Shafiei
2014-08-15
We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.
Infinite dimensional symmetries of self-dual Yang-Mills
NASA Astrophysics Data System (ADS)
Mansfield, Paul; Wardlow, Adam
2009-08-01
We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra in the group algebra of isometries.
The Pythagorean Theorem: II. The infinite discrete case
Kadison, Richard V.
2002-01-01
The study of the Pythagorean Theorem and variants of it as the basic result of noncommutative, metric, Euclidean Geometry is continued. The emphasis in the present article is the case of infinite discrete dimensionality. PMID:16578869
Impedance of pistons on a two-layer medium in a planar infinite rigid baffle.
Hassan, Scott E
2007-07-01
An integral transform technique is used to develop a general solution for the impedance of rigid pistons acting on a two-layer medium. The medium consists of a semi-infinite acoustic fluid on a viscoelastic thick plate in a rigid infinite baffle. The stresses acting on the planar baffle, as a result of piston motion, are determined using theory of linear elasticity and are therefore unrestricted in terms of applicable frequency range. The special case of a circular piston is considered and expressions for the self-and mutual impedances are developed and evaluated numerically. Numerical results are compared with classical piston impedance functions and finite-element model results. At low frequencies (k(0)a<1), the self-impedances vary significantly from the classical piston impedance functions due to the shear properties of the viscoelastic medium. In the midfrequency range (1
Aspects of infinite dimensional ℓ-super Galilean conformal algebra
NASA Astrophysics Data System (ADS)
Aizawa, N.; Segar, J.
2016-12-01
In this work, we construct an infinite dimensional ℓ-super Galilean conformal algebra, which is a generalization of the ℓ = 1 algebra found in the literature. We give a classification of central extensions, the vector field representation, the coadjoint representation, and the operator product expansion of the infinite dimensional ℓ-super Galilean conformal algebra, keeping possible applications in physics and mathematics in mind.
A notion of graph likelihood and an infinite monkey theorem
NASA Astrophysics Data System (ADS)
Banerji, Christopher R. S.; Mansour, Toufik; Severini, Simone
2014-01-01
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of vertices. We present an algorithm to compute this graph invariant and closed formulas for some infinite classes. We have to leave the computational complexity of the likelihood as an open problem.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2002-02-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.
Packing Infinite Number of Cubes in a Finite Volume Box
ERIC Educational Resources Information Center
Yao, Haishen; Wajngurt, Clara
2006-01-01
Packing an infinite number of cubes into a box of finite volume is the focus of this article. The results and diagrams suggest two ways of packing these cubes. Specifically suppose an infinite number of cubes; the side length of the first one is 1; the side length of the second one is 1/2 , and the side length of the nth one is 1/n. Let n approach…
Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques
NASA Technical Reports Server (NTRS)
Banks, H. T.; Wang, C.
1989-01-01
A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.
Constructing an autonomous system with infinitely many chaotic attractors
NASA Astrophysics Data System (ADS)
Zhang, Xu; Chen, Guanrong
2017-07-01
Some classical chaotic systems such as the Lorenz system and Chua system have finite numbers of chaotic attractors. This letter develops a simple, effective method for constructing lower-dimensional autonomous systems with infinitely many chaotic attractors. As an application, a Lorenz-type system and a Rössler-type system with infinitely many chaotic attractors are constructed with bifurcation analysis, and with an extension to the fractional-order setting.
NASA Technical Reports Server (NTRS)
Sheu, Y. C.; Fu, L. S.
1983-01-01
The extended method of equivalent inclusions is applied to study the specific wave problems: (1) the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and (2) the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. Eigenstrains are expanded as a geometric series and a method of integration based on the inhomogeneous Helmholtz operator is adopted. This study compares results, obtained by using limited number of terms in the eigenstrain expansion, with exact solutions for the layer problem and that for a perfect sphere.
Elastic properties of minerals
Aleksandrov, K.S.; Prodaivoda, G.T.
1993-09-01
Investigations of the elastic properties of the main rock-forming minerals were begun by T.V. Ryzhova and K.S. Aleksandrov over 30 years ago on the initiative of B.P. Belikov. At the time, information on the elasticity of single crystals in general, and especially of minerals, was very scanty. In the surveys of that time there was information on the elasticity of 20 or 30 minerals. These, as a rule, did not include the main rock-forming minerals; silicates were represented only by garnets, quartz, topaz, tourmaline, zircon, beryl, and staurolite, which are often found in nature in the form of large and fairly high-quality crystals. Then and even much later it was still necessary to prove a supposition which now seems obvious: The elastic properties of rocks, and hence the velocities of elastic (seismic) waves in the earth`s crust, are primarily determined by the elastic characteristics of the minerals composing these rocks. Proof of this assertion, with rare exceptions of mono-mineralic rocks (marble, quartzite, etc.) cannot be obtained without information on the elasticities of a sufficiently large number of minerals, primarily framework, layer, and chain silicates which constitute the basis of most rocks. This also served as the starting point and main problem of the undertakings of Aleksandrov, Ryzhova, and Belikov - systematic investigations of the elastic properties of minerals and then of various rocks. 108 refs., 7 tabs.
Elastic wave invariants for acoustic emission
NASA Astrophysics Data System (ADS)
Pardee, W. J.
1981-07-01
It is shown that there are four conserved properties of an elastic wave in an infinite isotropic plate: the energy, the two components of wave momentum parallel to the surface, and wave angular momentum normal to the surface. All four invariants are volume integrals of quadratic functions of the spatial (Eulerian) coordinates. The canonical energy-momentum density tensor and the orbital, spin, and total angular momentum density tensors are constructed and sufficient conditions for their conservation are demonstrated. A procedure for measuring the wave momentum of a surface wave is proposed. It is argued that these invariants are likely to be particularly useful characterizations of acoustic emission, e.g., from a growing crack. Experimental tests are proposed, and possible applications to practical monitoring problems described.
Sun, Qicheng; Jin, Feng; Wang, Guangqian; Song, Shixiong; Zhang, Guohua
2015-01-01
Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles. These structures have internal structural degrees of freedom in addition to the translational degree of freedom. The resultant granular elasticity, which exhibits intrinsic variations and inevitable relaxation, is a key quantity that accounts for macroscopic solid- or fluid-like properties and the transitions between them. In this work, we propose a potential energy landscape (PEL) with local stable basins and low elastic energy barriers to analyse the nature of granular elasticity. A function for the elastic energy density is proposed for stable states and is further calibrated with ultrasonic measurements. Fluctuations in the elastic energy due to the evolution of internal structures are proposed to describe a so-called configuration temperature Tc as a counterpart of the classical kinetic granular temperature Tk that is attributed to the translational degrees of freedom. The two granular temperatures are chosen as the state variables, and a fundamental equation is established to develop non-equilibrium thermodynamics for granular materials. Due to the relatively low elastic energy barrier in the PEL, granular elasticity relaxes more under common mechanical loadings, and a simple model based on mean-field theory is developed to account for this behaviour. PMID:25951049
Drops with non-circular footprints
NASA Astrophysics Data System (ADS)
Ravazzoli, Pablo D.; González, Alejandro G.; Diez, Javier A.
2016-04-01
In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. These drops are consequence of the breakup processes occurring in thin films when anisotropic contact line motions take place. The anisotropy is basically due to the hysteresis of the contact angle since there is a wetting process in some parts of the contact line, while a dewetting occurs in other parts. Here, we obtain a characteristic drop shape from the rupture of a long liquid filament sitting on a solid substrate. We analyze its shape and contact angles by means of goniometric and refractive techniques. We also find a non-trivial steady state solution for the drop shape within the long wave approximation (lubrication theory), and we compare most of its features with experimental data. This solution is presented both in Cartesian and polar coordinates, whose constants must be determined by a certain group of measured parameters. Besides, we obtain the dynamics of the drop generation from numerical simulations of the full Navier-Stokes equation, where we emulate the hysteretic effects with an appropriate spatial distribution of the static contact angle over the substrate.
Non-Circular Wheels: Reuleaux and Squares
ERIC Educational Resources Information Center
Mills, Allan
2011-01-01
Circular wheels are so familiar on vehicles of all types that it is seldom realized that alternatives do exist. This short non-mathematical article describes Reuleaux and square wheels that, rolling along appropriate tracks, can maintain a moving platform at a constant height. Easily made working models lend themselves to demonstrations at science…
Non-Circular Wheels: Reuleaux and Squares
ERIC Educational Resources Information Center
Mills, Allan
2011-01-01
Circular wheels are so familiar on vehicles of all types that it is seldom realized that alternatives do exist. This short non-mathematical article describes Reuleaux and square wheels that, rolling along appropriate tracks, can maintain a moving platform at a constant height. Easily made working models lend themselves to demonstrations at science…
Elastic membranes in confinement
NASA Astrophysics Data System (ADS)
Bostwick, Joshua; Miksis, Michael; Davis, Stephen
2014-11-01
An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and DNA, have finer internal structure in which a membrane (or elastic member) is geometrically ``confined'' by another object. We study the shape stability of elastic membranes in a ``confining'' box and introduce repulsive van der Waals forces to prevent the membrane from intersecting the wall. We aim to define the parameter space associated with mitochondria-like deformations. We compare the confined to `unconfined' solutions and show how the structure and stability of the membrane shapes changes with the system parameters.
Elastic scattering phenomenology
NASA Astrophysics Data System (ADS)
Mackintosh, R. S.
2017-04-01
We argue that, in many situations, fits to elastic scattering data that were historically, and frequently still are, considered "good", are not justifiably so describable. Information about the dynamics of nucleon-nucleus and nucleus-nucleus scattering is lost when elastic scattering phenomenology is insufficiently ambitious. It is argued that in many situations, an alternative approach is appropriate for the phenomenology of nuclear elastic scattering of nucleons and other light nuclei. The approach affords an appropriate means of evaluating folding models, one that fully exploits available empirical data. It is particularly applicable for nucleons and other light ions.
Contact problems for a finitely deformed incompressible elastic halfspace
NASA Astrophysics Data System (ADS)
Selvadurai, A. P. S.
2015-01-01
This paper examines the class of problems related to the interaction between a finitely deformed incompressible elastic halfspace and contacting elements that include smooth, flat rigid indenters with elliptical and circular shapes and a thick plate of infinite extent. The contact between the finitely deformed elastic halfspace and the contacting elements is assumed to be bilateral. The interaction between both the rigid circular indenter and the finitely deformed halfspace is induced by a Mindlin force that acts at the interior of the halfspace regions and by exterior loads. Similar considerations apply for the contact between the flexible plate of infinite extent and the finitely deformed elastic halfspace. The theory of small deformations superposed on large deformations proposed by Green et al. (Proc R Soc Ser A 211:128-155, 1952) is used as the basis for the formulation of the problem, and results of potential theory and integral transform techniques are used to develop the analytical results. In particular, explicit results are presented for the displacement of the rigid elliptical indenter and the maximum deflection of the flexible plate induced by the Mindlin forces, when the finitely deformed halfspace region has a strain energy function of the Mooney-Rivlin form.
On the impedance of infinite LC ladder networks
NASA Astrophysics Data System (ADS)
Klimo, Paul
2017-01-01
The subject of electrical impedance is on the syllabi of most undergraduate courses in physics and electrical engineering. For example, Richard Feynman in his famous undergraduate text Lectures on Physics shows how to calculate the impedance of an infinite LC ladder. However, the formula he obtains has no useful physical interpretation if considered in the steady state frequency domain. In fact the value of this impedance becomes infinite unless one assumes that the energy flow along the infinite LC ladder is spatially uniform and in one direction only. This ad-hoc assumption, which renders the solution non-causal, is entirely unnecessary if the problem is considered in the time domain. It is important for students to appreciate that the concept of impedance works well only in dissipative circuits where the effects of transients are largely short lived. The purpose of this paper is to show that the same problem treated in the time domain by the Laplace transform method provides a qualitatively different and more satisfying explanation. We show that the current response of an infinite LC ladder, which is in the zero state before a causal harmonic driving voltage is applied, contains a significant non-harmonic component. This component, which is present in addition to the forced harmonic waveform, decays only very slowly and extracts an infinite amount of energy from the source.
Representations of Canonical Commutation Relations Describing Infinite Coherent States
NASA Astrophysics Data System (ADS)
Joye, Alain; Merkli, Marco
2016-10-01
We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.
Dissipation-Induced Instability Phenomena in Infinite-Dimensional Systems
NASA Astrophysics Data System (ADS)
Krechetnikov, Rouslan; Marsden, Jerrold E.
2009-11-01
This paper develops a rigorous notion of dissipation-induced instability in infinite dimensions as an extension of the classical concept implicitly introduced by Thomson and Tait for finite degree of freedom mechanical systems over a century ago. Here we restrict ourselves to a particular form of infinite-dimensional systems—partial differential equations—whose inherent function-analytic differences from finite-dimensional systems make uncovering this notion more intricate. In building the concept of dissipation-induced instability in infinite dimensions we found Arnold’s and Yudovich’s nonlinear stability methods, for conservative and dissipative systems respectively, along with some new existence theory for solutions, to be the essential foundation. However, when proving the results for classical solutions, as motivated by their direct physical significance, we had to overcome a number of fundamental difficulties associated with existing stability analysis methods, which has led to new techniques. In particular, in this work we establish the connection of existence and general stability theories in strong and weak topologies and provide new insights into the physics and geometry of the dissipation-induced instability phenomena in infinite-dimensional systems. As a paradigm and the first infinite-dimensional example to be rigorously analyzed, we use a two-layer quasi-geostrophic beta-plane model, which describes the fundamental baroclinic instability in atmospheric and ocean dynamics; early formal linear approximate studies suggested that this system can be destabilized after the introduction of dissipation.
Measures of correlations in infinite-dimensional quantum systems
NASA Astrophysics Data System (ADS)
Shirokov, M. E.
2016-05-01
Several important measures of correlations of the state of a finite-dimensional composite quantum system are defined as linear combinations of marginal entropies of this state. This paper is devoted to infinite-dimensional generalizations of such quantities and to an analysis of their properties. We introduce the notion of faithful extension of a linear combination of marginal entropies and consider several concrete examples, the simplest of which are quantum mutual information and quantum conditional entropy. Then we show that quantum conditional mutual information can be defined uniquely as a lower semicontinuous function on the set of all states of a tripartite infinite-dimensional system possessing all the basic properties valid in finite dimensions. Infinite-dimensional generalizations of some other measures of correlations in multipartite quantum systems are also considered. Applications of the results to the theory of infinite-dimensional quantum channels and their capacities are considered. The existence of a Fawzi-Renner recovery channel reproducing marginal states for all tripartite states (including states with infinite marginal entropies) is shown. Bibliography: 47 titles.
NASA Astrophysics Data System (ADS)
Godoy, Eduardo; Boccardo, Valeria; Durán, Mario
2017-01-01
The Dirichlet-to-Neumann finite element method (DtN FEM) has proven to be a powerful numerical approach to solve boundary-value problems formulated in exterior domains. However, its application to elastic semi-infinite domains, which frequently arise in geophysical applications, has been rather limited, mainly due to the lack of explicit closed-form expressions for the DtN map. In this paper, we present a DtN FEM procedure for boundary-value problems of elastostatics in semi-infinite domains with axisymmetry about the vertical axis. A semi-spherical artificial boundary is used to truncate the semi-infinite domain and to obtain a bounded computational domain, where a FEM scheme is employed. By using a semi-analytical procedure of solution in the unbounded residual domain lying outside the artificial boundary, the exact nonlocal boundary conditions provided by the DtN map are numerically approximated and efficiently coupled with the FEM scheme. Numerical results are provided to demonstrate the effectiveness and accuracy of the proposed method.
Mechanism of Resilin Elasticity
Qin, Guokui; Hu, Xiao; Cebe, Peggy; Kaplan, David L.
2012-01-01
Resilin is critical in the flight and jumping systems of insects as a polymeric rubber-like protein with outstanding elasticity. However, insight into the underlying molecular mechanisms responsible for resilin elasticity remains undefined. Here we report the structure and function of resilin from Drosophila CG15920. A reversible beta-turn transition was identified in the peptide encoded by exon III and for full length resilin during energy input and release, features that correlate to the rapid deformation of resilin during functions in vivo. Micellar structures and nano-porous patterns formed after beta-turn structures were present via changes in either the thermal or mechanical inputs. A model is proposed to explain the super elasticity and energy conversion mechanisms of resilin, providing important insight into structure-function relationships for this protein. Further, this model offers a view of elastomeric proteins in general where beta-turn related structures serve as fundamental units of the structure and elasticity. PMID:22893127
NASA Astrophysics Data System (ADS)
Quilliet, Catherine; Quemeneur, François; Marmottant, Philippe; Imhof, Arnout; Pépin-Donat, Brigitte; van Blaaderen, Alfons
2010-03-01
The deflation of elastic spherical surfaces has been numerically investigated, and show very different types of deformations according the range of elastic parameters, some of them being quantitatively explained through simple calculations. This allows to retrieve various shapes observed on hollow shells (from colloidal to centimeter scale), on lipid vesicles, or on some biological objects. The extension of this process to other geometries allows to modelize vegetal objects such as the ultrafast trap of carnivorous plants.
Joyce, Duncan
2017-01-01
In Parnell & Abrahams (2008 Proc. R. Soc. A 464, 1461–1482. (doi:10.1098/rspa.2007.0254)), a homogenization scheme was developed that gave rise to explicit forms for the effective antiplane shear moduli of a periodic unidirectional fibre-reinforced medium where fibres have non-circular cross section. The explicit expressions are rational functions in the volume fraction. In that scheme, a (non-dilute) approximation was invoked to determine leading-order expressions. Agreement with existing methods was shown to be good except at very high volume fractions. Here, the theory is extended in order to determine higher-order terms in the expansion. Explicit expressions for effective properties can be derived for fibres with non-circular cross section, without recourse to numerical methods. Terms appearing in the expressions are identified as being associated with the lattice geometry of the periodic fibre distribution, fibre cross-sectional shape and host/fibre material properties. Results are derived in the context of antiplane elasticity but the analogy with the potential problem illustrates the broad applicability of the method to, e.g. thermal, electrostatic and magnetostatic problems. The efficacy of the scheme is illustrated by comparison with the well-established method of asymptotic homogenization where for fibres of general cross section, the associated cell problem must be solved by some computational scheme. PMID:28588412
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ (N) using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C(1) maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS
OTT, WILLIAM; RIVAS, MAURICIO A.; WEST, JAMES
2016-01-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝN using a ‘typical’ nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time-T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence). PMID:28066028
Permittivity and permeability of semi-infinite metamaterial
NASA Astrophysics Data System (ADS)
Porvatkina, O. V.; Tishchenko, A. A.; Strikhanov, M. N.
2016-08-01
In our work we investigate dielectric and magnetic properties of semi-infinite metamaterial consisting of particles of different possible nature: atoms, molecules, nanoparticles, etc. It is important that these particles would have magnetic properties. Polarization of a near-surface layer is known to differ from its bulk value for non-magnetic materials; for magnetic materials, including metamaterials, the situation should be similar, which is the subject of our research. We obtain analogues of the Clausius-Mossotti relation both for permittivity and permeability taking into account the local field effects in the longwave approximation for semi-infinite metamaterial. These relations describe the connection between macroscopic characteristics of the semi-infinite metamaterial (permittivity and permeability) and characteristics of constituent particles (dielectric polarizability and magnetic polarizability), which is a bright example of multi-scale approach - method very popular today in physical and computer simulating.
Escape rate scaling in infinite measure preserving systems
NASA Astrophysics Data System (ADS)
Munday, Sara; Knight, Georgie
2016-02-01
We investigate the scaling of the escape rate from piecewise linear dynamical systems displaying intermittency due to the presence of an indifferent fixed point. Strong intermittent behaviour in the dynamics can result in the system preserving an infinite measure. We define a neighbourhood of the indifferent fixed point to be a hole through which points escape and investigate the scaling of the rate of this escape as the length of the hole decreases, both in the finite measure preserving case and infinite measure preserving case. In the infinite measure preserving systems we observe logarithmic corrections to and polynomial scaling of the escape rate with hole length. Finally we conjecture a relationship between the wandering rate and the observed scaling of the escape rate.
String-inspired Infinite Derivative theories of Gravity
NASA Astrophysics Data System (ADS)
Biswas, Tirthabir; Mazumdar, Anupam
2015-04-01
In String Theory there often appears a rather interesting class of higher derivative theories containing an infinite set of derivatives in the form of an exponential. These theories may provide a way to tame ultra-violet divergences without introducing ghost-like states. In this talk we provide a brief overview on the progress that has been made over the last decade to construct such infinite derivative theories of gravity. We will mostly focus on the status of the classical singularities, viz. Big Bang and the Black hole singularities, but we will also briefly discuss the recent progress that has been made on understanding quantum aspects of such infinite derivative theories. In the process we will present some general results that can be applied to any covariant torsion-free metric theory of gravity. We would like to thank W. Siegel, A. Koshelev, T. Koivisto, E. Gerwick, S. Vernov and S. Talaganis for several fruitful collaborations on the subject.
Quantum control of infinite-dimensional many-body systems
NASA Astrophysics Data System (ADS)
Bliss, Roger S.; Burgarth, Daniel
2014-03-01
A major challenge to the control of infinite-dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space domain and show that by utilizing the implications of the quantum recurrence theorem this irreversibility may be overcome, in the case of individual states more generally, but also in certain specified cases over larger subsets of the Hilbert space. We discuss briefly the possibility of using these results in the control of infinite-dimensional coupled harmonic oscillators and also draw attention to some of the issues and open questions arising from this and related work.
Role of infinite invariant measure in deterministic subdiffusion
NASA Astrophysics Data System (ADS)
Akimoto, Takuma; Miyaguchi, Tomoshige
2010-09-01
Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time difference is much smaller than the total observation time, the time-averaged mean square displacement depends linearly on the time difference. Furthermore, the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the Mittag-Leffler distribution.
Robust Consumption-Investment Problem on Infinite Horizon
Zawisza, Dariusz
2015-12-15
In our paper we consider an infinite horizon consumption-investment problem under a model misspecification in a general stochastic factor model. We formulate the problem as a stochastic game and finally characterize the saddle point and the value function of that game using an ODE of semilinear type, for which we provide a proof of an existence and uniqueness theorem for its solution. Such equation is interested on its own right, since it generalizes many other equations arising in various infinite horizon optimization problems.
Infinite tension limit of the pure spinor superstring
NASA Astrophysics Data System (ADS)
Berkovits, Nathan
2014-03-01
Mason and Skinner recently constructed a chiral infinite tension limit of the Ramond-Neveu-Schwarz superstring which was shown to compute the Cachazo-He-Yuan formulae for tree-level d = 10 Yang-Mills amplitudes and the NS-NS sector of tree-level d = 10 supergravity amplitudes. In this letter, their chiral infinite tension limit is generalized to the pure spinor superstring which computes a d = 10 superspace version of the Cachazo-He-Yuan formulae for tree-level d = 10 super-Yang-Mills and supergravity amplitudes.
Infinite time interval backward stochastic differential equations with continuous coefficients.
Zong, Zhaojun; Hu, Feng
2016-01-01
In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).
NASA Astrophysics Data System (ADS)
Campbell, C. S.
2014-12-01
The dry granular flowmap can be broken into two broad categories, the Elastic and the Inertial. Elastic flows are dominated by force chains and stresses are generated by the compression of the interparticle contacts within those chains, and thus are proportional to the stiffness of the contacts. The Elastic zone can be subdivided into two regimes, the Elastic-Quasistatic where forces are independent of the shear rate which at high shear rates transitions to Elastic-Inertial where the particle inertia is reflected in the forces and the stresses increase linearly with the shear rate. In the Inertial regime, the stresses vary with the square of the shear rate. It also is divided into two regimes, the Dense-Inertial where the flow is dominated by clusters of particles, and the Inertial-Collisional where the flow is dominated by binary collisions. Appropriately the elastic theory grew out of an old study of landslides. But like most such studies, all of the above depend on idealized computer simulations of uniform sized spherical particles. Real particles are never round, never of uniform size, and the process of flowing changes surface properties and may even shatter the particles. But all indications are that real systems still fit into the pattern drawn out in the last paragraph. A grave problem facing the field is how to incorporate these effects without losing a fundamental understanding of the internal rheological processes. This talk will begin with an overview of the Elastic flowmap and the behaviors associated with each flow regime. It will then discuss early work to include effects of particle shape and size mixtures and perhaps some effects of particle breakage.
Elasticity of plagioclase feldspars
NASA Astrophysics Data System (ADS)
Brown, J. Michael; Angel, Ross J.; Ross, Nancy L.
2016-02-01
Elastic properties are reported for eight plagioclase feldspars that span compositions from albite (NaSi3AlO8) to anorthite (CaSi2Al2O8). Surface acoustic wave velocities measured using Impulsive Stimulated Light Scattering and compliance sums from high-pressure X-ray compression studies accurately determine all 21 components of the elasticity tensor for these triclinic minerals. The overall pattern of elasticity and the changes in individual elastic components with composition can be rationalized on the basis of the evolution of crystal structures and chemistry across this solid-solution join. All plagioclase feldspars have high elastic anisotropy; a* (the direction perpendicular to the b and c axes) is the softest direction by a factor of 3 in albite. From albite to anorthite the stiffness of this direction undergoes the greatest change, increasing twofold. Small discontinuities in the elastic components, inferred to occur between the three plagioclase phases with distinct symmetry (C1>¯, I1>¯, and P1>¯), appear consistent with the nature of the underlying conformation of the framework-linked tetrahedra and the associated structural changes. Measured body wave velocities of plagioclase-rich rocks, reported over the last five decades, are consistent with calculated Hill-averaged velocities using the current moduli. This confirms long-standing speculation that previously reported elastic moduli for plagioclase feldspars are systematically in error. The current results provide greater assurance that the seismic structure of the middle and lower crusts can be accurately estimated on the basis of specified mineral modes, chemistry, and fabric.
Fracture and contact problems for an elastic wedge
NASA Technical Reports Server (NTRS)
Erdogan, F.; Arin, K.
1976-01-01
The paper deals with the plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.
Fracture and contact problems for an elastic wedge
NASA Technical Reports Server (NTRS)
Erdogan, F.; Arin, K.
1974-01-01
The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.
Normal waves in elastic bars of rectangular cross section.
Krushynska, Anastasiia A; Meleshko, Viatcheslav V
2011-03-01
This paper addresses a theoretical study of guided normal waves in elastic isotropic bars of rectangular cross-section by an analytical superposition method. Dispersion properties of propagating and evanescent modes for four families are analyzed in detail at various geometric and physical parameters of the bar. A comparison of the obtained results with the well-known properties for waves in infinite plates and circular cylinders is provided. The complicated structure of dispersion spectra is explained. High-frequency limiting values for phase and group velocities of normal waves are established for the first time. Calculated data agree well with the available experimental results.
NASA Astrophysics Data System (ADS)
O'Neill, Bridget; Bass, Jay D.; Rossman, George R.; Geiger, Charles A.; Langer, Klaus
1991-03-01
Brillouin spectroscopy was used to measure the single crystal elastic properties of a pure synthetic pyrope and a natural garnet containing 89.9 mol% of the pyrope end member (Mg3Al2Si3O12). The elastic moduli, c ij , of the two samples are entirely consistent and agree with previous estimates of the elastic properties of pyrope based upon the moduli of solid solutions. Our results indicate that the elastic moduli of pyrope end-member are c 11=296.2±0.5, c 12=111.1±0.6, c 44=91.6±0.3, Ks=172.8±0.3, μ=92.0±0.2, all in units of GPa. These results differ by several percent from those reported previously for synthetic pyrope, but are based upon a much larger data set. Although the hydrous components of the two samples from the present study are substantially different, representing both ‘dry’ and ‘saturated’ samples, we find no discernable effect of structurally bound water on the elastic properties. This is due to the small absolute solubility of water in pyrope, as compared with other garnets such as grossular.
Finding Sums for an Infinite Class of Alternating Series
ERIC Educational Resources Information Center
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
Infinite Coordination Polymer Nano- and Micro-Particles
2015-06-12
Capacity17 Nanoporous materials such as MOFs form an important class of materials that can potentially be used for the separation and storage of...SECURITY CLASSIFICATION OF: Infinite coordination polymer (ICP) particles and metal-organic frameworks (MOFs) are attractive materials for a diverse...nano- materials possess certain shortcomings that require further examination through fundamental studies. Towards overcoming these shortcomings, we
Coherent States for Supersymmetric Partners of the Infinite Well
NASA Astrophysics Data System (ADS)
Hussin, V.; Morales-Salgado, V. S.
2017-05-01
We define linear and quadratic coherent states for the supersymmetric partners of the quantum infinite well through formal series expansions of the energy eigenfunctions of the systems and we study the appropriateness of this definitions as coherent states by means of their properties. In particular, we examine the localization in position and time evolution, minimum uncertainty relations and the behavior of the Wigner function.
Activity coefficients of chlorophenols in water at infinite dilution
Tabai, S.; Rogalski, M.; Solimando, R.; Malanowski, S.K.
1997-11-01
The total pressure of aqueous solutions of chlorophenols was determined by a ebulliometric total pressure method for the aqueous solutions of phenol, 2-chlorophenol, 3-chlorophenol, 4-chlorophenol, and 2,4-dichlorophenol in the temperature range from 40 to 90 C. The activity coefficients at infinite dilution and the Henry constants were derived.
On Hamilton-Jacobi equation in infinite dimensions
Sritharan, S.S.
1994-12-31
A relationship between the notion of viscosity solution in the sense of Crandall and Lions and the generalized solution in the sense of Clarke for the infinite dimensional Hamilton-Jacobi-Bellman equation is established. This problem arises in optimal control of fluids.
Entropy of a black hole in infinite-derivative gravity
NASA Astrophysics Data System (ADS)
Myung, Yun Soo
2017-05-01
We compute the Wald entropy of the Schwarzschild black hole in the ghost-free, infinite-derivative gravity that is quadratic in curvature. This is not given purely by the area law but includes an additional contribution depending on the power of the d'Alembertian operator, when requiring that the massless graviton be the only propagating mode in the Minkowski spacetime.
Functional DNA: Teaching Infinite Series through Genetic Analogy
ERIC Educational Resources Information Center
Kowalski, R. Travis
2011-01-01
This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…
Large Deviations for Infinite Dimensional Stochastic Dynamical Systems
2007-03-27
exotic function spaces (e.g., Hölder spaces, spaces of diffeomorphisms , etc.). Standard approaches to small noise LDP for infinite dimensional SDE...24] J. Ren and X. Zhang. Schilder theorem for the Brownian motion on the diffeomorphism group of the circle. J. Funct. Anal., 224(1): 107–133, 2005
Infinite Töplitz Lipschitz matrices and operators
NASA Astrophysics Data System (ADS)
Eliasson, H. L.; Kuksin, S. B.
2008-01-01
We introduce a class of infinite matrices {(A_{ss', s, s' in mathbb{Z}^d)} , which are asymptotically ( as | s| + | s'| → ∞) close to Hankel Töplitz matrices. We prove that this class forms an algebra, and that flow-maps of nonautonomous linear equations with coefficients from the class also belong to it.
Reparametrization of the Relativistic Infinitely Extended Charged Particle Action
NASA Astrophysics Data System (ADS)
Saadat, Hassan; Pourhassan, Behnam
2016-09-01
In this letter, relativistic infinitely extended particles formulated. Correct form of action with possibility of reparametrization obtained and effect of electric field considered. It may be one of the first step to re-introduce theory of every things given by Nakano and Hessaby many years ago.
Explaining Infinite Series--An Exploration of Students' Images
ERIC Educational Resources Information Center
Champney, Danielle Dawn
2013-01-01
This study uses self-generated representations (SGR)--images produced in the act of explaining--as a means of uncovering what university calculus students understand about infinite series convergence. It makes use of student teaching episodes, in which students were asked to explain to a peer what that student might have missed had they been…
Functional DNA: Teaching Infinite Series through Genetic Analogy
ERIC Educational Resources Information Center
Kowalski, R. Travis
2011-01-01
This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…
Explaining Infinite Series--An Exploration of Students' Images
ERIC Educational Resources Information Center
Champney, Danielle Dawn
2013-01-01
This study uses self-generated representations (SGR)--images produced in the act of explaining--as a means of uncovering what university calculus students understand about infinite series convergence. It makes use of student teaching episodes, in which students were asked to explain to a peer what that student might have missed had they been…
Plasmonic waves of a semi-infinite random nanocomposite
Moradi, Afshin
2013-10-15
The dispersion curves of the plasmonic waves of a semi-infinite random metal-dielectric nanocomposite, consisting of bulk metal embedded with dielectric inclusions, are presented. Two branches of p-polarized surface plasmon-polariton modes are found to exist. The possibility of experimentally observing the surface waves by attenuated total reflection is demonstrated.
How Fragile Is Consolidated Knowledge? Ben's Comparisons of Infinite Sets
ERIC Educational Resources Information Center
Tsamir, Pessia; Dreyfus, Tommy
2005-01-01
This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…
What Causes Adverbial Infinitives to Spread? Evidence from Romance
ERIC Educational Resources Information Center
Schulte, K.
2007-01-01
It is cross-linguistically common for languages to undergo a diachronic increase in the range of adverbial notions that can be expressed by means of infinitival constructions, and the Romance languages are a good example of this process. Examining the development of adverbial "prepositional infinitive" constructions in Spanish, Portuguese and…
The Limits of Some Infinite Families of Complex Contracting Mappings
NASA Astrophysics Data System (ADS)
Pagon, Dušan
2008-11-01
Self-similarity is strongly presented in modern mathematics and physics. We study a broad class of planar fractals—strongly self-similar sets of points in complex plane, obtained from a unit interval as geometric limits of certain infinite families of contracting mappings. Different 1-1 correspondences between the constructed set and the initial unit interval are established.
Finding Sums for an Infinite Class of Alternating Series
ERIC Educational Resources Information Center
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-01-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the…
Finding sums for an infinite class of alternating series
NASA Astrophysics Data System (ADS)
Chen, Zhibo; Wei, Sheng; Xiao, Xuerong
2012-07-01
Calculus II students know that many alternating series are convergent by the Alternating Series Test. However, they know few alternating series (except geometric series and some trivial ones) for which they can find the sum. In this article, we present a method that enables the students to find sums for infinitely many alternating series in the following form ?
The physics of FEL in an infinite electron beam
Wang, G.; Litvinenko, V.N.; Webb, S.
2010-10-07
We solve linearized Vlasov-Maxwell FEL equations for a 3-D perturbation in the infinite electron beam with Lorentzian energy distributions using paraxial approximation. We present analytical solutions for various initial perturbations and discuss the effect of optical guiding in such system.
Infinite S-expansion with ideal subtraction and some applications
NASA Astrophysics Data System (ADS)
Peñafiel, D. M.; Ravera, L.
2017-08-01
According to the literature, the S-expansion procedure involving a finite semigroup is valid no matter what the structure of the original Lie (super)algebra is; however, when something about the structure of the starting (super)algebra is known and when certain particular conditions are met, the S-expansion method (with its features of resonance and reduction) is able not only to lead to several kinds of expanded (super)algebras but also to reproduce the effects of the standard as well as the generalized Inönü-Wigner contraction. In the present paper, we propose a new prescription for S-expansion, involving an infinite abelian semigroup S(∞ ) and the subtraction of an infinite ideal subalgebra. We show that the subtraction of the infinite ideal subalgebra corresponds to a reduction. Our approach is a generalization of the finite S-expansion procedure presented in the literature, and it offers an alternative view of the generalized Inönü-Wigner contraction. We then show how to write the invariant tensors of the target (super)algebras in terms of those of the starting ones in the infinite S-expansion context presented in this work. We also give some interesting examples of application on algebras and superalgebras.
The Limits of Some Infinite Families of Complex Contracting Mappings
Pagon, Dusan
2008-11-13
Self-similarity is strongly presented in modern mathematics and physics. We study a broad class of planar fractals--strongly self-similar sets of points in complex plane, obtained from a unit interval as geometric limits of certain infinite families of contracting mappings. Different 1-1 correspondences between the constructed set and the initial unit interval are established.
NASA Astrophysics Data System (ADS)
Yu, Betty; Kang, Soo-Young; Akthakul, Ariya; Ramadurai, Nithin; Pilkenton, Morgan; Patel, Alpesh; Nashat, Amir; Anderson, Daniel G.; Sakamoto, Fernanda H.; Gilchrest, Barbara A.; Anderson, R. Rox; Langer, Robert
2016-08-01
We report the synthesis and application of an elastic, wearable crosslinked polymer layer (XPL) that mimics the properties of normal, youthful skin. XPL is made of a tunable polysiloxane-based material that can be engineered with specific elasticity, contractility, adhesion, tensile strength and occlusivity. XPL can be topically applied, rapidly curing at the skin interface without the need for heat- or light-mediated activation. In a pilot human study, we examined the performance of a prototype XPL that has a tensile modulus matching normal skin responses at low strain (<40%), and that withstands elongations exceeding 250%, elastically recoiling with minimal strain-energy loss on repeated deformation. The application of XPL to the herniated lower eyelid fat pads of 12 subjects resulted in an average 2-grade decrease in herniation appearance in a 5-point severity scale. The XPL platform may offer advanced solutions to compromised skin barrier function, pharmaceutical delivery and wound dressings.
Sewell, T. D.; Bedrov, D.; Menikoff, Ralph; Smith, G. D.
2001-01-01
Atomistic molecular dynamics simulations have been used to calculate isothermal elastic properties for {beta}-, {alpha}-, and {delta}-HMX. The complete elastic tensor for each polymorph was determined at room temperature and pressure via analysis of microscopic strain fluctuations using formalism due to Rahman and Parrinello [J. Chem. Phys. 76,2662 (1982)]. Additionally, the isothermal compression curve was computed for {beta}-HMX for 0 {le} p {le} 10.6 GPa; the bulk modulus K and its pressure derivative K{prime} were obtained from two fitting forms employed previously in experimental studies of the {beta}-HMX equation of state. Overall, the results indicate good agreement between the bulk modulus predicted from the measured and calculated compression curves. The bulk modulus determined directly from the elastic tensor of {beta}-HMX is in significant disagreement with the compression curve-based results. The explanation for this discrepancy is an area of current research.
Peselnick, L.; Robie, R.A.
1962-01-01
The recent measurements of the elastic constants of calcite by Reddy and Subrahmanyam (1960) disagree with the values obtained independently by Voigt (1910) and Bhimasenachar (1945). The present authors, using an ultrasonic pulse technique at 3 Mc and 25??C, determined the elastic constants of calcite using the exact equations governing the wave velocities in the single crystal. The results are C11=13.7, C33=8.11, C44=3.50, C12=4.82, C13=5.68, and C14=-2.00, in units of 1011 dyncm2. Independent checks of several of the elastic constants were made employing other directions and polarizations of the wave velocities. With the exception of C13, these values substantially agree with the data of Voigt and Bhimasenachar. ?? 1962 The American Institute of Physics.
Dynamics and ergodicity of the infinite harmonic crystal
NASA Astrophysics Data System (ADS)
van Hemmen, J. L.
1980-10-01
This is a comprehensive, relatively formal study of the a priori infinite harmonic crystal. A phase space is introduced and the equations of motion of a harmonic crystal, which need not be a primitive one, are explicitly solved by several methods. The crystal is taken infinite right at the beginni ng. Exploiting the fact that the dynamics is known we derive the thermal equilibrium state of the infinite system. In so doing we use the classical Kubo-Martin-Schwinger (KMS) condition. The thermal equilibrium state is a, so-called, gaussian measure on the phase space. The traditional procedure of the thermodynamic limit is considered as well. In both cases we exploit the advantages of the technique of Fourier transforms of measures. This technique is elucidated in a separate section, where the many connections with Euclidean quantum field theory are also indicated. Finally we settle the problem of the existence of a crystalline state in its appropriate setting: the infinite system. The system is a “crystal” only if it is three-dimensional. The three essential ingredients of the ergodic analysis are a phase space, a dynamics, and an invariant state, here the thermal equilibrium state. A system is ergodic when the time average of any observable equals its phase average. There are, however, stronger notions of ergodicity which are classified in an “ergodic hierarchy”. When a system is Bernoulli it is at the top of this hierarchy. A finite harmonic system is never ergodic. Here it is shown that, generally speaking, a perfect, infinite harmonic crystal in thermal equilibrium has to be Bernoulli. A detailed discussion of the physical relevance of this result has been included.
Elastic model of supercoiling.
Benham, C J
1977-01-01
An elastic model for the supercoiling of duplex DNA is developed. The simplest assumptions regarding the elastic properties of double-helical DNA (homogeneous, isotropic, of circular cross section, and remaining straight when unstressed) will generate two orders of superhelicity when stressed. Recent experimental results [Brady, G.W., Fein, D.B. & Brumberger, H. (1976) Nature 264, 231-234] suggest that in supercoiled DNA molecules there are regions where two distinct orders of supercoiling arise, as predicted by this model. PMID:267934
NASA Astrophysics Data System (ADS)
Quilliet, Catherine
2011-03-01
The deflation of elastic spherical surfaces has been numerically investigated, and show very different types of deformations according the range of elastic parameters, some of them being quantitatively understood through simple theoretical considerations. In particular, the role of the Poisson ratio is closely investigated. This work allowed to retrieve various shapes observed on hollow deformable shells (from colloidal to centimeter scale), on lipid vesicles, or on some simple biological objects. Conversely, it shows how high deformations can tell observers about mechanical properties of a body. Such investigations have been extended to other geometries, in order to provide clues to understand deformations of vegetal or animal tissues.
ERIC Educational Resources Information Center
Cocco, Alberto; Masin, Sergio Cesare
2010-01-01
Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight--a cognitive law analogous to Hooke's law of elasticity. Participants also estimated the total imagined elongation of springs joined…
Elastic and Inelastic Collisions
ERIC Educational Resources Information Center
Gluck, Paul
2010-01-01
There have been two articles in this journal that described a pair of collision carts used to demonstrate vividly the difference between elastic and inelastic collisions. One cart had a series of washers that were mounted rigidly on a rigid wooden framework, the other had washers mounted on rubber bands stretched across a framework. The rigidly…
ERIC Educational Resources Information Center
Gordon, Warren B.
2006-01-01
This paper examines the elasticity of demand, and shows that geometrically, it may be interpreted as the ratio of two simple distances along the tangent line: the distance from the point on the curve to the x-intercept to the distance from the point on the curve to the y-intercept. It also shows that total revenue is maximized at the transition…
Hydrodynamic Elastic Magneto Plastic
Wilkins, M. L.; Levatin, J. A.
1985-02-01
The HEMP code solves the conservation equations of two-dimensional elastic-plastic flow, in plane x-y coordinates or in cylindrical symmetry around the x-axis. Provisions for calculation of fixed boundaries, free surfaces, pistons, and boundary slide planes have been included, along with other special conditions.
Elastic swimming I: Optimization
NASA Astrophysics Data System (ADS)
Lauga, Eric; Yu, Tony; Hosoi, Anette
2006-03-01
We consider the problem of swimming at low Reynolds number by oscillating an elastic filament in a viscous liquid, as investigated by Wiggins and Goldstein (1998, Phys Rev Lett). In this first part of the study, we characterize the optimal forcing conditions of the swimming strategy and its optimal geometrical characteristics.
Elastic swimming II: Experiments
NASA Astrophysics Data System (ADS)
Yu, Tony; Lauga, Eric; Hosoi, Anette
2006-03-01
We consider the problem of swimming at low Reynolds number by oscillating an elastic filament in a viscous liquid, as investigated by Wiggins and Goldstein (1998, Phys Rev Lett). In this second part of the study, we present results of a series of experiments characterizing the performance of the propulsive mechanism.
Elastic and Inelastic Collisions
ERIC Educational Resources Information Center
Gluck, Paul
2010-01-01
There have been two articles in this journal that described a pair of collision carts used to demonstrate vividly the difference between elastic and inelastic collisions. One cart had a series of washers that were mounted rigidly on a rigid wooden framework, the other had washers mounted on rubber bands stretched across a framework. The rigidly…
Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids
NASA Astrophysics Data System (ADS)
Piriz, S. A.; Piriz, A. R.; Tahir, N. A.
2017-05-01
A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT=1 , the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998), 10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.
Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids.
Piriz, S A; Piriz, A R; Tahir, N A
2017-05-01
A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes into account the finite transit time of the elastic waves across the slab thickness. For Atwood number A_{T}=1, the asymptotic growth rate is found to be in excellent agreement with the exact solution [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.
NASA Astrophysics Data System (ADS)
Campbell, Charles
2006-03-01
There is no fundamental understanding of the mechanics of granular solids. Partially this is because granular flows have historically been divided into two very distinct flow regimes, (1) the slow, quasistatic regime, in which the bulk friction coefficient is taken to be a material constant, and (2) the fast, rapid-flow regime, where the particles interact collisionally. But slow hopper flow simulations indicate that the bulk friction coefficient is not a constant. Rapidly moving large scale landslide simulations never entered the collisional regime and operate in a separate intermediate flow regime. In other words, most realistic granular flows are not described by either the quasistatic or rapid flow models and it is high time that the field look beyond those early models. This talk will discuss computer simulation studies that draw out the entire flowmap of shearing granular materials, spanning the quasistatic, rapid and the intermediate regimes. The key was to include the elastic properties of the solid material in the set of rheological parameters; in effect, this puts solid properties back into the rheology of granular solids. The solid properties were previously unnecessary in the plasticity and kinetic theory formalisms that respectively form the foundations of the quasistatic and rapid-flow theories. Granular flows can now be divided into two broad categories, the Elastic Regimes, in which the particles are locked in force chains and interact elastically over long duration contact with their neighbors and the Inertial regimes, where the particles have broken free of the force chains. The Elastic regimes can be further subdivided into the Elastic-Quasistatic regime (the old quasistatic regime) and the Elastic-Inertial regime. The Elastic-Inertial regime is the ``new'' regime observed in the landslide simulations, in which the inertially induced stresses are significant compared to the elastically induced stresses. The Inertial regime can also be sub
Three-dimensional fundamental thermo-elastic solutions applied to contact problems
NASA Astrophysics Data System (ADS)
Wang, Z. P.; Wang, T.; Li, P. D.; Li, X. Y.; Chen, W. Q.; Müller, R.
2016-11-01
This paper aims to develop three-dimensional fundamental thermo-elastic solutions for an infinite/half-infinite space of a two-dimensional hexagonal quasi-crystal, which is subjected to a point heat source. Starting from the newly developed general solution in terms of quasi-harmonic potential functions, the corresponding fundamental solutions are derived by means of the trial-and-error technique. Six appropriate potential functions involved in the general solution are observed. The present fundamental solutions are applied to construct boundary integral equations governing the contact problems. Numerical calculations are performed to show the distributions of the thermo-elastic coupling field variables in a half-space subjected to a point thermal source.
NASA Technical Reports Server (NTRS)
Sheu, Y. C.; Fu, L. S.
1982-01-01
The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.
NASA Astrophysics Data System (ADS)
Vattré, A.
2017-08-01
A parametric energy-based framework is developed to describe the elastic strain relaxation of interface dislocations. By means of the Stroh sextic formalism with a Fourier series technique, the proposed approach couples the classical anisotropic elasticity theory with surface/interface stress and elasticity properties in heterogeneous interface-dominated materials. For any semicoherent interface of interest, the strain energy landscape is computed using the persistent elastic fields produced by infinitely periodic hexagonal-shaped dislocation configurations with planar three-fold nodes. A finite element based procedure combined with the conjugate gradient and nudged elastic band methods is applied to determine the minimum-energy paths for which the pre-computed energy landscapes yield to elastically favorable dislocation reactions. Several applications on the Au/Cu heterosystems are given. The simple and limiting case of a single set of infinitely periodic dislocations is introduced to determine exact closed-form expressions for stresses. The second limiting case of the pure (010) Au/Cu heterophase interfaces containing two crossing sets of straight dislocations investigates the effects due to the non-classical boundary conditions on the stress distributions, including separate and appropriate constitutive relations at semicoherent interfaces and free surfaces. Using the quantized Frank-Bilby equation, it is shown that the elastic strain landscape exhibits intrinsic dislocation configurations for which the junction formation is energetically unfavorable. On the other hand, the mismatched (111) Au/Cu system gives rise to the existence of a minimum-energy path where the fully strain-relaxed equilibrium and non-regular intrinsic hexagonal-shaped dislocation rearrangement is accompanied by a significant removal of the short-range elastic energy.
Defocusing of null rays in infinite derivative gravity
NASA Astrophysics Data System (ADS)
Conroy, Aindriú; Koshelev, Alexey S.; Mazumdar, Anupam
2017-01-01
Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any ansatz to solve the full equations of motion.
Dynamical Crossing of an Infinitely Degenerate Critical Point
NASA Astrophysics Data System (ADS)
Bachmann, Sven; Fraas, Martin; Graf, Gian Michele
2017-05-01
We study the evolution of a driven harmonic oscillator with a time-dependent frequency $\\omega_t \\propto |t|$. At time $t=0$ the Hamiltonian undergoes a point of infinite spectral degeneracy. If the system is initialized in the instantaneous vacuum in the distant past then the asymptotic future state is a squeezed state whose parameters are explicitly determined. We show that the squeezing is independent on the sweeping rate. This manifests the failure of the adiabatic approximation at points where infinitely many eigenvalues collide. We extend our analysis to the situation where the gap at $t=0$ remains finite. We also discuss the natural geometry of the manifold of squeezed states. We show that it is realized by the Poincar\\'e disk model viewed as a K\\"ahler manifold.
Accelerated Gibbs Sampling for Infinite Sparse Factor Analysis
Andrzejewski, D M
2011-09-12
The Indian Buffet Process (IBP) gives a probabilistic model of sparse binary matrices with an unbounded number of columns. This construct can be used, for example, to model a fixed numer of observed data points (rows) associated with an unknown number of latent features (columns). Markov Chain Monte Carlo (MCMC) methods are often used for IBP inference, and in this technical note, we provide a detailed review of the derivations of collapsed and accelerated Gibbs samplers for the linear-Gaussian infinite latent feature model. We also discuss and explain update equations for hyperparameter resampling in a 'full Bayesian' treatment and present a novel slice sampler capable of extending the accelerated Gibbs sampler to the case of infinite sparse factor analysis by allowing the use of real-valued latent features.
Newtonian potential and geodesic completeness in infinite derivative gravity
NASA Astrophysics Data System (ADS)
Edholm, James; Conroy, Aindriú
2017-08-01
Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.
Infinite-Order Symmetries for Quantum Separable Systems
Miller, W.; Kalnins, E.G.; Kress, J.M.; Pogosyan, G.S.
2005-10-01
We develop a calculus to describe the (in general) infinite-order differential operator symmetries of a nonrelativistic Schroedinger eigenvalue equation that admits an orthogonal separation of variables in Riemannian n space. The infinite-order calculus exhibits structure not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. Among the simple consequences of the calculus is that one can generate algorithmically a canonical basis for the space. Similarly, we can develop a calculus for conformal symmetries of the time-dependent Schroedinger equation if it admits R separation in some coordinate system. This leads to energy-shifting symmetries.
Elastic properties of hybrid composites by the effective field approach
NASA Astrophysics Data System (ADS)
Kanaun, S. K.; Jeulin, D.
2001-10-01
The work is dedicated to the calculation of the overall elastic properties of matrix composite materials containing two different populations of inclusions (three phase hybrid composites). The application of the well known Mori-Tanaka method or self-consistent effective medium method to the solution of this problem gives overall elastic moduli tensors of such composites that do not have the necessary symmetry (the symmetry with respect to the first and second pairs of indices). In this work, a new version of the effective field method that takes into account specific features of the microstructure of three phase composites is developed. In this version, the field that acts on every inclusion in the composite is assumed to be different for inclusions of different populations. It is shown that the modified effective field method gives a correct symmetry of the overall elastic moduli tensors of three phase composites. The method allows us to describe the influence of the peculiarities in spatial distributions of inclusions on the overall elastic constants. The cases of media containing infinite cylindrical fibers and thin ellipsoidal disks or spherical pores are considered. Various boolean type probabilistic models of random sets of such inclusions are proposed and the elastic moduli tensors of the corresponding three phase composites are obtained and analyzed. It turns out that these tensors strongly depend on statistical properties of the random fields of inclusions. It is shown that for two phase composites, the Mori-Tanaka method is a particular case of the effective field method. In the case of three phase composites, the formulas of the Mori-Tanaka method follow from the equations of the effective field method if a general property of the symmetry of cross-correlation functions of different populations of inclusions is violated. As a result, the overall elastic moduli tensors obtained by Mori-Tanaka method lose their natural symmetry.
Acoustic Characterization of a Stretched Vortex in an Infinite Medium
NASA Astrophysics Data System (ADS)
Manneville, Sebastien; Maurel, Agnes; Bottausci, Frederic; Petitjeans, Philippe
A new experimental device is presented, that allows to isolate and control a stretched vortex in an "`infinite" medium. Acoustic measurements based on the ultrasound-flow interaction yield the main vortex characteristics (position, circulation, core size). This global and non-invasive method also allows a dynamical tracking of the vortex. Experimental results on the mean vortex characteristics as a function of the control parameters are presented, together with some examples of transitory regimes and of precession motion.
Private algebras in quantum information and infinite-dimensional complementarity
Crann, Jason; Kribs, David W.; Levene, Rupert H.; Todorov, Ivan G.
2016-01-15
We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.
Subdifferential of Optimal Value Functions in Nonlinear Infinite Programming
Huy, N. Q. Giang, N. D.; Yao, J.-C.
2012-02-15
This paper presents an exact formula for computing the normal cones of the constraint set mapping including the Clarke normal cone and the Mordukhovich normal cone in infinite programming under the extended Mangasarian-Fromovitz constraint qualification condition. Then, we derive an upper estimate as well as an exact formula for the limiting subdifferential of the marginal/optimal value function in a general Banach space setting.
Toroidal insulating inhomogeneity in an infinite space and related problems
Radi, E.
2016-01-01
An analytic solution for the steady-state temperature distribution in an infinite conductive medium containing an insulated toroidal inhomogeneity and subjected to remotely applied uniform heat flux is obtained. The temperature flux on the torus surface is then determined as a function of torus parameters. This result is used to calculate the resistivity contribution tensor for the toroidal inhomogeneity required to evaluate the effective conductive properties of a material containing multiple inhomogeneities of this shape. PMID:27118919
Analysis of Multiple Cracks in an Infinite Functionally Graded Plate
NASA Technical Reports Server (NTRS)
Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.
1999-01-01
A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.
Infinite Phased Array of Microstrip Dipoles in Two Layers
1989-01-01
Green’s function appropriate to the two-layer substrate- superstrate structure was used in the formulation of the method of moMents - (continued on back) 20...analysis is presented for an infinite phased array of microstrip dipoles embedded within a two layer substrate structure (sub- strate- superstrate ...characterization of input impedance as a function of phase scan angle. Results for several sub- strate- superstrate structures illustrate the utility of the single
Fuhrman, Marco Hu, Ying
2007-09-15
In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.
Infinite variance in fermion quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
Infinitely Many Heteroclinic Orbits of a Complex Lorenz System
NASA Astrophysics Data System (ADS)
Wang, Haijun; Li, Xianyi
2017-06-01
The existence of heteroclinic orbits of a chaotic system is a difficult yet interesting mathematical problem. Nowadays, a rigorous analytical proof for the existence of a heteroclinic orbit can be carried out only for some special chaotic and hyperchaotic systems, and few results are known for the complex systems. In this paper, by revisiting a complex Lorenz system, it is found that this system possesses an infinite set of heteroclinic orbits to the origin and its circle equilibria. However, it is impossible for the corresponding real Lorenz system to have infinitely many heteroclinic orbits. The theoretical tools for proving the main results are Lyapunov functions and the definitions of α-limit set and ω-limit set. Numerical simulations show the effectiveness and correctness of the theoretical conclusions. The investigations not only enrich the related results for the complex Lorenz system, but also find the essential difference between the complex Lorenz system and its corresponding real version: the complex Lorenz system has infinitely many heteroclinic orbits whereas its corresponding real one does not.
Single file diffusion into a semi-infinite tube.
Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D
2015-11-23
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
Single file diffusion into a semi-infinite tube
NASA Astrophysics Data System (ADS)
Farrell, Spencer G.; Brown, Aidan I.; Rutenberg, Andrew D.
2015-12-01
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
Drop impact onto semi-infinite solid surface
NASA Astrophysics Data System (ADS)
Chen, Huanchen; Amirfazli, Alidad
2016-11-01
The drop impact onto solid surfaces has been studied intensively due to its importance in different applications, e.g. spray coating, inkjet printing and agricultural sprays. The previous studies on this topic were typically focused either on the drop impact onto an infinite solid surface (i.e. a solid surface that is large, and the impact happens far away from the surface edges), or onto a finite solid surface (e.g. drop impact onto a target smaller than the droplet). However, in practice, it is also possible for the impact onto a large surface but close to its edge (named as semi-infinite surface). In this first study of its kind, the process of drop impact onto a semi-infinite surface (both hydrophobic and hydrophilic) was investigated experimentally. During the impact process, part of the liquid lamella can spread out of the surface (free lamella). Depending on the distance between the impact point and surface edge, the free lamella can recede, or partially recede back to the surface, or completely break apart at the surface edge. The behavior of free lamella can also affect the morphology of the part of liquid lamella which remains in contact with the solid surface, especially in the receding phase (e.g. occurrence of drop rebound). Various morphologies observed for lamella breakage at the surface edge will also be discussed for surfaces of different wettabilities.
Infinite slope stability under steady unsaturated seepage conditions
Lu, N.; Godt, J.
2008-01-01
[1] We present a generalized framework for the stability of infinite slopes under steady unsaturated seepage conditions. The analytical framework allows the water table to be located at any depth below the ground surface and variation of soil suction and moisture content above the water table under steady infiltration conditions. The framework also explicitly considers the effect of weathering and porosity increase near the ground surface on changes in the friction angle of the soil. The factor of safety is conceptualized as a function of the depth within the vadose zone and can be reduced to the classical analytical solution for subaerial infinite slopes in the saturated zone. Slope stability analyses with hypothetical sandy and silty soils are conducted to illustrate the effectiveness of the framework. These analyses indicate that for hillslopes of both sandy and silty soils, failure can occur above the water table under steady infiltration conditions, which is consistent with some field observations that cannot be predicted by the classical infinite slope theory. A case study of shallow slope failures of sandy colluvium on steep coastal hillslopes near Seattle, Washington, is presented to examine the predictive utility of the proposed framework. Copyright 2008 by the American Geophysical Union.
Infinite slope stability under steady unsaturated seepage conditions
NASA Astrophysics Data System (ADS)
Lu, Ning; Godt, Jonathan
2008-11-01
We present a generalized framework for the stability of infinite slopes under steady unsaturated seepage conditions. The analytical framework allows the water table to be located at any depth below the ground surface and variation of soil suction and moisture content above the water table under steady infiltration conditions. The framework also explicitly considers the effect of weathering and porosity increase near the ground surface on changes in the friction angle of the soil. The factor of safety is conceptualized as a function of the depth within the vadose zone and can be reduced to the classical analytical solution for subaerial infinite slopes in the saturated zone. Slope stability analyses with hypothetical sandy and silty soils are conducted to illustrate the effectiveness of the framework. These analyses indicate that for hillslopes of both sandy and silty soils, failure can occur above the water table under steady infiltration conditions, which is consistent with some field observations that cannot be predicted by the classical infinite slope theory. A case study of shallow slope failures of sandy colluvium on steep coastal hillslopes near Seattle, Washington, is presented to examine the predictive utility of the proposed framework.
Entanglement and Nonlocality in Infinite 1D Systems
NASA Astrophysics Data System (ADS)
Wang, Zizhu; Singh, Sukhwinder; Navascués, Miguel
2017-06-01
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.
Verifying the Simulation Hypothesis via Infinite Nested Universe Simulacrum Loops
NASA Astrophysics Data System (ADS)
Sharma, Vikrant
2017-01-01
The simulation hypothesis proposes that local reality exists as a simulacrum within a hypothetical computer's dimension. More specifically, Bostrom's trilemma proposes that the number of simulations an advanced 'posthuman' civilization could produce makes the proposition very likely. In this paper a hypothetical method to verify the simulation hypothesis is discussed using infinite regression applied to a new type of infinite loop. Assign dimension n to any computer in our present reality, where dimension signifies the hierarchical level in nested simulations our reality exists in. A computer simulating known reality would be dimension (n-1), and likewise a computer simulating an artificial reality, such as a video game, would be dimension (n +1). In this method, among others, four key assumptions are made about the nature of the original computer dimension n. Summations show that regressing such a reality infinitely will create convergence, implying that the verification of whether local reality is a grand simulation is feasible to detect with adequate compute capability. The action of reaching said convergence point halts the simulation of local reality. Sensitivities to the four assumptions and implications are discussed.
Infinite variance in fermion quantum Monte Carlo calculations.
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.
NASA Astrophysics Data System (ADS)
Williamson, Matthew M.
1995-01-01
This thesis presents the design, construction, control and evaluation of a novel for controlled actuator. Traditional force controlled actuators are designed from the premise that 'Stiffer is better'. This approach gives a high bandwidth system, prone to problems of contact instability, noise, and low power density. The actuator presented in this thesis is designed from the premise that 'Stiffness isn't everything'. The actuator, which incorporates a series elastic element, trades off achievable bandwidth for gains in stable, low noise force control, and protection against shock loads. This thesis reviews related work in robot force control, presents theoretical descriptions of the control and expected performance from a series elastic actuator, and describes the design of a test actuator constructed to gather performance data. Finally the performance of the system is evaluated by comparing the performance data to theoretical predictions.
NASA Astrophysics Data System (ADS)
Revenough, Justin
Elastic waves propagating in simple media manifest a surprisingly rich collection of phenomena. Although some can't withstand the complexities of Earth's structure, the majority only grow more interesting and more important as remote sensing probes for seismologists studying the planet's interior. To fully mine the information carried to the surface by seismic waves, seismologists must produce accurate models of the waves. Great strides have been made in this regard. Problems that were entirely intractable a decade ago are now routinely solved on inexpensive workstations. The mathematical representations of waves coded into algorithms have grown vastly more sophisticated and are troubled by many fewer approximations, enforced symmetries, and limitations. They are far from straightforward, and seismologists using them need a firm grasp on wave propagation in simple media. Linear Elastic Waves, by applied mathematician John G. Harris, responds to this need.
NASA Technical Reports Server (NTRS)
Oline, L.; Medaglia, J.
1972-01-01
The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.
NASA Astrophysics Data System (ADS)
Osorio Iregui, Juan; Troyer, Matthias; Corboz, Philippe
2017-09-01
In spite of their intrinsic one-dimensional nature, matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected entangled-pair states as the method of choice, we assess the relative performance of infinite matrix product states and infinite projected entangled-pair states on cylindrical geometries. By considering the Heisenberg and half-filled Hubbard models on the square lattice as our benchmark cases, we evaluate their variational energies as a function of both bond dimension and cylinder width. In both examples, we find crossovers at moderate cylinder widths, i.e., for the largest bond dimensions considered, we find an improvement on the variational energies for the Heisenberg model by using projected entangled-pair states at a width of about eleven sites, whereas for the half-filled Hubbard model, this crossover occurs at about seven sites.
Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language
ERIC Educational Resources Information Center
Blom, Elma
2007-01-01
This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…
Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language
ERIC Educational Resources Information Center
Blom, Elma
2007-01-01
This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…
NASA Astrophysics Data System (ADS)
Sankovich, Vladimir
1998-12-01
The goal of this paper is to build a consistent physical theory of the dynamics of the bat-ball interaction. This requires creating realistic models for both the softball bat and the softball. Some of the features of these models are known phenomenologically, from experiments conducted in our laboratory, others will be introduced and computed from first principles here for the first time. Both interacting objects are treated from the viewpoint of the theory of elasticity, and it is shown how a computer can be used to accurately calculate all the relevant characteristics of batball collisions. It is shown also how the major elastic parameters of the material constituting the interior of a softball can be determined using the existing experimental data. These parameters, such as the Young's modulus, the Poisson ratio and the damping coefficient are vital for the accurate description of the ball's dynamics. We are demonstrating how the existing theories of the elastic behavior of solid bars and hollow shells can be augmented to simplify the resulting equations and make the subsequent computer analysis feasible. The standard system of fourth-order PDE's is reduced to a system of the second order, because of the inclusion of the usually ignored effects of the shear forces in the bat.
NASA Astrophysics Data System (ADS)
Spagnolie, Saverio; Lauga, Eric
2009-11-01
We address the question of optimality for slender swimming bodies or flagella in viscous fluid environments. Our novel approach is to define an energy which includes not only the work performed against the surrounding fluid, but also the energy stored elastically in the bending of the body, the energy stored elastically in internal shearing (such as the relative sliding of microtubules internal to a flagellum), and viscous dissipation due to the presence of an internal fluid. The shape of the optimal periodic planar wave is determined numerically and in some cases analytically which maximizes a related efficiency measure. We find that bending or internal dissipation costs regularize the optimal shape, but elastic shearing costs do not. For bodies of finite length, we show that the number of wavelengths expressed by the body is determined by a competition between bending costs and the work done on the fluid associated with body rotations. The hydrodynamic efficiency is shown to be less sensitive to the morphology than the bending costs, which may help us to better understand the locomotory forms observed in nature.
Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags
NASA Astrophysics Data System (ADS)
Karmakar, R.; Sur, A.; Kanoria, M.
2016-07-01
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.
NASA Astrophysics Data System (ADS)
Govardhan, R.; Williamson, C. H. K.
2002-12-01
In this paper, we study the transverse vortex-induced vibrations of a cylinder with no structural restoring force (k = 0). In terms of the conventionally used normalized flow velocity, U*, the present experiments correspond to an infinite value (where U* = U/fND, fN = natural frequency, D = diameter). A reduction of mass ratios m* (mass/displaced mass) from the classically studied values of order m* = 100, down to m* = 1, yields negligible oscillations. However, a further reduction in mass exhibits a surprising result: large-amplitude vigorous vibrations suddenly appear for values of mass less than a critical mass ratio, m*crit = 0.54. The classical assumption, since the work of den Hartog (1934), has been that resonant large-amplitude oscillations exist only over a narrow range of velocities, around U*[similar]5, where the vortex shedding frequency is comparable with the natural frequency. However, in the present study, we demonstrate that, so long as the body’s mass is below this critical value, the regime of normalized velocities (U*) for resonant oscillations is infinitely wide, beginning at around U*[similar]5 and extending to U*[rightward arrow][infty infinity]. This result is in precise accordance with the predictions put forward by Govardhan & Williamson (2000), based on elastically mounted vibration studies (where k > 0). We deduce a condition under which this unusual concept of an infinitely wide regime of resonance will occur in any generic vortex-induced vibration system.
The elastic pendulum: A nonlinear paradigm
NASA Astrophysics Data System (ADS)
Breitenberger, Ernst; Mueller, Robert D.
1981-06-01
A pendulum with an elastic instead of an inextensible suspension is the simplest realization of an autonomous, conservative, oscillatory system of several degrees of freedom with nonlinear coupling; it can also have an internal 1:2 resonance. A fairly complete study of this system at and near resonance is here undertaken by means of the ''slow-fluctuation'' approximation which consists in developing the x2y-type interaction into a trigonometric polynomial and keeping only the term with the slowest frequency. Extensive computations showed that up to moderately large amplitudes the approximate solutions were virtually as accurate as numerical integrations of the exact equations of motion. The slow-fluctuation equations of motion can be completely integrated by quadratures. Explicit solutions for amplitudes and phases are given in terms of elliptic functions, and can be linked to initial conditions. There exist two branches of purely periodic, harmonic, constant-amplitude motions which are orbitally stable but Liapunov unstable. The pure suspension motion is Liapunov unstable and remains orbitally stable only up to and including a critical amplitude; the standard ''method of variational equations'' leads to a slightly different stability criterion but is shown to be unreliable. In the dynamical neighborhood of the unstable pure suspension mode are motions which convert to it after infinite time. When a motion has an amplitude modulation minimum at or near zero, a phase reversal of the suspension takes place which is shown to be an artefact inherent in the description in terms of amplitudes and phases. In addition there is in the pendulum (but not in the exactly soluble system having the slow-fluctuation Hamiltonian) a fast phase transient which vitiates the slow-fluctuation technique for a few periods around the suspension amplitude minimum; this is the only restriction on the method. An appendix outlines formal isomorphisms between the elastic pendulum and the
Scattering of Airy elastic sheets by a cylindrical cavity in a solid.
Mitri, F G
2017-11-01
The prediction of the elastic scattering by voids (and cracks) in materials is an important process in structural health monitoring, phononic crystals, metamaterials and non-destructive evaluation/imaging to name a few examples. Earlier analytical theories and numerical computations considered the elastic scattering by voids in plane waves of infinite extent. However, current research suggesting the use of (limited-diffracting, accelerating and self-healing) Airy acoustical-sheet beams for non-destructive evaluation or imaging applications in elastic solids requires the development of an improved analytical formalism to predict the scattering efficiency used as a priori information in quantitative material characterization. Based on the definition of the time-averaged scattered power flow density, an analytical expression for the scattering efficiency of a cylindrical empty cavity (i.e., void) encased in an elastic medium is derived for compressional and normally-polarized shear-wave Airy beams. The multipole expansion method using cylindrical wave functions is utilized. Numerical computations for the scattering energy efficiency factors for compressional and shear waves illustrate the analysis with particular emphasis on the Airy beam parameters and the non-dimensional frequency, for various elastic materials surrounding the cavity. The ratio of the compressional to the shear wave speed stimulates the generation of elastic resonances, which are manifested as a series of peaks in the scattering efficiency plots. The present analysis provides an improved method for the computations of the scattering energy efficiency factors using compressional and shear-wave Airy beams in elastic materials as opposed to plane waves of infinite extent. Copyright © 2017 Elsevier B.V. All rights reserved.
Dipole and slot elements and arrays on semi-infinite substrates
NASA Technical Reports Server (NTRS)
Kominami, M.; Pozar, D. M.; Schaubert, D. H.
1985-01-01
The printed dipole or slot antenna on a semi-infinite substrate and infinite phased arrays of these elements are investigated. The solution is based on the moment method in the Fourier transform domain. The generalized impedance or admittance matrix can be expressed in rapidly converging infinite-integral or infinite-summation forms, allowing the accurate determination of the current distributions. Using the present formulation, the input impedance, resonant length, and radiation pattern for the isolated antennas, and the reflection coefficient for infinite phased arrays, are calculated.
Probabilistic Elastography: Estimating Lung Elasticity
Risholm, Petter; Ross, James; Washko, George R.; Wells, William M.
2011-01-01
We formulate registration-based elastography in a probabilistic framework and apply it to study lung elasticity in the presence of emphysematous and fibrotic tissue. The elasticity calculations are based on a Finite Element discretization of a linear elastic biomechanical model. We marginalize over the boundary conditions (deformation) of the biomechanical model to determine the posterior distribution over elasticity parameters. Image similarity is included in the likelihood, an elastic prior is included to constrain the boundary conditions, while a Markov model is used to spatially smooth the inhomogeneous elasticity. We use a Markov Chain Monte Carlo (MCMC) technique to characterize the posterior distribution over elasticity from which we extract the most probable elasticity as well as the uncertainty of this estimate. Even though registration-based lung elastography with inhomogeneous elasticity is challenging due the problem's highly underdetermined nature and the sparse image information available in lung CT, we show promising preliminary results on estimating lung elasticity contrast in the presence of emphysematous and fibrotic tissue. PMID:21761697
Probabilistic elastography: estimating lung elasticity.
Risholm, Petter; Ross, James; Washko, George R; Wells, William M
2011-01-01
We formulate registration-based elastography in a probabilistic framework and apply it to study lung elasticity in the presence of emphysematous and fibrotic tissue. The elasticity calculations are based on a Finite Element discretization of a linear elastic biomechanical model. We marginalize over the boundary conditions (deformation) of the biomechanical model to determine the posterior distribution over elasticity parameters. Image similarity is included in the likelihood, an elastic prior is included to constrain the boundary conditions, while a Markov model is used to spatially smooth the inhomogeneous elasticity. We use a Markov Chain Monte Carlo (MCMC) technique to characterize the posterior distribution over elasticity from which we extract the most probable elasticity as well as the uncertainty of this estimate. Even though registration-based lung elastography with inhomogeneous elasticity is challenging due the problem's highly underdetermined nature and the sparse image information available in lung CT, we show promising preliminary results on estimating lung elasticity contrast in the presence of emphysematous and fibrotic tissue.
Geometric MCMC for infinite-dimensional inverse problems
NASA Astrophysics Data System (ADS)
Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.
2017-04-01
Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.
Scan blindness in infinite phased arrays of printed dipoles
NASA Technical Reports Server (NTRS)
Pozar, D. M.; Schaubert, D. H.
1984-01-01
A comprehensive study of infinite phased arrays of printed dipole antennas is presented, with emphasis on the scan blindness phenomenon. A rigorous and efficient moment method procedure is used to calculate the array impedance versus scan angle. Data are presented for the input reflection coefficient for various element spacings and substrate parameters. A simple theory, based on coupling from Floquet modes to surface wave modes on the substrate, is shown to predict the occurrence of scan blindness. Measurements from a waveguide simulator of a blindness condition confirm the theory.
Approaching infinite temperature upon repeated measurements of a quantum system
Yi, Juyeon; Talkner, Peter; Ingold, Gert-Ludwig
2011-09-15
The influence of repeated projective measurements on the dynamics of the state of a quantum system is studied as a function of the time lag {tau} between successive measurements. In the limit of infinitely many measurements of the occupancy of a single state the total system approaches a uniform state. The asymptotic approach to this state is exponential in the case of finite Hilbert space dimension. The rate characterizing this approach undergoes a sharp transition from a monotonically increasing to an erratically varying function of the time between subsequent measurements.
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
Lattice bosons with infinite-range checkerboard interactions
NASA Astrophysics Data System (ADS)
Sundar, Bhuvanesh; Mueller, Erich J.
2016-09-01
Motivated by experiments performed by Landig et al. [Nature (London) 532, 476 (2016), 10.1038/nature17409], we consider a two-dimensional Bose gas in an optical lattice, trapped inside a single mode superradiant Fabry-Perot cavity. The cavity mediates infinite-range checkerboard interactions between the atoms, which produces competition between Mott insulator, charge-density wave, superfluid, and supersolid phases. We calculate the phase diagram of this Bose gas in a homogeneous system and in the presence of a harmonic trap.
A Generic Result in Linear Semi-Infinite Optimization
Goberna, Miguel A. Lopez, Marco A. Todorov, Maxim I.
2003-10-15
In this paper we consider the space of all the linear semi-infinite programming problems with the same index set, endowed with a suitable topology. We provide a constructive proof of the following generic result:if we confine ourselves to the class of problems having a bounded set of coefficient vectors (those vectors appearing in the left-hand side of the constraints), the set of those problems which have a strongly unique optimal solution contains an open and dense subset of the set of solvable problems in the same class.
Capabilities and Limitations of Infinite-Time Computation
NASA Astrophysics Data System (ADS)
Long, James Thomas, III
The relatively new field of infinitary computability strives to characterize the capabilities and limitations of infinite-time computation; that is, computations of potentially transfinite length. Throughout our work, we focus on the prototypical model of infinitary computation: Hamkins and Lewis' infinite-time Turing machine (ITTM), which generalizes the classical Turing machine model in a natural way. This dissertation adopts a novel approach to this study: whereas most of the literature, starting with Hamkins and Lewis' debut of the ITTM model, pursues set-theoretic questions using a set-theoretic approach, we employ arguments that are truly computational in character. Indeed, we fully utilize analogues of classical results from finitary computability, such as the s mn Theorem and existence of universal machines, and for the most part, judiciously restrict our attention to the classical setting of computations over the natural numbers. In Chapter 2 of this dissertation, we state, and derive, as necessary, the aforementioned analogues of the classical results, as well as some useful constructs for ITTM programming. With this due paid, the subsequent work in Chapters 3 and 4 requires little in the way of programming, and that programming which is required in Chapter 5 is dramatically streamlined. In Chapter 3, we formulate two analogues of one of Rado's busy beaver functions from classical computability, and show, in analogy with Rado's results, that they grow faster than a wide class of infinite-time computable functions. Chapter 4 is tasked with developing a system of ordinal notations via a natural approach involving infinite-time computation, as well as an associated fast-growing hierarchy of functions over the natural numbers. We then demonstrate that the busy beaver functions from Chapter 3 grow faster than the functions which appear in a significant portion of this hierarchy. Finally, we debut, in Chapter 5, two enhancements of the ITTM model which can self
Infinite volume of noncommutative black hole wrapped by finite surface
NASA Astrophysics Data System (ADS)
Zhang, Baocheng; You, Li
2017-02-01
The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.
Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ganesh, R.; Suganya, S.
2012-12-01
The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
Infinite invariant densities due to intermittency in a nonlinear oscillator
NASA Astrophysics Data System (ADS)
Meyer, Philipp; Kantz, Holger
2017-08-01
Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e., a physical model in continuous time, whose properties in terms of weak ergodity breaking and aging have a one-to-one correspondence to the properties of the Pomeau-Manneville map. So for both systems in a wide range of parameters no physical invariant density exists. We show how this regime can be characterized quantitatively using the techniques of infinite invariant densities and the Thaler-Dynkin limit theorem. We see how expectation values exhibit aging in terms of scaling in time.
Convex aggregative modelling of infinite memory nonlinear systems
NASA Astrophysics Data System (ADS)
Wachel, Paweł
2016-08-01
The convex aggregation technique is applied for modelling general class of nonlinear systems with unknown structure and infinite memory. The finite sample size properties of the algorithm are formally established and compared to the standard least-squares counterpart of the method. The proposed algorithm demonstrates its advantages when the a-priori knowledge and the measurement data are both scarce, that is, when the information about the actual system structure is unknown or uncertain and the measurement set is small and disturbed by a noise. Numerical experiments illustrate application and practical benefits of the method for various nonlinear systems.
Parameter Estimation for ARMA Models with Infinite Variance Innovations
1993-12-30
application of Theorem 3.1 of Rosinski and Woyczynski (1987) yields for some C2 > 0 1 n-nInI+lgP(JV21 > ) -5 IC2-In + log4 • 1=1 h=m+t+l Note that for x E (0...infinite variance ARMA models 35 Rosinski and Woyczynski (1987) have shown that for some c > 0 P (ZIZ2 > z)ɝCz-’ (l+Io09+ Z-’). Similar arguments as in the...W.E. (1990). The rate of escape of random walk. Ann. Probab. 18, 1417-1461. ROSINSKI , J. AND WOYCZYNSKI, W.A. (1987). Multilinear forms in Pareto- like
Examples of infinite direct sums of spectral triples
NASA Astrophysics Data System (ADS)
Falk, Kevin
2017-02-01
We study two ways of summing an infinite family of noncommutative spectral triples. First, we propose a definition of the integration of spectral triples and give an example using algebras of Toeplitz operators acting on weighted Bergman spaces over the unit ball of Cn. Secondly, we construct a spectral triple associated to a general polygonal self-similar set in C using algebras of Toeplitz operators on Hardy spaces. In this case, we show that we can recover the Hausdorff dimension of the fractal set.
Limiting equilibrium and liquefaction potential in infinite submarine slopes
Denlinger, R.P.; Iverson, R.M.
1990-01-01
Stability evaluation of submarine slopes is hampered by the difficulty of making field measurements. Owing to the scarcity of detailed field data, stability is commonly assessed by assuming homogenous infinite slopes with steady seepage. For these conditions, it is necessary to measure only the slope angle, friction angle, cohesion, and pore pressure at some distance into the sediment to evaluate stability. Examination of available data shows that conditions close to those required for liquefaction are necessary for Coulomb failure in many continental shelf areas. This favors long landslide runouts and flow of sediment subsequent to failure. -from Authors
J-integral estimates for cracks in infinite bodies
NASA Technical Reports Server (NTRS)
Dowling, N. E.
1986-01-01
An analysis and discussion is presented of existing estimates of the J-integral for cracks in infinite bodies. Equations are presented which provide convenient estimates for Ramberg-Osgood type elastoplastic materials containing cracks and subjected to multiaxial loading. The relationship between J and the strain normal to the crack is noted to be only weakly dependent on state of stress. But the relationship between J and the stress normal to the crack is strongly dependent on state of stress. A plastic zone correction term often employed is found to be arbitrary, and its magnitude is seldom significant.
J-integral estimates for cracks in infinite bodies
NASA Technical Reports Server (NTRS)
Dowling, N. E.
1987-01-01
An analysis and discussion is presented of existing estimates of the J-integral for cracks in infinite bodies. Equations are presented which provide convenient estimates for Ramberg-Osgood type elasto-plastic materials containing cracks and subjected to multiaxial loading. The relationship between J and the strain normal to the crack is noted to be only weakly dependent on state of stress. But the relationship between J and the stress normal to the crack is strongly dependent on state of stress. A plastic zone correction term often employed is found to be arbitrary, and its magnitude is seldom significant.
Elastic pion Compton scattering
Kowalewski, R.V.; Berg, D.; Chandlee, C.; Cihangir, S.; Ferbel, T.; Huston, J.; Jensen, T.; Kornberg, R.; Lobkowicz, F.; Ohshima, T.
1984-03-01
We present evidence for elastic pion Compton scattering as observed via the Primakoff process on nulcear targets. We find production cross sections for ..pi../sup -/A..--> pi../sup -/..gamma..A on lead and copper of 0.249 +- 0.027 and 0.029 +- 0.006 mb, respectively, in agreement with the values expected from the one-photon-exchange mechanism of 0.268 +- 0.018 and 0.035 +- 0.004 mb in the region of our experimental acceptance. This reaction provides a clean test of the Primakoff formalism.
Design guidance for elastic followup
Naugle, F.V.
1983-01-01
The basic mechanism of elastic followup is discussed in relation to piping design. It is shown how mechanistic insight gained from solutions for a two-bar problem can be used to identify dominant design parameters and to determine appropriate modifications where elastic followup is a potential problem. It is generally recognized that quantitative criteria are needed for elastic followup in the creep range where badly unbalanced lines can pose potential problems. Approaches for criteria development are discussed.
Loewenthal, M.; Loseke, K.; Dow, T.A.; Scattergood, R.O.
1988-12-01
Elastic emission polishing, also called elastic emission machining (EEM), is a process where a stream of abrasive slurry is used to remove material from a substrate and produce damage free surfaces with controlled surface form. It is a noncontacting method utilizing a thick elasto-hydrodynamic film formed between a soft rotating ball and the workpiece to control the flow of the abrasive. An apparatus was built in the Center, which consists of a stationary spindle, a two-axis table for the workpiece, and a pump to circulate the working fluid. The process is controlled by a programmable computer numerical controller (CNC), which presently can operate the spindle speed and movement of the workpiece in one axis only. This apparatus has been used to determine material removal rates on different material samples as a function of time, utilizing zirconium oxide (ZrO{sub 2}) particles suspended in distilled water as the working fluid. By continuing a study of removal rates the process should become predictable, and thus create a new, effective, yet simple tool for ultra-precision mechanical machining of surfaces.
Theory of epithelial elasticity
NASA Astrophysics Data System (ADS)
Krajnc, Matej; Ziherl, Primož
2015-11-01
We propose an elastic theory of epithelial monolayers based on a two-dimensional discrete model of dropletlike cells characterized by differential surface tensions of their apical, basal, and lateral sides. We show that the effective tissue bending modulus depends on the apicobasal differential tension and changes sign at the transition from the flat to the fold morphology. We discuss three mechanisms that stabilize the finite-wavelength fold structures: Physical constraint on cell geometry, hard-core interaction between non-neighboring cells, and bending elasticity of the basement membrane. We show that the thickness of the monolayer changes along the waveform and thus needs to be considered as a variable rather than a parameter. Next we show that the coupling between the curvature and the thickness is governed by the apicobasal polarity and that the amplitude of thickness modulation along the waveform is proportional to the apicobasal differential tension. This suggests that intracellular stresses can be measured indirectly by observing easily measurable morphometric parameters. We also study the mechanics of three-dimensional structures with cylindrical symmetry.
Spectra of Semi-Infinite Quantum Graph Tubes
NASA Astrophysics Data System (ADS)
Shipman, Stephen P.; Tillay, Jeremy
2016-10-01
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation {D(λ,k_1,k_2)=0} with {(k_1,k_2)in({C}/2π{Z})^2} subject to the constraint {a k_1 + b k_2 ≡ 0} (mod {2π}), where a and b are integers. The number of Floquet modes for a given {λin{R}} is {2max{ a, b }}. Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.
Nuclear Matter Phase Transition in Infinite and Finite Systems
NASA Astrophysics Data System (ADS)
Terranova, S.; Bonasera, A.
2005-04-01
A new "semiclassical" model of the nuclear matter, composed of u, d colored quarks, is proposed. The approach, named Constrained Molecular Dynamics (CoMD) is based on the molecular dynamics simulation of the quarks, which interact through the Richardson's potential, and on a constraint due to Pauli blocking. With a suitable choice of the quark masses, some possible Equation of State (EOS) of the nuclear matter, at temperature equal to zero and finite baryon density, are obtained. These equations of state, not only present some known properties of the nuclear matter, as the Quark-Gluon Plasma (QGP) phase transition, but also shown the existence of a new state, the Exotic Color Clustering (ECC) state, in which cluster of quarks with the same color are formed. Some new quantities, "indicators" of the phase transition, are introduced: three order parameters, Mc2, Mc3, Mc4 defined trough the Gell-Mann matrices λα, and the lifetime of the J/Ψ particle. The behavior of the J/Ψ particle is studied also in the "finite" systems, obtained by expanding the corresponding "infinite" systems. It seems that the dynamics and the finite size effects do not wash completely the phase transition occurred in infinite systems, and the J/Ψ particle is still a good signature.
Quantitative determination of infinite inhibition concentrations of antimicrobial agents.
Marwan, A G; Nagel, C W
1986-01-01
We developed a method to determine the infinite inhibition concentrations (IICs) of antimicrobial agents. This method was based on finding the relative effectiveness of an inhibitor at various concentrations. Benzoic acid and parabens were tested on Saccharomyces bayanus, Hansenula sp., and Pseudomonas fluorescens. The relative effectiveness values of these compounds were established. A plot of the inhibitor concentration versus the reciprocal of relative effectiveness was linear. The chi-axis intercept was the concentration of the inhibitor which gave infinite microbial inhibition. For S. bayanus the IICs were 330, 930, 480, and 220 ppm (330, 930, 480, and 220 ml/liter) for benzoic acid and methyl-, ethyl-, and propylparabens, respectively. For Hansenula sp. the IIC was 180 ppm for benzoic acid. For P. fluorescens the IICs were 1,310, 960, and 670 ppm for methyl-, ethyl-, and propylparabens, respectively. Our results indicated that the IIC is affected by the growth medium. The advantages and applications of this method are discussed. PMID:3083773
Conformal field theories with infinitely many conservation laws
NASA Astrophysics Data System (ADS)
Todorov, Ivan
2013-02-01
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Unitary positive energy representations of scalar bilocal fields," Commun. Math. Phys. 271, 223-246 (2007), 10.1007/s00220-006-0182-2; e-print arXiv:math-ph/0604069v3; B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Infinite dimensional Lie algebras in 4D conformal quantum field theory," J. Phys. A Math Theor. 41, 194002 (2008), 10.1088/1751-8113/41/19/194002; e-print arXiv:0711.0627v2 [hep-th
Infinite dilution activity coefficients from ab initio solvation calculations
Lin, S.T.; Sandler, S.I.
1999-12-01
A Group Contribution Solvation (GCS) model was developed to calculate infinite dilution activity coefficients ({gamma}{sup {chi}}) based on modern computational chemistry. The GCS model results in an average error of 7% in {gamma}{sup {chi}} for the limited number of data points among water, n-hexane, acetonitrile and n-octanol, whereas the errors are 47% and 52% with the UNIFAC model and the modified UNIFAC model, respectively. GCS was also used to calculate infinite dilution partition coefficients, which can be used to determine how a dilute solute partitions between two solvents. Solutes were examined in three different liquid-liquid systems: water/n-hexane, water/acetonitrile, and water/n-octanol. With GCS, the average errors are 22% (for 18 solutes), 18% (for 14 solutes) and 14% (for 15 solutes) for these solvent systems, while comparable errors are 237%, 286% and 226% with UNIFAC; and 342%, 414% and 306% with modified UNIFAC. The GCS model is a powerful new tool to predict the octanol-water partition coefficients.
Evolution in random fitness landscapes: the infinite sites model
NASA Astrophysics Data System (ADS)
Park, Su-Chan; Krug, Joachim
2008-04-01
We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution g(w). This is the finite population version of Kingman's house of cards model (Kingman 1978 J. Appl. Probab. 15 1). In contrast to Kingman's work, the focus here is on unbounded distributions g(w) which lead to an indefinite growth of the population fitness. The model is solved analytically in the limit of infinite population size N \\to \\infty and simulated numerically for finite N. When the genome-wide mutation probability U is small, the long-time behavior of the model reduces to a point process of fixation events, which is referred to as a diluted record process (DRP). The DRP is similar to the standard record process except that a new record candidate (a number that exceeds all previous entries in the sequence) is accepted only with a certain probability that depends on the values of the current record and the candidate. We develop a systematic analytic approximation scheme for the DRP. At finite U the fitness frequency distribution of the population decomposes into a stationary part due to mutations and a traveling wave component due to selection, which is shown to imply a reduction of the mean fitness by a factor of 1-U compared to the U \\to 0 limit.
NASA Technical Reports Server (NTRS)
Bensoussan, A.; Delfour, M. C.; Mitter, S. K.
1976-01-01
Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.
NASA Astrophysics Data System (ADS)
Ruiz, Franklin J.
estimate the elastic properties of cemented porous grain aggregates at all cement concentrations. Therefore, the porous grain model allows for (a) varying the grain contact friction coefficient gamma in the whole range from 0 to 1, for smooth to infinitely rough grains, respectively; (b) combining the self-consistent approximation with the cementation theory to account for intergranular cement volume fractions from 0 to 1; and (c) considering porous grain textures and the effect of frequency. (Abstract shortened by UMI.)
An inclusion in one of two joined isotropic elastic half-spaces
NASA Astrophysics Data System (ADS)
Walpole, L. J.
1997-10-01
Two dissimilar, homogeneous and istropic, elastic half-spaces are bonded together over thier infinite plane of contract. An arbitrarily shaped finite part of one of them (an inclusion) tends spontaneously to undergo a unifrom infinitesimal strain, but, as it remains attached to and restrained by the surrounding material, an equilibrated state of stress and strain is established everywhere instead. By adopting a convenient expression for the fundamental field of a point force, we transformed inclusion. For a general shape of the inclussion and for particular spherical and finite cylindrical shapes in detail, we consider the evaluation of the elastic strain energy, especially of the interaction term which depends on the location of the inclusion and both pairs of elastic moduli, and which is of great significance in physical applications.
NASA Astrophysics Data System (ADS)
Lacivita, V.; Erba, A.; Noël, Y.; Orlando, R.; D'Arco, Ph.; Dovesi, R.
2013-06-01
Structural, vibrational, elastic, and dielectric properties of ZnO single-walled nanotubes are investigated theoretically. Calculations are carried out by using a Gaussian basis set and the B3LYP hybrid functional as implemented in the periodic ab initio CRYSTAL code. Nanotubes with increasing radius display asymptotic limits to the infinite monolayer. One soft phonon mode is recognized, whose vibration frequency is shown to be connected to the elastic constant C11 of the monolayer as the 1D → 2D transition is approached. The value of Young's elastic modulus of the nanotubes denotes a remarkable flexibility. Electronic and ionic contributions to the polarizability turn out to be comparable in magnitude. In particular, geometry relaxations at increasing radii show large influence on the transverse vibrational polarizability.
NASA Technical Reports Server (NTRS)
Brunelle, Eugene J.
1994-01-01
The first few viewgraphs describe the general solution properties of linear elasticity theory which are given by the following two statements: (1) for stress B.C. on S(sub sigma) and zero displacement B.C. on S(sub u) the altered displacements u(sub i)(*) and the actual stresses tau(sub ij) are elastically dependent on Poisson's ratio nu alone: thus the actual displacements are given by u(sub i) = mu(exp -1)u(sub i)(*); and (2) for zero stress B.C. on S(sub sigma) and displacement B.C. on S(sub u) the actual displacements u(sub i) and the altered stresses tau(sub ij)(*) are elastically dependent on Poisson's ratio nu alone: thus the actual stresses are given by tau(sub ij) = E tau(sub ij)(*). The remaining viewgraphs describe the minimum parameter formulation of the general classical laminate theory plate problem as follows: The general CLT plate problem is expressed as a 3 x 3 system of differential equations in the displacements u, v, and w. The eighteen (six each) A(sub ij), B(sub ij), and D(sub ij) system coefficients are ply-weighted sums of the transformed reduced stiffnesses (bar-Q(sub ij))(sub k); the (bar-Q(sub ij))(sub k) in turn depend on six reduced stiffnesses (Q(sub ij))(sub k) and the material and geometry properties of the k(sup th) layer. This paper develops a method for redefining the system coefficients, the displacement components (u,v,w), and the position components (x,y) such that a minimum parameter formulation is possible. The pivotal steps in this method are (1) the reduction of (bar-Q(sub ij))(sub k) dependencies to just two constants Q(*) = (Q(12) + 2Q(66))/(Q(11)Q(22))(exp 1/2) and F(*) - (Q(22)/Q(11))(exp 1/2) in terms of ply-independent reference values Q(sub ij); (2) the reduction of the remaining portions of the A, B, and D coefficients to nondimensional ply-weighted sums (with 0 to 1 ranges) that are independent of Q(*) and F(*); and (3) the introduction of simple coordinate stretchings for u, v, w and x,y such that the process is
Bulk solitary waves in elastic solids
NASA Astrophysics Data System (ADS)
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
NASA Astrophysics Data System (ADS)
Fain, Boris; Rudnick, Joseph
1997-03-01
Short segments of DNA assume shapes that minimize their elastic energy. Modeling of the various mechanisms involving the molecule - replication, transcription, packaging, etc. - requires a description of the conformations of DNA under constraints. We develop a formalism that obtains analytic expressions for shape, link, twist and extension of a segment subject to sufficient number of constraints. We apply our technique to two particular cases: a) Stretched twisted linear DNA. This is an interesting test for our formalism, especially in light of recent experiments(Strick T.R., Allemand J.-F., Bensimon A., Croquette V. Science) 271 1835-1837, (1996). The molecule remains extended until a critical twist is reached, at which point it undergoes a plectonemic transition. b) Closed circular DNA. Describing the shapes of such molecules has been an outstanding problem for some time. We obtain a family of curves classified by their deviation in link from the plain circle.
Collapse and Fragmentation of Magnetically-Supported Infinite Sheets
NASA Astrophysics Data System (ADS)
Boss, A. P.
2004-12-01
The collapse and fragmentation of initially sheet-like, magnetic molecular clouds is calculated in three dimensions with a gravitational, radiative hydrodynamics code. The code includes a crude representation of magnetic field effects and ambipolar diffusion, through the magnetic pressure and magnetic tension approximations, and a simple parameterization based on previous magnetohydrodynamical calculations, respectively. The computational volume is a spherical portion of an initially isothermal, infinite sheet of self-gravitating gas, symmetric about its midplane, with the portion of the cloud exterior to the spherical volume being represented through its effect on the gravitational potential inside the spherical volume. The gas layer is initially in hydrostatic equilibrium, but with a mass equal to or greater than the critical mass ( ˜ 1 M⊙) for the growth of gravitational instability. The magnetic field pressure acts to further stabilize the initial cloud. Over 106 active grid points are employed in the models, sufficient to resolve the Jeans length and so avoid artificial fragmentation. The parameters varied are the ratio of the ambipolar diffusion time to the midplane free fall time (10 or 20), the cloud's reference magnetic field strength (100 or 200 microgauss), the ratio of rotational to gravitational energy of the sheet (0.0 or 0.01), and the form of the initial density perturbation applied to the infinite sheet. Three types of outcomes are observed: formation of one or two protostars near the edge of the spherical volume, formation of a protostar near (but not at) the center of the cloud, or formation of a rotating ring near the center of the cloud, which appears likely to fragment into two or more protostars. Flow speeds of ˜ 0.1 km s-1 are generated as the sheet begins to break-up into collapsing protostars. The forming protostars are separated by distances approximately equal to the cloud diameter, consistent with the spacing predicted by the linear
Larkin, A. I.; Khmelnitskii, D. E.
2013-09-15
Friction of elastic bodies is connected with the passing through the metastable states that arise at the contact of surfaces rubbing against each other. Three models are considered that give rise to the metastable states. Friction forces and their dependence on the pressure are calculated. In Appendix A, the contact problem of elasticity theory is solved with adhesion taken into account.
ERIC Educational Resources Information Center
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
Valve designed with elastic seat
NASA Technical Reports Server (NTRS)
Mac Glashan, W. F., Jr.
1965-01-01
Absolute valve closure is accomplished by a machined valve with an axially annular channel which changes the outlet passage into a thin tubular elastic seat member with a retainer backup ring. The elasticity of the seat provides tight conformity to ball irregularity.
PAGOSA Sample Problem. Elastic Precursor
Weseloh, Wayne N.; Clancy, Sean Patrick
2016-02-03
A PAGOSA simulation of a flyer plate impact which produces an elastic precursor wave is examined. The simulation is compared to an analytic theory for the Mie-Grüneisen equation of state and an elastic-perfectly-plastic strength model.
ERIC Educational Resources Information Center
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
NASA Astrophysics Data System (ADS)
Lefèvre, Victor; Lopez-Pamies, Oscar
2017-02-01
This paper puts forth homogenization solutions for the macroscopic elastic dielectric response-under finite deformations and finite electric fields-of ideal elastic dielectric composites with two-phase isotropic particulate microstructures. Specifically, solutions are presented for three classes of microstructures: (i) an isotropic iterative microstructure wherein the particles are infinitely polydisperse in size, (ii) an isotropic distribution of polydisperse spherical particles of a finite number of different sizes, and (iii) an isotropic distribution of monodisperse spherical particles. The solution for the iterative microstructure, which corresponds to the viscosity solution of a Hamilton-Jacobi equation in five "space" variables, is constructed by means of a novel high-order WENO finite-difference scheme. On the other hand, the solutions for the microstructures with spherical particles are constructed by means of hybrid finite elements. Prompted by the functional features shared by all three obtained solutions, a simple closed-form approximation is proposed for the macroscopic elastic dielectric response of ideal elastic dielectric composites with any type of (non-percolative) isotropic particulate microstructure. As elaborated in a companion paper, the proposed approximate solution proves particularly useful as a fundamental building block to generate approximate solutions for the macroscopic elastic dielectric response of dielectric elastomer composites made up of non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles.
Exact solutions of a modified fractional diffusion equation in the finite and semi-infinite domains
NASA Astrophysics Data System (ADS)
Guo, Gang; Li, Kun; Wang, Yuhui
2015-01-01
We investigate the solutions of a modified fractional diffusion equation which has a secondary fractional time derivative acting on a diffusion operator. We obtain analytical solutions for the modified equation in the finite and semi-infinite domains subject to absorbing boundary conditions. Most of the results have been derived by using the Laplace transform, the Fourier Cosine transform, the Mellin transform and the properties of Fox H function. We show that the semi-infinite solution can be expressed using an infinite series of Fox H functions similar to the infinite case, while the finite solution requires double infinite series including both Fox H functions and trigonometric functions instead of one infinite series. The characteristic crossover between more and less anomalous behaviour as well as the effect of absorbing boundary conditions are clearly demonstrated according to the analytical solutions.
Elasticity of Flowing Soap films
NASA Astrophysics Data System (ADS)
Kim, Ildoo; Mandre, Shreyas
2016-11-01
The robustness of soap films and bubbles manifests their mechanical stability. The single most important factor underlying the mechanical stability of soap films is its elasticity. Non-destructive measurement of the elasticity in these films has been cumbersome, because of its flowing nature. Here we provide a convenient, reproducible, and non-destructive method for measuring the elasticity by generating and inspecting Marangoni waves. Our method is based on generating an oblique shock by inserting a thin cylindrical obstacle in the flowing film, and converting the measured the shock angle to elasticity. Using this method, we find a constant value for the elasticity of 22 dyne/cm in the commonly used range of film widths, thicknesses or flow rates, implying that the surface of the film is chemically saturated with soap molecules.
New infinite-dimensional algebras, sine brackets, and SU (infinity)
Zachos, C.K.; Fairlie, D.B.
1989-01-01
We investigate the infinite dimensional algebras we have previously introduced, which involve trigonometric functions in their structure constants. We find a realization for them which provides a basis-independent formulation, identified with the algebra of sine brackets. A special family of them, the cyclotomic ones, contain SU(N) as invariant subalgebras. In this basis, it is evident by inspection that the algebra of SU(infinity) is equivalent to the centerless algebra of SDiff/sub 0/ on two-dimensional manifolds. Gauge theories of SU(infinity) are thus simply reformulated in terms of surface (sheet) coordinates. Spacetime-independent configurations of their gauge fields describe strings through the quadratic Schild action. 11 refs.
Quantum correlations at infinite temperature: The dynamical Nagaoka effect
NASA Astrophysics Data System (ADS)
Kanász-Nagy, Márton; Lovas, Izabella; Grusdt, Fabian; Greif, Daniel; Greiner, Markus; Demler, Eugene A.
2017-07-01
Do quantum correlations play a role in high-temperature dynamics of many-body systems? A common expectation is that thermal fluctuations lead to fast decoherence and make dynamics classical. In this paper we provide a striking example that a single particle created in a featureless, infinite temperature spin bath not only exhibits nonclassical dynamics but it also induces strong long-lived correlations between the surrounding spins. We study the nonequilibrium dynamics of a hole created in a Mott insulator in the atomic limit, which corresponds to a degenerate spin system. In the absence of interactions, the spin correlations arise purely from quantum interference. Furthermore, these correlations are both antiferromagnetic and ferromagnetic, in striking contrast to the equilibrium Nagaoka effect. These results are relevant for a number of condensed matter spin systems and should be observable using state of the art bosonic or fermionic quantum gas microscopes.
Quantum dynamics of a semi-infinite homogeneous harmonic chain
NASA Astrophysics Data System (ADS)
Prato, Domingo; Lamberti, Pedro W.
1993-07-01
The quantum dynamics of a semi-infinite homogeneous harmonic chain is studied. Assuming the system to be in its ground state, a harmonic motion, A sin(ω t), is imposed on the mass at the beginning of the chain. The quantum state of the system for t>0 is calculated by means of the evolution operator. Two different regimes occur: one for angular frequencies ω outside the allowed band ω>ω 0 and the other one for ω inside the band. After a transient the time derivative of the total energy of the chain vanishes for the first regime and tends to a constant for the second one. The mean values of the displacements from their equilibrium position are also calculated for masses along the chain. These averaged displacements and the time derivative of the total energy are shown to give exactly the same expression as in the classical case.
Predictive optimized adaptive PSS in a single machine infinite bus.
Milla, Freddy; Duarte-Mermoud, Manuel A
2016-07-01
Power System Stabilizer (PSS) devices are responsible for providing a damping torque component to generators for reducing fluctuations in the system caused by small perturbations. A Predictive Optimized Adaptive PSS (POA-PSS) to improve the oscillations in a Single Machine Infinite Bus (SMIB) power system is discussed in this paper. POA-PSS provides the optimal design parameters for the classic PSS using an optimization predictive algorithm, which adapts to changes in the inputs of the system. This approach is part of small signal stability analysis, which uses equations in an incremental form around an operating point. Simulation studies on the SMIB power system illustrate that the proposed POA-PSS approach has better performance than the classical PSS. In addition, the effort in the control action of the POA-PSS is much less than that of other approaches considered for comparison. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Three-body hyperspherical method with infinite angular expansions
Han Huili; Tang Liyan; Shi Tingyun
2011-12-15
The hyperspherical method based on infinite angular expansions is introduced. We approximate the cusp behavior of a wave function using B-spline techniques. Calculations for the ground-state energies of the atomic helium and the e{sup +}Li system are presented as two examples for testing this method. The computed ground-state energy of He is -2.903 724 a.u. with single particle orbitals l{sub max}=8. For the e{sup +}Li system, with l{sub max}=9, the ground-state energy is -0.250 83 a.u., which is better than the configuration interaction result of -0.250 107 82 a.u. with l{sub max}=30.
Infinite geometric frustration in a cubic dipole cluster
NASA Astrophysics Data System (ADS)
Schönke, Johannes; Schneider, Tobias M.; Rehberg, Ingo
2015-01-01
The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry, and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of eight interacting dipoles in a cubic cluster is investigated in detail. Instead of discrete equilibria we find a type of ground state consisting of infinitely many orientations. This continuum of energetically degenerate states represents a yet unknown form of magnetic frustration. The corresponding dipole rotations in the flat potential valley of this Goldstone mode enable the construction of frictionless magnetic couplings. Using computer-assisted algebraic geometry methods, we moreover completely enumerate all equilibrium configurations. The seemingly simple cubic system allows for exactly 9536 unstable discrete equilibria falling into 183 distinct energy families.
Doubly infinite separation of quantum information and communication
NASA Astrophysics Data System (ADS)
Liu, Zi-Wen; Perry, Christopher; Zhu, Yechao; Koh, Dax Enshan; Aaronson, Scott
2016-01-01
We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015), 10.1103/PhysRevLett.115.030504] for which there exist instances where the quantum information complexity tends to zero as the size of the input n increases. By showing that the quantum communication complexity of these games scales at least logarithmically in n , we obtain our result. We further show that the established lower bounds and gaps still hold even if we allow a small probability of error. However in this case, the n -qubit quantum message of the zero-error strategy can be compressed polynomially.
Solutions of evolution equations associated to infinite-dimensional Laplacian
NASA Astrophysics Data System (ADS)
Ouerdiane, Habib
2016-05-01
We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).
Infinite finitely generated fields are biinterpretable with {{N}}
NASA Astrophysics Data System (ADS)
Scanlon, Thomas
2008-07-01
Using the work of several other mathematicians, principally the results of Poonen refining the work of Pop that algebraic independence is definable within the class of finitely generated fields and of Rumely that the ring of rational integers is uniformly interpreted in global fields, and a theorem on the definability of valuations on function fields of curves, we show that each infinite finitely generated field considered in the ring language is parametrically biinterpretable with {N} . As a consequence, for any finitely generated field there is a first-order sentence in the language of rings which is true in that field but false in every other finitely generated field and, hence, Pop's conjecture that elementarily equivalent finitely generated fields are isomorphic is true.
Luminescent infinite coordination polymer materials from metal-terpyridine ligation.
Eryazici, Ibrahim; Farha, Omar K; Compton, Owen C; Stern, Charlotte; Hupp, Joseph T; Nguyen, SonBinh T
2011-09-28
A new class of infinite coordination polymers (CP) was synthesized using a tetrahedral tetrakis[4-(4'-phenyl-2,2':6',2''-terpyridine)phenyl]methane ligand as an organic node to direct the three-dimensional growth of the network and M(II) (M = Zn, Fe, Ni, and Ru) ions as inorganic linkers, an approach that is the opposite of the metal-as-a-node strategy used in the construction of metal-organic frameworks (MOFs). The unusual rod-like morphology of the resulting microporous materials can be tuned via solvents and reaction conditions. The covalent entrapment of a [Ru(tpy)(2)](2+) moiety in the skeleton of the 3D-network enables the Ru-CP to exhibit room-temperature luminescence.
Defect energy of infinite-component vector spin glasses.
Lee, L W; Young, A P
2005-09-01
We compute numerically the zero-temperature defect energy DeltaE of the vector spin glass in the limit of an infinite number of spin components m , for a range of dimensions 2< or d < or =5 . Fitting to DeltaE approximately L(theta) , where L is the system size, we obtain: theta similar to-1.54 (d=2) , theta similar to-1.04 (d=3) , theta similar to -0.67 (d=4) , and theta similar to -0.37 (d=5) . These results show that the lower critical dimension dl (the dimension where theta changes sign) is significantly higher for m=infinity than for finite m (where 2< dl <3 ).
Double resonance in the infinite-range quantum Ising model.
Han, Sung-Guk; Um, Jaegon; Kim, Beom Jun
2012-08-01
We study quantum resonance behavior of the infinite-range kinetic Ising model at zero temperature. Numerical integration of the time-dependent Schrödinger equation in the presence of an external magnetic field in the z direction is performed at various transverse field strengths g. It is revealed that two resonance peaks occur when the energy gap matches the external driving frequency at two distinct values of g, one below and the other above the quantum phase transition. From the similar observations already made in classical systems with phase transitions, we propose that the double resonance peaks should be a generic feature of continuous transitions, for both quantum and classical many-body systems.
Light bending in infinite derivative theories of gravity
NASA Astrophysics Data System (ADS)
Feng, Lei
2017-04-01
Light bending is one of the significant predictions of general relativity (GR) and it has been confirmed with great accuracy during the past one hundred years. In this paper, we semiclassically calculate the deflection angle for the photons that just graze the Sun in the infinite derivative theories of gravity (IDG) which is a ghost and singularity free theory of gravity. From our calculations, we find that the deflection angle θ only depends on Λ /E . θ →θE when Λ /E →∞ and decrease to zero when Λ /E →0 . The transition interval occurs at 1 04
Broadband computation of the scattering coefficients of infinite arbitrary cylinders.
Blanchard, Cédric; Guizal, Brahim; Felbacq, Didier
2012-07-01
We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.
Infinite occupation number basis of bosons: Solving a numerical challenge
NASA Astrophysics Data System (ADS)
Geißler, Andreas; Hofstetter, Walter
2017-06-01
In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to Nc lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.
Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments
NASA Astrophysics Data System (ADS)
Vojta, Thomas; Hoyos, José A.
2015-11-01
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of temporal disorder on nonequilibrium processes. We also discuss how general this exotic critical behavior is, we illustrate the results by computer simulations, and we touch upon experimental applications of our theory.
Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments
NASA Astrophysics Data System (ADS)
Vojta, Thomas; Hoyos, Jose
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of temporal disorder on nonequilibrium processes. We also discuss how general this exotic critical behavior is, we illustrate the results by computer simulations, and we touch upon experimental applications of our theory. Supported by the NSF under Grant No. DMR-1205803, by Simons Foundation, by FAPESP under Grant No. 2013/09850-7, and by CNPq under Grant Nos. 590093/2011-8 and 305261/2012-6.
On q-deformed infinite-dimensional n-algebra
NASA Astrophysics Data System (ADS)
Ding, Lu; Jia, Xiao-Yu; Wu, Ke; Yan, Zhao-Wen; Zhao, Wei-Zhong
2016-03-01
The q-deformation of the infinite-dimensional n-algebras is investigated. Based on the structure of the q-deformed Virasoro-Witt algebra, we derive a nontrivial q-deformed Virasoro-Witt n-algebra which is nothing but a sh-n-Lie algebra. Furthermore in terms of the pseud-differential operators, we construct the (co)sine n-algebra and the q-deformed S Diff (T2)n-algebra. We find that they are the sh-n-Lie algebras for the n even case. In terms of the magnetic translation operators, an explicit physical realization of the (co)sine n-algebra is given.
On the mechanism of bandgap formation in locally resonant finite elastic metamaterials
NASA Astrophysics Data System (ADS)
Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper
2016-10-01
Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.
NASA Astrophysics Data System (ADS)
Lubarda, Vlado A.
2016-03-01
The Peach-Koehler expressions for the glide and climb components of the force exerted on a straight dislocation in an infinite isotropic medium by another straight dislocation are derived by evaluating the plane and antiplane strain versions of J integrals around the center of the dislocation. After expressing the elastic fields as the sums of elastic fields of each dislocation, the energy momentum tensor is decomposed into three parts. It is shown that only one part, involving mixed products from the two dislocation fields, makes a nonvanishing contribution to J integrals and the corresponding dislocation forces. Three examples are considered, with dislocations on parallel or intersecting slip planes. For two edge dislocations on orthogonal slip planes, there are two equilibrium configurations in which the glide and climb components of the dislocation force simultaneously vanish. The interactions between two different types of screw dislocations and a nearby circular void, as well as between parallel line forces in an infinite or semi-infinite medium, are then evaluated.
Constructing a Chaotic System with an Infinite Number of Equilibrium Points
NASA Astrophysics Data System (ADS)
Pham, Viet-Thanh; Jafari, Sajad; Kapitaniak, Tomasz
2016-12-01
The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology.
Infinitely extended Kac table of solvable critical dense polymers
NASA Astrophysics Data System (ADS)
Pearce, Paul A.; Rasmussen, Jørgen; Villani, Simon P.
2013-05-01
Solvable critical dense polymers is a Yang-Baxter integrable model of polymers on the square lattice. It is the first member LM(1,2) of the family of logarithmic minimal models LM(p,p^{\\prime }). The associated logarithmic conformal field theory admits an infinite family of Kac representations labelled by the Kac labels r, s = 1, 2, …. In this paper, we explicitly construct the conjugate boundary conditions on the strip. The boundary operators are labelled by the Kac fusion labels (r, s) = (r, 1)⊗(1, s) and involve a boundary field ξ. Tuning the field ξ appropriately, we solve exactly for the transfer matrix eigenvalues on arbitrary finite-width strips and obtain the conformal spectra using the Euler-Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double-row transfer matrices. The transfer matrix eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane. This yields selection rules for the physically relevant solutions to the inversion identity which takes the form of a decomposition into irreducible blocks corresponding combinatorially to finitized characters given by generalized q-Catalan polynomials. This decomposition is in accord with the decomposition of the Kac characters into irreducible characters. In the scaling limit, we confirm the central charge c = -2 and the Kac formula for the conformal weights \\Delta _{r,s}=\\frac{(2r-s)^2-1}{8} for r, s = 1, 2, 3, … in the infinitely extended Kac table.
NASA Astrophysics Data System (ADS)
Matveenko, V. P.; Sevodina, N. V.; Fedorov, A. Yu.
2013-09-01
The stress state in adhesive lap joints with various geometric shapes of spew fillet is studied. It is noted that the applied design models of the considered problem include singular points at which infinite stress values are possible if one uses the linear elasticity theory to calculate the stress state. Based on the conclusions of the solution of the geometry optimization problem in the vicinity of the singular points of elastic bodies, variants of the geometry of spew fillet, which provide the most significant decrease in the concentration of stresses in adhesive lap joints, are proposed.
NASA Technical Reports Server (NTRS)
Hardrath, Herbert F; Ohman, Lachlan
1953-01-01
Six large 24s-t3 aluminum-alloy-sheet specimens containing various notches or fillets were tested in tension to determine their stress concentration factors in both the elastic and plastic ranges. The elastic stress concentration factors were found to be slightly higher than those calculated by Neuber's method and those obtained photoelastically by Frocht. The results showed further that the stress concentration factor decreases as strains at the discontinuity enter the plastic range. A generalization of Stowell's relation for the plastic stress concentration factor at a circular hole in an infinite plate was applied to the specimen shapes tested and gave good agreement with test results.
Elastic wave propagation along a set of parallel fractures
NASA Astrophysics Data System (ADS)
Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.
2002-08-01
Previous studies on elastic wave propagation in fractured media have demonstrated that a single planar fracture supports fracture interface waves and that two plane parallel fractures support fracture channel waves. Here, the results are presented for plane wave propagation through an infinite number of plane parallel fractures with equal fracture spacing and fracture stiffnesses. Analysis of the dispersion equations for this fractured system demonstrates that these waves exhibit symmetric and antisymmetric particle motions, degenerate to classical Rayleigh-Lamb plate waves when the fractures are completely open, and possess dispersive velocities that are functions of both the fracture stiffness and spacing. Time-frequency analysis performed on a series of laboratory ultrasonic transmission measurements on a fractured rock analog shows good agreement with the theoretical predictions.
Semi-infinite photocarrier radiometric model for the characterization of semiconductor wafer
NASA Astrophysics Data System (ADS)
Liu, Xianming; Li, Bincheng; Huang, Qiuping
2010-03-01
The analytical expression is derived to describe the photocarrier radiometric (PCR) signal for a semi-infinite semiconductor wafer excited by a square-wave modulated laser. For comparative study, the PCR signals are calculated by the semi-infinite model and the finite thickness model with several thicknesses. The fitted errors of the electronic transport properties by semi-infinite model are analyzed. From these results it is evident that for thick samples or at high modulation frequency, the semiconductor can be considered as semi-infinite.
NASA Astrophysics Data System (ADS)
Li, FengLian; Wang, YueSheng; Zhang, ChuanZeng
2016-06-01
A boundary element method (BEM) is presented to compute the transmission spectra of two-dimensional (2-D) phononic crystals of a square lattice which are finite along the x-direction and infinite along the y-direction. The cross sections of the scatterers may be circular or square. For a periodic cell, the boundary integral equations of the matrix and the scatterers are formulated. Substituting the periodic boundary conditions and the interface continuity conditions, a linear equation set is formed, from which the elastic wave transmission can be obtained. From the transmission spectra, the band gaps can be identified, which are compared with the band structures of the corresponding infinite systems. It is shown that generally the transmission spectra completely correspond to the band structures. In addition, the accuracy and the efficiency of the boundary element method are analyzed and discussed.
NASA Astrophysics Data System (ADS)
Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.
2017-05-01
Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of
NASA Astrophysics Data System (ADS)
Ruge, P.; Birk, C.
2007-07-01
This paper deals with the dynamic analysis of infinite beam models. The translational and the rotational dynamic stiffness of both Timoshenko and Euler-Bernoulli beams on Winkler foundation are derived and compared in the frequency-domain. The situation of vanishing elastic foundation is included as a special case. Here, special emphasis is placed on the asymptotic behaviour of the derived stiffness expressions for high frequencies, since this is of importance in case of transient excitations. It is shown that the dynamic stiffness of the infinite Timoshenko beam follows a linear function of iω, whereas rational powers of iω are involved in case of Euler-Bernoulli's model. The stiffness formulations can be transformed into the time-domain using the mixed-variables technique. This is based on a rational approximation of the low-frequency force-displacement relationship and a subsequent algebraic splitting process. At the same time, the high-frequency asymptotic dynamic stiffness is transformed into the time-domain in closed-form. It is shown that the Timoshenko beam is equivalent to a simple dashpot in the high-frequency limit, whereas Euler-Bernoulli's beam model leads to fractional derivatives of the unknown state variables in an equivalent time-domain description. This finding confirms the superiority of Timoshenko's model especially for high frequencies and transient excitations. Numerical examples illustrate the differences with respect to the two beam models and demonstrate the applicability of the proposed method for the time-domain transformation of force-displacement relationships.
Elasticity of crystalline molecular explosives
Hooks, Daniel E.; Ramos, Kyle J.; Bolme, C. A.; ...
2015-04-14
Crystalline molecular explosives are key components of engineered explosive formulations. In precision applications a high degree of consistency and predictability is desired under a range of conditions to a variety of stimuli. Prediction of behaviors from mechanical response and failure to detonation initiation and detonation performance of the material is linked to accurate knowledge of the material structure and first stage of deformation: elasticity. The elastic response of pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), and cyclotetramethylene tetranitramine (HMX), including aspects of material and measurement variability, and computational methods are described in detail. Experimental determinations of elastic tensors are compared, andmore » an evaluation of sources of error is presented. Furthermore, computed elastic constants are also compared for these materials and for triaminotrinitrobenzene (TATB), for which there are no measurements.« less
Elasticity of crystalline molecular explosives
Hooks, Daniel E.; Ramos, Kyle J.; Bolme, C. A.; Cawkwell, Marc J.
2015-04-14
Crystalline molecular explosives are key components of engineered explosive formulations. In precision applications a high degree of consistency and predictability is desired under a range of conditions to a variety of stimuli. Prediction of behaviors from mechanical response and failure to detonation initiation and detonation performance of the material is linked to accurate knowledge of the material structure and first stage of deformation: elasticity. The elastic response of pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), and cyclotetramethylene tetranitramine (HMX), including aspects of material and measurement variability, and computational methods are described in detail. Experimental determinations of elastic tensors are compared, and an evaluation of sources of error is presented. Furthermore, computed elastic constants are also compared for these materials and for triaminotrinitrobenzene (TATB), for which there are no measurements.
Measuring How Elastic Arteries Function.
ERIC Educational Resources Information Center
DeMont, M. Edwin; MacGillivray, Patrick S.; Davison, Ian G.; McConnell, Colin J.
1997-01-01
Describes a procedure used to measure force and pressure in elastic arteries. Discusses the physics of the procedure and recommends the use of bovine arteries. Explains the preparation of the arteries for the procedure. (DDR)
Measuring How Elastic Arteries Function.
ERIC Educational Resources Information Center
DeMont, M. Edwin; MacGillivray, Patrick S.; Davison, Ian G.; McConnell, Colin J.
1997-01-01
Describes a procedure used to measure force and pressure in elastic arteries. Discusses the physics of the procedure and recommends the use of bovine arteries. Explains the preparation of the arteries for the procedure. (DDR)
Elastic protectors for ultrasound injection
Barkhatov, V.A.; Nesterova, L.A.
1995-07-01
A new material has been developed for elastic protectors on ultrasonic probes: sonar rubber. This combines low ultrasonic absorption, high strength, and wear resistance, and so the rubber can be used in sensor designs.
Flame resistant elastic elastomeric fibers
NASA Technical Reports Server (NTRS)
Howarth, J. T.; Massucco, A. A.
1972-01-01
Development of materials to improve flame resistance of elastic elastomeric fibers is discussed. Two approaches, synthesis of polyether based urethanes and modification of synthesized urethanes with flame ratardant additives, are described. Specific applications of both techniques are presented.
Hilbert complexes of nonlinear elasticity
NASA Astrophysics Data System (ADS)
Angoshtari, Arzhang; Yavari, Arash
2016-12-01
We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.
Elastic waves in quasiperiodic structures
NASA Astrophysics Data System (ADS)
Velasco, V. R.; Zárate, J. E.
2001-08-01
We study the transverse and sagittal elastic waves in different quasiperiodic structures by means of the full transfer-matrix technique and surface Green-function matching method. The quasiperiodic structures follow Fibonacci, Thue-Morse and Rudin-Shapiro sequences, respectively. We consider finite structures having stress-free bounding surfaces and different generation orders, including up to more than 1000 interfaces. We obtain the dispersion relations for elastic waves and spatial localization of the different modes. The fragmentation of the spectrum for different sequences is evident for intermediate generation orders, in the case of transverse elastic waves, whereas, for sagittal elastic waves, higher generation orders are needed to show clearly the spectrum fragmentation. The results of Fibonacci and Thue-Morse sequences exhibit similarities not present in the results of Rudin-Shapiro sequences.
Elastic Properties of Mantle Minerals
NASA Astrophysics Data System (ADS)
Duffy, T. S.; Stan, C. V.
2012-12-01
The most direct information about the interior structure of the Earth comes from seismic wave velocities. Interpretation of seismic data requires an understanding of how sound velocities and elastic properties of minerals vary with pressure, temperature, crystal structure, and composition as well as the role of anelasticity, melts, etc. More generally, elastic moduli are important for understanding many solid-state phenomena including mechanical stability, interatomic interactions, material strength, compressibility, and phase transition mechanisms. The database of mineral elasticity measurements has been growing rapidly in recent years. In this work, we report initial results of an ongoing survey of our current knowledge of mineral elasticity at both ambient conditions and high pressures and temperatures. The analysis is selective, emphasizing single crystal measurements but also incorporating polycrystalline measurements and volume compression data as appropriate. The goal is to synthesize our current understanding of mineral elasticity in terms of structure and composition, and to identify the major remaining needs for experimental and theoretical work. Clinopyroxenes (Cpx) provide an example of our approach. A wide range of clinopyroxene compositions are found geologically and Mg-, Ca-, and Na-rich clinopyroxenes are expected to be important components in the upper mantle. The single-crystal elastic properties of a number of endmember Cpx compositions have been measured and these exhibit a range of ~25% in shear velocity. Those with monovalent cations (spodumene, jadeite) in the M2 site exhibit the highest velocities while Fe-rich (hendenbergit, acmite) compositions have the lowest velocities. The effects on velocity due to a wide range of chemical substitutions can be defined, but there are important discrepancies and omissions in the database. New measurements of omphacites, intermediate diopside-hedenbergite compositions, aegerine/acmite, augite, etc. are
Masiero, Federica
2007-05-15
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
A Corpus-Based Study of the Infinitive Errors Made by Chinese College Students
ERIC Educational Resources Information Center
Xia, Lixin
2012-01-01
The paper discusses the infinitive errors made by Chinese college students. From the CLEC, all infinitive errors tagged as [vp5] are collected, and then the general distribution of the errors among 4 groups of college students is shown. Moreover, these errors are classified into 12 categories according to the characteristics of the usage. After…
The planar Green`s function in an infinite multiplying medium
Kornreich, D.E.; Ganapol, B.D.
1996-10-01
Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green`s function in an infinite medium. The Green`s function problem considers an infinite planar source emitting neutral particles in the single directions`. Recently, this Green`s function has been used to obtain solutions for finite media. These solutions, which hinge on accurate and fast evaluation of the infinite medium Green`s function, use Fourier and Laplace transform inversion techniques for the evaluation. Until now, only absorbing media have been considered, and applications were therefore limited to non-multiplying media. In an effort to relax this limitation, the infinite medium Green`s function is numerically evaluated for an infinite multiplying medium using the double-sided Laplace transform inversion. Of course, no steady-state mathematical solution exists for an infinite multiplying medium with a source present; however, the non-physical solution in an infinite medium can be used in finite media problems where the solution is physically realizable.
Monreal, Marisa J; Seaman, Lani A; Goff, George S; Michalczyk, Ryszard; Morris, David E; Scott, Brian L; Kiplinger, Jaqueline L
2016-03-07
Two organometallic 1D infinite coordination polymers and two organometallic monometallic complexes of thorium diazide have been synthesized and characterized. Steric control of these self-assembled arrays, which are dense in thorium and nitrogen, has also been demonstrated: infinite chains can be circumvented by using steric bulk either at the metallocene or with a donor ligand in the wedge.
Maxwell-Higgs self-dual solitons on an infinite cylinder
NASA Astrophysics Data System (ADS)
Casana, Rodolfo; Sourrouille, Lucas
2015-07-01
We have studied the Maxwell-Higgs model on the surface of an infinite cylinder. In particular, we show that this model supports self-dual topological soliton solutions on the infinite tube. Finally, the Bogomol’nyi-type equations are studied from theoretical and numerical point of view.
ERIC Educational Resources Information Center
Tsamir, Pessia
1999-01-01
Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…
Confusing Aspects in the Calculation of the Electrostatic Potential of an Infinite Line of Charge
ERIC Educational Resources Information Center
Jimenez, J. L.; Campos, I.; Roa-Neri, J. A. E.
2012-01-01
In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…
Confusing Aspects in the Calculation of the Electrostatic Potential of an Infinite Line of Charge
ERIC Educational Resources Information Center
Jimenez, J. L.; Campos, I.; Roa-Neri, J. A. E.
2012-01-01
In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…
Stress distribution in a semi-infinite body symmetrically loaded over a circular area
NASA Technical Reports Server (NTRS)
Mcginness, H.
1980-01-01
Algorithms are developed for computing stresses in a semi-infinite body when loaded by a uniform pressure acting over a circular area. The algorithm allows easy determination of any stress component in a semi-infinite body having a known Poisson's ratio. Example curves are plotted for Portland cement grout and metal representative values.
An Infinite Mixture Model for Coreference Resolution in Clinical Notes
Liu, Sijia; Liu, Hongfang; Chaudhary, Vipin; Li, Dingcheng
2016-01-01
It is widely acknowledged that natural language processing is indispensable to process electronic health records (EHRs). However, poor performance in relation detection tasks, such as coreference (linguistic expressions pertaining to the same entity/event) may affect the quality of EHR processing. Hence, there is a critical need to advance the research for relation detection from EHRs. Most of the clinical coreference resolution systems are based on either supervised machine learning or rule-based methods. The need for manually annotated corpus hampers the use of such system in large scale. In this paper, we present an infinite mixture model method using definite sampling to resolve coreferent relations among mentions in clinical notes. A similarity measure function is proposed to determine the coreferent relations. Our system achieved a 0.847 F-measure for i2b2 2011 coreference corpus. This promising results and the unsupervised nature make it possible to apply the system in big-data clinical setting. PMID:27595047
Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions
Goreac, D.
2009-08-15
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y-component of the solution there is still another one acting on the Z-component. With the help of this dual equation we then deduce the duality between approximate controllability and observability. Finally, under the assumption that the unbounded operator acting on the state process of the forward equation is an infinitesimal generator of an exponentially stable semigroup, we show that the generalized Hautus test provides a necessary condition for the approximate controllability. The paper generalizes former results by Buckdahn, Quincampoix and Tessitore (Stochastic Partial Differential Equations and Applications, Series of Lecture Notes in Pure and Appl. Math., vol. 245, pp. 253-260, Chapman and Hall, London, 2006) and Goreac (Applied Analysis and Differential Equations, pp. 153-164, World Scientific, Singapore, 2007) from the finite dimensional to the infinite dimensional case.
A conformal truncation framework for infinite-volume dynamics
Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.
2016-07-28
Here, we present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, P, and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ Cmax, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preservemore » the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N) CFT deformed by a mass term and a non-perturbative quartic interaction at large-N. In all cases, the truncation scheme correctly reproduces known analytic results. As a result, we also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.« less
Infinite bandwidth of a Mott-Hubbard insulator
NASA Astrophysics Data System (ADS)
Freericks, James; Cohn, Jeffrey; van Dongen, Peter; Krishnamurthy, Hulikal
The conventional viewpoint of the strongly correlated electron metal-insulator transition is that a single band splits into two upper and lower Hubbard bands at the metal-insulator transition. Much work has investigated whether this transition is continuous or discontinuous. Here we focus on another aspect and ask the question of whether there are additional upper and lower Hubbard bands, which stretch all the way out to infinity|leading to an infinite bandwidth for the Mott insulator. While we are not yet able to provide a rigorous proof of this result, we use exact diagonalization studies on small clusters to motivate the existence of these additional bands, and we discuss some different methods that might be utilized to provide a rigorous proof of this result. Even though the extra upper and lower Hubbard bands have very low total spectral weight, those states are expected to have extremely long lifetimes, leading to a nontrivial contribution to the transport density of states for dc transport and modifying the high temperature limit for the electrical resistivity. JKF supported by the Department of Energy, Office of Basic Energy Sciences, under Grant No. DE-FG02-08ER46542, and by the McDevitt bequest at Georgetown University. HRK supported by the Indian Science Foundation.
Spectral Methods Using Rational Basis Functions on an Infinite Interval
NASA Astrophysics Data System (ADS)
Boyd, John P.
1987-03-01
By using the map y = L cot( t) where L is a constant, differential equations on the interval yɛ [- ∞, ∞] can be transformed into tɛ [0, π] and solved by an ordinary Fourier series. In this article, earlier work by Grosch and Orszag ( J. Comput. Phys.25, 273 (1977)), Cain, Ferziger, and Reynolds ( J. Comput. Phys.56, 272 (1984)), and Boyd ( J. Comput. Phys.25, 43 (1982); 57, 454 (1985); SIAM J. Numer. Anal. (1987)) is extended in several ways. First, the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y-plane. Second, Galerkin's method will convert differential equations with polynomial or rational coefficients into banded matrix problems. Third, with orthogonal rational functions it is possible to obtain exponential convergence even for u( y) that asymptote to a constant although this behavior would wreck alternatives such as Hermite or sinc expansions. Fourth, boundary conditions are usually "natural" rather than "essential" in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions. Fifth, mapping a finite interval to an infinite one and then applying the rational Chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities. These concepts are illustrated by five numerical examples.
Second law analysis of an infinitely segmented magnetohydrodynamic generator
NASA Astrophysics Data System (ADS)
Arash, Ardeshir; Saidi, Mohammad Hassan; Najafi, Mohammad
2017-03-01
The performance of an infinitely segmented magnetohydrodynamic generator is analyzed using the second law of thermodynamics entropy generation criterion. The exact analytical solution of the velocity and temperature fields are provided by applying the modified Hartmann flow model, taking into account the occurrence of the Hall effect in the considered generator. Contributions of heat transfer, fluid friction, and ohmic dissipation to the destruction of useful available work are found, and the nature of irreversibilities in the considered generator is determined. In addition, the electrical isotropic efficiency scheme is used to evaluate the generator performance. Finally, the implication of the Hall parameter, Hartmann number, and load factor for the entropy generation and the generator performance are studied and the optimal operating conditions are determined. The results show that the heat transfer has the smallest contribution to the entropy generation compared to that of the friction and ohmic dissipation. The application of the Hall effect on the system showed an appreciable augmentation of entropy generation rate which is along with what the logic implies. A parametric study is conducted and its results provide the generated entropy and also efficiency diagrams which show the influence of the Hall effect on the considered generator.
Causal field theory with an infinite speed of sound
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-15
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Superposition, Transition Probabilities and Primitive Observables in Infinite Quantum Systems
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Størmer, Erling
2015-10-01
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I∞ factors. Such funnels are used in the description of infinite systems, appearing for example in quantum field theory or in quantum statistical mechanics; their respective constituents are interpreted as algebras of observables localized in an increasing family of nested spacetime regions. Given a generic reference state (expectation functional) on a funnel, e.g. a ground state or a thermal equilibrium state, it is shown that irrespective of the global type of this state all of its excitations, generated by the adjoint action of elements of the funnel, can coherently be superimposed in a meaningful manner. Moreover, these states are the extreme points of their convex hull and as such are analogues of pure states. As further support of this analogy, transition probabilities are defined, complete families of orthogonal states are exhibited and a one-to-one correspondence between the states and families of minimal projections on a Hilbert space is established. The physical interpretation of these quantities relies on a concept of primitive observables. It extends the familiar framework of observable algebras and avoids some counter intuitive features of that setting. Primitive observables admit a consistent statistical interpretation of corresponding measurements and their impact on states is described by a variant of the von Neumann-Lüders projection postulate.
Semiclassical limits of quantum partition functions on infinite graphs
Güneysu, Batu
2015-02-15
We prove that if H denotes the operator corresponding to the canonical Dirichlet form on a possibly locally infinite weighted graph (X, b, m), and if v : X → ℝ is such that H + v/ħ is well-defined as a form sum for all ħ > 0, then the quantum partition function tr(e{sup −βħ(H+v/ħ)}) converges to ∑{sub x∈X}e{sup −βv(x)} as ħ → 0 +, for all β > 0, regardless of the fact whether e{sup −βv} is a priori summable or not. This fact can be interpreted as a semiclassical limit, and it allows geometric Weyl-type convergence results. We also prove natural generalizations of this semiclassical limit to a large class of covariant Schrödinger operators that act on sections in Hermitian vector bundle over (X, m, b), a result that particularly applies to magnetic Schrödinger operators that are defined on (X, m, b)
Bifurcation analysis of an infinite array of von Karman Streets
NASA Astrophysics Data System (ADS)
Ghaemi Oskouei, Babak; Kanso, Eva; Newton, Paul K.
2008-11-01
This research investigates the behavior of an infinite array of (inverse) von Karman streets. Primary motivation is to model the wake dynamics in large fish schools. Ignoring the fish we focus on the dynamic interaction of multiple wakes. In particular, we investigate the problem of fluid transport between adjacent vortex streets for its relevance to understanding the transport of oxygen and nutrients to inner fish in large schools as well as understanding flow barriers to passive locomotion. We prove that the configuration of vortices is in relative equilibrium, meaning that the streamline pattern remains steady in the frame moving with vortices. We look at the topology of these streamline patterns plotted in the moving frame which lends insight to fluid transport through the mid-wake region. Fluid is advected along different paths depending on the distance separating two adjacent streets. When the streets are far apart, the dynamics is decoupled and fluid is transported globally between two adjacent streets. When the streets get closer to each other, the number of streets that enter into partnership in transporting fluid among themselves increases. This observation motivates a bifurcation analysis which links the distance between streets to the maximum number of streets transporting fluid among themselves.
Causal field theory with an infinite speed of sound
NASA Astrophysics Data System (ADS)
Afshordi, Niayesh; Chung, Daniel J. H.; Geshnizjani, Ghazal
2007-04-01
We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.
Communication Tasks with Infinite Quantum-Classical Separation.
Perry, Christopher; Jain, Rahul; Oppenheim, Jonathan
2015-07-17
Quantum resources can be more powerful than classical resources-a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two parties' inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than their classical counterpart. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n. Next, we consider a version of the task where the parties may have access to entanglement. With this assistance, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n. The task is related to the Pusey-Barrett-Rudolph theorem which arises in the context of the foundations of quantum theory.
Infinite hidden conditional random fields for human behavior analysis.
Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja
2013-01-01
Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF), which is a nonparametric model based on hierarchical Dirichlet processes and is capable of automatically learning the optimal number of hidden states for a classification task. We show how we learn the model hyperparameters with an effective Markov-chain Monte Carlo sampling technique, and we explain the process that underlines our iHCRF model with the Restaurant Franchise Rating Agencies analogy. We show that the iHCRF is able to converge to a correct number of represented hidden states, and outperforms the best finite HCRFs--chosen via cross-validation--for the difficult tasks of recognizing instances of agreement, disagreement, and pain. Moreover, the iHCRF manages to achieve this performance in significantly less total training, validation, and testing time.
A conformal truncation framework for infinite-volume dynamics
Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.
2016-07-28
Here, we present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, P, and conformal Casimir, C. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with C ≤ C_{max}, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free O(N) CFT deformed by a mass term and a non-perturbative quartic interaction at large-N. In all cases, the truncation scheme correctly reproduces known analytic results. As a result, we also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.
Tamm plasmon modes on semi-infinite metallodielectric superlattices.
Isić, Goran; Vuković, Slobodan; Jašić, Zoran; Belić, Milivoj
2017-06-16
We analyze the fundamental properties of optical waves referred to as Tamm plasmon modes (TPMs) which are tied to the interface of a semi-infinite two-phase metallodielectric superlattice with an arbitrary homogeneous capping medium. Such modes offer new ways of achieving high electromagnetic field localization and spontaneous emission enhancement in the vicinity of the interface in conjunction with absorption loss management, which is crucial for future applications. The homointerface, formed when the capping medium has the same permittivity as one of the superlattice constituents, is found to support a TPM whose dispersion overlaps the single-interface surface plasmon polariton (SPP) dispersion but which has a cut off at the topological transition point. In contrast, a heterointerface formed for an arbitrary capping medium, is found to support multiple TPMs whose origin can be traced by considering the interaction between a single-interface SPP and the homointerface TPM burried under the top layer of the superlattice. By carrying out a systematic comparison between TPMs and single-interface SPPs, we find that the deviations are most pronounced in the vicinity of the transition frequency for superlattices in which dielectric layers are thicker than metallic ones.
Electromagnetic field interacting with a semi-infinite plasma.
Apostol, M; Vaman, G
2009-07-01
Plasmon and polariton modes are derived for an ideal semi-infinite (half-space) plasma by using a general, unifying procedure based on the equation of motion of the polarization and the electromagnetic potentials. Known results are reproduced in a much more direct manner, and new ones are derived. The approach consists of representing the charge disturbances by a displacement field in the positions of the moving particles (electrons). The propagation of an electromagnetic wave in this plasma is treated by using the retarded electromagnetic potentials. The resulting integral equations are solved, and the reflected and refracted fields are computed, as well as the reflection coefficient. Generalized Fresnel relations are thereby obtained for any incidence angle and polarization. Bulk and surface plasmon-polariton modes are identified. As is well known, the field inside the plasma is either damped (evanescent) or propagating (transparency regime), and the reflection coefficient exhibits an abrupt enhancement on passing from the propagating regime to the damped one (total reflection).
A simple extrapolation of thermodynamic perturbation theory to infinite order
Ghobadi, Ahmadreza F.; Elliott, J. Richard
2015-09-21
Recent analyses of the third and fourth order perturbation contributions to the equations of state for square well spheres and Lennard-Jones chains show trends that persist across orders and molecular models. In particular, the ratio between orders (e.g., A{sub 3}/A{sub 2}, where A{sub i} is the ith order perturbation contribution) exhibits a peak when plotted with respect to density. The trend resembles a Gaussian curve with the peak near the critical density. This observation can form the basis for a simple recursion and extrapolation from the highest available order to infinite order. The resulting extrapolation is analytic and therefore cannot fully characterize the critical region, but it remarkably improves accuracy, especially for the binodal curve. Whereas a second order theory is typically accurate for the binodal at temperatures within 90% of the critical temperature, the extrapolated result is accurate to within 99% of the critical temperature. In addition to square well spheres and Lennard-Jones chains, we demonstrate how the method can be applied semi-empirically to the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT)
Infinite dimensional variational inequalities and dynamic network disequilibrium modeling
Friesz, T.; Bernstein, D.
1994-12-31
In this paper we explain the importance of modeling disequilibrium flow patterns occurring on networks, with special emphasis on automobile networks and the role of information technology. We show how elementary notions of disequilibrium, whether abstract, physical or economic in nature, give rise to an adjustment process expressible as a dynamical system. We comment that when such a system is autonomous its steady states can be given the traditional finite dimensional variational inequality/fixed point representations common to static network equilibria. Beyond this, and unique to our work, we show that if the disequilibrium dynamical system is nonautonomous it may tend toward moving or dynamic (instead of static) network equilibria expressible as infinite dimensional variational inequalities. Using concepts of fast and slow dynamic systems, we show how day-to-day and within-day aspects of automobile travel decision making can be combined to yield a nonautonomous dynamical system with the mathematical properties reviewed previously. We introduce axioms for a proper predictive model of urban network flows which integrates both day-to-day and within-day considerations and postulate one such model for further study.
A study on Rayleigh wave dispersion in bone according to Mindlin's Form II gradient elasticity.
Vavva, Maria G; Gergidis, Leonidas N; Protopappas, Vasilios C; Charalambopoulos, Antonios; Polyzos, Demosthenes; Fotiadis, Dimitrios I
2014-05-01
The classical elasticity cannot effectively describe bone's mechanical behavior since only homogeneous media and local stresses are assumed. Additionally, it cannot predict the dispersive nature of the Rayleigh wave which has been reported in experimental studies and was also demonstrated in a previous computational study by adopting Mindlin's Form II gradient elasticity. In this work Mindlin's theory is employed to analytically determine the dispersion of Rayleigh waves in a strain gradient elastic half-space. An isotropic semi-infinite space is considered with properties equal to those of bone and dynamic behavior suffering from microstructural effects. Microstructural effects are considered by incorporating four intrinsic parameters in the stress analysis. The results are presented in the form of group and phase velocity dispersion curves and compared with existing computational results and semi-analytical curves calculated for a simpler case of Rayleigh waves in dipolar gradient elastic half-spaces. Comparisons are also performed with the velocity of the first-order antisymmetric mode propagating in a dipolar plate so as to observe the Rayleigh asymptotic behavior. It is shown that Mindlin's Form II gradient elasticity can effectively describe the dispersive nature of Rayleigh waves. This study could be regarded as a step toward the ultrasonic characterization of bone.
Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates.
Destrade, Michel; Fu, Yibin; Nobili, Andrea
2016-09-01
The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.
NASA Astrophysics Data System (ADS)
Hammad, F.
2010-05-01
In a series of recent papers Padmanabhan et al. derived Einstein equations for gravity by introducing an entropy functional for space-time viewed as an elastic medium. They showed that the same entropy functional applied to the thermodynamics of horizons yields an entropy that is always proportional to the area of the horizon. Following the same philosophy as theirs we first note that it may be arrived at Einstein equations, with a cosmological constant as an integration constant, using a slightly different route from theirs that also results in the same final expression for the entropy functional. We generalize the fundamental equations of three-dimensional elasticity to four dimensions and propose that the elastic deformation of space-time be constrained by those equations. A general Lagrangian describing the elastic deformation of space-time is deduced. When applied to the special case of a Schwarzschild black hole, viewed as an infinite line defect in space-time, the approach developed here permits to recover the black hole’s mass from the elastic deformation it caused to space-time, to reproduce the Hawking temperature, and to yield an entropy that is also in agreement with the Bekenstein-Hawking formula.
Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates
NASA Astrophysics Data System (ADS)
Destrade, Michel; Fu, Yibin; Nobili, Andrea
2016-09-01
The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.
Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids.
Bevzenko, Dmytro; Lubchenko, Vassiliy
2014-11-07
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant--which is enhanced by adding polar molecules to the system--the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid, respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the random first order transition theory.
Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates
Fu, Yibin
2016-01-01
The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff–Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix. PMID:27713663
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
Stresses and elastic constants of crystalline sodium, from molecular dynamics
Schiferl, S.K.
1985-02-01
The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340K. The total adiabatic potential of a system of sodium atoms is represented by pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the results to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. 45 refs., 10 figs., 4 tabs.
An elastic strip with multiple cracks and applications to tapered specimens
NASA Technical Reports Server (NTRS)
Liu, X.-H.; Erdogan, F.
1985-01-01
In this paper an infinite elastic strip containing arbitrarily oriented cracks and subjected to uniform tension and a pair of concentrated forces is formulated in terms of a system of singular integral equations. Even though the technique is sufficiently general to solve new multiple crack problem, with the objective of applying the results to tapered specimens, only a certain symmetric crack geometry and loading conditions are considered. The stress intensity factors are calculated for edge cracks in the strip under uniform tension and for a 'compact' and a 'slender' tapered specimen (the latter simulating the double cantilever beam) under concentrated forces or crack surface wedge forces.
Response Due to Concentrated Force in Micropolar Elastic Solid with Voids
NASA Astrophysics Data System (ADS)
Singh, R.; Singh, K.
2014-11-01
The eigen value approach, following Laplace and Fourier transforms has been employed to find the general solution of the field equation in a micropolar elastic solid with voids for the plane strain problem. An application of an infinite space with impulsive force has been taken to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to get result in physical domain. The result in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components has been obtained numerically and illustrated graphically to depict the effect of micropolarity and voids.
Lamb waves propagation in elastic plane layers with a joint strip.
Predoi, Mihai Valentin; Rousseau, Martine
2005-06-01
The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.
Axial gravitational perturbations of an infinite static line source
NASA Astrophysics Data System (ADS)
Gleiser, Reinaldo J.
2015-03-01
The Levi-Civita metric, which contains a naked singularity that has been interpreted as an infinite static line source, appears, for instance, as the possible end point in the collapse of cylindrically symmetric objects such as shells of dust. The analysis of its gravitational stability should therefore be relevant in the contexts of the cosmic censorship and hoop conjectures. In this paper we study axial gravitational perturbations of the Levi-Civita metric. The perturbations are restricted to axial symmetry but break the cylindrical symmetry of the background metric. We analyze the gauge issues that arise in setting up the appropriate form of the perturbed metric and show that it is possible to restrict the perturbations to diagonal terms but that this does not fix the gauge completely. We derive and solve the perturbation equations. The solutions contain gauge-trivial parts, and we show how to extract the gauge-nontrivial components. We impose appropriate boundary conditions on the solutions and show that these lead to a boundary value problem that determines the allowed functional forms of the perturbation modes. The associated eigenvalues determine a sort of ‘dispersion relation’ for the frequencies and corresponding ‘wave vector’ components. The central result of this analysis is that the spectrum of allowed frequencies contains one unstable (imaginary frequency) mode for every possible choice of the background metric. The completeness of the mode expansion in relation to the initial value problem and to the gauge problem is discussed in detail, and we show that the perturbations contain an unstable component for generic initial data and therefore that the Levi-Civita space times are gravitationally unstable. We also include, for completeness, a set of approximate eigenvalues and examples of the functional form of the solutions.
Stability of infinite slopes under transient partially saturated seepage conditions
NASA Astrophysics Data System (ADS)
Godt, Jonathan W.; ŞEner-Kaya, BaşAk; Lu, Ning; Baum, Rex L.
2012-05-01
Prediction of the location and timing of rainfall-induced shallow landslides is desired by organizations responsible for hazard management and warnings. However, hydrologic and mechanical processes in the vadose zone complicate such predictions. Infiltrating rainfall must typically pass through an unsaturated layer before reaching the irregular and usually discontinuous shallow water table. This process is dynamic and a function of precipitation intensity and duration, the initial moisture conditions and hydrologic properties of the hillside materials, and the geometry, stratigraphy, and vegetation of the hillslope. As a result, pore water pressures, volumetric water content, effective stress, and thus the propensity for landsliding vary over seasonal and shorter time scales. We apply a general framework for assessing the stability of infinite slopes under transient variably saturated conditions. The framework includes profiles of pressure head and volumetric water content combined with a general effective stress for slope stability analysis. The general effective stress, or suction stress, provides a means for rigorous quantification of stress changes due to rainfall and infiltration and thus the analysis of slope stability over the range of volumetric water contents and pressure heads relevant to shallow landslide initiation. We present results using an analytical solution for transient infiltration for a range of soil texture and hydrological properties typical of landslide-prone hillslopes and show the effect of these properties on the timing and depth of slope failure. We follow by analyzing field-monitoring data acquired prior to shallow landslide failure of a hillside near Seattle, Washington, and show that the timing of the slide was predictable using measured pressure head and volumetric water content and show how the approach can be used in a forward manner using a numerical model for transient infiltration.
Dynamically crowded solutions of infinitely thin Brownian needles
NASA Astrophysics Data System (ADS)
Leitmann, Sebastian; Höfling, Felix; Franosch, Thomas
2017-07-01
We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.
Quantum critical phase with infinite projected entangled paired states
NASA Astrophysics Data System (ADS)
Poilblanc, Didier; Mambrini, Matthieu
2017-07-01
A classification of SU(2)-invariant projected entangled paired states (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al. [M. Mambrini, R. Orús, and D. Poilblanc, Phys. Rev. B 94, 205124 (2016), 10.1103/PhysRevB.94.205124]. It is not clear whether such SU(2)-invariant PEPS can either (i) exhibit long-range magnetic order (such as in the Néel phase) or (ii) describe a genuine quantum critical point (QCP) or quantum critical phase (QCPh) separating two ordered phases. Here, we identify a specific family of SU(2)-invariant PEPS of the classification which provides excellent variational energies for the J1-J2 frustrated Heisenberg model, especially at J2=0.5 , corresponding to the approximate location of the QCP or QCPh separating the Néel phase from a dimerized phase. The PEPS are built from virtual states belonging to the 1/2⊗N⊕0 SU(2) representation, i.e., with N "colors" of virtual spin-1/2 . Using a full-update infinite-PEPS approach directly in the thermodynamic limit, based on the corner transfer matrix renormalization algorithm supplemented by a conjugate gradient optimization scheme, we provide evidence of (i) the absence of magnetic order and of (ii) diverging correlation lengths (i.e., showing no sign of saturation with increasing environment dimension) in both the singlet and triplet channels, when the number of colors N ≥3 . We argue that such a PEPS gives a qualitative description of the QCP or QCPh of the J1-J2 model.
User's manual for GILDA: An infinite lattice diffusion theory calculation
Le, T.T.
1991-11-01
GILDA is a static two-dimensional diffusion theory code that performs either buckling (B[sup 2]) or k-effective (k[sub eff]) calculations for an infinite hexagonal lattice which is constructed by repeating identical seven-cell zones (one cell is one or seven identical homogenized hexes). GILDA was written by J. W. Stewart in 1973. This user's manual is intended to provide all of the information necessary to set up and execute a GILDA calculation and to interpret the output results. It is assumed that the user is familiar with the computer (VAX/VMS or IBM/MVS) and the JOSHUA system database on which the code is implemented. Users who are not familiar with the JOSHUA database are advised to consult additional references to understand the structure of JOSHUA records and data sets before turning to section 4 of this manual. Sections 2 and 3 of this manual serve as a theory document in which the basic diffusion theory and the numerical approximations behind the code are described. Section 4 describes the functions of the program's subroutines. Section 5 describes the input data and tutors the user how to set up a problem. Section 6 describes the output results and the error messages which may be encountered during execution. Users who only wish to learn how to run the code without understanding the theory can start from section 4 and use sections 2 and 3 as references. Finally, the VAX/VMS and the IBM execution command files together with sample input records are provided in the appendices at the end of this manual.
Elastic wavefield migration and tomography
NASA Astrophysics Data System (ADS)
Duan, Yuting
Wavefield migration and tomography are well-developed under the acoustic assumption; however, multicomponent recorded seismic data include shear waves (S-modes) in addition to the compressional waves (P-modes). Constructing multicomponent wavefields and considering multiparameter model properties make it possible to utilize information provided by various wave modes, and this information allows for better characterization of the subsurface. In my thesis, I apply popular wavefield imaging and tomography to elastic media, and propose methods to address challenges posed by elastic multicomponent wavefields and multiparameter models. The key novelty of my research consists of new elastic imaging conditions, which generate elastic images with improved qualities and clear physical meaning. Moreover, I demonstrate an elastic wavefield tomography method to obtain realistic elastic models which benefits elastic migration. Migration techniques, including conventional RTM, extended RTM, and least-squares RTM (LSRTM), provide images of subsurface structures. I propose one imaging condition that computes potential images (PP, PS, SP, and SS). This imaging condition exploits pure P- and S-modes obtained by Helmholtz decomposition and corrects for the polarity reversal in PS and SP images. Using this imaging condition, I propose methods for conventional RTM and extended RTM. The extended imaging condition makes it possible to compute angle gathers for converted waves. The amplitudes of the scalar images indicate reflectivities, which can be used for amplitude verse offset (AVO) analysis; however, this imaging condition requires knowledge of the geologic dip. I propose a second imaging condition that computes perturbation images, i.e., P and S velocity perturbations. Because these images correspond to perturbations to material properties that are angle-independent, they do not have polarity reversals; therefore, they do not need dip information for polarity correction. I use this
Elastic actuation for legged locomotion
NASA Astrophysics Data System (ADS)
Cao, Chongjing; Conn, Andrew
2017-04-01
The inherent elasticity of dielectric elastomer actuators (DEAs) gives this technology great potential in energy efficient locomotion applications. In this work, a modular double cone DEA is developed with reduced manufacturing and maintenance time costs. This actuator can lift 45 g of mass (5 times its own weight) while producing a stroke of 10.4 mm (23.6% its height). The contribution of the elastic energy stored in antagonistic DEA membranes to the mechanical work output is experimentally investigated by adding delay into the DEA driving voltage. Increasing the delay time in actuation voltage and hence reducing the duty cycle is found to increase the amount of elastic energy being recovered but an upper limit is also noticed. The DEA is then applied to a three-segment leg that is able to move up and down by 17.9 mm (9% its initial height), which demonstrates the feasibility of utilizing this DEA design in legged locomotion.
Photoacoustic elastic oscillation and characterization.
Gao, Fei; Feng, Xiaohua; Zheng, Yuanjin
2015-08-10
Photoacoustic imaging and sensing have been studied extensively to probe the optical absorption of biological tissue in multiple scales ranging from large organs to small molecules. However, its elastic oscillation characterization is rarely studied and has been an untapped area to be explored. In literature, photoacoustic signal induced by pulsed laser is commonly modelled as a bipolar "N-shape" pulse from an optical absorber. In this paper, the photoacoustic damped oscillation is predicted and modelled by an equivalent mass-spring system by treating the optical absorber as an elastic oscillator. The photoacoustic simulation incorporating the proposed oscillation model shows better agreement with the measured signal from an elastic phantom, than conventional photoacoustic simulation model. More interestingly, the photoacoustic damping oscillation effect could potentially be a useful characterization approach to evaluate biological tissue's mechanical properties in terms of relaxation time, peak number and ratio beyond optical absorption only, which is experimentally demonstrated in this paper.
Functors of White Noise Associated to Characters of the Infinite Symmetric Group
NASA Astrophysics Data System (ADS)
Bożejko, Marek; Guţă, Mădălin
The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state:
NASA Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.
1983-01-01
The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.
Biaxial load effects on the crack border elastic strain energy and strain energy rate
NASA Technical Reports Server (NTRS)
Eftis, J.; Subramonian, N.; Liebowitz, H.
1977-01-01
The validity of the singular solution (first term of a series representation) is investigated for the crack tip stress and displacement field in an infinite sheet with a flat line crack with biaxial loads applied to the outer boundaries. It is shown that if one retains the second contribution to the series approximations for stress and displacement in the calculation of the local elastic strain energy density and elastic strain energy rate in the crack border region, both these quantities have significant biaxial load dependency. The value of the J-integral does not depend on the presence of the second term of the series expansion for stress and displacement. Thus J(I) is insensitive to the presence of loads applied parallel to the plane of the crack.
Anti-phase synchronization and ergodicity in arrays of oscillators coupled by an elastic force
NASA Astrophysics Data System (ADS)
Dilão, Rui
2014-04-01
We have proposed a mechanism of interaction between two non-linear dissipative oscillators, leading to exact and robust anti-phase and in-phase synchronization. The system we have analyzed is a model for the Huygens's two pendulum clocks system, as well as a model for synchronization mediated by an elastic media. Here, we extend these results to arrays, finite or infinite, of conservative pendula coupled by linear elastic forces. We show that, for two interacting pendula, this mechanism leads always to synchronized anti-phase small amplitude oscillations, and it is robust upon variation of the parameters. For three or more interacting pendula, this mechanism leads always to ergodic non-synchronized oscillations. In the continuum limit, the pattern of synchronization is described by a quasi-periodic longitudinal wave.
Dynamic Wrinkling and Strengthening of an Elastic Filament in a Viscous Fluid
NASA Astrophysics Data System (ADS)
Chopin, Julien; Dasgupta, Moumita; Kudrolli, Arshad
2017-08-01
We investigate the wrinkling dynamics of an elastic filament immersed in a viscous fluid submitted to compression at a finite rate with experiments and by combining geometric nonlinearities, elasticity, and slender body theory. The drag induces a dynamic lateral reinforcement of the filament leading to growth of wrinkles that coarsen over time. We discover a new dynamical regime characterized by a time scale with a nontrivial dependence on the loading rate, where the growth of the instability is superexponential and the wave number is an increasing function of the loading rate. We find that this time scale can be interpreted as the characteristic time over which the filament transitions from the extensible to the inextensible regime. In contrast with our analysis with moving boundary conditions, Biot's analysis in the limit of infinitely fast loading leads to rate independent exponential growth and wavelength.
NASA Astrophysics Data System (ADS)
Hashimoto, Hiroshi; Kim, Min-Geun; Abe, Kazuhisa; Cho, Seonho
2013-10-01
This paper presents a level set-based topology optimization method for noise barriers formed from an assembly of scatterers. The scattering obstacles are modeled by elastic bodies arranged periodically along the wall. Due to the periodicity, the problem can be reduced to that in a unit cell. The interaction between the elastic scatterers and the acoustic field is described in the context of the level set analysis. The semi-infinite acoustic wave regions located on the both sides of the barrier are represented by impedance matrices. The objective function is defined by the energy transmission passing the barrier. The design sensitivity is evaluated analytically by the aid of adjoint equations. The dependency of the optimal profile on the stiffness of scatterers and on the target frequency band is examined. The feasibility of the developed optimization method is proved through numerical examples.
NASA Astrophysics Data System (ADS)
Baek, Dooyoung; Hemthavy, Pasomphone; Takahashi, Kunio
2014-08-01
Contact between a silica glass lens and silicone rubber is experimentally investigated by simultaneously measuring displacement, force and contact radius. The relationship between these three parameters is derived using elastic theory. The discrepancy between the theoretical relationship and the experimental results is observed to increase as the deformation of the silicone rubber increases. Under smaller deformation conditions, the elastic theory shows good agreement with the experimental results, although infinite stress on the edge of the contact area is predicted in the theory, and time dependence and adhesion hysteresis are observed in all experiments. It is suggested that time dependence and adhesion hysteresis in contact are not induced by the deformation of the bulk of the silicone rubber, but are induced by surface effects. The result suggests that the applicability limit of the elastic theory must be carefully considered in the JKR analysis of point contact for polymers.
Thermal Fluctuations and Rubber Elasticity
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Goldbart, Paul M.; Radzihovsky, Leo
2007-02-01
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.
Thermal fluctuations and rubber elasticity.
Xing, Xiangjun; Goldbart, Paul M; Radzihovsky, Leo
2007-02-16
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.
NASA Technical Reports Server (NTRS)
Bhatia, A. K.
2003-01-01
Precision calculations for e^{-}-H and e^{-}-He^{+} for S-wave scattering in the elastic region have been carried out using the optical potential approach. This formalism is now extended to e^{-}-H P-wave scattering in the elastic region. The scattering equations are solved by the non-iterative method. Phase shifts are calculated using Hylleraas-type correlation functions up to 84 terms. Results are rigorous lower bounds to the exact phase shifts and they are compared to those obtained in previous calculations.
Cellular Uptake of Elastic Nanoparticles
NASA Astrophysics Data System (ADS)
Yi, Xin; Shi, Xinghua; Gao, Huajian
2011-08-01
A fundamental understanding of cell-nanomaterial interaction is of essential importance to nanomedicine and safe applications of nanotechnology. Here we investigate the adhesive wrapping of a soft elastic vesicle by a lipid membrane. We show that there exist a maximum of five distinct wrapping phases based on the stability of full wrapping, partial wrapping, and no wrapping states. The wrapping phases depend on the vesicle size, adhesion energy, surface tension of membrane, and bending rigidity ratio between vesicle and membrane. These results are of immediate interest to the study of vesicular transport and endocytosis or phagocytosis of elastic particles into cells.
Wave excited motion of a body floating on water confined between two semi-infinite ice sheets
NASA Astrophysics Data System (ADS)
Ren, K.; Wu, G. X.; Thomas, G. A.
2016-12-01
The wave excited motion of a body floating on water confined between two semi-infinite ice sheets is investigated. The ice sheet is treated as an elastic thin plate and water is treated as an ideal and incompressible fluid. The linearized velocity potential theory is adopted in the frequency domain and problems are solved by the method of matched eigenfunctions expansion. The fluid domain is divided into sub-regions and in each sub-region the velocity potential is expanded into a series of eigenfunctions satisfying the governing equation and the boundary conditions on horizontal planes including the free surface and ice sheets. Matching is conducted at the interfaces of two neighbouring regions to ensure the continuity of the pressure and velocity, and the unknown coefficients in the expressions are obtained as a result. The behaviour of the added mass and damping coefficients of the floating body with the effect of the ice sheets and the excitation force are analysed. They are found to vary oscillatorily with the wave number, which is different from that for a floating body in the open sea. The motion of the body confined between ice sheets is investigated, in particular its resonant behaviour with extremely large motion found to be possible under certain conditions. Standing waves within the polynya are also observed.
The influence of gravity on the steady propagation of a semi-infinite bubble into a flexible channel
NASA Astrophysics Data System (ADS)
Hazel, Andrew L.; Heil, Matthias
2008-09-01
Motivated by discrepancies between recent bench-top experiments [A. Juel and A. Heap, J. Fluid Mech. 572, 287 (2007)] and numerical simulations [A. L. Hazel and M. Heil, ASME J. Biomech. Eng. 128, 573 (2006)] we employ computational methods to examine the effects of transverse gravity on the steady propagation of a semi-infinite, inviscid air finger into a two-dimensional elastic channel filled with a Newtonian fluid. The special case of propagation in a rigid channel is also discussed in Appendix B. The coupled free-surface, fluid-structure-interaction problem is solved numerically using the object-oriented multiphysics finite-element library OOMPH-LIB. In the absence of gravity the relationship between the applied pressure and the propagation speed of the finger is nonmonotonic, with a turning point at small values of the propagation speed. We demonstrate that the turning point disappears when a modest gravitational force is applied and conjecture that it is this effect of gravity rather than any instability of the zero-gravity solution, as postulated in previous studies, that explains why the turning point has never been observed in experiments. At large propagation speeds, the presence of transverse gravity is shown to increase the pressure required to drive the air finger at a given speed, which is consistent with the observed discrepancies between previous zero-gravity simulations and the experimental results. Finally, we briefly discuss the possible implications of our results for the physiological problem of pulmonary airway reopening.
Order and Chaos in Some Deterministic Infinite Trigonometric Products
NASA Astrophysics Data System (ADS)
Albert, Leif; Kiessling, Michael K.-H.
2017-08-01
It is shown that the deterministic infinite trigonometric products \\prod _{n\\in N}[ 1- p +p cos ( style n^{-s}_{_{}}t) ] =: {{ Cl }_{p;s}^{}}(t) with parameters p\\in (0,1] & s>1/2, and variable t\\in R, are inverse Fourier transforms of the probability distributions for certain random series Ω p^ζ (s) taking values in the real ω line; i.e. the {{ Cl }_{p;s}^{}}(t) are characteristic functions of the Ω p^ζ (s). The special case p=1=s yields the familiar random harmonic series, while in general Ω p^ζ (s) is a "random Riemann-ζ function," a notion which will be explained and illustrated—and connected to the Riemann hypothesis. It will be shown that Ω p^ζ (s) is a very regular random variable, having a probability density function (PDF) on the ω line which is a Schwartz function. More precisely, an elementary proof is given that there exists some K_{p;s}^{}>0, and a function F_{p;s}^{}(|t|) bounded by |F_{p;s}^{}(|t|)|!≤ \\exp \\big (K_{p;s}^{} |t|^{1/(s+1)}), and C_{p;s}^{} =-1/s\\int _0^∞ ln |{1-p+p cos ξ }|1/ξ ^{1+1/s}{d}ξ , such that \\forall t\\in R:\\quad {{ Cl }_{p;s}^{}}(t) = \\exp \\bigl ({- C_{p;s}^{} |t|^{1/s}\\bigr )F_{p;s}^{}(|t|)}; the regularity of Ω p^ζ (s) follows. Incidentally, this theorem confirms a surmise by Benoit Cloitre, that ln {{ Cl }_{{{1}/{3}};2}^{}}(t) ˜ -C√{t} ( t→ ∞) for some C>0. Graphical evidence suggests that {{ Cl }_{{{1}/{3}};2}^{}}(t) is an empirically unpredictable (chaotic) function of t. This is reflected in the rich structure of the pertinent PDF (the Fourier transform of {{ Cl }_{{{1}/{3}};2}^{}}), and illustrated by random sampling of the Riemann-ζ walks, whose branching rules allow the build-up of fractal-like structures.
Instability of flow around a rotating, semi-infinite cylinder
NASA Astrophysics Data System (ADS)
Derebail Muralidhar, Srikanth; Pier, Benoît; Scott, Julian F.
2016-09-01
Stability of flow around a rotating, semi-infinite cylinder placed in an axial stream is investigated. Assuming large Reynolds number, the basic flow is computed numerically as described by Derebail Muralidhar et al. [Proc. R. Soc. London, Ser. A 472, 20150850 (2016), 10.1098/rspa.2015.0850], while numerical solution of the local stability equations allows calculation of the modal growth rates and hence determination of flow stability or instability. The problem has three nondimensional parameters: the Reynolds number Re , the rotation rate S , and the axial location Z . Small amounts of rotation are found to strongly affect flow stability. This is the result of a nearly neutral mode of the nonrotating cylinder which controls stability at small S . Even small rotation can produce a sufficient perturbation that the mode goes from decaying to growing, with obvious consequences for stability. Without rotation, the flow is stable below a Reynolds number of about 1060 and also beyond a threshold Z . With rotation, no matter how small, instability is no longer constrained by a minimum Re nor a maximum Z . In particular, the critical Reynolds number goes to zero as Z →∞ , so the flow is always unstable at large enough axial distances from the nose. As Z is increased, the flow goes from stability at small Z to instability at large Z . If the critical Reynolds number is a monotonic decreasing function of Z , as it is for S between about 0.0045 and 5, there is a single boundary in Z , which separates the stable from the unstable part of the flow. On the other hand, when the critical Reynolds number is nonmonotonic, there can, depending on the choice of Re , be several such boundaries and flow stability switches more than once as Z is increased. Detailed results showing the critical Reynolds number as a function of Z for different rotation rates are given. We also obtain an asymptotic expansion of the critical Reynolds number at large Z and use perturbation theory to
Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth
NASA Astrophysics Data System (ADS)
Mohapatra, Smrutiranjan
2017-08-01
In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.
Spin and wedge representations of infinite-dimensional Lie algebras and groups
Kac, Victor G.; Peterson, Dale H.
1981-01-01
We suggest a purely algebraic construction of the spin representation of an infinite-dimensional orthogonal Lie algebra (sections 1 and 2) and a corresponding group (section 4). From this we deduce a construction of all level-one highest-weight representations of orthogonal affine Lie algebras in terms of creation and annihilation operators on an infinite-dimensional Grassmann algebra (section 3). We also give a similar construction of the level-one representations of the general linear affine Lie algebra in an infinite-dimensional “wedge space.” Along these lines we construct the corresponding representations of the universal central extension of the group SLn(k[t,t-1]) in spaces of sections of line bundles over infinite-dimensional homogeneous spaces (section 5). PMID:16593029
High-energy scatterings in infinite-derivative field theory and ghost-free gravity
NASA Astrophysics Data System (ADS)
Talaganis, Spyridon; Mazumdar, Anupam
2016-07-01
In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet.
NASA Astrophysics Data System (ADS)
Chainais, P.
2006-05-01
The framework of infinitely divisible scaling was first developed to analyse the statistical intermittency of turbulence in fluid dynamics. It also reveals a powerful tool to describe and model various situations including Internet traffic, financial time series, textures ... A series of recent works introduced the infinitely divisible cascades in 1 dimension, a family of multifractal processes that can be easily synthesized numerically. This work extends the definition of infinitely divisible cascades from 1 dimension to d dimensions in the scalar case. Thus, a class of models is proposed both for data analysis and for numerical simulation in dimension d≥1. In this article, we give the definitions and main properties of infinitely divisible cascades in d dimensions. Then we focus on the modelling of statistical intermittency in turbulent flows. Several other applications are considered.
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
Robustness Elasticity in Complex Networks
Matisziw, Timothy C.; Grubesic, Tony H.; Guo, Junyu
2012-01-01
Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems. PMID:22808060
Elastic modes and their computation
Hedstrom, G.W.
1995-04-01
In this note we summarize the theory of modes in stratified elastic media, and we discuss some of the considerations necessary to achieve reliable numerical computations. We also point out the consequences of the fact that the corresponding eigenvalue problem is not selfadjoint. 14 refs.
Duration of an Elastic Collision
ERIC Educational Resources Information Center
de Izarra, Charles
2012-01-01
With a pedagogical goal, this paper deals with a study of the duration of an elastic collision of an inflatable spherical ball on a planar surface suitable for undergraduate studies. First, the force generated by the deformed spherical ball is obtained under assumptions that are discussed. The study of the motion of the spherical ball colliding…
[Use of elastic compression stockings].
Kallestrup, Lisbeth; Søgaard, Tine; Schjødt, Inge; Grove, Erik Lerkevang
2014-08-04
Post-thrombotic syndrome (PTS) is caused by venous insufficiency and is a frequent complication of deep venous thrombosis. Patients with PTS have reduced quality of life and an increased risk of recurrent deep venous thrombosis. Importantly, the risk of PTS is halved by the use of elastic compression stockings. This review outlines important practical aspects related to correct clinical use of these stockings.
Duration of an Elastic Collision
ERIC Educational Resources Information Center
de Izarra, Charles
2012-01-01
With a pedagogical goal, this paper deals with a study of the duration of an elastic collision of an inflatable spherical ball on a planar surface suitable for undergraduate studies. First, the force generated by the deformed spherical ball is obtained under assumptions that are discussed. The study of the motion of the spherical ball colliding…
HEMP. Hydrodynamic Elastic Magneto Plastic
Wilkins, M.L.; Levatin, J.A.
1985-02-01
The HEMP code solves the conservation equations of two-dimensional elastic-plastic flow, in plane x-y coordinates or in cylindrical symmetry around the x-axis. Provisions for calculation of fixed boundaries, free surfaces, pistons, and boundary slide planes have been included, along with other special conditions.
Pilot Study of Debt Elasticity
ERIC Educational Resources Information Center
Greiner, Keith; Girardi, Tony
2006-01-01
This report examines the relationship between student loan debt and the manner in which that debt is described. It focuses on three forms of description: (1) monthly payments, (2) total debt, and (3) income after graduation. The authors used the term elasticity to describe the relationship between consumers' college choices and the retention…
NASA Astrophysics Data System (ADS)
Catrysse, Peter B.; Fan, Shanhui
2015-03-01
Media that are described by extreme electromagnetic parameters, such as very large/small permittivity/permeability, have generated significant fundamental and applied interest in recent years. Notable examples include epsilon-near-zero, ultra-low refractive-index, and ultra-high refractive-index materials. Many photonic structures, such as waveguides, lenses, and photonic band gap materials, benefit greatly from the large index contrast provided by such media. In this paper, I discuss our recent work on media with infinite anisotropy, i.e., infinite permittivity (permeability) in one direction and finite in the other directions. As an illustration of the unusual optical behaviors that result from infinite anisotropy, I describe efficient light transport in deep-subwavelength apertures filled with infinitely anisotropic media. I then point out some of the opportunities that exist for controlling light at the nano-scale using infinitely anisotropic media by themselves. First, I show that a single medium with infinite anisotropy enables diffraction-free propagation of deep-subwavelength beams. Next, I demonstrate interfaces between two infinitely anisotropic media that are impedancematched for complete deep-subwavelength beams and enable reflection-free routing with zero bend radius that is entirely free from diffraction effects even when deep-subwavelength information is encoded on the beams. These behaviors indicate an unprecedented possibility to use media with infinite anisotropy to manipulate beams with deepsubwavelength features, including complete images. To illustrate physical realizability, I demonstrate a metamaterial design using existing materials in a planar geometry, which can be implemented using well-established nanofabrication techniques. This approach provides a path to deep-subwavelength routing of information-carrying beams and far-field imaging unencumbered by diffraction and reflection.
Infinite product expansion of the Fokker–Planck equation with steady-state solution
Martin, R. J.; Craster, R. V.; Kearney, M. J.
2015-01-01
We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples. PMID:26346100
Noise Prevents Infinite Stretching of the Passive Field in a Stochastic Vector Advection Equation
NASA Astrophysics Data System (ADS)
Flandoli, Franco; Maurelli, Mario; Neklyudov, Mikhail
2014-09-01
A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.
Distributed Reinforcement Learning for Policy Synchronization in Infinite-Horizon Dec-POMDPs
2012-01-01
REPORT Distributed Reinforcement Learning for PolicySynchronization in Infinite-Horizon Dec-POMDPs 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: In many...ADDRESSES U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Dec-POMDPs, reinforcement learning , multi...Rev 8/98) Prescribed by ANSI Std. Z39.18 - Distributed Reinforcement Learning for PolicySynchronization in Infinite-Horizon Dec-POMDPs Report
Harding, R.M.; Martinson, J.J.; Flint, J.; Clegg, J.B.; Boyce, A.J. )
1993-11-01
Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. The authors show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. The authors use sampling theory to confirm the intrinsically poor fit to the infinite model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. 25 refs., 20 figs., 4 tabs.
NASA Astrophysics Data System (ADS)
Camacho, Miguel; Boix, Rafael R.; Medina, Francisco
2016-06-01
The authors present a computationally efficient technique for the analysis of extraordinary transmission through both infinite and truncated periodic arrays of slots in perfect conductor screens of negligible thickness. An integral equation is obtained for the tangential electric field in the slots both in the infinite case and in the truncated case. The unknown functions are expressed as linear combinations of known basis functions, and the unknown weight coefficients are determined by means of Galerkin's method. The coefficients of Galerkin's matrix are obtained in the spatial domain in terms of double finite integrals containing the Green's functions (which, in the infinite case, is efficiently computed by means of Ewald's method) times cross-correlations between both the basis functions and their divergences. The computation in the spatial domain is an efficient alternative to the direct computation in the spectral domain since this latter approach involves the determination of either slowly convergent double infinite summations (infinite case) or slowly convergent double infinite integrals (truncated case). The results obtained are validated by means of commercial software, and it is found that the integral equation technique presented in this paper is at least two orders of magnitude faster than commercial software for a similar accuracy. It is also shown that the phenomena related to periodicity such as extraordinary transmission and Wood's anomaly start to appear in the truncated case for arrays with more than 100 (10 ×10 ) slots.
Spectral-infinite-element Simulations of Self-gravitating Seismic Wave Propagation
NASA Astrophysics Data System (ADS)
Gharti, H. N.; Tromp, J.
2015-12-01
Gravitational perturbations induced by particle motions are governed by the Poisson/Laplace equation, whosedomain includes all of space. Due to its unbounded nature, obtaining an accurate numerical solution is verychallenging. Consequently, gravitational perturbations are generally ignored in simulations of global seismicwave propagation, and only the unperturbed equilibrium gravitational field is taken into account. This so-called"Cowling approximation" is justified for relatively short-period waves (periods less than 250 s), but is invalidfor free-oscillation seismology. Existing methods are usually based on spherical harmonic expansions. Mostmethods are either limited to spherically symmetric models or have to rely on costly iterative implementationprocedures. We propose a spectral-infinite-element method to solve wave propagation in a self-gravitating Earthmodel. The spectral-infinite-element method combines the spectral-element method with the infinite-elementmethod. Spectral elements are used to capture the internal field, and infinite elements are used to represent theexternal field. To solve the weak form of the Poisson/Laplace equation, we employ Gauss-Legendre-Lobattoquadrature in spectral elements. In infinite elements, Gauss-Radau quadrature is used in the radial directionwhereas Gauss-Legendre-Lobatto quadrature is used in the lateral directions. Infinite elements naturally integratewith spectral elements, thereby avoiding an iterative implementation. We demonstrate the accuracy of themethod by comparing our results with a spherical harmonics method. The new method empowers us to tackleseveral problems in long-period seismology accurately and efficiently.
Elastic And Plastic Deformations In Butt Welds
NASA Technical Reports Server (NTRS)
Verderaime, V.
1992-01-01
Report presents study of mathematical modeling of stresses and strains, reaching beyond limits of elasticity, in bars and plates. Study oriented toward development of capability to predict stresses and resulting elastic and plastic strains in butt welds.
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2016-10-01
Stemming from the law of the conservation of energy in an elastic medium, this work extends the scope of the previous analysis for a scatterer immersed in a nonviscous liquid [F. G. Mitri, Ultrasonics 62, 20-26 (2015)] to the case of a (viscous) fluid circular cylinder cross-section encased in a homogeneous, isotropic, elastic matrix. Analytical expressions for the absorption, scattering, and extinction efficiencies (or cross-sections) are derived for "elastic-sheets" (i.e., finite beams in 2D propagating in elastic media) of arbitrary wavefront, in contrast to the ideal case of plane waves of infinite extent. The mathematical expressions are formulated in generalized partial-wave series expansions in cylindrical coordinates involving the beam-shape coefficients of finite elastic-sheet beams with arbitrary wavefront, and the scattering coefficients of the fluid cylinder encased in the elastic matrix. The analysis shows that in elastodynamic scattering, both the scattered L-wave as well as the scattered T-wave contribute to the time-averaged scattered efficiency (or power). However, the extinction efficiency only depends on the scattering coefficients characterizing the same type (L or T) as the incident wave. Numerical computations for the (non-dimensional energy) efficiency factors such as the absorption, scattering, and extinction efficiencies of a circular cylindrical viscous fluid cavity embedded in an elastic aluminum matrix are performed for nonparaxial focused Gaussian and Airy elastic-sheet beams with arbitrary longitudinal and transverse normally-polarized (shear) wave incidences in the Rayleigh and resonance regimes. A series of elastic resonances are manifested in the plots of the efficiencies as the non-dimensional size parameters for the L- and T-waves are varied. As the beam waist for the nonparaxial Gaussian beam increases, the plane wave result is recovered, while for a tightly focused wavefront, some of the elastic resonances can be suppressed
On the anisotropic elastic properties of hydroxyapatite.
NASA Technical Reports Server (NTRS)
Katz, J. L.; Ukraincik, K.
1971-01-01
Experimental measurements of the isotropic elastic moduli on polycrystalline specimens of hydroxyapatite and fluorapatite are compared with elastic constants measured directly from single crystals of fluorapatite in order to derive a set of pseudo single crystal elastic constants for hydroxyapatite. The stiffness coefficients thus derived are given. The anisotropic and isotropic elastic properties are then computed and compared with similar properties derived from experimental observations of the anisotropic behavior of bone.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
2015-07-01
approximate 3D solution for the stress distribution around a circular cylindrical hole in an infinite plate of arbitrary thickness. They did this by...UNCLASSIFIED UNCLASSIFIED Linear-Elastic 2D and 3D Finite Element Contact Analysis of a Hole Containing a Circular Insert in a Fatigue Test...large numbers of circular holes that are fitted with fasteners such as bolts or rivets. During the service life of aircraft, fatigue damage often occurs
NASA Astrophysics Data System (ADS)
Zhao, Xue-Hui; Tian, Bo; Liu, De-Yin; Wu, Xiao-Yu; Chai, Jun; Guo, Yong-Jiang
2017-01-01
Under investigation in this paper is a generalized (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain. Lax pair and infinitely-many conservation laws are derived, indicating the existence of the multi-soliton solutions for such an equation. Via the Hirota method with an auxiliary function, bilinear forms, dark one-, two- and three-soliton solutions are derived. Propagation and interactions for the dark solitons are illustrated graphically: Velocity of the solitons is linearly related to the coefficients of the second- and fourth-order dispersion terms, while amplitude of the solitons does not depend on them. Interactions between the two solitons are shown to be elastic, while those among the three solitons are pairwise elastic.
21 CFR 880.5075 - Elastic bandage.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Elastic bandage. 880.5075 Section 880.5075 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL... § 880.5075 Elastic bandage. (a) Identification. An elastic bandage is a device consisting of either a...
21 CFR 880.5075 - Elastic bandage.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Elastic bandage. 880.5075 Section 880.5075 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL... § 880.5075 Elastic bandage. (a) Identification. An elastic bandage is a device consisting of either a...
21 CFR 880.5075 - Elastic bandage.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Elastic bandage. 880.5075 Section 880.5075 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL... § 880.5075 Elastic bandage. (a) Identification. An elastic bandage is a device consisting of either a...
A strain-consistent elastic plate model with surface elasticity
NASA Astrophysics Data System (ADS)
Ru, C. Q.
2016-03-01
A strain-consistent elastic plate model is formulated in which both initial surface tension and the induced residual stress are treated as finite values, and the exactly same strain expressions are consistently employed for both the surface and the bulk plate. Different than most of previous related models which follow the original Gurtin-Murdoch model and include some non-strain displacement gradient terms (which cannot be expressed in terms of the surface infinitesimal strains or the von Karman-type strains) in the surface stress-strain relations, the present model does not include any non-strain displacement gradient terms in the surface stress-strain relations. For a free elastic plate with in-plane movable edges, the present model predicts that initial surface tension exactly cancels out the induced residual compressive stress. On the other hand, if all edges are in-plane immovable, residual stress cannot develop in the plate and the initial surface tension causes a tensile net membrane force. In addition, the present model predicts that initial surface tension reduces the effective bending rigidity of the plate, while this reduction does not depend on Poisson ratio. In particular, self-buckling of a free elastic plate under tensile surface tension cannot occur unless the effective bending rigidity of plate vanishes or becomes negative.
Elastic heterogeneity in metallic glasses.
Dmowski, , W.; Iwashita, T.; Chuang, C.-P.; Almer, J. D; Egami, T.; X-Ray Science Division; Univ. of Tennessee; ORNL
2010-01-01
When a stress is applied on a metallic glass it deforms following Hook's law. Therefore it may appear obvious that a metallic glass deforms elastically. Using x-ray diffraction and anisotropic pair-density function analysis we show that only about 3/4 in volume fraction of metallic glasses deforms elastically, whereas the rest of the volume is anelastic and in the experimental time scale deform without resistance. We suggest that this anelastic portion represents residual liquidity in the glassy state. Many theories, such as the free-volume theory, assume the density of defects in the glassy state to be of the order of 1%, but this result shows that it is as much as a quarter.
Linear elastic fracture mechanics primer
NASA Technical Reports Server (NTRS)
Wilson, Christopher D.
1992-01-01
This primer is intended to remove the blackbox perception of fracture mechanics computer software by structural engineers. The fundamental concepts of linear elastic fracture mechanics are presented with emphasis on the practical application of fracture mechanics to real problems. Numerous rules of thumb are provided. Recommended texts for additional reading, and a discussion of the significance of fracture mechanics in structural design are given. Griffith's criterion for crack extension, Irwin's elastic stress field near the crack tip, and the influence of small-scale plasticity are discussed. Common stress intensities factor solutions and methods for determining them are included. Fracture toughness and subcritical crack growth are discussed. The application of fracture mechanics to damage tolerance and fracture control is discussed. Several example problems and a practice set of problems are given.
Vibrations of elastically restrained frames
NASA Astrophysics Data System (ADS)
Albarracín, Carlos Marcelo; Grossi, Ricardo Oscar
2005-07-01
This paper deals with the determination of eigenfrequencies of a frame which consists of a beam supported by a column and is submitted to intermediate elastic constraints. The ends of the frame are elastically restrained against rotation and translation. The individual members of the frame are assumed to be governed by the transverse and axial vibration theory of an Euler-Bernoulli beam. The boundary and eigenvalue problem which governs the dynamical behavior of the frame structure is derived using the techniques of calculus of variations. Exact values of eigenfrequencies are determined by the application of the separation of variables method. Also, results are obtained by the use of the finite element method. The natural frequencies and mode shapes are presented for a wide range of values of the restraint parameters. Several particular cases are presented and some of these have been compared with those available in the literature.
Elastic modulus of viral nanotubes
NASA Astrophysics Data System (ADS)
Zhao, Yue; Ge, Zhibin; Fang, Jiyu
2008-09-01
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5nm indentation depths and Hertz theory in 1.5nm indentation depths. The derived radial Young’s modulus of TMV nanotubes is 0.92±0.15GPa from finite-element analysis and 1.0±0.2GPa from the Hertz model, which are comparable with the reported axial Young’s modulus of 1.1GPa [Falvo , Biophys. J. 72, 1396 (1997)].
Elastic Heterogeneity in Metallic Glasses
NASA Astrophysics Data System (ADS)
Dmowski, W.; Iwashita, T.; Chuang, C.-P.; Almer, J.; Egami, T.
2010-11-01
When a stress is applied on a metallic glass it deforms following Hook’s law. Therefore it may appear obvious that a metallic glass deforms elastically. Using x-ray diffraction and anisotropic pair-density function analysis we show that only about (3)/(4) in volume fraction of metallic glasses deforms elastically, whereas the rest of the volume is anelastic and in the experimental time scale deform without resistance. We suggest that this anelastic portion represents residual liquidity in the glassy state. Many theories, such as the free-volume theory, assume the density of defects in the glassy state to be of the order of 1%, but this result shows that it is as much as a quarter.
Elastic cone for Chinese calligraphy
NASA Astrophysics Data System (ADS)
Cai, Fenglei; Li, Haisheng
2014-01-01
The brush plays an important role in creating Chinese calligraphy. We regard a single bristle of a writing brush as an elastic rod and the brush tuft absorbing ink as an elastic cone, which naturally deforms according to the force exerted on it when painting on a paper, and the brush footprint is formed by the intersection region between the deformed tuft and the paper plane. To efficiently generate brush strokes, this paper introduces interpolation and texture mapping approach between two adjacent footprints, and automatically applies bristle-splitting texture to the stroke after long-time painting. Experimental results demonstrate that our method is effective and reliable. Users can create realistic calligraphy in real time.
Structure and elasticity of glaucophane
NASA Astrophysics Data System (ADS)
Bezacier, L.; Mookherjee, M.
2012-12-01
We report equation of state and elasticity of glaucophane amphibole [Na2Mg3Al2Si8O22(OH)2] up to 9 GPa, which encompasses its experimentally observed stability field. The full elastic constant tensor reveals significantly larger stiffness along (100) plane. The [100] direction is relatively softer. This anisotropy is related to the stacking of the stiffer tetrahedral units along [010] and [001] directions within the crystal structure. Glaucophane is a dominant mineral constituent of blueschist facies rock, and has significantly lower velocities compared to garnet bearing eclogites. In addition, glaucophane is anisotropic and could account for the observed low velocity layer (LVL) in the subducting slabs at depth range within the thermodynamic stability of glaucophane.
Elastic sealants for surgical applications.
Annabi, Nasim; Yue, Kan; Tamayol, Ali; Khademhosseini, Ali
2015-09-01
Sealants have emerged as promising candidates for replacing sutures and staples to prevent air and liquid leakages during and after the surgeries. Their physical properties and adhesion strength to seal the wound area without limiting the tissue movement and function are key factors in their successful implementation in clinical practice. In this contribution, the advances in the development of elastic sealants formed from synthetic and natural materials are critically reviewed and their shortcomings are pointed out. In addition, we highlight the applications in which elasticity of the sealant is critical and outline the limitations of the currently available sealants. This review will provide insights for the development of novel bioadhesives with advanced functionality for surgical applications.
Stability of elastically supported columns
NASA Technical Reports Server (NTRS)
Niles, Alfred S; Viscovich, Steven J
1942-01-01
A criterion is developed for the stiffness required of elastic lateral supports at the ends of a compression member to provide stability. A method based on this criterion is then developed for checking the stability of a continuous beam-column. A related method is also developed for checking the stability of a member of a pin-jointed truss against rotation in the plane of the truss.
1992-12-16
12 = (K,, + )- (29) K 2 (see [3]). The parameter KM represents the amplitude of the periodic curva - ture function and sm denotes the value at which K...Additamentum De curvis elasticis. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Ser. 1., Vol. 24, Lausanne 1744. 17 [10...Mathematical Theory of Elasticity. 4th. ed., Cambridge University Press, 1927. [12] G. Nielson. Bernstein/ Bezier Curves and Splines on Spheres based upon
Improved Indentation Test for Measuring Nonlinear Elasticity
NASA Technical Reports Server (NTRS)
Eldridge, Jeffrey I.
2004-01-01
A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.
Teaching nonlinear dynamics through elastic cords
NASA Astrophysics Data System (ADS)
Chacón, R.; Galán, C. A.; Sánchez-Bajo, F.
2011-01-01
We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.
Normal stresses in elastic networks
NASA Astrophysics Data System (ADS)
Cioroianu, Adrian R.; Storm, Cornelis
2013-11-01
When loaded in simple shear deformation, polymeric materials may develop so-called normal stresses: stresses perpendicular to the direction of the applied shear. These normal stresses are intrinsically nonlinear: basic symmetry considerations dictate they may only enter at O(γ2), with γ the dimensionless shear strain. There is no fundamental restriction on their sign, and normal stresses may be positive (pushing outward) or negative (pulling inward). Most materials tend to dilate in the normal direction, but a wide variety of biopolymer networks including fibrin and actin gels have been reported to present anomalously large, negative normal stresses—a feature which has been ascribed to the intrinsic elastic nonlinearity of semiflexible fibers. In this work, we present analytical results on a model nonlinear network, which we expand to the required nonlinear order to show that due to geometric, rather than elastic, nonlinearities (negative) normal stresses generically arise in filamentous networks—even in networks composed of linear, Hookean springs. We investigate analytically and numerically how the subsequent addition of elastic nonlinearities, nonaffine deformations, and filament persistence through cross-linkers augment this basic behavior.
Phase diagram of elastic spheres.
Athanasopoulou, L; Ziherl, P
2017-02-15
Experiments show that polymeric nanoparticles often self-assemble into several non-close-packed lattices in addition to the face-centered cubic lattice. Here, we explore theoretically the possibility that the observed phase sequences may be associated with the softness of the particles, which are modeled as elastic spheres interacting upon contact. The spheres are described by two finite-deformation theories of elasticity, the modified Saint-Venant-Kirchhoff model and the neo-Hookean model. We determine the range of indentations where the repulsion between the spheres is pairwise additive and agrees with the Hertz theory. By computing the elastic energies of nine trial crystal lattices at densities far beyond the Hertzian range, we construct the phase diagram and find the face- and body-centered cubic lattices as well as the A15 lattice and the simple hexagonal lattice, with the last two being stable at large densities where the spheres are completely faceted. These results are qualitatively consistent with observations, suggesting that deformability may indeed be viewed as a generic property that determines the phase behavior in nanocolloidal suspensions.
Elastic proteins: biological roles and mechanical properties.
Gosline, John; Lillie, Margo; Carrington, Emily; Guerette, Paul; Ortlepp, Christine; Savage, Ken
2002-01-01
The term 'elastic protein' applies to many structural proteins with diverse functions and mechanical properties so there is room for confusion about its meaning. Elastic implies the property of elasticity, or the ability to deform reversibly without loss of energy; so elastic proteins should have high resilience. Another meaning for elastic is 'stretchy', or the ability to be deformed to large strains with little force. Thus, elastic proteins should have low stiffness. The combination of high resilience, large strains and low stiffness is characteristic of rubber-like proteins (e.g. resilin and elastin) that function in the storage of elastic-strain energy. Other elastic proteins play very different roles and have very different properties. Collagen fibres provide exceptional energy storage capacity but are not very stretchy. Mussel byssus threads and spider dragline silks are also elastic proteins because, in spite of their considerable strength and stiffness, they are remarkably stretchy. The combination of strength and extensibility, together with low resilience, gives these materials an impressive resistance to fracture (i.e. toughness), a property that allows mussels to survive crashing waves and spiders to build exquisite aerial filters. Given this range of properties and functions, it is probable that elastic proteins will provide a wealth of chemical structures and elastic mechanisms that can be exploited in novel structural materials through biotechnology. PMID:11911769
Elastic fingering patterns in confined lifting flows.
Fontana, João V; Miranda, José A
2016-09-01
The elastic fingering phenomenon occurs when two confined fluids are brought into contact, and due to a chemical reaction, the interface separating them becomes elastic. We study elastic fingering pattern formation in Newtonian fluids flowing in a lifting (time-dependent gap) Hele-Shaw cell. Using a mode-coupling approach, nonlinear effects induced by the interplay between viscous and elastic forces are investigated and the weakly nonlinear behavior of the fluid-fluid interfacial patterns is analyzed. Our results indicate that the existence of the elastic interface allows the development of unexpected morphological behaviors in such Newtonian fluid flow systems. More specifically, we show that depending on the values of the governing physical parameters, the observed elastic fingering structures are characterized by the occurrence of either finger tip splitting or side branching. The impact of the elastic interface on finger-competition events is also discussed.
Elastic and transition form factors of the Δ(1232)
Segovia, Jorge; Chen, Chen; Cloet, Ian C.; ...
2013-12-10
Predictions obtained with a confining, symmetry-preserving treatment of a vector Ⓧ vector contact interaction at leading-order in a widely used truncation of QCD’s Dyson–Schwinger equations are presented for Δ and Ω baryon elastic form factors and the γN → Δ transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest.more » The Δ elastic form factors are very sensitive to mΔ. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-baryon’s quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Δ-baryon’s deformation in the infinite momentum frame. Furthermore, results for analogous properties of the Ω baryon are less contentious. In connection with the N → Δ transition, the Ash-convention magnetic transition form factor falls faster than the neutron’s magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.« less
Elastic and transition form factors of the Δ(1232)
Segovia, Jorge; Chen, Chen; Cloet, Ian C.; Roberts, Craig D.; Schmidt, Sebastian M.; Wan, Shaolong
2013-12-10
Predictions obtained with a confining, symmetry-preserving treatment of a vector Ⓧ vector contact interaction at leading-order in a widely used truncation of QCD’s Dyson–Schwinger equations are presented for Δ and Ω baryon elastic form factors and the γN → Δ transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The Δ elastic form factors are very sensitive to m_{Δ}. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-baryon’s quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Δ-baryon’s deformation in the infinite momentum frame. Furthermore, results for analogous properties of the Ω baryon are less contentious. In connection with the N → Δ transition, the Ash-convention magnetic transition form factor falls faster than the neutron’s magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.
Emittance Growth in Intense Non-Circular Beams
NASA Astrophysics Data System (ADS)
Anderson, O. A.
1997-05-01
The electrostatic energy of intense beams in linear uniform focusing channels is minimized when the initial beam configuration is both uniform and round.(In the case of quadrupole focusing, this means round on the average.) Deviations from either uniformity or roundness produce free energy and emittance growth. Over the past 25 years, the consequences of beam nonuniformity have been thoroughly investigated for the case of round beams. Recently, there has been interest in more complex beam configurations such as those that occur in Heavy Ion Fusion (HIF) combiners or splitters. We discuss free energy and emittance growth for a variety of cases: (a) square beams, (b) hexagonal beams, (c) beams bounded by a quadrant or sextant of a circle, (d) rectangular beams, (e) elliptical beams, (f) pairs of beamlets, and (g) arrays of many beamlets. Cases (a) and (b) are approximations for large arrays of beamlets as proposed for HIF combiners or for negative-ion sources. Beam splitting, suggested for a particular HIF final focus scheme, leads to (c). The large emittance growth in cases (d)-(f), calculated by a new method,(O.A. Anderson, Proceedings of EPAC 96 conference.) illustrates the importance of maintaining symmetry. Practical examples are given for several cases.
NASA Technical Reports Server (NTRS)
Walker, Kevin P.; Freed, Alan D.; Jordan, Eric H.
1993-01-01
Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.
Interaction between one-dimensional dark spatial solitons and semi-infinite dark stripes
NASA Astrophysics Data System (ADS)
Hansinger, Peter; Maleshkov, Georgi; Gorunski, Nasko; Dimitrov, Nikolay; Dreischuh, Alexander; Paulus, Gerhard G.
2014-02-01
In this work we numerically study the evolution and interaction of one-dimensional (1-D) dark spatial solitons and semi-infinite dark stripes (SIDSs) in a local self-defocusing Kerr nonlinear medium. The experimental results in the linear regime of propagation confirm that the SIDS bending and fusion with the infinite 1-D dark beam modeled for negative nonlinearity is due to the opposite phase semi-helicities of SID beam ends. Results for several interaction scenaria show that bending ends of the semi-infinite dark stripes splice to the 1-D dark beam to form structures resembling waveguide couplers/branchers. Well pronounced modulational stability of 1-D dark spatial solitons under strong symmetric background beam modulation from decaying SIDSs is predicted.
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.
Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I
2008-12-19
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.
The effect of semi-infinite crystalline electrodes on transmission of gold atomic wires using DFT
NASA Astrophysics Data System (ADS)
Sattar, Abdul; Amjad, Raja Junaid; Yasmeen, Sumaira; Javed, Hafsa; Latif, Hamid; Mahmood, Hasan; Iqbal, Azmat; Usman, Arslan; Akhtar, Majid Niaz; Khan, Salman Naeem; Dousti, M. R.
2016-05-01
First principle calculations of the conductance of gold atomic wires containing chain of 3-8 atoms each with 2.39 Å bond lengths are presented using density functional theory. Three different configurations of wire/electrodes were used. For zigzag wire with semi-infinite crystalline electrodes, even-odd oscillation is observed which is consistent with the previously reported results. A lower conductance is observed for the chain in semi-infinite crystalline electrodes compared to the chains suspended in wire-like electrode. The calculated transmission spectrum for the straight and zig-zag wires suspended between semi-infinite crystalline electrodes showed suppression of transmission channels due to electron scattering occurring at the electrode-wire interface.
On the way from infinite layer compounds to atomic engineering of superconducting cuprates
NASA Astrophysics Data System (ADS)
Lagues, Michel; Beuran, C. F.; Deville Cavellin, C.; Eustache, B.; Germain, Philippe; Hatterer, C.; Mairet, V.; Partiot, C.; Xie, X. M.; Xu, Xiang Z.
1996-07-01
The quest for new cuprates compounds exhibiting superconducting properties at elevated temperatures was intensified recently. The synthesis under high pressure led first to an increased Tc record of around 160K with Hg compounds, and second to new bulk compounds including Cu, CO3 and infinite layer families. Meanwhile the results concerning thin films of new cuprates, even grown by atomic layering, were not as convincing. We describe here the growth of infinite layer related compounds with emphasis on the growth mechanisms. The deposition is performed in the range of 500 to 550 degrees C under atomic oxygen, using real time control by RHEED intensity. Various deposition sequences were used leading mainly to two basic families. The first one belongs to the infinite layer family, while the other one seems to belong to the spin ladder Can-1Cun+1O2n family. Transport properties in a wide range of temperatures are presented and discussed.
Energy-fluctuation relaxation towards equilibrium in an infinite chain of anharmonic oscillators
NASA Astrophysics Data System (ADS)
Mannella, R.; Fronzoni, L.
1991-05-01
This study tries to extend results observed in finite chains, like slowing-down effects and stretched-exponential decays, into the thermodynamic limit. An infinite chain of nonlinear oscillators is related to pairs of coupled anharmonic modes, where each mode is coupled to an infinite number of harmonic oscillators (thermal baths). For the model of the two coupled infinite chains, the analytical treatment leads very naturally to a ``critical'' energy below which slowing-down effects and stretched-exponential decays should appear. Also, the model yields a zero-energy threshold for the onset of energy sharing between modes, suggesting that chaos should set in for arbitrarily small energies of the Hamiltonian. The theory is confirmed by digital simulations. These results seem to support the phenomenology observed in models with finite degrees of freedom, suggesting that this behavior survives in the thermodynamic limit and it is perhaps a common feature of chains of coupled anharmonic oscillators.
Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data
NASA Astrophysics Data System (ADS)
Côte, Delphine; Côte, Raphaël
2017-03-01
We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).
Monte Carlo method for critical systems in infinite volume: The planar Ising model.
Herdeiro, Victor; Doyon, Benjamin
2016-10-01
In this paper we propose a Monte Carlo method for generating finite-domain marginals of critical distributions of statistical models in infinite volume. The algorithm corrects the problem of the long-range effects of boundaries associated to generating critical distributions on finite lattices. It uses the advantage of scale invariance combined with ideas of the renormalization group in order to construct a type of "holographic" boundary condition that encodes the presence of an infinite volume beyond it. We check the quality of the distribution obtained in the case of the planar Ising model by comparing various observables with their infinite-plane prediction. We accurately reproduce planar two-, three-, and four-point of spin and energy operators. We also define a lattice stress-energy tensor, and numerically obtain the associated conformal Ward identities and the Ising central charge.
Distributions of time averages for weakly chaotic systems: The role of infinite invariant density
NASA Astrophysics Data System (ADS)
Korabel, Nickolay; Barkai, Eli
2013-09-01
Distributions of time averaged observables are investigated using deterministic maps with N indifferent fixed points and N-state continuous time random walk processes associated with them. In a weakly chaotic phase, namely when separation of trajectories is subexponential, maps are characterized by an infinite invariant density. We find that the infinite density can be used to calculate the distribution of time averages of integrable observables with a formula recently obtained by Rebenshtok and Barkai. As an example we calculate distributions of the average position of the particle and average occupation fractions. Our work provides the distributional limit theorem for time averages for a wide class of nonintegrable observables with respect to the infinite invariant density, in other words it deals with the situation where the Darling-Kac-Aaronson theorem does not hold.
NASA Astrophysics Data System (ADS)
Hwang, M.; Podloucky, R.; Gonis, A.; Freeman, A. J.
1986-01-01
Results of exact and analytic calculations of the electronic densities of states (DOS's) associated with semi-infinite substitutionally disordered chains are presented using the exact position-space renormalization-group (PSRG) method, the augmented-space (AS) formalism, and the embedded-cluster method (ECM). In addition to total DOS's, the PSRG method allows the calculation of exact partial DOS's associated with local atomic configurations in a disordered material. Comparisons with the exact results indicate that as in the case of infinite materials the ECM provides a reliable method for the calculation of single-particle properties, such as the DOS, of semi-infinite systems. Furthermore, the ECM is found to be much more accurate than the AS formalism, especially in the case of concentrated substitutionally disordered alloys.
Infinite-Dimensional Schur-Weyl Duality and the Coxeter-Laplace Operator
NASA Astrophysics Data System (ADS)
Tsilevich, N. V.; Vershik, A. M.
2014-05-01
We extend the classical Schur-Weyl duality between representations of the groups and to the case of and the infinite symmetric group . Our construction is based on a "dynamic," or inductive, scheme of Schur-Weyl dualities. It leads to a new class of representations of the infinite symmetric group, which has not appeared earlier. We describe these representations and, in particular, find their spectral types with respect to the Gelfand-Tsetlin algebra. The main example of such a representation acts in an incomplete infinite tensor product. As an important application, we consider the weak limit of the so-called Coxeter-Laplace operator, which is essentially the Hamiltonian of the XXX Heisenberg model, in these representations.
Stationary solutions of SPDEs and infinite horizon BDSDEs with non-Lipschitz coefficients
NASA Astrophysics Data System (ADS)
Zhang, Qi; Zhao, Huaizhong
We prove a general theorem that the Lρ2(R;R)⊗Lρ2(R;R)-valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the Lρ2(R;R)⊗Lρ2(R;R)-valued solutions for backward doubly stochastic differential equations on finite and infinite horizon with linear growth without assuming Lipschitz conditions, but under the monotonicity condition. Therefore the solution of finite horizon problem gives the solution of the initial value problem of the corresponding stochastic partial differential equations, and the solution of the infinite horizon problem gives the stationary solution of the SPDEs according to our general result.
Hu, Zhonghan
2014-12-09
We present a unified derivation of the Ewald sum for electrostatics in a three-dimensional infinite system that is periodic in one, two, or three dimensions. The derivation leads to the Ewald3D sum being expressed as a sum of a real space contribution and a reciprocal space contribution, as in previous work. However, the k → 0 term in the reciprocal space contribution is analyzed further and found to give an additional contribution that is not part of previous reciprocal space contributions. The transparent derivation provides a unified view of the existing conducting infinite boundary term, the vacuum spherical infinite boundary term and the vacuum planar infinite boundary term for the Ewald3D sum. The derivation further explains that the infinite boundary term is conditional for the Ewald3D sum because it depends on the asymptotic behavior that the system approaches the infinite in 3D but it becomes a definite term for the Ewald2D or Ewald1D sum irrespective of the asymptotic behavior in the reduced dimensions. Moreover, the unified derivation yields two formulas for the Ewald sum in one-dimensional periodicity, and we rigorously prove that the two formulas are equivalent. These formulas might be useful for simulations of organic crystals with wirelike shapes or liquids confined in uniform cylinders. More importantly, the Ewald3D, Ewald2D, and Ewald1D sums are further written as sums of well-defined pairwise potentials overcoming the difficulty in splitting the total Coulomb potential energy into contributions from each individual group of charges. The pairwise interactions with their clear physical meaning of the explicit presence of the periodic images thus can be used to consistently perform analysis based on the trajectories from computer simulations of bulk or interfaces.
Euler-Lagrange Elasticity: elasticity without stress or strain
NASA Astrophysics Data System (ADS)
Hardy, Humphrey
2014-03-01
A Euler-Lagrange (E-L) approach to elasticity is proposed that produces differential equations of elasticity without the need to define stress or strain tensors. The positions of the points within the body are the independent parameters instead of strain. Force replaces stress. The advantage of this approach is that the E-L differential equations are the same for both infinitesimal and finite deformations. Material properties are expressed in terms of the energy of deformation. The energy is expressed as a function of the principal invariants of the deformation gradient tensor. This scalar invariant representation of the energy of deformation enters directly into the E-L differential equations so that there is no need to define fourth order tensor material properties. By experimentally measuring the force and displacement of materials the functional form of the energy of deformation can be determined. The E-L differential equations can be input directly into finite element, finite difference, or other numerical models. If desired, stress and stain can be calculated as dependent parameters.
Pikhitsa, Stanislaw
2017-01-01
We provide a complete classification of possible configurations of mutually pairwise-touching infinite cylinders in Euclidian three-dimensional space. It turns out that there is a maximum number of such cylinders possible in three dimensions independently of the shape of the cylinder cross-sections. We give the explanation of the uniqueness of the non-trivial configuration of seven equal mutually touching round infinite cylinders found earlier. Some results obtained for the chirality matrix, which is equivalent to the Seidel adjacency matrix, may be found useful for the theory of graphs. PMID:28280575
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1988-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
Infinite hierarchy of nonlinear Schrödinger equations and their solutions.
Ankiewicz, A; Kedziora, D J; Chowdury, A; Bandelow, U; Akhmediev, N
2016-01-01
We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.
Density functional theory study of the conformational space of an infinitely long polypeptide chain
NASA Astrophysics Data System (ADS)
Ireta, Joel; Scheffler, Matthias
2009-08-01
The backbone conformational space of infinitely long polyalanine is investigated with density-functional theory and mapping the potential energy surface in terms of (L, θ) cylindrical coordinates. A comparison of the obtained (L, θ) Ramachandran-like plot with results from an extended set of protein structures shows excellent conformity, with the exception of the polyproline II region. It is demonstrated the usefulness of infinitely long polypeptide models for investigating the influence of hydrogen bonding and its cooperative effect on the backbone conformations. The results imply that hydrogen bonding together with long-range electrostatics is the main actuator for most of the structures assumed by protein residues.
NASA Technical Reports Server (NTRS)
Balas, M. J.; Kaufman, H.; Wen, J.
1985-01-01
A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.
NASA Astrophysics Data System (ADS)
Papkov, S. O.
2015-03-01
A new asymptotically exact solution is obtained for the problem of transverse vibrations of a rectangular orthotropic plate with free edges. The general solution to the vibration equation is constructed as the sum of Fourier series with unknown coefficients, which are related by a homogeneous quasi-regular infinite system of linear algebraic equations. Analysis of the infinite system makes it possible to determine the power-law asymptotics for a nontrivial solution to the system, which makes it possible to calculate the natural vibration frequencies and to construct the corresponding eigenmodes. Examples of numerical calculations for real materials are presented.
Negative, positive, and infinite mass properties of a rotating electron beam
French, David M.; Lau, Y. Y.; Gilgenbach, R. M.; Hoff, Brad W.
2010-09-13
An electron rotating under a uniform axial magnetic field and a radial electric field exhibits an effective mass that may be negative, positive, or infinite, in response to an azimuthal electric field. This paper reports simulation results that show instability and stability when the effective mass are negative and positive, respectively, depending on the magnitude and orientation of the radial electric field. Thus, the inverted magnetron would have a much faster startup than the conventional magnetron, an important consideration for pulsed operation. When the effective mass is infinite, the electrons hardly respond to an azimuthal ac electric field.
A Paley-Wiener theorem for generalized entire functions on infinite-dimensional spaces
NASA Astrophysics Data System (ADS)
Khrennikov, A. Yu; Petersson, H.
2001-04-01
We study entire functions on infinite-dimensional spaces. The basis is the study of spaces of Gateaux holomorphic functions that are bounded on certain subsets (bounded entire functions). The main goal is to characterize the Fourier image of the corresponding spaces of generalized entire functions (ultra-distributions) by an infinite-dimensional Paley-Wiener theorem. We introduce entire functions of exponential type and prove a generalization of the classical Paley-Wiener theorem. The crucial point of our theory is the dimension-invariant estimate given by Lemma 4.12.
NASA Technical Reports Server (NTRS)
Sidi, Avram
1987-01-01
In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability and that the W-transformation can be applied to them without any modifications. Convergence results are stated and numerical examples given.
Infinite disorder and correlation fixed point in the Ising model with correlated disorder
NASA Astrophysics Data System (ADS)
Chatelain, Christophe
2017-03-01
Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations of the Ising model (q = 2), directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percolation fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations.