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)
Zenkour, Ashraf M.; Abbas, Ibrahim A.
2015-12-01
The electro-magneto-thermo-elastic analysis problem of an infinite functionally graded (FG) hollow cylinder is studied in the context of Green-Naghdi's (G-N) generalized thermoelasticity theory (without energy dissipation). Material properties are assumed to be graded in the radial direction according to a novel power-law distribution in terms of the volume fractions of the metal and ceramic constituents. The inner surface of the FG cylinder is pure metal whereas the outer surface is pure ceramic. The equations of motion and the heat-conduction equation are used to derive the governing second-order differential equations. A finite element scheme is presented for the numerical purpose. The system of differential equations is solved numerically and some plots for displacement, radial and electromagnetic stresses, and temperature are presented. The radial displacement, mechanical stresses and temperature as well as the electromagnetic stress are all investigated along the radial direction of the infinite cylinder.
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.
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.
Linear stability of plane Poiseuille flow in an infinite elastic medium and volcanic tremors
NASA Astrophysics Data System (ADS)
Sakuraba, Ataru; Yamauchi, Hatsuki
2014-12-01
The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastic media was investigated with the aim of explaining the excitation of volcanic tremors. Our results show that there are several regimes of instability, and the nature of stability significantly depends on the symmetry of oscillatory fluid and solid motion. It has been shown that long-wave symmetric instability occurs at a very small value of the Reynolds number, but it is unlikely that this is the cause of volcanic tremors. We show that antisymmetric (flexural) instability also occurs, involving two parallel Rayleigh waves traveling against the Poiseuille flow, but the critical flow speed is faster than that of symmetric instability. However, if the basic flow profile is nonparabolic because of a nonuniform driving force or nonuniform viscosity, the critical flow speed of antisymmetric instability can be considerably slower than that of symmetric instability. Based on numerical calculations and analytical consideration, we conclude that this anomalous antisymmetric instability is possibly produced by a basaltic magma flow of a few meters per second through a dike with thickness of 1 m and extending for several kilometers; this origin can explain some of the characteristics of volcanic tremors.
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 Technical Reports Server (NTRS)
Batdorf, S B; Houbolt, John C
1946-01-01
An exact solution and a closely concurring approximate energy solution are given for the buckling of an infinitely long flat plate under combined shear and transverse direct stress with edges elastically restrained against rotation. It was found that an appreciable fraction of the critical stress in pure shear may be applied to the plate without any reduction in the transverse compressive stress necessary to produce buckling. An interaction formula in general use was shown to be decidedly conservative for the range in which it is supposed to apply.
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.
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.
Lasaygues, Philippe; Le Marrec, Loïc
2008-01-01
Comparisons were made between the results obtained using two quantitative ultrasound imaging methods on the solid cross section of a cylindrical tube that is infinite in the axial direction. The first method tested was the classical reflection tomography method based on the first-order Born approximation, which can only be used under conditions to obtain limited reconstruction of the external boundaries of the high contrast scatterer. The results were compared with those obtained using another inversion scheme based on the Intercepting Canonical Body Approximation (ICBA) in a large frequency range, which gives accurate complete geometrical information about the tube (thickness measurements). The numerical and experimental results obtained show the feasibility of the latter approach. PMID:18564595
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. PMID:27475169
Stress intensity factors in a cracked infinite elastic wedge loaded by a rigid punch
NASA Technical Reports Server (NTRS)
Erdogan, F.; Civelek, M. B.
1978-01-01
A plane elastic wedge-shaped solid was split through the application of a rigid punch. It was assumed that the coefficient of friction on the the contact area was constant, and the problem had a plane of symmetry with respect to loading and geometry, with the crack in the plane of symmetry. The problem was formulated in terms of a system of integral equations with the contact stress and the derivative of the crack surface displacement as the unknown functions. The solution was obtained for an internal crack and for an edge crack. The results include primarily the stress intensity factors at the crack tips, and the measure of the stress singularity at the wedge apex, and at the end points of the contact area.
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.
Wave propagation in semi-infinite bar with random imperfections of density and elasticity module
NASA Astrophysics Data System (ADS)
Náprstek, J.
2008-02-01
Mathematical modeling and properties of a linear longitudinal wave propagating in a slender bar with random imperfections of material density and Young modulus of elasticity is discussed. Fluctuation components of material properties are considered as continuous stochastic functions of the length coordinate. Two types of fluctuation and their influence on response properties have been investigated, in particular the delta correlated and a diffusion-type processes. Investigation itself is based on Markov processes and corresponding Fokker-Planck-Kolmogorov equation. The stochastic moments closure as a solution method has been used. Many effects due to the stochastic nature of the problem have been detected. Along the bar a drop of the mean value of the response with the simultaneous increase of the response variance have been observed. This effect does not represent any conventional damping, but a gradual drop of the deterministic and an increase of the stochastic components of the overall response. The rate of the response indeterminacy increases with the increase of the length coordinate. Increasing values of material imperfection variances and the rising excitation frequency can lead to a critical state when the length of the propagating wave is comparable with the correlation length of imperfections. This state will manifest itself as a radical change of the response character. The problem will pass beyond the boundaries of stochastic mechanics and lose its physical meaning. Similar effects can be observed in the FEM analysis, where there is also a certain permissible upper boundary of the excitation frequency corresponding with the size and type of the element used.
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.
NASA Astrophysics Data System (ADS)
Dai, Ming; Schiavone, Peter; Gao, Cun-Fa
2016-06-01
We re-examine the conclusion established earlier in the literature that in the presence of a homogeneously imperfect interface, the circular inhomogeneity is the only shape of inhomogeneity which can achieve a uniform internal strain field in an isotropic or anisotropic material subjected to anti-plane shear. We show that under certain conditions, it is indeed possible to design such non-circular inhomogeneities despite the limitation of a homogeneously imperfect interface. Our method proceeds by prescribing a uniform strain field inside a non-circular inhomogeneity via perturbations of the uniform strain field inside the analogous circular inhomogeneity and then subsequently identifying the corresponding (non-circular) shape via the use of a conformal mapping whose unknown coefficients are determined from a system of nonlinear equations. We illustrate our results with several examples. We note also that, for a given size of inhomogeneity, the minimum value of the interface parameter required to guarantee the desired uniform internal strain increases as the elastic constants of the inclusion approach those of the matrix. Finally, we discuss in detail the relationship between the curvature of the interface and the displacement jump across the interface in the design of such inhomogeneities.
Searching for Non-Circular Motions in Halpha Velocity Fields
NASA Astrophysics Data System (ADS)
Peters, Wesley; Kuzio de Naray, Rachel
2016-01-01
We present Halpha velocity fields for four spiral galaxies: NGC 2654, NGC 2841, NGC 5746 and NGC 6674. These velocity fields were constructed from SparsePak IFU data taken on the WIYN telescope at KPNO. We use the DiskFit code to model the kinematics of these galaxies and to determine a rotation curve for each object. We find that two of these galaxies, NGC 2654 and NGC 5746, are nearly edge-on and display both photometric and kinematic evidence of a bar. NGC 6674 is closer to face-on and shows the signatures of a bar and ring. The velocity field of NGC 2841 does not show evidence for significant non-circular motions in the disk.
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
2016-01-01
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
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. PMID:27274658
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.
Okada, O.; DeLucia, J.; Okabayashi, M.
1980-10-01
An analytical study is made of the external field required to produce non-circular toroidal MHD equilibria. Here the external magnetic flux pattern is formulated with a series of multipole moments expanded around the magnetic axis. The present approach provides a common description of the external field characteristics of various devices rather than specifying location of poloidal coils. Furthermore, the preconceptual design of noncircular devices can be simplified since the arrangement of poloidal coil location is decoupled from the physics requirement.
Non-circular chainring improves aerobic cycling performance in non-cyclists.
Hintzy, Frédérique; Horvais, Nicolas
2016-06-01
Non-circular chainrings alter the crank velocity profile over a pedalling cycle. The aim of this study was to investigate the effect of this altered crank velocity profile on the aerobic performance compared to a circular chainring (CC). Ten male non-cyclists performed two incremental maximal tests at 80 rpm on a cycle ergometer: one with a circular (Shimano) and the other with a non-circular chainring Osymetric(®) (Somovedi), at least 50 h apart. Each test started with a workload of 100 W lasting 3 min. During the first 12 min, the workload was increased by 30 W every 3 min. Thereafter, the workload was increased by 30 W every 2 min until exhaustion. The power output, the intra-cycle crank angular velocity and the physiological parameters were monitored continuously, averaged over the last 30 s of each increment and at exhaustion, and compared for the two chainrings. Results showed a higher maximal aerobic power attained with the non-circular chainring (362.6 ± 37.9 vs. 338.8 ± 32.6 W, p < .001; moderate effect), which could be explained by a significantly lower energy expenditure during the first increment at 100 W. It could be hypothesised that the use of the non-circular chainring allowed saving a small part of energy expenditure throughout the test, allowing the exhaustion of the subject at a higher increment for a similar maximal energy expenditure, in comparison with a CC. Although this improvement is obtained only for non-cyclists, it allowed highlighting the link between cycling equipment modifying the pedalling motion and physiological responses. PMID:26406359
Hα kinematics of S4G spiral galaxies - II. Data description and non-circular motions
NASA Astrophysics Data System (ADS)
Erroz-Ferrer, Santiago; Knapen, Johan H.; Leaman, Ryan; Cisternas, Mauricio; Font, Joan; Beckman, John E.; Sheth, Kartik; Muñoz-Mateos, Juan Carlos; Díaz-García, Simón; Bosma, Albert; Athanassoula, E.; Elmegreen, Bruce G.; Ho, Luis C.; Kim, Taehyun; Laurikainen, Eija; Martinez-Valpuesta, Inma; Meidt, Sharon E.; Salo, Heikki
2015-07-01
We present a kinematical study of 29 spiral galaxies included in the Spitzer Survey of Stellar Structure in Galaxies, using Hα Fabry-Perot (FP) data obtained with the Galaxy Hα Fabry-Perot System instrument at the William Herschel Telescope in La Palma, complemented with images in the R band and in Hα. The primary goal is to study the evolution and properties of the main structural components of galaxies through the kinematical analysis of the FP data, complemented with studies of morphology, star formation and mass distribution. In this paper we describe how the FP data have been obtained, processed and analysed. We present the resulting moment maps, rotation curves, velocity model maps and residual maps. Images are available in FITS format through the NASA/IPAC Extragalactic Database and the Centre de Données Stellaires. With these data products we study the non-circular motions, in particular those found along the bars and spiral arms. The data indicate that the amplitude of the non-circular motions created by the bar does not correlate with the bar strength indicators. The amplitude of those non-circular motions in the spiral arms does not correlate with either arm class or star formation rate along the spiral arms. This implies that the presence and the magnitude of the streaming motions in the arms is a local phenomenon.
Performance limits of ion extraction systems with non-circular apertures.
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. PMID:27131665
Estimating non-circular motions in barred galaxies using numerical N-body simulations
NASA Astrophysics Data System (ADS)
Randriamampandry, T. H.; Combes, F.; Carignan, C.; Deg, N.
2015-12-01
The observed velocities of the gas in barred galaxies are a combination of the azimuthally averaged circular velocity and non-circular motions, primarily caused by gas streaming along the bar. These non-circular flows must be accounted for before the observed velocities can be used in mass modelling. In this work, we examine the performance of the tilted-ring method and the DISKFIT algorithm for transforming velocity maps of barred spiral galaxies into rotation curves (RCs) using simulated data. We find that the tilted-ring method, which does not account for streaming motions, under-/overestimates the circular motions when the bar is parallel/perpendicular to the projected major axis. DISKFIT, which does include streaming motions, is limited to orientations where the bar is not aligned with either the major or minor axis of the image. Therefore, we propose a method of correcting RCs based on numerical simulations of galaxies. We correct the RC derived from the tilted-ring method based on a numerical simulation of a galaxy with similar properties and projections as the observed galaxy. Using observations of NGC 3319, which has a bar aligned with the major axis, as a test case, we show that the inferred mass models from the uncorrected and corrected RCs are significantly different. These results show the importance of correcting for the non-circular motions and demonstrate that new methods of accounting for these motions are necessary as current methods fail for specific bar alignments.
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 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. 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 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
Instability waves in supersonic jets confined in non-circular ducts
NASA Astrophysics Data System (ADS)
Viswanathan, Krishnamurthy; Morris, Philip J.; Chen, G.
1992-01-01
The instability of supersonic jets confined in circular and non-circular ducts is investigated both analytically and numerically. A technique based on the boundary element method is developed to study jets confined in ducts of non-circular geometry. It is shown that the presence of an outer wall introduces additional instability modes for the circular outer duct case. A highly supersonic unconfined jet possesses many modes of instability. These include the Kelvin-Helmholtz instability and supersonic instabilities. The modifications of these instabilities by a coflowing stream and an outer wall are examined. It is shown that the presence of an outer wall alters the instability modes of the jet. For the case of a circular jet in a circular duct, both the vortex sheet model and a model that includes the effect of finite shear layer thickness are considered. The results of these calculations are compared with those for unconfined supersonic jets with external flow. Finally, the effects of changes in the duct geometry on the instability modes are examined.
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".
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.
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.
NASA Astrophysics Data System (ADS)
Fathollahi Khalkhali, T.; Bananej, A.
2016-06-01
In this study, we analyze the tunability of complete photonic band gap of square and triangular photonic crystal slabs composed of square and hexagonal air holes in anisotropic tellurium background with SiO2 as cladding material. The non-circular holes are infiltrated with liquid crystal. Using the supercell method based on plane wave expansion, we study the variation of complete band gap by changing the optical axis orientation of liquid crystal. Our numerical results show that noticeable tunability of complete photonic band gap can be obtained in both square and triangular structures with non-circular holes.
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
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.)
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
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
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 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.
Finite and infinite wavelength elastocapillary instabilities with cylindrical geometry
NASA Astrophysics Data System (ADS)
Biggins, John; Xuan, Chen
In an elastic cylinder with shear modulus μ, radius R0 and surface tension γ we can define an emergent elastocapillary length l = γ / μ . When this length becomes comparable to R0 the cylinder becomes undergoes a Rayleigh-Plateaux type instability, but surprisingly, with infinite wavelength λ rather than with wavelength λ ~R0 ~ l . Here we take advantage of this infinite wavelength behaviour to construct a simple 1-D model of the elastocapillary instability in a cylindrical gel which permits a high-amplitude fully non-linear treatment. In particular, we show that the instability is sub-critical and entirely dependent on the elastic cylinder being subject to tension. We also discuss elastocapillary instabilities in a range of other cylindrical geometries, such a cylindrical cavities through a bulk elastic solid, or a solid cylinder embedded in a bulk elastic solid, and show that in these cases instability has finite wavelength. Thus infinite wavelength behaviour is a curiosity of elastic cylinders rather than the generic behaviour or elasto-capiliarity. Also Fudan University Shanghai.
NASA Astrophysics Data System (ADS)
Lenci, Marco
2010-09-01
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, testing them on a prototypical class of infinite measure-preserving dynamical systems, namely, the random walks.
NASA Astrophysics Data System (ADS)
Lee, Hanshin; Hart, Michael; Hill, Gary J.; Rafal, Marc D.
2010-07-01
Wavefront sensing (WFS) is one of the key elements for active alignment of the new Wide-Field Corrector (WFC), as it tracks sidereal motion, with respect to the fixed Hobby-Eberly Telescope (HET) primary mirror. During a track, part of the 10m-pupil of the WFC can lie outside the primary periphery and be clipped off. An additional field-dependent central obscuration by the holes and baffles of the WFC leads to complex pupil geometries. The combination of these is a complicated dynamically varying non-circular telescope pupil. This unique problem to the WFS on the HET needs to be dealt with by choosing an appropriate set of orthonormal aberration polynomials during wavefront reconstruction. In this paper, three ways of computing orthonormal aberration polynomials and their coefficients are discussed. These are based on the Gram-Schmidt (GS) process, but differ in the way of computing key integrals during the GS process. The first method analytically computes the integrals, where a computer algebra program is used. The second uses the Gaussian quadrature over triangulated pupil geometries that approximate the true pupil shape. The last uses indirect numerical estimates of the integrals, which turned out to be natural by-products of the usual least-square Zernike polynomials fit. It is shown that the first method is limited to cases of simple pupil shapes, while the second can be applied to more general pupil shapes. However, when dealing with complicated dynamically varying non-circular pupils, the last method can be vastly more efficient than the second and enables the possibility of estimating orthonormal aberration coefficient on the fly. Also noticed is that the last method naturally takes into account the pixelation effect of pupil geometries due to pixel-based imaging sensors (e.g. CCDs). With these benefits, the last method can be used as a viable tool in real-time wavefront analysis over dynamically changing pupils as in the Hobby- Eberly Telescope, which is
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.
NASA Astrophysics Data System (ADS)
Pant, Nidhi; Das, Santanu; Rotti, Aditya; Mitra, Sanjit; Souradeep, Tarun
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.
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. PMID:22319461
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…
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.
Word learning under infinite uncertainty.
Blythe, Richard A; Smith, Andrew D M; Smith, Kenny
2016-06-01
Language learners must learn the meanings of many thousands of words, despite those words occurring in complex environments in which infinitely many meanings might be inferred by the learner as a word's true meaning. This problem of infinite referential uncertainty is often attributed to Willard Van Orman Quine. We provide a mathematical formalisation of an ideal cross-situational learner attempting to learn under infinite referential uncertainty, and identify conditions under which word learning is possible. As Quine's intuitions suggest, learning under infinite uncertainty is in fact possible, provided that learners have some means of ranking candidate word meanings in terms of their plausibility; furthermore, our analysis shows that this ranking could in fact be exceedingly weak, implying that constraints which allow learners to infer the plausibility of candidate word meanings could themselves be weak. This approach lifts the burden of explanation from 'smart' word learning constraints in learners, and suggests a programme of research into weak, unreliable, probabilistic constraints on the inference of word meaning in real word learners. PMID:26927884
Infinite dimensional quantum information geometry
NASA Astrophysics Data System (ADS)
Grasselli, Matheus R.
2001-02-01
We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian H0. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing the dual mixture connection
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. PMID:26864541
Spring back of infinite honeycomb sheets beyond plastic deformation
NASA Astrophysics Data System (ADS)
Bonfanti, A.; Bhaskar, A.
2015-02-01
Cellular structures are promising for applications where high stiffness and strength are required with the minimal use of material. They are often used in applications where the plastic deformation plays an important role, such as those involving crashworthiness, energy absorption, and stents. The elastic analysis of a honeycomb sheet has been carried out in the past [1]. The present analysis extends this classical work in the elasto-plastic regime. Recoil analysis due to elastic recovery is absent from the published literature. This work aims to develop an analytical model to calculate the spring back for a simplified case, that of an infinite honeycomb sheet. An elastic-perfectly plastic material model is assumed. The recoil for a clamped beam with a load and moment applied at the free edge is analytically calculated first. This is carried out by relating the stress distribution of the cross section to the final deformed shape. The part corresponding to the elastic contribution is subsequently subtracted in order to obtain the final configuration after the external load is removed. This simple elasto-plastic analysis is then incorporated into the analysis of an infinite sheet made of uniform hexagonal cells. The translational symmetry of the lattice is exploited along with the analysis of a beam under tip loading through to plastic stage and recoil. The final shape of the struts upon the removal of the remote stress is completely determined by the plastic deformation which cannot be recovered. The expression for the beam thus obtained is then used to build an analytical model for an infinite honeycomb sheet loaded in both directions.
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. PMID:27171012
Logic of infinite quantum systems
NASA Astrophysics Data System (ADS)
Mundici, Daniele
1993-10-01
Limits of sequences of finite-dimensional (AF) C *-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AF C *-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate the noncommutative logic properties of general AF C *-algebras, and their corresponding systems. We stress the interplay between Gödel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AF C *-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “ twenty questions” game with lies.
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. PMID:19905274
Squashed entanglement in infinite dimensions
NASA Astrophysics Data System (ADS)
Shirokov, M. E.
2016-03-01
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
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.
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.
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…
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…
Inspiring Examples in Rearrangements of Infinite Products
ERIC Educational Resources Information Center
Ramasinghe, W.
2007-01-01
It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…
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.
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. PMID:6544755
Are There Infinite Irrigation Trees?
NASA Astrophysics Data System (ADS)
Bernot, M.; Caselles, V.; Morel, J. M.
2006-08-01
In many natural or artificial flow systems, a fluid flow network succeeds in irrigating every point of a volume from a source. Examples are the blood vessels, the bronchial tree and many irrigation and draining systems. Such systems have raised recently a lot of interest and some attempts have been made to formalize their description, as a finite tree of tubes, and their scaling laws [25], [26]. In contrast, several mathematical models [5], [22], [10], propose an idealization of these irrigation trees, where a countable set of tubes irrigates any point of a volume with positive Lebesgue measure. There is no geometric obstruction to this infinitesimal model and general existence and structure theorems have been proved. As we show, there may instead be an energetic obstruction. Under Poiseuille law R(s) = s -2 for the resistance of tubes with section s, the dissipated power of a volume irrigating tree cannot be finite. In other terms, infinite irrigation trees seem to be impossible from the fluid mechanics viewpoint. This also implies that the usual principle analysis performed for the biological models needs not to impose a minimal size for the tubes of an irrigating tree; the existence of the minimal size can be proven from the only two obvious conditions for such irrigation trees, namely the Kirchhoff and Poiseuille laws.
NASA Technical Reports Server (NTRS)
Shivakumar, V.; Forman, R. G.; Rosencranz, R., Jr.
1983-01-01
Stress-intensity factors are obtained for point loaded equal length cracks emanating from a circular hole in an infinite plate. A series approach and the Muskhelishvili formulation in the two-dimensional theory of elasticity are used to derive the solution. The applicability of the solution is demonstrated by using it as a Green's function to obtain stress-intensity factors in the case of (1) biaxial tension and pure shear of an infinite plate and (2) tension and pin loading of a plate with cracks emanating from one hole in a row of holes.
Where Infinite Spin Particles are Localizable
NASA Astrophysics Data System (ADS)
Longo, Roberto; Morinelli, Vincenzo; Rehren, Karl-Henning
2016-07-01
Particle states transforming in one of the infinite spin representations of the Poincaré group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state cannot exist. While it is known that infinite spin states localized in a spacelike cone are dense in the one-particle space, we show here that the subspace of states localized in any double cone is trivial. This implies that the free field theory associated with infinite spin has no observables localized in bounded regions. In an interacting theory, if the vacuum vector is cyclic for a double cone local algebra, then the theory does not contain infinite spin representations. We also prove that if a Doplicher-Haag-Roberts representation (localized in a double cone) of a local net is covariant under a unitary representation of the Poincaré group containing infinite spin, then it has infinite statistics. These results hold under the natural assumption of the Bisognano-Wichmann property, and we give a counter-example (with continuous particle degeneracy) without this property where the conclusions fail. Our results hold true in any spacetime dimension s + 1 where infinite spin representations exist, namely {s≥ 2}.
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.
NASA Astrophysics Data System (ADS)
Roy, J. S.; Nayak, P.
1981-09-01
An iteration procedure is used to solve fluid dynamics equations describing viscoelastic incompressible flow between two infinite parallel porous plates, one oscillating and the other in uniform motion. The solutions obtained are valid for small values of the elastic parameter S. The effects of the Reynolds number and the elastic parameter S on the velocity distribution and the shearing stress at the plates are analyzed.
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
Understanding the behaviour of infinite ladder circuits
NASA Astrophysics Data System (ADS)
Ucak, C.; Yegin, K.
2008-11-01
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 not change when a new block of impedance is added. However, the impedance derived from this assumption may lead to incorrect conclusions if it is not treated carefully. Sometimes, in the literature, the input impedance behaviour of infinite ladder circuits is referred to as a paradox, leaving students and educators in doubt. This study intends to clarify this confusion and help to better comprehend the behaviour of the input impedance of infinite ladder circuits.
Semi-infinite cohomology and string theory.
Frenkel, I B; Garland, H; Zuckerman, G J
1986-11-01
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
NASA Astrophysics Data System (ADS)
Moraru, Gheorghe; Mursa, Condrat
2006-12-01
In this book we present the basic concepts of the theory of elasticity: stress and deformation states (plane and three-dimensional) and generalized Hooke's law. We present a number of problems which have applications in strength analysis. The book includes a synthesis of the theory of elasticity and modern methods of applied mathematics. This book is designed for students, post graduate students and specialists in strength analysis. the book contains a number of appendixes which includes: elements of matrix-calculation, concepts of tensorial calculation, the Fourier transform, the notion of improper integrals,singular and hypersingular integrals, generalized functions, the Dirac Delta function
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. PMID:21361428
Seismic stability of gentle infinite slopes
Hadj-Hamou, T.; Kavazanjian, E.
1985-06-01
Deterministic and probabilistic analyses of the stability of gentle infinite slopes subject to seismically induced excess pore pressures and inertia forces are developed. In the deterministic analysis, classical equations for infinite slope stability are rewritten to explicitly include excess pore pressure and seismic acceleration. Equations for the factor of safety are developed that include these factors. In the probabilistic analysis, the seismic acceleration, excess pore pressure, and effective friction angle are considered random variables. Acceleration peaks are considered Rayleigh distributed. Excess pore pressure is predicted using a model that considers Rayleigh distributed shear stress peaks. The friction angle is modeled with a Beta distribution. Acceleration and pore pressure development within the gentle infinite slope are assumed the same as those in a horizontal deposit of the same average thicknesss. Finite element analyses are performed to investigate the limits of this assumption. Results from both analyses are compared to documented case histories of lateral spreading.
Theory and experiment for infinite microstrip arrays
NASA Astrophysics Data System (ADS)
Wright, S. M.; Lo, Y. T.
1985-01-01
Microstrip antennas are well suited for use in large scanning arrays. To obtain greater bandwidth, it is useful to use thicker substrates, which can increase the effects of mutual coupling and lead to significant mismatch or blindness for certain scan angles. Using an infinite array formulation, the impedance of a single element in an infinite array environment was solved with the method of moments. Mutual coupling is built into the solution, and the presence of surface waves is accounted for by using the periodic Green's function for the grounded dielectric substrate. Blindness in arrays of microstrip dipoles on various substrates, both with and without radomes is demonstrated.
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
Lyashenko, I. A.; Popov, V. L.
2015-01-01
An impact of an elastic sphere with an elastic half space under no-slip conditions (infinitely large coefficient of friction) is studied numerically using the method of dimensionality reduction. It is shown that the rebound velocity and angular velocity, written as proper dimensionless variables, are determined by a function of only the ratio of tangential and normal stiffness ("Mindlin-ratio"). The obtained numerical results can be approximated by a simple analytical expression. PMID:25684339
Efficient analysis for infinite microstrip dipole arrays
NASA Astrophysics Data System (ADS)
Wright, S. M.; Lo, Y. T.
1983-11-01
A moment method analysis of infinite microstrip dipole arrays which uses an efficient technique to evaluate the generalized impedance matrix is described. A particularly simple formulation is obtained through the use of the periodic Green function. Results for the reflection coefficient magnitude against scan angle are given for a typical array.
Stress on Second Conjugation Infinitives in Italian.
ERIC Educational Resources Information Center
Davis, Stuart; And Others
1987-01-01
Reviews the limited amount of research regarding ways in which primary stress is assigned to second conjugation infinitives in Italian and then proposes a new perspective taking into consideration root vowels, root-final consonants, syllable onset, monosyllabic vs. polysyllabic roots, and canonical form. (CB)
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.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-15
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.
On infinite-dimensional state spaces
NASA Astrophysics Data System (ADS)
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
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.
Semi-Infinite Cohomology of Loop Spaces
NASA Astrophysics Data System (ADS)
Shutler, Paul Maurice Edmund
Available from UMI in association with The British Library. Requires signed TDF. This thesis attempts to construct a de Rham model for the Floer homology of the space of free loops on a symplectic manifold. It derives its inspiration principally from the work of Witten on topological quantum field theories. Chapter 1 consist of a review of background material followed by a number of elementary results. It is seen how Floer homology should naturally be representable by a semi-infinite generalisation of the ordinary de Rham theory associated to a manifold. In Chapter 2 the main attempt at constructing such a semi-infinite theory is made by defining an exterior derivative. Two different kinds of divergences are encountered and resolved. A suitable space of semi-infinite forms is constructed and some remarks are made about the likelihood that this model captures the Floer homology. In Chapter 3 the obstruction to the existence of a chiral factorisation of the bundle of fermionic Fock spaces over the loop space of the two-sphere is computed. For this purpose the ordinary cohomology ring of the loop space is calculated, also the action of the deck transformation on the cohomology of the simply connected covering space. In Chapter 4 the supersymmetric path integral approach to quantising topological field theories is developed formally. The semi-infinite dimensionality of the differential forms involved emerges naturally. The Floer homology of loop space is shown to be a ring. Its structure is calculated for the simple case of complex projective space. Chapter 5 concludes the thesis with some remarks about the action of the super-Virasoro algebra on the space of ordinary and semi-infinite differential forms respectively. Two short appendices are included describing a polynomial generating function for spherical harmonics and the spectrum of curl on vector fields on the three -sphere.
NASA Astrophysics Data System (ADS)
Bufetov, A. I.
2016-04-01
The second paper in this series is devoted to the convergence of sequences of infinite determinantal measures, understood as the convergence of sequences of the corresponding finite determinantal measures. Besides the weak topology in the space of probability measures on the space of configurations, we also consider the natural immersion (defined almost surely with respect to the infinite Bessel process) of the space of configurations into the space of finite measures on the half-line, which induces a weak topology in the space of finite measures on the space of finite measures on the half-line. The main results of the present paper are sufficient conditions for the tightness of families and the convergence of sequences of induced determinantal processes as well as for the convergence of processes corresponding to finite-rank perturbations of operators.
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)
Entanglement convertibility for infinite-dimensional pure bipartite states
Owari, Masaki; Matsumoto, Keiji; Murao, Mio
2004-11-01
It is shown that the order property of pure bipartite states under stochastic local operations and classical communications (SLOCC) changes radically when dimensionality shifts from finite to infinite. In contrast to finite-dimensional systems where there is no pure incomparable state, the existence of infinitely many mutually SLOCC incomparable states is shown for infinite-dimensional systems even under the bounded energy and finite information exchange condition. These results show that the effect of the infinite dimensionality of Hilbert space, the 'infinite workspace' property, remains even in physically relevant infinite-dimensional systems.
Attenuation of Elastic Waves due to Scattering from Spherical Cavities and Elastic Inclusions.
NASA Astrophysics Data System (ADS)
Hinders, Mark Karl
1990-01-01
The attenuation of elastic waves due to scattering from a spherical inclusion of arbitrary size in an infinitely extended medium is investigated. The spherical scatterer and the exterior medium are isotropic, homogeneous, and linearly elastic, but of arbitrarily differing material parameters, with compressional and shear waves supported in both media. Exact expressions for scattered and transmitted fields caused by an incident plane compressional or shear wave of unit amplitude are calculated analytically and general expressions for extinction and scattering cross -sections are derived for both lossy and lossless scattering. Application to ultrasonic determination of porosity in cast aluminum is investigated.
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. PMID:27352146
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.
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.
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.
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. PMID:26353136
Structural analysis of infinite layer superlattices grown by pulsed laser deposition
NASA Astrophysics Data System (ADS)
Del Vecchio, A.; Tapfer, L.; Aruta, C.; Balestrino, G.; Petrocelli, G.
1996-07-01
In this work we investigate the structural properties of SrCuO2/CaCuO2 infinite layer superlattices by high-resolution x-ray diffraction and x-ray specular reflectivity measurements. The infinite layer superlattices are grown by pulsed laser deposition on slightly misoriented (001) SrTiO3 substrates. We demonstrate that good quality superlattices with few monolayers thick constituent SrCuO2 and CaCuO2 layers can be grown having an interface roughness of less than 3-4 Å. A strain analysis of the epitaxial film shows that the SrCuO2 layers are completely relaxed with respect to the substrate. However, the CaCuO2 layers are elastically strained with respect to the SrCuO2 layer. The Poisson ratio of the CaCuO2 is estimated to be 0.40±0.08.
On the principal and strictly particular solutions to infinite systems
NASA Astrophysics Data System (ADS)
Ivanova, O. F.; Pavlov, N. N.; Fedorov, F. M.
2016-03-01
The concepts of the principal solution to infinite systems of linear algebraic equations and the reduction method are defined more precisely. The principal solution, if it exists, is a strictly particular solution to the infinite system. If the reduction method is convergent, then it necessarily converges to Kramer's determinant; however, Kramer's determinant is not always a solution to the infinite system. To confirm the obtained results, analytical and numerical solutions of specific infinite system are considered.
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…
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
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
Infinite Maxwell fisheye inside a finite circle
NASA Astrophysics Data System (ADS)
Liu, Yangjié; Chen, Huanyang
2015-12-01
This manuscript proposes a two-dimensional heterogeneous imaging medium composed of an isotropic refractive index. We exploit conformal-mapping to transfer the full Maxwell fisheye into a finite circle. Unlike our previous design that requires a mirror of Zhukovski airfoil shape, this approach can work without a mirror, while offering a comparable imaging resolution. This medium may also be used as an isotropic gradient index lens to transform a light source inside it into two identical sources of null interference. A merit of this approach is reduction of the near-zero-index area from an infinite zone into a finite one, which shall ease its realization.
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.
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. PMID:24187221
Infinite densities for Lévy walks
NASA Astrophysics Data System (ADS)
Rebenshtok, A.; Denisov, S.; Hänggi, P.; Barkai, E.
2014-12-01
Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments <|x (t ) |q> with q below a critical value qc exhibit diffusive scaling while for q >qc a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α , and the diffusion coefficient Kα. We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.
Configuration interaction calculations with infinite angular = expansions
Goldman, S.P.; Glickman, T.
1996-05-01
The Modified Configuration Interaction (MCI) method improves the angular convergence of Configuration Interaction (CI) calculations by several orders of magnitude by mixing a priori a large number of angular basis functions. With MCI one can therefore use basis functions with very large angular momentum quantum numbers, overcoming an important limitation of conventional CI. Although this is desirable given the excellent convergence obtained, the large number of angular integrations and the calculation of n-j symbols with large values of l to high accuracy, make the angular calculations lengthy. In this work a new angular representation for CI calculations is presented that is much more efficient and powerful. Instead of the large number of angular functions of MCI the authors use a basis set containing an infinite linear combination of angular functions. All the necessary integrations involving these infinite expansions are done in closed form and are actually easy and fast to compute. The linear coefficients in the angular expansion are optimized in terms of a few non-linear parameters. Several examples will be presented with applications to two-electron systems.
Statistical Mechanics of Infinite Gravitating Systems
NASA Astrophysics Data System (ADS)
Saslaw, William C.
2008-01-01
The cosmological many-body problem was stated over 300 years ago, but its solution is quite recent and still incomplete. Imagine an infinite expanding universe essentially containing a very large number of objects moving in response to their mutual gravitational forces. What will be the spatial and velocity distributions of these objects and how will they evolve? This question fascinates on many levels. Though inherently non-linear, it turns out to be one of the few analytically solvable problems of statistical mechanics with long range forces. The partition function can be calculated. From this all the thermodynamic properties of the system can be obtained for the grand canonical ensemble. They confirm results derived independently directly from the first and second laws of thermodynamics. The behavior of infinite gravitating systems is quite different from their finite relations such as star clusters. Infinite gravitating systems have regimes of negative specific heat, an unusual type of phase transition, and a very close relation to the observed large-scale structure of our universe. This last feature provides an additional astronomical motivation, especially since the statistical mechanics may be generalized to include effects of dark matter haloes around galaxies. Previously the cosmological many-body problem has mostly been studied using the BBGKY hierarchy (not so suitable in the non-linear regime) and by direct computer integrations of the objects' orbits. The statistical mechanics agrees with and substantially extends these earlier results. Most astrophysicists had previously thought that a statistical thermodynamic approach would not be applicable because: a) many-body gravitational systems have no rigorous equilibrium state, b) the unshielded nature of the long-range force would cause the partition function to diverge on large scales, and c) point masses would produce divergences on small scales. However, deeper considerations show that these are not
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.
Infinite Index Subfactors and the GICAR Categories
NASA Astrophysics Data System (ADS)
Jones, Vaughan F. R.; Penneys, David
2015-10-01
Given a II1-subfactor of arbitrary index, we show that the rectangular GICAR category, also called the rectangular planar rook category, faithfully embeds as A - A bimodule maps among the bimodules . As a corollary, we get a lower bound on the dimension of the centralizer algebras for infinite index subfactors, and we also get that is nonabelian for , where is the Jones tower for . We also show that the annular GICAR/planar rook category acts as maps amongst the A-central vectors in , although this action may be degenerate. We prove these results in more generality using bimodules. The embedding of the GICAR category builds on work of Connes and Evans, who originally found GICAR algebras inside Temperley-Lieb algebras with finite modulus.
Nonlinear Shear Instabilities in an Infinite Slab
NASA Astrophysics Data System (ADS)
Nepveu, M.
1982-08-01
The dynamical evolution of an infinite slab moving in denser and noisy (turbulent) surroundings is investigated with a 2D hydrodynamic code. The applicability of the results to astrophysical jets is discussed. Inviscid beams show internal shocks at regular intervals of a few beamwidths. Kinks are not obvious. In viscous beams shocks are less outspoken, but turbulence is triggered with maximum scales of a few beamwidths. These viscous beams broaden. Linear stability analysis may hold up to a few e-folding times, although the seed disturbance field is not infinitesimal. The computations suggest that viscous astrophysical beams may become blurred quite suddenly and may give rise to sudden change in radiation patterns (NGC 1265).
Simulating infinite vortex lattices in superfluids.
Mingarelli, Luca; Keaveny, Eric E; Barnett, Ryan
2016-07-20
We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross-Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general 'synthetic' gauge fields. PMID:27219843
Simulating infinite vortex lattices in superfluids
NASA Astrophysics Data System (ADS)
Mingarelli, Luca; Keaveny, Eric E.; Barnett, Ryan
2016-07-01
We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross–Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau-level regime. While we focus on rotating scalar superfluids for simplicity, the framework can be naturally extended to treat multicomponent systems and systems under more general ‘synthetic’ gauge fields.
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.
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. PMID:26836289
Wave propagation in polar elastic superlattices
NASA Astrophysics Data System (ADS)
Green, W. A.; Green, E. Rhian
1994-08-01
This paper examines the passband and stop band regions for time-periodic waves travelling normal to the layering through an infinite medium composed of alternating layers of two different elastic materials. The materials are such that the elastic energy density is a function of the strains and the strain gradients and, in consequence, a deformation gives rise to both the usual Cauchy stress and to a hyperstress or couple-stress. Such materials can exhibit a non-uniform wrinkling deformation at a free surface and similar non-uniform deformations can arise at interfaces between two different media. The presence of the strain derivatives in the elastic energy function introduces a natural length scale l into the material and the depth of the non-uniform deformation is of the order of this length scale. This model can give rise to enhanced elastic response when the layer depths are comparable with l and it is of interest as a possible mathematical model of nanolayered structures. The model also includes a non-standard set of continuity conditions at material interfaces. These arise from the elastic interaction energy of the two materials at the boundary and their effect is localized in a boundary layer whose depth is of order l. The periodic layering gives rise to displacements which are periodic with a frequency-dependent wave number, the Floquet wave number. Dispersion curves, relating circular frequency to the Floquet wave number, are obtained for different ratios of the layer depth to the natural length l and for different values of the elastic interface coupling parameters.
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.
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…
A New Look at Infinitives in Business and Technical Writing.
ERIC Educational Resources Information Center
Myers, Marshall
2002-01-01
Argues the infinitive phrase has not been taken seriously in writing because writers have been too concerned with Bishop Robert Lowth's proscription against the split infinitive. Notes that examination of three types of technical prose (instructions, annual reports, and "junk mail") reveals that more than one sentence in four contains an…
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)
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.
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.
Control system for an infinitely variable transmission
Sakai, Y.
1986-12-09
This patent describes a control system for an infinitely variable belt-drive transmission having a selector device including a drive range position and a neutral position, a drive pulley having a hydraulically shiftable disc and a servo chamber for shifting the disc, and a driven pulley having a hydraulically shiftable disc and a servo chamber for shifting the disc. It also has a belt engaged with both the pulleys, a hydraulic control circuit for supplying oil to the servo chambers and for draining the servo chambers. The hydraulic control circuit is provided with a pressure regulator valve for providing a line pressure and a transmission ratio control valve for applying the line pressure to the servo chamber of the drive pulley. The improvement described here comprises: a lubricating oil circuit provided in the hydraulic control circuit for supplying lubricating oil to the drive and driven pulleys; a passage for supplying a part of the lubricating oil to the servo chamber of the drive pulley; a check valve provided in the passage for preventing the reverse flow of the lubricating oil; and a select position detecting valve for enabling the supply of the lubricating oil to the servo chamber at the selection of the neutral position.
Control system for an infinitely variable transmission
Morimoto, Y.
1987-07-21
A system is described for controlling an infinitely variable transmission for transmitting the power of an internal combustion engine through a clutch for driving a motor vehicle. The transmission comprises a drive pulley having a hydraulically shiftable disc and a hydraulic cylinder for shifting the disc, a driven pulley having a hydraulically shiftable disc and a hydraulic cylinder for operating the disc of the driven pulley, and a belt engaged with both pulleys. The system includes a pressure oil circuit having a pump for supplying pressurized oil, and a transmission ratio control valve having a spool for controlling the pressurized oil so as to move the disc of the drive pulley to change the actual transmission ratio of the transmission. The improvement in the system comprises: first means for moving the spool of the transmission ratio control valve; second means responsive to disengagement of the clutch, when speed of the vehicle is below a predetermined speed, for producing a coasting signal; third means responsive to the coasting signal for producing a drive pulley speed set signal; fourth means responsive to the drive pulley speed set signal for producing a shifting signal representing a quantity of shifting the spool of the transmission ratio control valve in upshifting direction, and fifth means responsive to the shifting signal for shifting the spool of the transmission ratio control valve in the upshifting direction via the first means thereby decreasing the drive pulley speed.
Countable Infinite Sets and Inflationary Models
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
2000-04-01
Unreasonable effectiveness of mathematics (E.Wigner) recasts pythagorean "all things are made of numbers". Hypotheses of eternal inflation (A.Linde) and/or quantum branching (H.Everett) buttressed by platonic pressure principle (PPP) resonates with "for deriving all from nothing there suffices a single principle" (G.W.Leibnitz). Externalization of PPP uses patterns of factorizations of super-long integers (tower exponents, TE). PPP-TE explosive emergence of space-time-matter-energy rests on infinite complexity of factorizational and iterational patterns of integers. Thus, PPP is direct translation of metaphysical principle to physics of material world ("metaphysics works"). Countability of quantum states of bounded systems allows "listing" of all states of all baby universes through Godel-like counting with TE of primes. At each breeding step upper (Nth) prime of TE stack p1...pN counts (by multidimensional Cantor diagonal scheme) all universes AND all states in them. Exclusive use of primes in TEs assures non-overlapping counting. Cantor counting with non-crossing subsets of primes (and actual PPP emergence) can proceed both in "forward" and "backward" direction in megauniversal ("Newtonian") time. format.
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.
Motion of a mirror under infinitely fluctuating quantum vacuum stress
NASA Astrophysics Data System (ADS)
Wang, Qingdi; Unruh, William G.
2014-04-01
The actual value of the quantum vacuum energy density is generally regarded as irrelevant in nongravitational physics. However, this paper presents a nongravitational system where this value does have physical significance. The system is a mirror with an internal degree of freedom that interacts with a scalar field. We find that the force exerted on the mirror by the field vacuum undergoes wild fluctuations with a magnitude proportional to the value of the vacuum energy density, which is mathematically infinite. This infinite fluctuating force gives infinite instantaneous acceleration of the mirror. We show that this infinite fluctuating force and infinite instantaneous acceleration make sense because they will not result in infinite fluctuation of the mirror's position. On the contrary, the mirror's fluctuating motion will be confined in a small region due to two special properties of the quantum vacuum: (1) the vacuum friction that resists the mirror's motion and (2) the strong anticorrelation of vacuum fluctuations that constantly changes the direction of the mirror's infinite instantaneous acceleration and thus cancels the effect of infinities to make the fluctuation of the mirror's position finite.
On the Atkinson-Johnson Homogeneous Solution for Infinite Systems
NASA Astrophysics Data System (ADS)
Laraudogoitia, Jon Pérez
2015-05-01
This paper shows that the general homogeneous solution to equations of evolution for some infinite systems of particles subject to mutual binary collisions does not depend on a single arbitrary constant but on a potentially infinite number of such constants. This is because, as I demonstrate, a single self-excitation of a system of particles can depend on a potentially infinite number of parameters. The recent homogeneous solution obtained by Atkinson and Johnson, which depends on a single arbitrary constant, is only a particular case.
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.
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.
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.
Elastically Decoupling Dark Matter
NASA Astrophysics Data System (ADS)
Kuflik, Eric; Perelstein, Maxim; Lorier, Nicolas Rey-Le; Tsai, Yu-Dai
2016-06-01
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.
Elastically Decoupling Dark Matter.
Kuflik, Eric; Perelstein, Maxim; Lorier, Nicolas Rey-Le; Tsai, Yu-Dai
2016-06-01
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. PMID:27314712
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.
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.
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…
LED downlights with non-circular spots
NASA Astrophysics Data System (ADS)
Parkyn, William A.; Pelka, David G.
2005-09-01
The ubiquitous downlight inhabits our ceilings by the millions. Hot, inefficient, and electrically wasteful, it is next in line for replacement by the latest high-brightness, high-efficacy white LEDs. The conventional downlight configuration of a large incandescent spotlight in a low-cost, ceiling-recessed metal can, represents the culmination of old technology, fated never to improve significantly. Incandescent downlights add greatly both to direct and indirect electrical consumption, with the lamps requiring relatively frequent replacement. The small size of LED emitters means small optical elements can produce much higher-quality beams than incandescent spotlight-lamps can produce. Herein we introduce compact high-luminosity LED downlights with lenses that deliver uniform illumination to delimited targets such as tables. One version utilizes circular lenses and micro-diffuser films to deliver square outputs. The other uses lenses cut to the target shape. In particular, one of these lenses is the first to offer a semicircular spot suitable for gambling tables.
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.
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.
A unified approach to infinite-dimensional integration
NASA Astrophysics Data System (ADS)
Albeverio, S.; Mazzucchi, S.
2016-04-01
An approach to infinite-dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite-dimensional construction of integrals as linear functionals, as much as possible independent of the underlying topological and measure theoretical structure. Various applications are given, including, next to Feynman path integrals, Schrödinger and diffusion equations, as well as higher order hyperbolic and parabolic equations.
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
A piezoelectric-based infinite stiffness generation method for strain-type load sensors
NASA Astrophysics Data System (ADS)
Zhang, Shuwen; Shao, Shubao; Chen, Jie; Xu, Minglong
2015-11-01
Under certain application conditions like nanoindentation technology and the mechanical property measurement of soft materials, the elastic deformation of strain-type load sensors affects their displacement measurement accuracy. In this work, a piezoelectric-based infinite stiffness generation method for strain-type load sensors that compensates for this elastic deformation is presented. The piezoelectric material-based deformation compensation method is proposed. An Hottinger Baldwin Messtechnik GmbH (HBM) Z30A/50N load sensor acts as the foundation of the method presented in this work. The piezoelectric stack is selected based on its size, maximum deformation value, blocking force and stiffness. Then, a clamping and fixing structure is designed to integrate the HBM sensor with the piezoelectric stack. The clamping and fixing structure, piezoelectric stack and HBM load sensor comprise the sensing part of the enhanced load sensor. The load-deformation curve and the voltage-deformation curve of the enhanced load sensor are then investigated experimentally. Because a hysteresis effect exists in the piezoelectric structure, the relationship between the control signal and the deformation value of the piezoelectric material is nonlinear. The hysteresis characteristic in a quasi-static condition is studied and fitted using a quadratic polynomial, and its coefficients are analyzed to enable control signal prediction. Applied arithmetic based on current theory and the fitted data is developed to predict the control signal. Finally, the experimental effects of the proposed method are presented. It is shown that when a quasi-static load is exerted on this enhanced strain-type load sensor, the deformation is reduced and the equivalent stiffness appears to be almost infinite.
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.
Postinstability models in elasticity
NASA Technical Reports Server (NTRS)
Zak, M.
1984-01-01
It is demonstrated that the instability caused by the failure of hyperbolicity in elasticity and associated with the problem of unpredictability in classical mechanics expresses the incompleteness of the original model of an elastic medium. The instability as well as the ill-posedness of the Cauchy problem are eliminated by reformulating the original model.
Peng, Qing; De, Suvranu
2014-10-21
Silicane is a fully hydrogenated silicene-a counterpart of graphene-having promising applications in hydrogen storage with capacities larger than 6 wt%. Knowledge of its elastic limit is critical in its applications as well as tailoring its electronic properties by strain. Here we investigate the mechanical response of silicane to various strains using first-principles calculations based on density functional theory. We illustrate that non-linear elastic behavior is prominent in two-dimensional nanomaterials as opposed to bulk materials. The elastic limits defined by ultimate tensile strains are 0.22, 0.28, and 0.25 along armchair, zigzag, and biaxial directions, respectively, an increase of 29%, 33%, and 24% respectively in reference to silicene. The in-plane stiffness and Poisson ratio are reduced by a factor of 16% and 26%, respectively. However, hydrogenation/dehydrogenation has little effect on its ultimate tensile strengths. We obtained high order elastic constants for a rigorous continuum description of the nonlinear elastic response. The limitation of second, third, fourth, and fifth order elastic constants are in the strain range of 0.02, 0.08, and 0.13, and 0.21, respectively. The pressure effect on the second order elastic constants and Poisson's ratio were predicted from the third order elastic constants. Our results could provide a safe guide for promising applications and strain-engineering the functions and properties of silicane monolayers. PMID:25190587
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.
Proton Nucleus Elastic Scattering Data.
Energy Science and Technology Software Center (ESTSC)
1993-08-18
Version 00 The Proton Nucleus Elastic Scattering Data file PNESD contains the numerical data and the related bibliography for the differential elastic cross sections, polarization and integral nonelastic cross sections for elastic proton-nucleus scattering.
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
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.
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.
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
On the problem of quantum control in infinite dimensions
NASA Astrophysics Data System (ADS)
Vilela Mendes, R.; Man'ko, Vladimir I.
2011-04-01
In the framework of bilinear control of the Schrödinger equation, it has been proved that the reachable set has a dense complement in {S} \\cap {H}^{2}. Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand, it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this paper and, in particular, it is proved that the closure of the reachable set of bilinear control is dense in {S} \\cap {H}^{2}. The requirements for controllability in infinite dimensions are also related to the properties of the infinite-dimensional unitary group.
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.
Elastic Collisions and Gravity
NASA Astrophysics Data System (ADS)
Ball, Steven
2009-04-01
Elastic collisions are fascinating demonstrations of conservation principles. The mediating force must be conservative in an elastic collision. Truly elastic collisions take place only when the objects in collision do not touch, e.g. magnetic bumpers on low friction carts. This requires that we define a collision as a momentum transfer. Elastic collisions in 1-D can be solved in general and the implications are quite remarkable. For example, a heavy object moving initially towards a light object followed by an elastic collision results in a final velocity of the light object greater than either initial velocity. This is easily demonstrated with low friction carts. Gravitational elastic collisions involving a light spacecraft and an extremely massive body like a moon or planet can be approximated as 1-D collisions, such as the ``free return'' trajectory of Apollo 13 around the moon. The most fascinating gravitational collisions involve the gravitational slingshot effect used to boost spacecraft velocities. The maximum gravitational slingshot effect occurs when approaching a nearly 1-D collision, revealing that the spacecraft can be boosted to greater than twice the planet velocity, enabling the spacecraft to travel much further away from the Sun.
Dynamics with infinitely many derivatives: the initial value problem
NASA Astrophysics Data System (ADS)
Barnaby, Neil; Kamran, Niky
2008-02-01
Differential equations of infinite order are an increasingly important class of equations in theoretical physics. Such equations are ubiquitous in string field theory and have recently attracted considerable interest also from cosmologists. Though these equations have been studied in the classical mathematical literature, it appears that the physics community is largely unaware of the relevant formalism. Of particular importance is the fate of the initial value problem. Under what circumstances do infinite order differential equations possess a well-defined initial value problem and how many initial data are required? In this paper we study the initial value problem for infinite order differential equations in the mathematical framework of the formal operator calculus, with analytic initial data. This formalism allows us to handle simultaneously a wide array of different nonlocal equations within a single framework and also admits a transparent physical interpretation. We show that differential equations of infinite order do not generically admit infinitely many initial data. Rather, each pole of the propagator contributes two initial data to the final solution. Though it is possible to find differential equations of infinite order which admit well-defined initial value problem with only two initial data, neither the dynamical equations of p-adic string theory nor string field theory seem to belong to this class. However, both theories can be rendered ghost-free by suitable definition of the action of the formal pseudo-differential operator. This prescription restricts the theory to frequencies within some contour in the complex plane and hence may be thought of as a sort of ultra-violet cut-off. Our results place certain recent attempts to study inflation in the context of nonlocal field theories on a much firmer mathematical footing.
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.
Superlinear nonlocal fractional problems with infinitely many solutions
NASA Astrophysics Data System (ADS)
Binlin, Zhang; Molica Bisci, Giovanni; Servadei, Raffaella
2015-07-01
In this paper we study the existence of infinitely many weak solutions for equations driven by nonlocal integrodifferential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian where s ∈ (0, 1) is fixed. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-known Ambrosetti-Rabinowitz condition. In this framework we obtain three different results about the existence of infinitely many weak solutions for the problem under consideration, by using the Fountain Theorem. All these theorems extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.
Gravitational waves from kinks on infinite cosmic strings
Kawasaki, Masahiro; Miyamoto, Koichi; Nakayama, Kazunori
2010-05-15
Gravitational waves emitted by kinks on infinite strings are investigated using detailed estimations of the kink distribution on infinite strings. We find that gravitational waves from kinks can be detected by future pulsar timing experiments such as SKA for an appropriate value of the string tension, if the typical size of string loops is much smaller than the horizon at their formation. Moreover, the gravitational wave spectrum depends on the thermal history of the Universe and hence it can be used as a probe into the early evolution of the Universe.
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.
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.
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.
The infinite interface limit of multiple-region relaxed magnetohydrodynamics
Dennis, G. R.; Dewar, R. L.; Hole, M. J.; Hudson, S. R.
2013-03-15
We show the stepped-pressure equilibria that are obtained from a generalization of Taylor relaxation known as multi-region, relaxed magnetohydrodynamics (MRXMHD) are also generalizations of ideal magnetohydrodynamics (ideal MHD). We show this by proving that as the number of plasma regions becomes infinite, MRXMHD reduces to ideal MHD. Numerical convergence studies illustrating this limit are presented.
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.
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.
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.
Young Students Exploring Cardinality by Constructing Infinite Processes
ERIC Educational Resources Information Center
Kahn, Ken; Sendova, Evgenia; Sacristan, Ana Isabel; Noss, Richard
2011-01-01
In this paper, we describe the design and implementation of computer programming activities aimed at introducing young students (9-13 years old) to the idea of infinity, and in particular, to the cardinality of infinite sets. This research was part of the "WebLabs" project where students from several European countries explored topics in…
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…
On the sound fields of infinitely long strips.
Mellow, Tim; Kärkkäinen, Leo
2011-07-01
Exact solutions are derived for sound radiation from four kinds of infinitely-long strips: namely a rigid strip in a baffle of finite width, a resilient strip in free space, and a resilient or rigid strip in an infinite baffle. In one limit, the strip in a finite baffle becomes a rigid strip in free space and in the other, a line source in a finite baffle. Here "rigid" means that the surface velocity is uniform, whereas "resilient" means that the surface pressure is uniform, and the strip is assumed to have zero mass or stiffness, as if a force were driving the acoustic medium directly. According to the Babinet-Bouwkamp principle, radiation from a resilient strip in an infinite baffle is equivalent to diffraction of a plane wave through a slit in the same. Plots are shown for the radiation impedances, far-field directivity patterns, and on-axis pressure responses of the four kinds of strip. A simple relationship between the radiation admittance of the rigid strip in an infinite baffle and the resilient strip in free space is presented. The two-dimensional rectangular wave functions developed in this paper can be applied to related problems. PMID:21786886
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.
Infinite and Finite Games: Play and Visual Culture
ERIC Educational Resources Information Center
Hicks, Laurie E.
2004-01-01
In this article, I shall argue for the value of conceptualizing, and practicing art education as a kind of play or game, drawing inspiration from the concepts of finite and infinite games articulated by philosopher James Carse (1986). In so doing, I seek to encourage a continuing dialogue with the assumptions that constrain the theoretical basis…
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 ?
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…
Stability analysis of a stochastic logistic model with infinite delay
NASA Astrophysics Data System (ADS)
Liu, Meng; Fan, Dejun; Wang, Ke
2013-09-01
This report is concerned with a stochastic logistic equation with infinite delay. We establish the sufficient conditions for global asymptotical stability of the zero solution and the positive equilibrium. Some classical results are improved and extended. Several numerical simulations are introduced to illustrate the main results.
Explaining the Distribution of Infinitives of Impersonals in Russian
ERIC Educational Resources Information Center
Fortuin, Egbert
2011-01-01
In Russian infinitives of impersonal verbs have a peculiar distribution: they are not acceptable in most syntactic contexts, but there are also syntactic contexts in which they are perfectly acceptable. Based on a qualitative analysis of data from corpora, the Internet and an acceptability survey, it is argued that the restrictions on impersonals…
On the steady propagation of a semi-infinite crack
Paukshto, M.V.; Sulimov, M.G.
1994-12-25
We consider the rectilinear propagation of a semi-infinite crack with constant velocity in a crystal structure. We obtain the solutions of homogeneous boundary-value problems for the corresponding difference-differential operators in spaces of one and two dimensions. We give a justification of the computational aspect of the problem.
Eshelby tensor for a crack in an orthotropic elastic medium
NASA Astrophysics Data System (ADS)
Gruescu, Cosmin; Monchiet, Vincent; Kondo, Djimedo
2005-06-01
In the present Note, we provide new analytical expressions of the components of Hill tensor P (or equivalently the Eshelby tensor S) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005).
Extremely correlated Fermi liquids in the limit of infinite dimensions
Perepelitsky, Edward Sriram Shastry, B.
2013-11-15
We study the infinite spatial dimensionality limit (d→∞) of the recently developed Extremely Correlated Fermi Liquid (ECFL) theory (Shastry 2011, 2013) [17,18] for the t–J model at J=0. We directly analyze the Schwinger equations of motion for the Gutzwiller projected (i.e. U=∞) electron Green’s function G. From simplifications arising in this limit d→∞, we are able to make several exact statements about the theory. The ECFL Green’s function is shown to have a momentum independent Dyson (Mori) self energy. For practical calculations we introduce a partial projection parameter λ, and obtain the complete set of ECFL integral equations to O(λ{sup 2}). In a related publication (Zitko et al. 2013) [23], these equations are compared in detail with the dynamical mean field theory for the large U Hubbard model. Paralleling the well known mapping for the Hubbard model, we find that the infinite dimensional t–J model (with J=0) can be mapped to the infinite-U Anderson impurity model with a self-consistently determined set of parameters. This mapping extends individually to the auxiliary Green’s function g and the caparison factor μ. Additionally, the optical conductivity is shown to be obtainable from G with negligibly small vertex corrections. These results are shown to hold to each order in λ. -- Highlights: •Infinite-dimensional t–J model (J=0) studied within new ECFL theory. •Mapping to the infinite U Anderson model with self consistent hybridization. •Single particle Green’s function determined by two local self energies. •Partial projection through control variable λ. •Expansion carried out to O(λ{sup 2}) explicitly.
NASA Astrophysics Data System (ADS)
Zacharias, Mario; Paul, Indranil; Garst, Markus
2015-07-01
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T3 law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors.
Norris, Andrew N.
2014-01-01
We consider a periodic lattice structure in d=2 or 3 dimensions with unit cell comprising Z thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the effective elasticity of such frameworks. The method yields the effective cubic elastic constants for three-dimensional space-filling lattices with Z=4, 6, 8, 12 and 14, the last being the ‘stiffest’ lattice proposed by Gurtner & Durand (Gurtner & Durand 2014 Proc. R. Soc. A 470, 20130611. (doi:10.1098/rspa.2013.0611)). The analytical expressions provide explicit formulae for the effective properties of pentamode materials, both isotropic and anisotropic, obtained from the general formulation in the stretch-dominated limit for Z=d+1. PMID:25484608
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.
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. PMID:27159017
Elastic membranes in confinement.
Bostwick, J B; Miksis, M J; Davis, S H
2016-07-01
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 coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped. PMID:27440257
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.
Zacharias, Mario; Paul, Indranil; Garst, Markus
2015-07-10
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors. PMID:26207483
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.
NASA Astrophysics Data System (ADS)
Habibi, M.; Ribe, N. M.; Bonn, Daniel
2007-10-01
A rope falling onto a solid surface typically forms a series of regular coils. Here, we study this phenomenon using laboratory experiments (with cotton threads and softened spaghetti) and an asymptotic “slender-rope” numerical model. The excellent agreement between the two with no adjustable parameters allows us to determine a complete phase diagram for elastic coiling comprising three basic regimes involving different force balances (elastic, gravitational, and inertial) together with resonant “whirling string” and “whirling shaft” eigenmodes in the inertial regime.
Generalized topological sensitivity for inverse scattering of elastic waves
NASA Astrophysics Data System (ADS)
Chikichev, Ivan Sergeevich
The focus of this research is an extension of the concept of topological sensitivity, rooted in theories of shape optimization and elastostatics, to three-dimensional elastodynamics and its application toward preliminary reconstruction and characterization of inner defects by way of elastic waves. In particular the original concept, which exercises the idea of cavity nucleation, is generalized to permit germination of solid obstacles. The main result of the proposed generalization is an expression for topological sensitivity, explicit in terms of either the elastodynamic Green's function or the so-called adjoint solution, that is obtained by an asymptotic expansion of a misfit-type cost functional with respect to the nucleation of a dissimilar elastic inclusion in a defect-free "reference" solid. To cater for a variety of physical applications including shallow seismic exploration, material testing, and medical imaging, the proposed methodology is developed both in the frequency domain and the time domain. The featured formula, consisting of an inertial-contrast monopole term and an elasticity-contrast dipole term, is shown to be applicable to a variety of reference domains such as finite, semi-infinite, and infinite homogeneous solids as well as their heterogeneous counterparts with smoothly-varying elastic properties. Through numerical examples, it is shown that the generalized topological sensitivity can be used as a robust and computationally-effective obstacle indicator through an assembly of sampling points where it attains pronounced negative values. On varying the material characteristics of the nucleating obstacle, a new identification algorithm is developed that permits the use of the featured sensitivity as a preparatory tool for both geometric and material characterization of internal defects.
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…
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…
Elastically tailored composite structures
NASA Technical Reports Server (NTRS)
2000-01-01
Elastically tailored composite structures using out-of-autoclave processes. Several unsymetric autoclave-cured and electron-beam-cured composite laminates are compared. Cantilevered beam (unbalanced/asymetric laminate) used to demonstrate bend-twist coupling effects. Photographed in building 1145, photographic studio.
Hydrodynamic Elastic Magneto Plastic
Energy Science and Technology Software Center (ESTSC)
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.
Renormalization of curvature elastic constants for elastic and fluid membranes
NASA Astrophysics Data System (ADS)
Ami, S.; Kleinert, H.
1987-02-01
We study the fluctuations of membranes with area and curvature elasticity and calculate the renormalization of the curvature elastic constants due to thermal fluctuations. For the mean curvature elastic constant the result is the same as obtained previously for “ideal membranes” which resist only to curvature deformations. The renormalization of the gaussian curvature, on the other hand, depends on the elastic contants. In an incompressible membrane, it is five times weaker than in an ideal membrane.
Frequency dependent elastic impedance inversion for interstratified dispersive elastic parameters
NASA Astrophysics Data System (ADS)
Zong, Zhaoyun; Yin, Xingyao; Wu, Guochen
2016-08-01
The elastic impedance equation is extended to frequency dependent elastic impedance equation by taking partial derivative to frequency. With this equation as the forward solver, a practical frequency dependent elastic impedance inversion approach is presented to implement the estimation of the interstratified dispersive elastic parameters which makes full use of the frequency information of elastic impedances. Three main steps are included in this approach. Firstly, the elastic Bayesian inversion is implemented for the estimation of elastic impedances from different incident angle. Secondly, with those estimated elastic impedances, their variations are used to estimate P-wave velocity and S-wave velocity. Finally, with the prior elastic impedance and P-wave and S-wave velocity information, the frequency dependent elastic variation with incident angle inversion is presented for the estimation of the interstratified elastic parameters. With this approach, the interstratified elastic parameters rather than the interface information can be estimated, making easier the interpretation of frequency dependent seismic attributes. The model examples illustrate the feasibility and stability of the proposed method in P-wave velocity dispersion and S-wave velocity dispersion estimation. The field data example validates the possibility and efficiency in hydrocarbon indication of the estimated P-wave velocity dispersion and S-wave velocity dispersion.
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.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan
2013-02-15
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); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
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.
Predictive Rate-Distortion for Infinite-Order Markov Processes
NASA Astrophysics Data System (ADS)
Marzen, Sarah E.; Crutchfield, James P.
2016-06-01
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.
LES investigation of infinite staggered wind-turbine arrays
NASA Astrophysics Data System (ADS)
Yang, Xiaolei; Sotiropoulos, Fotis
2014-12-01
The layouts of turbines affect the turbine wake interactions and thus the wind farm performance. The wake interactions in infinite staggered wind-turbine arrays are investigated and compared with infinite aligned turbine arrays in this paper. From the numerical results we identify three types of wake behaviours, which are significantly different from wakes in aligned wind-turbine arrays. For the first type, each turbine wake interferes with the pair of staggered downstream turbine wakes and the aligned downstream turbine. For the second type, each turbine wake interacts with the first two downstream turbine wakes but does not show significant interference with the second aligned downstream turbine. For the third type, each turbine wake recovers immediately after passing through the gap of the first two downstream turbines and has little interaction with the second downstream turbine wakes The extracted power density and power efficiency are also studied and compared with aligned wind-turbine arrays.
The development of infinitives from three to five.
Eisenberg, S L; Cairns, H S
1994-10-01
This study investigated the form of infinitival sentences produced by young children and their knowledge of the control properties of this sentence form. Twenty-five children between the ages of 3;7 and 5;4 participated in a story completion task designed to elicit infinitive sentences and in an act-out comprehension task. Although the infinitive form was productive for even the youngest children in this study, development of this form was not complete even for the five-year-olds, nor did any child demonstrate adult knowledge of control. In addition, two competing claims regarding order of acquisition (that of Limber, 1973, and Hyams, 1985) were evaluated. PMID:7852479
Infinite number of MSSMs from heterotic line bundles?
NASA Astrophysics Data System (ADS)
Groot Nibbelink, Stefan; Loukas, Orestis; Ruehle, Fabian; Vaudrevange, Patrick K. S.
2015-08-01
We consider heterotic E8×E8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by letting their background flux quanta grow without bound. Even though we do not have a general proof, we find that all examples are at the boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which can be thought of as vanishing D-term conditions, cannot be satisfied inside the Kähler cone unless a growing number of scalar vacuum expectation values is switched on. As they are charged under various line bundles simultaneously, the gauge background gets deformed by these VEVs to a non-Abelian bundle. In general, our physical expectation is that such infinite sets of models should be impossible, since they never seem to occur in exact conformal field theory constructions.
Approximation of Optimal Infinite Dimensional Compensators for Flexible Structures
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Mingori, D. L.; Adamian, A.; Jabbari, F.
1985-01-01
The infinite dimensional compensator for a large class of flexible structures, modeled as distributed systems are discussed, as well as an approximation scheme for designing finite dimensional compensators to approximate the infinite dimensional compensator. The approximation scheme is applied to develop a compensator for a space antenna model based on wrap-rib antennas being built currently. While the present model has been simplified, it retains the salient features of rigid body modes and several distributed components of different characteristics. The control and estimator gains are represented by functional gains, which provide graphical representations of the control and estimator laws. These functional gains also indicate the convergence of the finite dimensional compensators and show which modes the optimal compensator ignores.
Predictive Rate-Distortion for Infinite-Order Markov Processes
NASA Astrophysics Data System (ADS)
Marzen, Sarah E.; Crutchfield, James P.
2016-05-01
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.
Global Stability for Infinite Delay Lotka-Volterra Type Systems
NASA Astrophysics Data System (ADS)
Kuang, Y.; Smith, H. L.
1993-06-01
In this paper, sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay, nonautonomous Lotka-Volterra type system. The present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions. We require the undelayed intraspecific competition to dominate the latter but not the former.
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.
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.
Some characterizations of quantum channel in infinite Hilbert spaces
Sun, Xiu-Hong; Li, Yuan
2014-05-15
We first show that for any quantum states ρ on H and σ on K there exists a quantum channel Φ such that Φ(ρ) = σ, where H and K are finite or infinite dimensional Hilbert spaces. Then we consider some conclusions for the quantum channel Φ such that Φ(ρ) = σ and Φ(I{sub H}) exists or Φ(I{sub H})=I{sub K}.
Single file diffusion into a semi-infinite tube.
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. PMID:26595123
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.
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.
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.
Symmetry-protected local minima in infinite DMRG
NASA Astrophysics Data System (ADS)
Pfeifer, Robert N. C.
2015-11-01
The infinite density matrix renormalization group (iDMRG) algorithm is a highly successful numerical algorithm for the study of low-dimensional quantum systems, and is also frequently used to initialize the more popular finite DMRG algorithm. Implementations of both finite and infinite DMRG frequently incorporate support for the protection and exploitation of symmetries of the Hamiltonian. In common with other variational tensor network algorithms, convergence of iDMRG to the ground state is not guaranteed, with the risk that the algorithm may become stuck in a local minimum. In this paper, I demonstrate the existence of a particularly harmful class of physically irrelevant local minima affecting both iDMRG and to a lesser extent also infinite time-evolving block decimation (iTEBD), for which the ground state is compatible with the protected symmetries of the Hamiltonian but cannot be reached using the conventional iDMRG or iTEBD algorithms. I describe a modified iDMRG algorithm which evades these local minima, and which also admits a natural interpretation on topologically ordered systems with a boundary.
Analysis of transitional separation bubbles on infinite swept wings
NASA Technical Reports Server (NTRS)
Davis, R. L.; Carter, J. E.
1986-01-01
A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.
NASA Astrophysics Data System (ADS)
Gallot, T.; Fehler, M. C.; Brown, S. R.; Buns, D.; Szabo, T.; Malcolm, A. E.
2013-12-01
The nonlinear mechanical behavior of rocks is a well known phenomenon at a laboratory scale and has been observed during earthquakes, slow slip events, volcanic activity, reservoir fracturing, etc. he present work explores the possibility of measuring nonlinear parameters in a semi-infinite medium. Contrary to existing methods that rely on vibrating a sample at a fixed resonant frequency, a pulsed wave is used to create a high amplitude perturbation (the pump) responsible for the nonlinear response. At the same time, a low amplitude wave probes the material to measure changes in elastic properties. Laboratory experiments have been performed in rocks (berea sandstones) to explore the possibility of using such a method for Earth imaging. The strain created by the pump (a shear wave in the tens of kHz), is on the order of a microstrain and is measured by laser vibrometry and extrapolated to the whole sample by a finite difference simulation. A compressional pulse (in the hundreds of kHz range) probes the 15-cm size sample. The variation in time of flight is related to a change in elasticity as described as a function of the strain through quadratic and cubic nonlinearities. Those nonlinear coefficients are shown to be sensitive to several environmental parameters such as temperature, humidity, and also physical properties such as the amplitude of the strain and the relative orientation of the pump and the probing wave. Experimental set-up: a P-wave transducer generates an ultrasonic pulse at 500 kHz recorded by an identical transducer after propagation through the sample. The medium is then perturbed with a S-wave transducer on the top of the sample at 50 kHz .
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 Technical Reports Server (NTRS)
Grissom, D. S.; Michalopoulos, C. D.
1973-01-01
A problem in the linear theory of elasticity is considered wherein a layer with a circular cylindrical hole is subjected to a nonuniform axisymmetric radial displacement. The solution utilizes Navier's equations of elasticity which are solved by means of extended Hankel transforms. A special case in which the radial displacement is a linear function of the axial coordinate is presented. Numerical results are given in graphical form for the case when hole radius and layer thickness are equal. The inversion integrals were evaluated numerically using Longman's technique for computing infinite integrals of oscillatory functions.
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 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.
Subsonic semi-infinite crack with a finite friction zone in a bimaterial
NASA Astrophysics Data System (ADS)
Antipov, Y. A.
2009-12-01
Propagation of a semi-infinite crack along the interface between an elastic half-plane and a rigid half-plane is analyzed. The crack advances at constant subsonic speed. It is assumed that, ahead of the crack, there is a finite segment where the conditions of Coulomb friction law are satisfied. The contact zone of unknown a priori length propagates with the same speed as the crack. The problem reduces to a vector Riemann-Hilbert problem with a piece-wise constant matrix coefficient discontinuous at three points, 0, 1, and ∞. The problem is solved exactly in terms of Kummer's solutions of the associated hypergeometric differential equation. Numerical results are reported for the length of the contact friction zone, the stress singularity factor, the normal displacement u2, and the dynamic energy release rate G. It is found that in the case of frictionless contact for both the sub-Rayleigh and super-Rayleigh regimes, G is positive and the stress intensity factor KII does not vanish. In the sub-Rayleigh case, the normal displacement is positive everywhere in the opening zone. In the super-Rayleigh regime, there is a small neighborhood of the ending point of the open zone where the normal displacement is negative.
Elastic properties of hedenbergite
NASA Astrophysics Data System (ADS)
Kandelin, John; Weidner, Donald J.
1988-02-01
The single-crystal elastic moduli of hedenbergite (CaFeSi2O6) hare been measured at 20°C and 1 bar using Brillouin spectroscopy. The moduli are (in gigapascals): C11 = 222, C22 = 176, C23 = 249, C44 = 55, C55 = 63, C66 = 60, C12 = 69, C13 = 79, C33, = 86, C15 = 12, C25 = 13, C35 = 26, C46 = -10. The comparison of elastic properties among Mg-Fe-Ca bearing pyroxenes, known as quadrilateral pyroxenes, reveals only weak variations with changes in composition. Of the four quadrilateral pyroxenes, orthoferrosilite has elastic properties distinctive from the others. The principal differences among these pyroxenes are due to subtle structural differences. In particular, the mechanical linkage between the M2 polyhedral chains in clinopyroxenes enhances the importance of the cation in this site. In contrast to the orthopyroxenes, the aggregate shear modulus μ of the calcium-bearing clinopyroxenes (diopside and hedenbergite) exhibits no dependence on the amount of iron (Fe2+) present in the structure, while the ratio K/μ does. As a result, the compressional and shear acoustic velocities of the calcium-bearing clinopyroxenes show a smaller dependency on iron content than do the orthopyroxenes.
NASA Astrophysics Data System (ADS)
Lazarev, L. A.
2015-07-01
An infinite panel with two types of resonators regularly installed on it is theoretically considered. Each resonator is an air-filled cavity hermetically closed by a plate, which executes piston vibrations. The plate and air inside the cavity play the roles of mass and elasticity, respectively. Every other resonator is reversed. At a certain ratio between the parameters of the resonators at the tuning frequency of the entire system, the acoustic-pressure force that directly affects the panel can be fully compensated by the action forces of the resonators. In this case, the sound-proofing ability (transmission loss) tends to infinity. The presented calculations show that a complete transmission-loss effect can be achieved even with low- Q resonators.
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.
Spin transport of weakly disordered Heisenberg chain at infinite temperature
NASA Astrophysics Data System (ADS)
Khait, Ilia; Gazit, Snir; Yao, Norman Y.; Auerbach, Assa
2016-06-01
We study the disordered Heisenberg spin chain, which exhibits many-body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as C ˜t-β , whereas the conductivity exhibits a low-frequency power law σ ˜ωα . The exponents depict subdiffusive behavior β <1 /2 ,α >0 at all finite disorders and convergence to the scaling result α +2 β =1 at large disorders.
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.
Rotor-router walk on a semi-infinite cylinder
NASA Astrophysics Data System (ADS)
Papoyan, Vl V.; Poghosyan, V. S.; Priezzhev, V. B.
2016-07-01
We study the rotor-router walk with the clockwise ordering of outgoing edges on the semi-infinite cylinder. Imposing uniform conditions on the boundary of the cylinder, we consider growth of the cluster of visited sites and its internal structure. The average width of the surface region of the cluster evolves with time to the stationary value by a scaling law whose parameters are close to the standard KPZ exponents. We introduce characteristic labels corresponding to closed clockwise contours formed by rotors and show that the sequence of labels has in average an ordered helix structure.
Anomalous properties of the Hubbard model in infinite dimensions
NASA Astrophysics Data System (ADS)
Jarrell, M.; Pruschke, Th.
1994-01-01
Anomalies are found in the resistivity ρ and NMR rate 1/T1 of the infinite-dimensional Hubbard model using quantum Monte Carlo calculations and the noncrossing approximation. For temperatures greater than the ``Kondo scale'' T0, we obtain 1/T1~a+bT and ρ~c+dT (a, b, c, d constants). For temperatures T<
Crack problems for a rectangular plate and an infinite strip
NASA Technical Reports Server (NTRS)
Civelek, M. B.; Erdogan, F.
1980-01-01
The general plane problem for an infinite strip containing multiple cracks perpendicular to its boundaries is considered. The problem is reduced to a system of singular integral equations. Two specific problems of practical interest are then studied in detail. The first problem explores the interaction effect of multiple edge cracks in a plate or beam under tension or bending. The second problem is that of a rectangular plate containing an arbitrarily oriented crack in the plane of symmetry. Particular emphasis is placed on the problem of a plate containing an edge crack and subjected to concentrated forces.
Infinite impulse response modal filtering in visible adaptive optics
NASA Astrophysics Data System (ADS)
Agapito, G.; Arcidiacono, C.; Quirós-Pacheco, F.; Puglisi, A.; Esposito, S.
2012-07-01
Diffraction limited resolution adaptive optics (AO) correction in visible wavelengths requires a high performance control. In this paper we investigate infinite impulse response filters that optimize the wavefront correction: we tested these algorithms through full numerical simulations of a single-conjugate AO system comprising an adaptive secondary mirror with 1127 actuators and a pyramid wavefront sensor (WFS). The actual practicability of the algorithms depends on both robustness and knowledge of the real system: errors in the system model may even worsen the performance. In particular we checked the robustness of the algorithms in different conditions, proving that the proposed method can reject both disturbance and calibration errors.
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
D. Day
2007-03-01
The nucleon form factors are still the subject of active investigation even after an experimental effort spanning 50 years. This is because they are of critical importance to our understanding of the electromagnetic properties of nuclei and provide a unique testing ground for QCD motivated models of nucleon structure. Progress in polarized beams, polarized targets and recoil polarimetry have allowed an important and precise set of data to be collected over the last decade. I will review the experimental status of elastic electron scattering from the nucleon along with an outlook for future progress.
NASA Astrophysics Data System (ADS)
Wisdom, Jack; Meyer, Jennifer
2016-04-01
This is an exploration of dynamic tides on elastic bodies. The body is thought of as a dynamical system described by its modes of oscillation. The dynamics of these modes are governed by differential equations that depend on the rheology. The modes are damped by dissipation. Tidal friction occurs as exterior bodies excite the modes and the modes act back on the tide raising body. The whole process is governed by a closed set of differential equations. Standard results from tidal theory are recovered in a two-timescale approximation to the solution of these differential equations.
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.
Probabilistic context-free grammars estimated from infinite distributions.
Corazza, Anna; Satta, Giorgio
2007-08-01
In this paper, we consider probabilistic context-free grammars, a class of generative devices that has been successfully exploited in several applications of syntactic pattern matching, especially in statistical natural language parsing. We investigate the problem of training probabilistic context-free grammars on the basis of distributions defined over an infinite set of trees or an infinite set of sentences by minimizing the cross-entropy. This problem has applications in cases of context-free approximation of distributions generated by more expressive statistical models. We show several interesting theoretical properties of probabilistic context-free grammars that are estimated in this way, including the previously unknown equivalence between the grammar cross-entropy with the input distribution and the so-called derivational entropy of the grammar itself. We discuss important consequences of these results involving the standard application of the maximum-likelihood estimator on finite tree and sentence samples, as well as other finite-state models such as Hidden Markov Models and probabilistic finite automata. PMID:17568142
Relativistic regular approximations revisited: An infinite-order relativistic approximation
Dyall, K.G.; van Lenthe, E.
1999-07-01
The concept of the regular approximation is presented as the neglect of the energy dependence of the exact Foldy{endash}Wouthuysen transformation of the Dirac Hamiltonian. Expansion of the normalization terms leads immediately to the zeroth-order regular approximation (ZORA) and first-order regular approximation (FORA) Hamiltonians as the zeroth- and first-order terms of the expansion. The expansion may be taken to infinite order by using an un-normalized Foldy{endash}Wouthuysen transformation, which results in the ZORA Hamiltonian and a nonunit metric. This infinite-order regular approximation, IORA, has eigenvalues which differ from the Dirac eigenvalues by order E{sup 3}/c{sup 4} for a hydrogen-like system, which is a considerable improvement over the ZORA eigenvalues, and similar to the nonvariational FORA energies. A further perturbation analysis yields a third-order correction to the IORA energies, TIORA. Results are presented for several systems including the neutral U atom. The IORA eigenvalues for all but the 1s spinor of the neutral system are superior even to the scaled ZORA energies, which are exact for the hydrogenic system. The third-order correction reduces the IORA error for the inner orbitals to a very small fraction of the Dirac eigenvalue. {copyright} {ital 1999 American Institute of Physics.}
Infinite Factorial Unbounded-State Hidden Markov Model.
Valera, Isabel; Ruiz, Francisco J R; Perez-Cruz, Fernando
2016-09-01
There are many scenarios in artificial intelligence, signal processing or medicine, in which a temporal sequence consists of several unknown overlapping independent causes, and we are interested in accurately recovering those canonical causes. Factorial hidden Markov models (FHMMs) present the versatility to provide a good fit to these scenarios. However, in some scenarios, the number of causes or the number of states of the FHMM cannot be known or limited a priori. In this paper, we propose an infinite factorial unbounded-state hidden Markov model (IFUHMM), in which the number of parallel hidden Markovmodels (HMMs) and states in each HMM are potentially unbounded. We rely on a Bayesian nonparametric (BNP) prior over integer-valued matrices, in which the columns represent the Markov chains, the rows the time indexes, and the integers the state for each chain and time instant. First, we extend the existent infinite factorial binary-state HMM to allow for any number of states. Then, we modify this model to allow for an unbounded number of states and derive an MCMC-based inference algorithm that properly deals with the trade-off between the unbounded number of states and chains. We illustrate the performance of our proposed models in the power disaggregation problem. PMID:26571511
Masses of atomic nuclei in the infinite nuclear matter model
Satpathy, L.; Nayak, R.C.
1988-07-01
We present mass excesses of 3481 nuclei in the range 18less than or equal toAless than or equal to267 using the infinite nuclear matter model based on the Hugenholtz-Van Hove theorem. In this model the ground-state energy of a nucleus of asymmetry ..beta.. is considered equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus the residual energy due to shell effects, deformation, etc., called the local energy eta. In this model there are two kinds of parameters: global and local. The five global parameters characterizing the properties of the above sphere are determined by fitting the mass of all nuclei (756) in the recent mass table of Wapstra et al. having error bar less than 30 keV. The local parameters are determined for 25 regions each spanning 8 or 10 A values. The total number of parameters including the five global ones is 238. The root-mean-square deviation for the calculated masses from experiment is 397 keV for the 1572 nuclei used in the least-squares fit. copyright 1988 Academic Press, Inc.
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Lu, M. C.; Erdogan, F.
1980-01-01
The numerical method is given for solving the plane problem for two bonded infinite dissimilar elastic strips which contain cracks of various configurations. The problem is intended to approximate a composite beam or a plate having cracks perpendicular to and on the interface of the two layers.
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
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)
Bik, W. M. A.; Habraken, F. H. P. M.
1993-07-01
In elastic recoil detection (ERD) one determines the yield and energy of particles ejected out of the surface region of samples under MeV ion bombardment. By application of this surface and thin film analysis technique one can obtain quantitative information concerning the depth distribution of light elements in a sample to be analysed. The quantitativity and the depth resolving power are based on knowledge of the recoil cross section and the stopping power of high-energy ions in matter. This paper reviews the fundamentals of this technique and the various experimental methods for recoil identification. Furthermore, important features for material analysis, such as detection limits, depth resolution and elemental range are discussed. Some emphasis is put on the conversion of the spectral contribution of the elements to atomic concentrations in the films for several representative cases. Throughout the review numerous examples are given to illustrate the features of ERD and to demonstrate empirically the accuracy of the quantification method.
Elastic instabilities in rubber
NASA Astrophysics Data System (ADS)
Gent, Alan
2009-03-01
Materials that undergo large elastic deformations can exhibit novel instabilities. Several examples are described: development of an aneurysm on inflating a rubber tube; non-uniform stretching on inflating a spherical balloon; formation of internal cracks in rubber blocks at a critical level of triaxial tension or when supersaturated with a dissolved gas; surface wrinkling of a block at a critical amount of compression; debonding or fracture of constrained films on swelling, and formation of ``knots'' on twisting stretched cylindrical rods. These various deformations are analyzed in terms of a simple strain energy function, using Rivlin's theory of large elastic deformations, and the results are compared with experimental measurements of the onset of unstable states. Such comparisons provide new tests of Rivlin's theory and, at least in principle, critical tests of proposed strain energy functions for rubber. Moreover the onset of highly non-uniform deformations has serious implications for the fatigue life and fracture resistance of rubber components. [4pt] References: [0pt] R. S. Rivlin, Philos. Trans. Roy. Soc. Lond. Ser. A241 (1948) 379--397. [0pt] A. Mallock, Proc. Roy. Soc. Lond. 49 (1890--1891) 458--463. [0pt] M. A. Biot, ``Mechanics of Incremental Deformations'', Wiley, New York, 1965. [0pt] A. N. Gent and P. B. Lindley, Proc. Roy. Soc. Lond. A 249 (1958) 195--205. [0pt] A. N. Gent, W. J. Hung and M. F. Tse, Rubb. Chem. Technol. 74 (2001) 89--99. [0pt] A. N. Gent, Internatl. J. Non-Linear Mech. 40 (2005) 165--175.
Infinite phased array of microstrip dipoles in two layers
NASA Astrophysics Data System (ADS)
Castaneda, Jesus A.
1989-01-01
A method has been devised for the analysis of the infinite printed strip dipole array in a two layer microstrip substrate structure. The complete dynamic Green's function appropriate to the two-layer substrate-superstrate structure was used in the formulation of the method of moments solution. In this way all the substrate effects, including the surface wave related phenomena, have been included in the development and solution. The solution provides a means by which the most important performance characteristics of the finite-but-large phase-scanned microstrip array can be studied. Attention has been focused on the characterization of the active input impedance as a function of the equivalent scan angle.
A General No-Cloning Theorem for an infinite Multiverse
NASA Astrophysics Data System (ADS)
Gauthier, Yvon
2013-10-01
In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.
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.
Second quantisation for skew convolution products of infinitely divisible measures
NASA Astrophysics Data System (ADS)
Applebaum, David; van Neerven, Jan
2015-03-01
Suppose λ1 and λ2 are infinitely divisible Radon measures on real Banach spaces E1 and E2, respectively and let T : E1 → E2 be a Borel measurable mapping so that T(λ1) * ρ = λ2 for some Radon probability measure ρ on E2. Extending previous results for the Gaussian and the Poissonian case, we study the problem of representing the "transition operator" PT : Lp(E2, λ2) → Lp(E1, λ1) given by $PTf(x) = ∫ E{2}f(T(x) + y)dρ (y)$ as the second quantisation of a contraction operator acting between suitably chosen "reproducing kernel Hilbert spaces" associated with λ1 and λ2.
Multipoint inverse design of an infinite cascade of airfoils
NASA Astrophysics Data System (ADS)
Selig, M. S.
1994-04-01
This paper describes a method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping and does not allow for multipoint design. The cascade blade is to determined is divided into a number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distributions is to be achieved. In this way multipoint design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all of the desired characteristucs. For example, the cascade blades may be bulbous or crossed. Through Newtonian iteration, however, the desired characteristics may be prescribed directly. Four examples will be illustrated to demonstrate the capability of the method.
Variational optimization with infinite projected entangled-pair states
NASA Astrophysics Data System (ADS)
Corboz, Philippe
2016-07-01
We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states, a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state of a local Hamiltonian. The method is based on a systematic summation of Hamiltonian contributions using the corner-transfer-matrix method. Benchmark results for challenging problems are presented, including the two-dimensional Heisenberg model, the Shastry-Sutherland model, and the t -J model, which show that the variational scheme yields considerably more accurate results than the previously best imaginary-time evolution algorithm, with a similar computational cost and with a faster convergence towards the ground state.
Recurrent kernel machines: computing with infinite echo state networks.
Hermans, Michiel; Schrauwen, Benjamin
2012-01-01
Echo state networks (ESNs) are large, random recurrent neural networks with a single trained linear readout layer. Despite the untrained nature of the recurrent weights, they are capable of performing universal computations on temporal input data, which makes them interesting for both theoretical research and practical applications. The key to their success lies in the fact that the network computes a broad set of nonlinear, spatiotemporal mappings of the input data, on which linear regression or classification can easily be performed. One could consider the reservoir as a spatiotemporal kernel, in which the mapping to a high-dimensional space is computed explicitly. In this letter, we build on this idea and extend the concept of ESNs to infinite-sized recurrent neural networks, which can be considered recursive kernels that subsequently can be used to create recursive support vector machines. We present the theoretical framework, provide several practical examples of recursive kernels, and apply them to typical temporal tasks. PMID:21851278
Unstable infinite nuclear matter in stochastic mean field approach
Colonna, M.; Chomaz, P. Laboratorio Nazionale del Sud, Viale Andrea Doria, Catania )
1994-04-01
In this article, we consider a semiclassical stochastic mean-field approach. In the case of unstable infinite nuclear matter, we calculate the characteristic time of the exponential growing of fluctuations and the diffusion coefficients associated to the unstable modes, in the framework of the Boltzmann-Langevin theory. These two quantities are essential to describe the dynamics of fluctuations and instabilities since, in the unstable regions, the evolution of the system will be dominated by the amplification of fluctuations. In order to make realistic 3D calculations feasible, we suggest to replace the complicated Boltzmann-Langevin theory by a simpler stochastic mean-field approach corresponding to a standard Boltzmann evolution, complemented by a simple noise chosen to reproduce the dynamics of the most unstable modes. Finally we explain how to approximately implement this method by simply tuning the noise associated to the use of a finite number of test particles in Boltzman-like calculations.
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.
Phases of the infinite U Hubbard model on square lattices.
Liu, Li; Yao, Hong; Berg, Erez; White, Steven R; Kivelson, Steven A
2012-03-23
We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n≳0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states. PMID:22540606
Exploring percolative landscapes: Infinite cascades of geometric phase transitions
NASA Astrophysics Data System (ADS)
Timonin, P. N.; Chitov, Gennady Y.
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2 D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters.
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.
Exploring percolative landscapes: Infinite cascades of geometric phase transitions.
Timonin, P N; Chitov, Gennady Y
2016-01-01
The evolution of many kinetic processes in 1+1 (space-time) dimensions results in 2D directed percolative landscapes. The active phases of these models possess numerous hidden geometric orders characterized by various types of large-scale and/or coarse-grained percolative backbones that we define. For the patterns originated in the classical directed percolation (DP) and contact process we show from the Monte Carlo simulation data that these percolative backbones emerge at specific critical points as a result of continuous phase transitions. These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones. The multitude of conceivable percolative backbones implies the existence of infinite cascades of such geometric transitions in the kinetic processes considered. We present simple arguments to support the conjecture that such cascades of transitions are a generic feature of percolation as well as of many other transitions with nonlocal order parameters. PMID:26871019
The gravitational field of an infinite flat slab
NASA Astrophysics Data System (ADS)
Fulling, S. A.; Bouas, J. D.; Carter, H. B.
2015-08-01
We study Einstein's equations with a localized plane-symmetric source, with close attention to gauge freedom/fixing and to listing all physically distinct solutions. In the vacuum regions there are only two qualitatively different solutions, one curved and one flat; in addition, on each of the two sides there is a free parameter describing how the slab is embedded into the vacuum region. Surprisingly, for a generic slab source the solution must be curved on one side and flat on the other. We treat infinitely thin slabs in full detail and indicate how thick slabs can increase the variety of external geometry pairs. Positive energy density seems to force external geometries with curvature singularities at some distance from the slab; we speculate that such singularities occur in regions where the solution cannot be physically relevant anyway.
Dynamics of Bubbles Rising in Finite and Infinite Media
C.C. Maneri; P.F. Vassallo
2000-10-27
The dynamic behavior of single bubbles rising in quiescent liquid Suva (R134a) in a duct has been examined through the use of a high speed video system. Size, shape and velocity measurements obtained with the video system reveal a wide variety of characteristics for the bubbles as they rise in both finite and infinite media. This data, coupled with previously published data for other working fluids, has been used to assess and extend a rise velocity model given by Fan and Tsuchiya. As a result of this assessment, a new rise velocity model has been developed which maintains the physically consistent characteristics of the surface tension in the distorted bubbly regime. In addition, the model is unique in that it covers the entire range of bubble sizes contained in the spherical, distorted and planar slug regimes.
Persistence in nonautonomous predator-prey systems with infinite delays
NASA Astrophysics Data System (ADS)
Teng, Zhidong; Rehim, Mehbuba
2006-12-01
This paper studies the general nonautonomous predator-prey Lotka-Volterra systems with infinite delays. The sufficient and necessary conditions of integrable form on the permanence and persistence of species are established. A very interesting and important property of two-species predator-prey systems is discovered, that is, the permanence of species and the existence of a persistent solution are each other equivalent. Particularly, for the periodic system with delays, applying these results, the sufficient and necessary conditions on the permanence and the existence of positive periodic solutions are obtained. Some well-known results on the nondelayed periodic predator-prey Lotka-Volterra systems are strongly improved and extended to the delayed case.
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.
Infinite-range Heisenberg model and high-temperature superconductivity
NASA Astrophysics Data System (ADS)
Tahir-Kheli, Jamil; Goddard, William A., III
1993-11-01
A strongly coupled variational wave function, the doublet spin-projected Néel state (DSPN), is proposed for oxygen holes in three-band models of high-temperature superconductors. This wave function has the three-spin system of the oxygen hole plus the two neighboring copper atoms coupled in a spin-1/2 doublet. The copper spins in the neighborhood of a hole are in an eigenstate of the infinite-range Heisenberg antiferromagnet (SPN state). The doublet three-spin magnetic polaron or hopping polaron (HP) is stabilized by the hopping terms tσ and tτ, rather than by the copper-oxygen antiferromagnetic coupling Jpd. Although, the HP has a large projection onto the Emery (Dg) polaron, a non-negligible amount of doublet-u (Du) character is required for optimal hopping stabilization. This is due to Jdd, the copper-copper antiferromagnetic coupling. For the copper spins near an oxygen hole, the copper-copper antiferromagnetic coupling can be considered to be almost infinite ranged, since the copper-spin-correlation length in the superconducting phase (0.06-0.25 holes per in-plane copper) is approximately equal to the mean separation of the holes (between 2 and 4 lattice spacings). The general DSPN wave function is constructed for the motion of a single quasiparticle in an antiferromagnetic background. The SPN state allows simple calculations of various couplings of the oxygen hole with the copper spins. The energy minimum is found at symmetry (π/2,π/2) and the bandwidth scales with Jdd. These results are in agreement with exact computations on a lattice. The coupling of the quasiparticles leads to an attraction of holes and its magnitude is estimated.
Infinite networks and variation of conductance functions in discrete Laplacians
NASA Astrophysics Data System (ADS)
Jorgensen, Palle; Tian, Feng
2015-04-01
For a given infinite connected graph G = (V, E) and an arbitrary but fixed conductance function c, we study an associated graph Laplacian Δc; it is a generalized difference operator where the differences are measured across the edges E in G; and the conductance function c represents the corresponding coefficients. The graph Laplacian (a key tool in the study of infinite networks) acts in an energy Hilbert space ℋE computed from c. Using a certain Parseval frame, we study the spectral theoretic properties of graph Laplacians. In fact, for fixed c, there are two versions of the graph Laplacian, one defined naturally in the l2 space of V and the other in ℋE. The first is automatically selfadjoint, but the second involves a Krein extension. We prove that, as sets, the two spectra are the same, aside from the point 0. The point zero may be in the spectrum of the second, but not the first. We further study the fine structure of the respective spectra as the conductance function varies, showing now how the spectrum changes subject to variations in the function c. Specifically, we study an order on the spectra of the family of operators Δc, and we compare it to the ordering of pairs of conductance functions. We show how point-wise estimates for two conductance functions translate into spectral comparisons for the two corresponding graph Laplacians, involving a certain similarity: We prove that point-wise ordering of two conductance functions c on E induces a certain similarity of the corresponding (Krein extensions computed from the) two graph Laplacians Δc. The spectra are typically continuous, and precise notions of fine-structure of spectrum must be defined in terms of equivalence classes of positive Borel measures (on the real line). Our detailed comparison of spectra is analyzed this way.
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)
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.
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…
Monreal, Marisa J; Seaman, Lani A; Goff, George S; Michalczyk, Ryszard; Morris, David E; Scott, Brian L; Kiplinger, Jaqueline L
2016-03-01
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. PMID:26865502
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.
Oscillating laminar electrokinetic flow in infinitely extended circular microchannels.
Bhattacharyya, A; Masliyah, J H; Yang, J
2003-05-01
This article addresses the problem of oscillating laminar electrokinetic liquid flow in an infinitely extended circular microchannel. Based on the Debye-Huckel approximation for low surface potential at the channel wall, a complex variable approach is used to obtain an analytical solution for the flow. The complex counterparts of the flow rate and the current are linearly dependent on the pressure gradient and the external electric field. This property is used to show that Onsager's principle of reciprocity continues to be valid (involving the complex quantities) for the stated problem. During oscillating pressure-driven flow, the electroviscous effect for a given value of the normalized reciprocal electrical double-layer (EDL) thickness is observed to attain a maximum at a certain normalized frequency. In general, an increasing normalized frequency results in a reduction of EDL effects, leading to (i). a volumetric flow rate in the case of streaming potential approaching that predicted by the theory without EDL effects, and (ii). a reduction in the volumetric flow rate in the case of electroosmosis. PMID:12725819
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. PMID:24808217
Isotropic probability measures in infinite-dimensional spaces
NASA Technical Reports Server (NTRS)
Backus, George
1987-01-01
Let R be the real numbers, R(n) the linear space of all real n-tuples, and R(infinity) the linear space of all infinite real sequences x = (x sub 1, x sub 2,...). Let P sub in :R(infinity) approaches R(n) be the projection operator with P sub n (x) = (x sub 1,...,x sub n). Let p(infinity) be a probability measure on the smallest sigma-ring of subsets of R(infinity) which includes all of the cylinder sets P sub n(-1) (B sub n), where B sub n is an arbitrary Borel subset of R(n). Let p sub n be the marginal distribution of p(infinity) on R(n), so p sub n(B sub n) = p(infinity) (P sub n to the -1 (B sub n)) for each B sub n. A measure on R(n) is isotropic if it is invariant under all orthogonal transformations of R(n). All members of the set of all isotropic probability distributions on R(n) are described. The result calls into question both stochastic inversion and Bayesian inference, as currently used in many geophysical inverse problems.
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
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. PMID:26230777
(1)/(N) expansion of the nonequilibrium infinite- U Anderson model
NASA Astrophysics Data System (ADS)
Ratiani, Zurab; Mitra, Aditi
2009-06-01
Results are presented for the nonequilibrium infinite- U Anderson model using a large N approach, where N is the degeneracy of the impurity level, and where nonequilibrium is established by coupling the level to two leads at two different chemical potentials so that there is current flow. A slave-boson representation combined with Keldysh functional integral methods is employed. Expressions for the static spin susceptibility χS and the conductance G are presented to O((1)/(N)) and for an applied voltage difference V less than the Kondo temperature. The correlation function for the slave boson is found to be significantly modified from its equilibrium form in that it acquires a rapid decay in time with a rate that equals the current-induced decoherence rate. Physical observables are found to have a rather complex dependence on the coupling strength to the two leads which can lead to asymmetric behavior χS(V)≠χS(-V) , G(V)≠G(-V) both in the mixed valence and in the Kondo regime.
Scattering by infinitely rising one-dimensional potentials
NASA Astrophysics Data System (ADS)
Ferreira, E. M.; Sesma, J.
2015-12-01
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the energy. Here we consider the problem of scattering by the members of a family of potentials Va(x) = - sgn(x) | x | a, where sgn represents the sign function and a is a positive rational number. The scattering function and the phase shifts are obtained from global solutions of the Schrödinger equation. For the determination of the Gamow states, associated to resonances, we exploit their close relation with the eigenvalues of the PT-symmetric Hamiltonians with potentials VaPT(x) = - i sgn(x) | x | a. Calculation of the time delay in the scattering at real energies is used to characterize the resonances. As an additional result, the breakdown of the PT-symmetry of the family of potentials VaPT for a < 3 may be conjectured.
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.
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)
Water waves as a spatial dynamical system; infinite depth case.
Barrandon, Matthieu; Iooss, Gérard
2005-09-01
We review the mathematical results on traveling waves in one or several superposed layers of potential flow, subject to gravity, with or without surface and interfacial tension, where the bottom layer is infinitely deep. The problem is formulated as a "spatial dynamical system," and it is shown that the linearized operator of the resulting reversible system has an essential spectrum filling the real line. We consider three cases where bifurcation occurs. (i) The first case is when, in moving a parameter, two pairs of imaginary eigenvalues merge into one pair of double eigenvalues, and then split into four symmetric complex conjugate eigenvalues. (ii) The second case is when one pair of imaginary eigenvalues meet in 0, and disappear; (iii) the third case is when the phenomenon described in (ii) is superposed to the presence of another pair of imaginary eigenvalues sitting at finite distance from 0. We give a physical example for each case and more specially study the solitary waves and generalized solitary waves, emphasizing the differences, in the methods and in the results, between these cases and the finite depth case. PMID:16253007
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.
A conformal truncation framework for infinite-volume dynamics
NASA Astrophysics Data System (ADS)
Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T.
2016-07-01
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. We also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.
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.
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
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., A3/A2, where A(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). PMID:26395687
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)
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)
Fingering in Confined Elastic Layers
NASA Astrophysics Data System (ADS)
Biggins, John; Mahadevan, L.; Wei, Z.; Saintyves, Baudouin; Bouchaud, Elizabeth
2015-03-01
Fingering has recently been observed in soft highly elastic layers that are confined between and bonded to two rigid bodies. In one case an injected fluid invades the layer in finger-like protrusions at the layer's perimeter, a solid analogue of Saffman-Taylor viscous fingering. In a second case, separation of the rigid bodies (with maintained adhesion to the layer) leads air to the formation of similar fingers at the layer's perimeter. In both cases the finger formation is reversible: if the fluid is removed or the separation reduced, the fingers vanish. In this talk I will discuss a theoretical model for such elastic fingers that shows that the origin of the fingers is large-strain geometric non-linearity in the elasticity of soft solids. Our simplified elastic model unifies the two types of fingering and accurately estimates the thresholds and wavelengths of the fingers.
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.
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, 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.
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.
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
Analysis of the Elastic Field in Functionally Graded Materials
NASA Astrophysics Data System (ADS)
Mohammadi, Mohsen
In this thesis, the elastic field in circular beams and pipes made of functionally graded materials is considered. The following aspects are presented. First, the thermoelastic stress field in a functionally graded curved beam, where the elastic stiffness varies in the radial direction, is considered. An analytical solution is obtained where the radial variation of the stiffness is represented by a fairly general form. The stress fields corresponding to two different cases for the elastic properties are examined. The flexural stress in the curved beam is then compared with that of a ring. A relatively simple approximate solution is then developed and this is shown to be in good agreement with the analytical results. Secondly, the effect of a nonconstant Poisson's ratio upon the elastic field in functionally graded axisymmetric solids is analyzed. Both of the elastic coefficients, i.e. Young's modulus and Poisson's ratio, are permitted to vary in the radial direction. These elastic coefficients are considered to be functions of composition and are related on this basis. This allows a closed form solution for the stress function to be obtained. Two cases are discussed in this investigation: a) both Young's modulus and Poisson's ratio are allowed to vary across the radius and the effect of spatial variation of Poisson's ratio upon the maximum radial displacement is investigated; b) Young's modulus is taken as constant and the change in the maximum hoop stress resulting from a variable Poisson's ratio is calculated. Thirdly, the stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young's modulus and Poisson's ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of
Acoustic and elastic multiple scattering and radiation from cylindrical structures
NASA Astrophysics Data System (ADS)
Amirkulova, Feruza Abdukadirovna
Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an
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)
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.
The effect of tissue elastic properties and surfactant on alveolar stability.
Andreassen, Steen; Steimle, Kristoffer L; Mogensen, Mads L; Bernardino de la Serna, Jorge; Rees, Stephen; Karbing, Dan S
2010-11-01
This paper presents a novel mathematical model of alveoli, which simulates the effects of tissue elasticity and surfactant on the stability of human alveoli. The model incorporates a spherical approximation to the alveolar geometry, the hysteretic behavior of pulmonary surfactant and tissue elasticity. The model shows that the alveolus without surfactant and the elastic properties of the lung tissue are always at an unstable equilibrium, with the capability both to collapse irreversibly and to open with infinite volume when the alveolus has small opening radii. During normal tidal breathing, the alveolus can becomes stable, if surfactant is added. Including the passive effect of tissue elasticity stabilizes the alveolus, further allowing the alveoli to be stable, even for lung volumes below residual volume. The model is the first to describe the combined effects of tissue elasticity and surfactant on alveolar stability. The model may be used as an integrated part of a more comprehensive model of the respiratory system, since it can predict opening pressures of alveoli. PMID:20724566
The infinite range Heisenberg model and high temperature superconductivity
NASA Astrophysics Data System (ADS)
Tahir-Kheli, Jamil
1992-01-01
The thesis deals with the theory of high temperature superconductivity from the standpoint of three-band Hubbard models.Chapter 1 of the thesis proposes a strongly coupled variational wavefunction that has the three-spin system of an oxygen hole and its two neighboring copper spins in a doublet and the background Cu spins in an eigenstate of the infinite range antiferromagnet. This wavefunction is expected to be a good "zeroth order" wavefunction in the superconducting regime of dopings. The three-spin polaron is stabilized by the hopping terms rather than the copper-oxygen antiferromagnetic coupling Jpd. Considering the effect of the copper-copper antiferromagnetic coupling Jdd, we show that the three-spin polaron cannot be pure Emery (Dg), but must have a non-negligible amount of doublet-u (Du) character for hopping stabilization. Finally, an estimate is made for the magnitude of the attractive coupling of oxygen holes.Chapter 2 presents an exact solution to a strongly coupled Hamiltonian for the motion of oxygen holes in a 1-D Cu-O lattice. The Hamiltonian separates into two pieces: one for the spin degrees of freedom of the copper and oxygen holes, and the other for the charge degrees of freedom of the oxygen holes. The spinon part becomes the Heisenberg antiferromagnet in 1-D that is soluble by the Bethe Ansatz. The holon piece is also soluble by a Bethe Ansatz with simple algebraic relations for the phase shifts.Finally, we show that the nearest neighbor Cu-Cu spin correlation increases linearly with doping and becomes positive at x [...] 0.70.
Commutative law for products of infinitely large isotropic random matrices.
Burda, Zdzislaw; Livan, Giacomo; Swiech, Artur
2013-08-01
Ensembles of isotropic random matrices are defined by the invariance of the probability measure under the left (and right) multiplication by an arbitrary unitary matrix. We show that the multiplication of large isotropic random matrices is spectrally commutative and self-averaging in the limit of infinite matrix size N→∞. The notion of spectral commutativity means that the eigenvalue density of a product ABC... of such matrices is independent of the order of matrix multiplication, for example, the matrix ABCD has the same eigenvalue density as ADCB. In turn, the notion of self-averaging means that the product of n independent but identically distributed random matrices, which we symbolically denote by AAA..., has the same eigenvalue density as the corresponding power A(n) of a single matrix drawn from the underlying matrix ensemble. For example, the eigenvalue density of ABCCABC is the same as that of A(2)B(2)C(3). We also discuss the singular behavior of the eigenvalue and singular value densities of isotropic matrices and their products for small eigenvalues λ→0. We show that the singularities at the origin of the eigenvalue density and of the singular value density are in one-to-one correspondence in the limit N→∞: The eigenvalue density of an isotropic random matrix has a power-law singularity at the origin ~|λ|(-s) with a power sε(0,2) when and only when the density of its singular values has a power-law singularity ~λ(-σ) with a power σ=s/(4-s). These results are obtained analytically in the limit N→∞. We supplement these results with numerical simulations for large but finite N and discuss finite-size effects for the most common ensembles of isotropic random matrices. PMID:24032775
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.
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.
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.
Effective medium theory for elastic metamaterials in thin elastic plates
NASA Astrophysics Data System (ADS)
Torrent, Daniel; Pennec, Yan; Djafari-Rouhani, Bahram
2014-09-01
An effective medium theory for resonant and nonresonant metamaterials for flexural waves in thin plates is presented. The theory provides closed-form expressions for the effective mass density, rigidity, and Poisson's ratio of arrangements of isotropic scatterers in thin plates, valid for low frequencies and moderate filling fractions. It is found that the effective Young's modulus and Poisson's ratio are induced by a combination of the monopolar and quadrupolar scattering coefficient, as it happens for bulk elastic waves, while the effective mass density is induced by the monopolar coefficient, contrarily as it happens for bulk elastic waves, where the effective mass density is induced by the dipolar coefficient. It is shown that resonant positive or negative effective elastic parameters are possible, being therefore the monopolar resonance responsible for creating an effective medium with negative mass density. Several examples are given for both nonresonant and resonant effective parameters and the results are numerically verified by multiple scattering theory and finite element analysis.
Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity
NASA Astrophysics Data System (ADS)
Mielke, Alexander
1988-09-01
Saint-Venant's problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross-sectional resultants of force and moment. Using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite-dimensional manifold. In particular, the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations. Moreover, the set of semi-inverse solutions can be analyzed locally.
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.
Hydrodynamic repulsion of elastic dumbbells
NASA Astrophysics Data System (ADS)
Ekiel-Jezewska, Maria L.; Bukowicki, Marek; Gruca, Marta
2015-11-01
Dynamics of two identical elastic dumbbells, settling under gravity in a viscous fluid at low Reynolds number are analyzed within the point-particle model. Initially, the dumbbells are vertical, their centers are aligned horizontally, and the springs which connect the dumbbell's beads are at the equilibrium. The motion of the beads is determined numerically with the use of the Runge-Kutta method. After an initial relaxation phase, the system converges to a universal time-dependent solution. The elastic dumbbells tumble while falling, but their relative motion is not periodic (as in case of rigid dumbbells or pairs of separated beads). The elastic constraints break the time-reversal symmetry of the motion. As the result, the horizontal distance between the dumbbells slowly increases - they are hydrodynamically repelled from each other. This effect can be very large even though the elastic forces are always much smaller than gravity. The dynamics described above are equivalent to the motion of a single elastic dumbbell under a constant external force which is parallel to a flat free surface. The dumbbell migrates away from the interface and its tumbling time increases.
Infinitely many generalized symmetries and Painlevé analysis of a (2 + 1)-dimensional Burgers system
NASA Astrophysics Data System (ADS)
Wang, Jian-Yong; Liang, Zu-Feng; Tang, Xiao-Yan
2014-02-01
Infinitely many generalized symmetries of a coupled (2 + 1)-dimensional Burgers system are obtained by means of the formal series symmetry approach. It is found that the generalized symmetries constitute a closed infinite-dimensional Lie algebra. Three interesting special cases are presented, including a closed infinite-dimensional Lie algebra and a Kac-Moody-Virasoro-type Lie symmetry algebra. From the first one of the positive flow, a new integrable coupled system of the modified Korteweg-de Vries equation and the potential Boiti-Leon-Manna-Pempinelli equation is constructed. In addition, it is demonstrated that the coupled Burgers system can pass the Painlevé test.
A new approach to the representation of trigonometric and hyperbolic functions by infinite products
NASA Astrophysics Data System (ADS)
Melnikov, Yu. A.
2008-08-01
An innovative technique is developed for obtaining infinite product representations for some elementary functions. The technique is based on the comparison of alternative expressions of Green's functions constructed by two different methods. Some standard boundary value problems are considered posed for two-dimensional Laplace equation on regions of a regular configuration. Classical closed analytic form of Green's functions for such problems are compared against those obtained by the method of images in the form of infinite products. This yields a number of new infinite product representations for trigonometric and hyperbolic functions.
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:
Hopf solitons and elastic rods
Harland, Derek; Sutcliffe, Paul; Speight, Martin
2011-03-15
Hopf solitons in the Skyrme-Faddeev model are stringlike topological solitons classified by the integer-valued Hopf charge. In this paper we introduce an approximate description of Hopf solitons in terms of elastic rods. The general form of the elastic rod energy is derived from the field theory energy and is found to be an extension of the classical Kirchhoff rod energy. Using a minimal extension of the Kirchhoff energy, it is shown that a simple elastic rod model can reproduce many of the qualitative features of Hopf solitons in the Skyrme-Faddeev model. Features that are captured by the model include the buckling of the charge three solution, the formation of links at charges five and six, and the minimal energy trefoil knot at charge seven.
Mapping Elasticity at the Nanoscale
NASA Astrophysics Data System (ADS)
Stan, Gheorghe; Price, William
2006-03-01
In the last few years Atomic Force Acoustic Microscopy has been developed to investigate the elastic response of materials at the nanoscale ^[1],[2]. We have extended this technique to the real-time mapping of nanomechanical properties of material surfaces. This mapping allows us to investigate the local variation of elastic properties with nanometer resolution and to reduce the uncertainties that arise from single measurements. Quantitative measurements are acquired by first performing an accurate calibration of the elastic properties of the Atomic Force Microscope’s probes with respect to single crystal reference materials. A wide variety of surfaces with different mechanical properties have been investigated to illustrate the applicability of this technique. ^[1] U. Rabe et al., Surf. Interface Anal. 33 , 65 (2002)^[2] D.C. Hurley et al., J. Appl. Phys. 94, 2347 (2003)
Duration of an elastic collision
NASA Astrophysics Data System (ADS)
de Izarra, Charles
2012-07-01
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 with the planar surface allows us to determine the duration of the elastic collision. In order to check the theoretical model, an experiment is proposed to measure the duration of the collision. A more refined model built with masses and springs gives good agreement between theoretical and experimental values.
Price and Income Elasticities of Iranian Exports
NASA Astrophysics Data System (ADS)
Atrkar Roshan, Sedigheh
This study investigates the export demand elasticities at the aggregate and disaggregated levels over the period 1977 to 2001 for Iran. By utilizing an export demand model and using time series techniques that account for the nonstationarity in the data, the price and income elasticities of demand are estimated by commodity class. As the elasticities of demand for various categories of exports are different, while they are crucial for policy determination. Based upon the estimated results, price and income elasticities are almost similar to those obtained in earlier studies in the case of developing countries. The main findings of this paper demonstrate that, price elasticities are smaller than -1 for all exports categories, whereas the income elasticities are found to be greater than one. The results also suggested, the income elasticities of industrial goods are higher compared to other export categories, while the lower elasticities are found in primary exports. The price and income elasticity estimates have also good statistical properties.
NASA Astrophysics Data System (ADS)
Yeh, C.-L.; Lo, W.-C.; Jan, C.-D.; Lee, J.-W.
2012-04-01
Based on the theoretical model derived by Yeh et al. (2010), this study simulates and analyzes reflection and refraction of incident elastic waves on a plane interface between two semi-infinite poroelastic half-spaces saturated by two different fluid mixtures. The amplitude and energy ratios of reflected and refracted waves considering the effect of motional modes, inertial and viscous couplings are determined for the first time with respect to water saturation of an incident P1 wave (the first dilatational wave). A plot of amplitude and energy ratios of reflected and refracted waves as a function of water saturation using an illustrative example with Lincoln sand containing an air-water mixture in the lower half-space and Columbia fine sandy loam bearing an oil-water mixture in the upper half-space. Analytical results indicate that the amplitude and energy ratios have the same magnitude order as phase speed, and the ratios of refracted and reflected waves are markedly affected by different physical parameters. This study further elucidates the difference in reflection and refraction between the oblique (30°) and normal (0°) incidences at the interface. The normal incident case have similar trend with the oblique case but no reflected and refracted SV waves exist. The sum of the energy ratio under each degree of water saturation equals unity. Additionally, amplitude and energy ratios of reflected and refracted waves are affected significantly by degree of saturation.
Managing competing elastic Grid and Cloud scientific computing applications using OpenNebula
NASA Astrophysics Data System (ADS)
Bagnasco, S.; Berzano, D.; Lusso, S.; Masera, M.; Vallero, S.
2015-12-01
Elastic cloud computing applications, i.e. applications that automatically scale according to computing needs, work on the ideal assumption of infinite resources. While large public cloud infrastructures may be a reasonable approximation of this condition, scientific computing centres like WLCG Grid sites usually work in a saturated regime, in which applications compete for scarce resources through queues, priorities and scheduling policies, and keeping a fraction of the computing cores idle to allow for headroom is usually not an option. In our particular environment one of the applications (a WLCG Tier-2 Grid site) is much larger than all the others and cannot autoscale easily. Nevertheless, other smaller applications can benefit of automatic elasticity; the implementation of this property in our infrastructure, based on the OpenNebula cloud stack, will be described and the very first operational experiences with a small number of strategies for timely allocation and release of resources will be discussed.
Transient response of a single-edge crack in an elastic half-plane
Chen, E.P.
1980-01-01
The elasto-dynamic response of a single-edge crack in a semi-infinite elastic medium is considered in this study. The crack is assumed to appear suddenly in an elastic half-plane that is being stretched by a remote stress field. Near the crack, the interactions between the wave emanating from the tip and those reflected from the free edge take place. This investigation focuses its attention on the determination of the effect of this interaction on the stress intensity factor. Laplace and Fourier transforms are used to reduce the solution to a pair of dual integral equations. A numerical Laplace inversion procedure is used to obtain the time dependence of the solution. Numerical results on the dynamic stress intensity factor are obtained and are presented in a graphical form.
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.
NASA Astrophysics Data System (ADS)
Fivez, J.
2016-01-01
Starting from the coupled thermoelastic equations, an analytic formula is obtained for the surface deformation of a semi-infinite homogeneous and isotropic solid in an impulsive stimulated scattering (ISS) experiment. The surface ripple consists of a transient diffusive grating and a standing Rayleigh wave. The time evolution of the diffusive part directly reveals the thermal diffusivity. The oscillatory part then reveals the elastic properties, and explicit formulae are presented for retrieving the elastic moduli as a function of the frequency and amplitude of the standing Rayleigh wave. The analytic formulae not only allow to avoid time-consuming and delicate numerical integration but they also demonstrate the uniqueness of the inversion from signal to material parameters and offer direct insight into the error propagation. The formulae are applied to real experimental data, illustrating the strength and the limitations of the ISS technique.
Impact buckling of thin bars in the elastic range for any end condition
NASA Technical Reports Server (NTRS)
Taub, Josef
1934-01-01
Following a qualitative discussion of the complicated process involved in a short-period, longitudinal force applied to an originally not quite straight bar, the actual process is substituted by an idealized process for the purpose of analytical treatment. The simplifications are: the assumption of an infinitely high rate of propagation of the elastic longitudinal waves in the bar, limitation to slender bars, disregard of material damping and of rotatory inertia, the assumption of consistently small elastic deformations, the assumption of cross-sectional dimensions constant along the bar axis, the assumption of a shock-load constant in time, and the assumption of eccentricities on one plane. Then follow the mathematical principles for resolving the differential equation of the simplified problem, particularly the developability of arbitrary functions with steady first and second and intermittently steady third and fourth derivatives into one convergent series, according to the natural functions of the homogeneous differential equation.
A remark on the computation of shear-horizontal and torsional modes in elastic waveguides.
Gravenkamp, Hauke
2016-07-01
When modeling the propagation of elastic guided waves in plates or cylinders, Finite Element based numerical methods such as the Scaled Boundary Finite Element Method (SBFEM) or the Semi-Analytical Finite Element (SAFE) Method lead to an eigenvalue problem to be solved at each frequency. For the particular case of shear horizontal modes in a homogeneous plate or torsional modes in a homogeneous cylinder, the problem can be drastically simplified. The eigenvalues become simple functions of the frequency, while the eigenvectors are constant. The current contribution discusses how this behavior is represented in the numerical formulation and derives the expressions for the eigenvalues and eigenvectors as well as the dynamic stiffness matrix of infinite elastic waveguides. PMID:27014855
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.
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.
State feedback control of real-time discrete event systems with infinite states
NASA Astrophysics Data System (ADS)
Park, Seong-Jin; Cho, Kwang-Hyun
2015-05-01
In this paper, we study a state feedback supervisory control of timed discrete event systems (TDESs) with infinite number of states modelled as timed automata. To this end, we represent a timed automaton with infinite number of untimed states (called locations) by a finite set of conditional assignment statements. Predicates and predicate transformers are employed to finitely represent the behaviour and specification of a TDES with infinite number of locations. In addition, the notion of clock regions in timed automata is used to identify the reachable states of a TDES with an infinite time space. For a real-time specification described as a predicate, we present the controllability condition for the existence of a state feedback supervisor that restricts the behaviour of the controlled TDES within the specification.
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
NASA Astrophysics Data System (ADS)
Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Zuo, Da-Wei
2016-01-01
Under investigation in this article is a (2+1)-dimensional generalised variable-coefficient shallow water wave equation, which describes the interaction of the Riemann wave propagating along the y axis with a long-wave propagating along the x axis in a fluid, where x and y are the scaled space coordinates. Bilinear forms, Bäcklund transformation, Lax pair, and infinitely many conservation law are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota method. Propagation and interaction of the solitons are illustrated graphically: (i) variable coefficients affect the shape of the multi-soliton interaction in the scaled space and time coordinates. (ii) Positions of the solitons depend on the sign of wave numbers after each interaction. (iii) Interaction of the solitons is elastic, i.e. the amplitude, velocity, and shape of each soliton remain invariant after each interaction except for a phase shift.
NASA Astrophysics Data System (ADS)
Zenkour, Ashraf M.; Abouelregal, Ahmed E.
2014-02-01
This paper is concerned with the determination of the thermoelastic displacement, stress, conductive temperature, and thermodynamic temperature in an infinite isotropic elastic body with a spherical cavity. A general solution to the problem based on the two-temperature generalized thermoelasticity theory (2TT) is introduced. The theory of thermal stresses based on the heat conduction equation with Caputo's time-fractional derivative of order α is used. Some special cases of coupled thermoelasticity and generalized thermoelasticity with one relaxation time are obtained. The general solution is provided by using Laplace's transform and state-space techniques. It is applied to a specific problem when the boundary of the cavity is subjected to thermomechanical loading (thermal shock). Some numerical analyses are carried out using Fourier's series expansion techniques. The computed results for thermoelastic stresses, conductive temperature, and thermodynamic temperature are shown graphically and the effects of two-temperature and fractional-order parameters are discussed.
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
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
Kinematic support using elastic elements
NASA Technical Reports Server (NTRS)
Geirsson, Arni; Debra, Daniel B.
1988-01-01
The design of kinematic supports using elastic elements is reviewed. The two standard methods (cone, Vee and flat and three Vees) are presented and a design example involving a machine tool metrology bench is given. Design goals included thousandfold strain attenuation in the bench relative to the base when the base strains due to temperature variations and shifting loads. Space applications are also considered.
A problem in micropolar elasticity.
NASA Technical Reports Server (NTRS)
Srinivas, S.
1973-01-01
In this paper a three-dimensional analysis for statics and dynamics of a class of simply supported rectangular plates made up of micropolar elastic material is presented. The solution is in the form of series, in which each term is explicitly determined. For free vibrations, the frequencies are obtained by the solution of a closed form characteristic equation.
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…
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…
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.
Harding, R. M.; Boyce, A. J.; Martinson, J. J.; Flint, J.; Clegg, J. B.
1993-01-01
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. We 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. We use sampling theory to confirm the intrinsically poor fit to the infinite alleles model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. PMID:8293988
Structure of local quantum operations and classical communication: Finite versus infinite rounds
NASA Astrophysics Data System (ADS)
Cohen, Scott M.
2015-04-01
Every measurement that can be implemented by local quantum operations and classical communication (LOCC) using an infinite number of rounds is the limit of a sequence of measurements, where each measurement in the sequence requires only a finite number of rounds. This rather obvious and well-known fact is nonetheless of interest as it shows that these infinite-round measurements can be approximated arbitrarily closely simply by using more and more rounds of communication. Here we demonstrate the perhaps less obvious result that (at least) for bipartite systems, the reverse relationship also holds. Specifically, we show that every finite-round bipartite LOCC measurement is the limit of a continuous sequence of LOCC measurements, where each measurement in that sequence can be implemented by LOCC, but only with the use of an infinite number of rounds. Thus, the set of LOCC measurements that require an infinite number of rounds is dense in the entirety of LOCC, as is the set of finite-round LOCC measurements. This means there exist measurements that can only be implemented by LOCC by using an infinite number of rounds, but can nonetheless be approximated closely by using one round of communication, and actually in some cases, no communication is needed at all. These results follow from a necessary condition presented here for finite-round LOCC, which is extremely simple to check, is very easy to prove, and which can be violated by utilizing an infinite number of rounds.
NASA Astrophysics Data System (ADS)
Nakagawa, Masaki; Aizawa, Yoji
2014-10-01
Universal aspects of a certain class of infinite ergodic systems are studied by using the infinite-modal maps with a special interest to their observed measures. It is shown that the ant-lion (AL) property is an important nature to realize the infinite ergodicity in the dissipative dynamics. The AL-property, which seems to be a little bit paradoxical one, is characterized by the monotonical relaxation of mean orbits into a singular stable point, but it causes the divergence of the Lyapunov exponent as well as the emergence of a number of absolutely-continuous invariant measures. Our main concern is to characterize the unique observed measure in those many admissible ergodic measures. To this end, firstly the randomization formulae are developed on the basis of the uniform distribution theorem by Weyl, to derive the stochastic aspects of the AL-property. Actually, it is shown that the statistical natures of the infinite-modal maps are well explained by the randomization formulae. Furthermore, it is shown that the observed measure derived from the randomization formulae is universal, and that the asymptotic form obeys the power law with the exponent -1, in agreement with numerical simulations.
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.
Calculation of the lining of a non-circular tunnel
Ilyushin, V.F.
1983-12-01
High-head hydroelectric stations located in mountainous regions have underground structures on which one of the main loads is the pressure of groundwaters. The most common noncircular cross-sectional shape of a tunnel is the horseshoe with a crown outlined over the arc of a circle and flat walls and invert. Such a shape is the most technologically efficient during construction. The lining has usually a minimum design thickness and can be concrete or reinforced. The reinforcement is installed in the crown in conformity with the diagram of moments and in the walls and invert in the middle of the lining thickness. The lining is equipped with drainage reducing the pressure of the groundwaters to a practically acceptable value. Residual pressure is absorbed by the lining of the crown having an efficient axis outlined over the arc of a circle and by the flat walls and invert transmitting forces through the anchors to the surrounding rock mass. There are no restrictions with respect to the conditions of hydraulics and seepage with respect to cavitation erosion and abrasion, and permissible gradients of the seepage flow through the lining. Methods are given for calculating the crown, concrete wall and invert, anchors, and concrete-rock walls and invert. 4 references, 2 figures.
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.
Illumination-redistribution lenses for non-circular spots
NASA Astrophysics Data System (ADS)
Parkyn, William A.; Pelka, David G.
2005-08-01
The design of illumination lenses is far easier under the regime of the small-source approximation, whereby central rays are taken as representative of the entire source. This implies that the lens is much larger than the source's active emitter, and its entire interior surface is nowhere close to the source. Also, a given source luminance requires a minimum lens area to achieve the candlepower necessary for target illumination. We introduce two-surface aspheric lenses for specific illuminations tasks involving ceiling-mounted downlights, lenses that achieve uniform illuminance at the output aperture as well as at the target. This means that squared-off lenses will produce square spots. In particular, a semicircular lens and a vertical mirror will produce a semicircular spot suitable for gambling tables.
The green function of an infinite, fluid loaded membrane
NASA Astrophysics Data System (ADS)
Crighton, D. G.
1983-02-01
In this paper the response of a fluid loaded plane structure (a membrane) to a concentrated line force excitation is considered in great detail. The normalized velocity response—here called the Green function G—depends upon a dimensionless range x0= km| x|, where km is the free wavenumber on the membrane in a vacuum, on the Mach number M= {k 0}/{k m}, the ratio of wave phase speed ω/ km on the unloaded membrane to the sound speed ω/ k0, and on a parameter ɛ which can be regarded as a measure of fluid loading at the "coincidence" condition M=1. In the analogous problem involving a thin elastic plate, the corresponding parameter is independent of frequency and plate thickness and may be regarded as an intrinsic measure of fluid loading; moreover, in cases of common interest (steel in water, aluminium in air) that parameter is small. In the present paper, the asymptotic structure of G( x0, M, ɛ) is therefore sought in the limit ɛ → 0. Naturally, no single asymptotic expansion can be expected to be valid throughout the ( x0, M) plane, and the programme therefore involves the delineation of regions of that plane in which distinct asymptotic results apply, the construction and discussion of those results, and the asymptotic matching (according to the procedures of the method of matched asymptotic expansions) of results holding in adjoining regions. The Fourier integral for G is broken into surface wave and acoustic components, and the asymptotic structure obtained for each. Previously obtained results for the behaviour at large distances are recovered, with a demonstration that very large distances indeed ( x0 ≫ ɛ-2) may be needed for their validity for some ranges of M; and the drive point behaviour, of G( x0=0, M, ɛ) as ɛ → 0 qua function of M, is shown to correspond to that already discussed in the literature. Elsewhere, in the covering of the whole ( x0, M) plane by different asymptotic expressions, a wide variety of analytical results is found
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.
Directional anisotropy, finite size effect and elastic properties of hexagonal boron nitride
NASA Astrophysics Data System (ADS)
Thomas, Siby; Ajith, K. M.; Valsakumar, M. C.
2016-07-01
Classical molecular dynamics simulations have been performed to analyze the elastic and mechanical properties of two-dimensional (2D) hexagonal boron nitride (h-BN) using a Tersoff-type interatomic empirical potential. We present a systematic study of h-BN for various system sizes. Young’s modulus and Poisson’s ratio are found to be anisotropic for finite sheets whereas they are isotropic for the infinite sheet. Both of them increase with system size in accordance with a power law. It is concluded from the computed values of elastic constants that h-BN sheets, finite or infinite, satisfy Born’s criterion for mechanical stability. Due to the the strong in-plane sp2 bonds and the small mass of boron and nitrogen atoms, h-BN possesses high longitudinal and shear velocities. The variation of bending rigidity with system size is calculated using the Foppl–von Karman approach by coupling the in-plane bending and out-of-plane stretching modes of the 2D h-BN.
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.
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)].
Linear elastic fracture mechanics primer
NASA Astrophysics Data System (ADS)
Wilson, Christopher D.
1992-07-01
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.
Elastic Flows Of Ellipsoidal Particles
NASA Astrophysics Data System (ADS)
Campbell, Charles S.
2009-06-01
Granular flow rheology can be divided into two global regimes, the Elastic, which is dominated by force chains and the inertial which are nearly free of force chains. The propensity of a material to form force chains is strongly influenced by particle shape. This paper is an attempt to assess the effect of particle shape on flow regime transitions, through computer simulations of shear flow of ellipsoidal particles. On one hand, the results show that at a given concentration, ellipsoidal particles generate smaller quasistatic stress than spheres, likely a result of their ability to form denser static packings. But at the same time, large aspect ratio ellipsoids more readily form force chains and demonstrate Elastic behavior at smaller concentrations than spheres.
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.
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.
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.
Partially penetrating fractures: Pressure transient analysis of an infinite conductivity fracture
Rodriguez, F.; Cinco-Ley, H.; Horne, R.N.
1984-04-01
The effect of the partial penetration of an infinite conductivity fracture on the transient pressure behavior of a vertically fractured well is investigated. Analysis of results shows that the pressure behavior of a well intersected by a partially-penetrating infinite conductivity vertical fracture can be divided into three flow periods: 1) the early time flow period which is characterized by a formation linear flow as in the case of a fully-penetrating infinite-conductivity vertical fracture, 2) the infinite-acting flow period and 3) the pseudoradial flow period which develops after the effects of the vertical boundaries of the reservoir are felt in the pressure behavior of the well. A log-log graph of log(h /SUB f/ /h)p /SUB wD/ versus log t /SUB Dxf/ shows a slope of one half during the early time flow period of a well with an infinite-conductivity partially penetrating fracture. The time for the end of the early time flow period is directly related to the square of the dimensionless height of the fracture, h /SUB fD/, which is defined as the ratio between the height of the fracture and its half length.
Avalanche dynamics of elastic interfaces.
Le Doussal, Pierre; Wiese, Kay Jörg
2013-08-01
Slowly driven elastic interfaces, such as domain walls in dirty magnets, contact lines wetting a nonhomogeneous substrate, or cracks in brittle disordered material proceed via intermittent motion, called avalanches. Here we develop a field-theoretic treatment to calculate, from first principles, the space-time statistics of instantaneous velocities within an avalanche. For elastic interfaces at (or above) their (internal) upper critical dimension d≥d(uc) (d(uc)=2,4 respectively for long-ranged and short-ranged elasticity) we show that the field theory for the center of mass reduces to the motion of a point particle in a random-force landscape, which is itself a random walk [Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model]. Furthermore, the full spatial dependence of the velocity correlations is described by the Brownian-force model (BFM) where each point of the interface sees an independent Brownian-force landscape. Both ABBM and BFM can be solved exactly in any dimension d (for monotonous driving) by summing tree graphs, equivalent to solving a (nonlinear) instanton equation. We focus on the limit of slow uniform driving. This tree approximation is the mean-field theory (MFT) for realistic interfaces in short-ranged disorder, up to the renormalization of two parameters at d=d(uc). We calculate a number of observables of direct experimental interest: Both for the center of mass, and for a given Fourier mode q, we obtain various correlations and probability distribution functions (PDF's) of the velocity inside an avalanche, as well as the avalanche shape and its fluctuations (second shape). Within MFT we find that velocity correlations at nonzero q are asymmetric under time reversal. Next we calculate, beyond MFT, i.e., including loop corrections, the one-time PDF of the center-of-mass velocity u[over ·] for dimension d
Dynamic Models of Robots with Elastic Hinges
NASA Astrophysics Data System (ADS)
Krakhmalev, O. N.
2016-04-01
Two dynamic models of robots with elastic hinges are considered. Dynamic models are the implementation of the method based on the Lagrange equation using the transformation matrices of elastic coordinates. Dynamic models make it possible to determine the elastic deviations from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. One model is the exact implementation of the Lagrange method and makes it possible to determine the total elastic deviation of the robot from the programmed motion trajectory. Another dynamic model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by two models are compared to the example of a two-link manipulator system. The considered models can be used when performing investigations of the mathematical accuracy of the robots.
Modified conduction shape factors for isothermal bodies embedded in a semi-infinite medium
Anteby, I.; Shai, I. . Pearlstone Centre for Aeronautical Engineering Studies)
1993-03-01
Numerical finite-element method calculations were performed for isothermal surfaces embedded in a semi-infinite medium with convection boundary conditions. A modified shape factor was defined that combines the conduction heat transfer in the medium and the convection to the environment, with the geometrical characteristics of the problem. Infinite finite elements are used; these form the last layer of elements in the infinite directions. The modified shape factors for a sphere and for a long horizontal cylinder are presented in graphs and correlations, both using nondimensional parameters. The heat flux distribution on the surface of the body and the temperature and heat transfer on the surface of the medium are also presented.
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.
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.
Localized energy pulse trains launched from an open, semi-infinite, circular waveguide
Shaarawi, A.M.; Besieris, I.M.; Ziolkowski, R.W.
1989-01-15
A new decomposition of exact solutions to the scalar wave equation into bidirectional, backward and forward traveling plane waves is described. These elementary blocks constitute a natural basis for synthesizing Brittinghamlike solutions. Examples of such solutions, besides Brittingham's original modes, are Ziolkowski's electromagnetic directed energy pulse trains (EDEPTs) and Hillion's spinor modes. A common feature of these solutions is the incorporation of certain parameters that can be tuned in order to achieve slow energy decay patterns. The aforementioned decomposition is used first to solve an initial boundary-value problem involving an infinite waveguide. This is followed by considering a semi-infinite waveguide excited by a localized initial pulse whose shape is related directly to parameters similar to those arising in Ziolkowski's EDEPT solutions. The far fields outside the semi-infinite waveguide are computed using Kirchhoff's integral formula with a time-retarded Green's function. The resulting approximate solutions are causal, have finite energy, and exhibit a slow energy decay behavior.
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. PMID:19113687
Seol, Jiwoong; Lee, Jong-Won; Kim, Do-Youn; Takeya, Satoshi; Ripmeester, John A; Lee, Huen
2010-01-21
This study focuses on the cage occupancy of guest molecules in the infinitely dilute state. At the extreme conditions of highly diluted guest concentrations the direct measurements of the cage occupancy ratio representing the competitive inclusion of multiguest species appear to be so difficult because of spectroscopic intensity limitation, but its thermodynamic significance might be considerable due to the fact that the infinite-dilution value of the cage occupancy ratio can provide the valuable thermodynamic information as a very unique and guest-specific parameter. To experimentally identify gaseous guest populations in structure I (sI) and structure II (sII) cages, we used the solid-state nuclear magnetic resonance (NMR), gas chromatography, and direct gas measurements. Furthermore, we derived the simple and generalized thermodynamic equation related to cage occupancies at infinite dilution from the van der Waals-Platteeuw model. Both experimental and predicted values agree well within the experimental error range. PMID:20000371
On the decay of infinite energy solutions to the Navier-Stokes equations in the plane
NASA Astrophysics Data System (ADS)
Bjorland, Clayton; Niche, César J.
2011-03-01
Infinite energy solutions to the Navier-Stokes equations in R2 may be constructed by decomposing the initial data into a finite energy piece and an infinite energy piece, which are then treated separately. We prove that the finite energy part of such solutions is bounded for all time and decays algebraically in time when the same can be said of heat energy starting from the same data. As a consequence, we describe the asymptotic behavior of the infinite energy solutions. Specifically, we consider the solutions of Gallagher and Planchon (2002) [2] as well as solutions constructed from a “radial energy decomposition”. Our proof uses the Fourier Splitting technique of M.E. Schonbek.
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.
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%.
Low formation energy and kinetic barrier of Stone-Wales defect in infinite and finite silicene
NASA Astrophysics Data System (ADS)
Manjanath, Aaditya; Singh, Abhishek K.
2014-01-01
Stone-Wales (SW) defects in materials having hexagonal lattice are the most common topological defects that affect the electronic and mechanical properties. Using first principles density functional theory based calculations, we study the formation energy and kinetic barrier of SW-defect in infinite and finite sheets of silicene. The formation energies as well as the barriers in both the cases are significantly lower than those of graphene. Furthermore, compared with the infinite sheets, the energy barriers and formation energies are lower for finite sheets. However, due to low barriers these defects are expected to heal out of the finite sheets.
NASA Astrophysics Data System (ADS)
Ding, Chikun; Lin, Siyuan; Li, Junfeng; Wang, Peng; Li, Qian; Zhang, Binqing
2013-03-01
It has recently been pointed out that infinite center of mass energies for the colliding particles can be attained when the black hole is exactly extremal and only at infinite time and on the horizon of the black hole. In this letter, we show that it cannot occur when the spacetime noncommutative effect is considered, i.e. the quantum effect of gravity is an other preventing mechanism. Additionally, the bigger of the black hole's mass is, the higher of center of mass energy that the particles obtain.
Calculating infinite-medium {alpha}-eigenvalue spectra with a transition rate matrix method
Betzler, B. R.; Kiedrowski, B. C.; Brown, F. B.; Martin, W. R.
2013-07-01
The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing {alpha}-eigenvalues and eigenvectors in an infinite medium. For this, a research Monte Carlo code called TORTE was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum. (authors)
Infinite hierarchy of nonlinear Schrödinger equations and their solutions
NASA Astrophysics Data System (ADS)
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.
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. PMID:26871072
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)
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.
Entanglement entropy at infinite-randomness fixed points in higher dimensions.
Lin, Yu-Cheng; Iglói, Ferenc; Rieger, Heiko
2007-10-01
The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions. PMID:17930713
Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
NASA Astrophysics Data System (ADS)
Odake, Satoru; Sasaki, Ryu
2011-08-01
Infinite families of multi-indexed orthogonal polynomials are discovered as the solutions of exactly solvable one-dimensional quantum mechanical systems. The simplest examples, the one-indexed orthogonal polynomials, are the infinite families of the exceptional Laguerre and Jacobi polynomials of types I and II constructed by the present authors. The totality of the integer indices of the new polynomials are finite and they correspond to the degrees of the 'virtual state wavefunctions' which are 'deleted' by the generalisation of Crum-Adler theorem. Each polynomial has another integer n which counts the nodes.
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.
Infinite invariant density determines statistics of time averages for weak chaos.
Korabel, N; Barkai, E
2012-02-10
Weakly chaotic nonlinear maps with marginal fixed points have an infinite invariant measure. Time averages of integrable and nonintegrable observables remain random even in the long time limit. Temporal averages of integrable observables are described by the Aaronson-Darling-Kac theorem. We find the distribution of time averages of nonintegrable observables, for example, the time average position of the particle, x[over ¯]. We show how this distribution is related to the infinite invariant density. We establish four identities between amplitude ratios controlling the statistics of the problem. PMID:22401047
Gobran, B.D.; Abbaszadeh-Dehghani, M.
1981-02-01
During a pressure drawdown test, all wells behave as if they are in an infinite reservoir for a brief period (termed the infinite-acting time). In an attempt to better determine this time for well locations in closed rectangular shapes, we have produced computer and hand calculator programs as well as contour graphs that yield the dimensionless time (in terms of area), t/sub DA/, which defines the end of the infinite-acting period.
Elasticity Imaging of Polymeric Media
Sridhar, Mallika; Liu, Jie; Insana, Michael F.
2009-01-01
Viscoelastic properties of soft tissues and hydropolymers depend on the strength of molecular bonding forces connecting the polymer matrix and surrounding fluids. The basis for diagnostic imaging is that disease processes alter molecular-scale bonding in ways that vary the measurable stiffness and viscosity of the tissues. This paper reviews linear viscoelastic theory as applied to gelatin hydrogels for the purpose of formulating approaches to molecular-scale interpretation of elasticity imaging in soft biological tissues. Comparing measurements acquired under different geometries, we investigate the limitations of viscoelastic parameters acquired under various imaging conditions. Quasistatic (step-and-hold and low-frequency harmonic) stimuli applied to gels during creep and stress relaxation experiments in confined and unconfined geometries reveal continuous, bimodal distributions of respondance times. Within the linear range of responses, gelatin will behave more like a solid or fluid depending on the stimulus magnitude. Gelatin can be described statistically from a few parameters of low-order rheological models that form the basis of viscoelastic imaging. Unbiased estimates of imaging parameters are obtained only if creep data are acquired for greater than twice the highest retardance time constant and any steady-state viscous response has been eliminated. Elastic strain and retardance time images are found to provide the best combination of contrast and signal strength in gelatin. Retardance times indicate average behavior of fast (1–10 s) fluid flows and slow (50–400 s) matrix restructuring in response to the mechanical stimulus. Insofar as gelatin mimics other polymers, such as soft biological tissues, elasticity imaging can provide unique insights into complex structural and biochemical features of connectives tissues affected by disease. PMID:17408331
Elastic mismatch enhances cell motility
NASA Astrophysics Data System (ADS)
Bresler, Yony; Palmieri, Benoit; Grant, Martin
In recent years, the study of physics phenomena in cancer has drawn considerable attention. In cancer metastasis, a soft cancer cell leaves the tumor, and must pass through the endothelium before reaching the bloodstream. Using a phase-field model we have shown that the elasticity mismatch between cells alone is sufficient to enhance the motility of thesofter cancer cell by means of bursty migration, in agreement with experiment. We will present further characterization of these behaviour, as well as new possible applications for this model.
Numerical investigation of elastic modes of propagation in helical waveguides.
Treyssède, Fabien
2007-06-01
Steel multi-wire cables are widely employed in civil engineering. They are usually made of a straight core and one layer of helical wires. In order to detect material degradation, nondestructive evaluation methods based on ultrasonics are one of the most promising techniques. However, their use is complicated by the lack of accurate cable models. As a first step, the goal of this paper is to propose a numerical method for the study of elastic guided waves inside a single helical wire. A finite element (FE) technique is used based on the theory of wave propagation inside periodic structures. This method avoids the tedious writing of equilibrium equations in a curvilinear coordinate system yielding translational invariance along the helix centerline. Besides, no specific programming is needed inside a conventional FE code because it can be implemented as a postprocessing step of stiffness, mass and damping matrices. The convergence and accuracy of the proposed method are assessed by comparing FE results with Pochhammer-Chree solutions for the infinite isotropic cylinder. Dispersion curves for a typical helical waveguide are then obtained. In the low-frequency range, results are validated with a helical Timoshenko beam model. Some significant differences with the cylinder are observed. PMID:17552691
Visco elasticity in 2D materials
NASA Astrophysics Data System (ADS)
Cortijo, Alberto; Ferreirós, Yago; Landsteiner, Karl; Vozmediano, María A. H.
2016-03-01
The combination of Dirac physics and elasticity has been explored at length in graphene where the so-called ‘elastic gauge fields’ have given rise to an entire new field of research and applications: straintronics. The fact that these elastic fields couple to fermions as the electromagnetic field, implies that many electromagnetic responses will have elastic counterparts not yet explored. In this work we will first show that the presence of elastic gauge fields is the rule rather than the exception in most of the topologically non-trivial materials in two- and three-dimensions. We will show that, associated to the physics of the anomalies, and as a counterpart of the Hall conductivity, elastic two-dimension materials will have a Hall viscosity with a coefficient orders of magnitude bigger than the previously studied response. The magnitude and generality of the new effect will greatly improve the chances for the experimental observation of this topological response.
Elastic, Conductive, Polymeric Hydrogels and Sponges
NASA Astrophysics Data System (ADS)
Lu, Yun; He, Weina; Cao, Tai; Guo, Haitao; Zhang, Yongyi; Li, Qingwen; Shao, Ziqiang; Cui, Yulin; Zhang, Xuetong
2014-07-01
As a result of inherent rigidity of the conjugated macromolecular chains resulted from the delocalized π-electron system along the polymer backbone, it has been a huge challenge to make conducting polymer hydrogels elastic by far. Herein elastic and conductive polypyrrole hydrogels with only conducting polymer as the continuous phase have been simply synthesized in the indispensable conditions of 1) mixed solvent, 2) deficient oxidant, and 3) monthly secondary growth. The elastic mechanism and oxidative polymerization mechanism on the resulting PPy hydrogels have been discussed. The resulting hydrogels show some novel properties, e.g., shape memory elasticity, fast functionalization with various guest objects, and fast removal of organic infectants from aqueous solutions, all of which cannot be observed from traditional non-elastic conducting polymer counterparts. What's more, light-weight, elastic, and conductive organic sponges with excellent stress-sensing behavior have been successfully achieved via using the resulting polypyrrole hydrogels as precursors.
Evaluation of a Hybrid Elastic EVA Glove
NASA Technical Reports Server (NTRS)
Korona, F. Adam; Akin, David
2002-01-01
The hybrid elastic design is based upon an American Society for Engineering Education (ASEE) glove designed by at the Space Systems Laboratory (SSL) in 1985. This design uses an elastic restraint layer instead of convolute joints to achieve greater dexterity and mobility during EVA (extravehicular activity). Two pilot studies and a main study were conducted using the hybrid elastic glove and 4000-series EMU (extravehicular activity unit) glove. Data on dexterity performance, joint range of motion, grip strength and perceived exertion was assessed for the EMU and hybrid elastic gloves with correlations to a barehanded condition. During this study, 30 test subjects performed multiple test sessions using a hybrid elastic glove and a 4000- series shuttle glove in a 4.3psid pressure environment. Test results to date indicate that the hybrid elastic glove performance is approximately similar to the performance of the 4000-series glove.
Elastic, Conductive, Polymeric Hydrogels and Sponges
Lu, Yun; He, Weina; Cao, Tai; Guo, Haitao; Zhang, Yongyi; Li, Qingwen; Shao, Ziqiang; Cui, Yulin; Zhang, Xuetong
2014-01-01
As a result of inherent rigidity of the conjugated macromolecular chains resulted from the delocalized π-electron system along the polymer backbone, it has been a huge challenge to make conducting polymer hydrogels elastic by far. Herein elastic and conductive polypyrrole hydrogels with only conducting polymer as the continuous phase have been simply synthesized in the indispensable conditions of 1) mixed solvent, 2) deficient oxidant, and 3) monthly secondary growth. The elastic mechanism and oxidative polymerization mechanism on the resulting PPy hydrogels have been discussed. The resulting hydrogels show some novel properties, e.g., shape memory elasticity, fast functionalization with various guest objects, and fast removal of organic infectants from aqueous solutions, all of which cannot be observed from traditional non-elastic conducting polymer counterparts. What's more, light-weight, elastic, and conductive organic sponges with excellent stress-sensing behavior have been successfully achieved via using the resulting polypyrrole hydrogels as precursors. PMID:25052015
Elastic constants of layers in isotropic laminates.
Heyliger, Paul R; Ledbetter, Hassel; Kim, Sudook; Reimanis, Ivar
2003-11-01
The individual laminae elastic constants in multilayer laminates composed of dissimilar isotropic layers were determined using ultrasonic-resonance spectroscopy and the linear theory of elasticity. Ultrasonic resonance allows one to measure the free-vibration response spectrum of a traction-free solid under periodic vibration. These frequencies depend on pointwise density, laminate dimensions, layer thickness, and layer elastic constants. Given a material with known mass but unknown constitution, this method allows one to extract the elastic constants and density of the constituent layers. This is accomplished by measuring the frequencies and then minimizing the differences between these and those calculated using the theory of elasticity for layered media to select the constants that best replicate the frequency-response spectrum. This approach is applied to a three-layer, unsymmetric laminate of WpCu, and very good agreement is found with the elastic constants of the two constituent materials. PMID:14649998
Elastic deformations of bolalipid membranes.
Galimzyanov, Timur R; Kuzmin, Peter I; Pohl, Peter; Akimov, Sergey A
2016-02-17
Archaeal membranes have unique mechanical properties that enable these organisms to survive under extremely aggressive environmental conditions. The so-called bolalipids contribute to this exceptional stability. They have two polar heads joined by two hydrocarbon chains. The two headgroups can face different sides of the membrane (O-shape conformation) or the same side (U-shape conformation). We have developed an elasticity theory for bolalipid membranes and show that the energetic contributions of (i) tilt deformations, (ii) area compression/stretching deformations, (iii) as well as those of Gaussian splay from the two membrane surfaces are additive, while splay deformations yield a cross-term. The presence of a small fraction of U-shaped molecules resulted in spontaneous membrane curvature. We estimated the tilt modulus to be approximately equal to that of membranes in eukaryotic cells. In contrast to conventional lipids, the bolalipid membrane possesses two splay moduli, one of which is estimated to be an order of magnitude larger than that of conventional lipids. The projected values of elastic moduli act to hamper pore formation and to decelerate membrane fusion and fission. PMID:26791255
Electron-Hydrogen Elastic Scattering
NASA Technical Reports Server (NTRS)
Bhatia, A. K.
2004-01-01
Scattering by single-electron systems is always of interest because the wave function of the target is known exactly. Various approximations have been employed to take into account distortion produced in the target. Among them are the method of polarized orbitals and the close coupling approximation. Recently, e-H and e-He+ S-wave scattering in the elastic region has been studied using the Feshbach projection operator formalism. In this approach, the usual Hartree-Fock and exchange potentials are augmented by an optical potential and the resulting phase shifts have rigorous lower bounds. Now this method is being applied to the e-H P-wave scattering in the elastic region. The number of terms in the Hylleraas-type wave function for the 1,3 P phase shifts is 84 and the resulting phase shifts (preliminary) are given. The results have been given up to five digits because to that accuracy they are rigorous lower bounds. They are in general agreement with the variational (VAR) results of Armstead, and those obtained from the intermediate energy R-matrix method (RM) of Scholz et al., and the finite element method (FEM) of Botero and Shertzer. The later two methods do not provide any bounds on phase shifts.
Hummingbird tongues are elastic micropumps
Rico-Guevara, Alejandro; Fan, Tai-Hsi; Rubega, Margaret A.
2015-01-01
Pumping is a vital natural process, imitated by humans for thousands of years. We demonstrate that a hitherto undocumented mechanism of fluid transport pumps nectar onto the hummingbird tongue. Using high-speed cameras, we filmed the tongue–fluid interaction in 18 hummingbird species, from seven of the nine main hummingbird clades. During the offloading of the nectar inside the bill, hummingbirds compress their tongues upon extrusion; the compressed tongue remains flattened until it contacts the nectar. After contact with the nectar surface, the tongue reshapes filling entirely with nectar; we did not observe the formation of menisci required for the operation of capillarity during this process. We show that the tongue works as an elastic micropump; fluid at the tip is driven into the tongue's grooves by forces resulting from re-expansion of a collapsed section. This work falsifies the long-standing idea that capillarity is an important force filling hummingbird tongue grooves during nectar feeding. The expansive filling mechanism we report in this paper recruits elastic recovery properties of the groove walls to load nectar into the tongue an order of magnitude faster than capillarity could. Such fast filling allows hummingbirds to extract nectar at higher rates than predicted by capillarity-based foraging models, in agreement with their fast licking rates. PMID:26290074
Hummingbird tongues are elastic micropumps.
Rico-Guevara, Alejandro; Fan, Tai-Hsi; Rubega, Margaret A
2015-08-22
Pumping is a vital natural process, imitated by humans for thousands of years. We demonstrate that a hitherto undocumented mechanism of fluid transport pumps nectar onto the hummingbird tongue. Using high-speed cameras, we filmed the tongue-fluid interaction in 18 hummingbird species, from seven of the nine main hummingbird clades. During the offloading of the nectar inside the bill, hummingbirds compress their tongues upon extrusion; the compressed tongue remains flattened until it contacts the nectar. After contact with the nectar surface, the tongue reshapes filling entirely with nectar; we did not observe the formation of menisci required for the operation of capillarity during this process. We show that the tongue works as an elastic micropump; fluid at the tip is driven into the tongue's grooves by forces resulting from re-expansion of a collapsed section. This work falsifies the long-standing idea that capillarity is an important force filling hummingbird tongue grooves during nectar feeding. The expansive filling mechanism we report in this paper recruits elastic recovery properties of the groove walls to load nectar into the tongue an order of magnitude faster than capillarity could. Such fast filling allows hummingbirds to extract nectar at higher rates than predicted by capillarity-based foraging models, in agreement with their fast licking rates. PMID:26290074
Inversion of elastic impedance for unconsolidated sediments
Lee, Myung W.
2006-01-01
Elastic properties of gas-hydrate-bearing sediments are important for quantifying gas hydrate amounts as well as discriminating the gas hydrate effect on velocity from free gas or pore pressure. This paper presents an elastic inversion method for estimating elastic properties of gas-hydrate-bearing sediments from angle stacks using sequential inversion of P-wave impedance from the zero-offset stack and S-wave impedance from the far-offset stack without assuming velocity ratio.
Elastic scattering with weakly bound projectiles
Figueira, J. M.; Abriola, D.; Arazi, A.; Capurro, O. A.; Marti, G. V.; Martinez Heinmann, D.; Pacheco, A. J.; Testoni, J. E.; Barbara, E. de; Fernandez Niello, J. O.; Padron, I.; Gomes, P. R. S.; Lubian, J.
2007-02-12
Possible effects of the break-up channel on the elastic scattering threshold anomaly has been investigated. We used the weakly bound 6,7Li nuclei, which is known to undergo break-up, as projectiles in order to study the elastic scattering on a 27Al target. In this contribution we present preliminary results of these experiments, which were analyzed in terms of the Optical Model and compared with other elastic scattering data using weakly bound nuclei as projectile.
Reply to Comment on ‘Wigner function for a particle in an infinite lattice’
NASA Astrophysics Data System (ADS)
Hinarejos, M.; Pérez, A.; Bañuls, M. C.
2013-06-01
In a recent paper (2012 New J. Phys. 14 103009), we proposed a definition of the Wigner function for a particle on an infinite lattice. Here we argue that the criticism to our work raised by Bizarro is not substantial and does not invalidate our proposal.
An Introduction to Differentials Based on Hyperreal Numbers and Infinite Microscopes
ERIC Educational Resources Information Center
Henry, Valerie
2010-01-01
In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In…
An Extended Optional Infinitive Stage in German-Speaking Children with Specific Language Impairment.
ERIC Educational Resources Information Center
Rice, Mabel L.; Noll, Karen Ruff; Grimm, Hannelore
1997-01-01
Predictions were formulated for extended Optional Infinitives (OIs) stage in German-speaking children with specific language impairment and evaluated in clinical sample of 8 SLI German-speaking children, ages 4; 0 to 4; 8; and control group of 8 younger utterance-equivalent children, ages 2; 1 to 2; 7. Samples reveal that affected group more…
Modeling the Development of Children's Use of Optional Infinitives in Dutch and English Using MOSAIC
ERIC Educational Resources Information Center
Freudenthal, Daniel; Pine, Julian M.; Gobet, Fernand
2006-01-01
In this study we use a computational model of language learning called model of syntax acquisition in children (MOSAIC) to investigate the extent to which the optional infinitive (OI) phenomenon in Dutch and English can be explained in terms of a resource-limited distributional analysis of Dutch and English child-directed speech. The results show…
NASA Technical Reports Server (NTRS)
Allaire, P. E.; Branagan, L. A.; Kocur, J. A.
1982-01-01
An unbounded eccentric centrifugal impeller with an infinite number of log spiral blades undergoing synchronous whirling in an incompressible fluid is considered. The forces acting on it due to coriolis forces, centripetal forces, changes in linear momentum, changes in pressure due to rotating and changes in pressure due to changes in linear momentum are evaluated.
Infinitives or Bare Stems? Are English-Speaking Children Defaulting to the Highest-Frequency Form?
ERIC Educational Resources Information Center
Räsänen, Sanna H. M.; Ambridge, Ben; Pine, Julian M.
2014-01-01
Young English-speaking children often produce utterances with missing 3sg -s (e.g., *He play). Since the mid 1990s, such errors have tended to be treated as Optional Infinitive (OI) errors, in which the verb is a non-finite form (e.g., Wexler, 1998; Legate & Yang, 2007). The present article reports the results of a cross-sectional…
ERIC Educational Resources Information Center
Hoover, Jill R.; Storkel, Holly L.; Rice, Mabel L.
2012-01-01
The effect of neighborhood density on optional infinitives was evaluated for typically developing (TD) children and children with Specific Language Impairment (SLI). Forty children, twenty in each group, completed two production tasks that assessed third person singular production. Half of the sentences in each task presented a dense verb, and…
Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle
NASA Astrophysics Data System (ADS)
Du, Lili; Duan, Ben
2016-04-01
This paper is a sequel to the earlier work Du and Duan (J Diff Equ 250:813-847, 2011) on well-posedness of steady subsonic Euler flows through infinitely long three-dimensional axisymmetric nozzles. In Du and Duan (J Diff Equ 250:813-847, 2011), the authors showed the existence and uniqueness of the global subsonic Euler flows through an infinitely long axisymmetric nozzle, when the variation of Bernoulli's function in the upstream is sufficiently small and the mass flux of the incoming flow is less than some critical value. The smallness of the variation of Bernoulli's function in the upstream prevents the attendance of the possible singularity in the nozzles, however, at the same time it also leads that the vorticity of the ideal flow is sufficiently small in the whole nozzle and the flows are indeed adjacent to axisymmetric potential flows. The purpose of this paper is to investigate the effects of the vorticity for the smooth subsonic ideal flows in infinitely long axisymmetric nozzles. We modify the formulation of the problem in the previous work Du and Duan (J Diff Equ 250:813-847, 2011) and the existence and uniqueness results on the smooth subsonic ideal polytropic flows in infinitely long axisymmetric nozzles without the restriction on the smallness of the vorticity are shown in this paper.
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. PMID:26259224
Dedekind's η-function and the cohomology of infinite dimensional Lie algebras
Garland, Howard
1975-01-01
We compute the cohomology of certain infinite dimensional Lie algebras which are subalgebras of Lie algebras introduced by Moody and Kac. We note a relation between our results and the cohomology of loop spaces of compact groups. Finally, we derive, by Euler-Poincaré, identities of Macdonald for powers of the Dedekind η-function. PMID:16592258
Dedekind's eta-function and the cohomology of infinite dimensional Lie algebras.
Garland, H
1975-07-01
We compute the cohomology of certain infinite dimensional Lie algebras which are subalgebras of Lie algebras introduced by Moody and Kac. We note a relation between our results and the cohomology of loop spaces of compact groups. Finally, we derive, by Euler-Poincaré, identities of Macdonald for powers of the Dedekind eta-function. PMID:16592258
ERIC Educational Resources Information Center
Ribbat, Christoph
2010-01-01
In a satiric chapter of David Foster Wallace's novel "Infinite Jest," a mock media expert reports how American consumers of the near future recoil from a new communication device known as "videophony" and return to the voice-only telephone of the Bell Era. This article explores the said chapter in the framework of media theories reading the…
ERIC Educational Resources Information Center
Gonzalez-Martin, Alejandro S.; Nardi, Elena; Biza, Irene
2011-01-01
The study we report here examines parts of what Chevallard calls the "institutional" dimension of the students' learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this…
An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations
NASA Astrophysics Data System (ADS)
Azuma, T.; Koikawa, T.
2007-08-01
The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and show that the 5D Reissner-Nordström solution and the 5D Majumdar-Papapetrou-type solution are included among the 2-soliton solutions.
Cooperation in an Infinite-Choice Continuous-Time Prisoner's Dilemma.
ERIC Educational Resources Information Center
Feeley, Thomas H.; Tutzauer, Frank; Young, Melissa J.; Rosenfeld, Heather L.
1997-01-01
The Prisoner's Dilemma (PD) game demonstrates how cooperative or competitive choices influence decision making between two people or groups. A study of 48 college students tested an infinite-choice, continuous-time version of the PD. Results indicated that oscillatory cooperation was the predominant over-time behavior, that players matched…
Diffusion in a generalized thermoelastic solid in an infinite body with a cylindrical cavity
NASA Astrophysics Data System (ADS)
Sharma, J. N.; Kumari, N.; Sharma, K. K.
2013-09-01
A dynamic problem of an infinite isotropic cylinder of radius r subjected to boundary conditions of the radial stress, temperature, or concentration of the diffusing substance is studied by using the equations of state of a elastothermodiffusive solid with one relaxation time and the Laplace transform technique. The distributions of the displacement, temperature, and concentration are displayed graphically and analytically.
Creating Visual Aids with Graphic Organisers on an Infinite Canvas--The Impact on the Presenter
ERIC Educational Resources Information Center
Casteleyn, Jordi; Mottart, Andre; Valcke, Martin
2015-01-01
Instead of the traditional set of slides, the visual aids of a presentation can now be graphic organisers (concept maps, knowledge maps, mind maps) on an infinite canvas. Constructing graphic organisers has a beneficial impact on learning, but this topic has not been studied in the context of giving a presentation. The present study examined this…
Novel photochromic infinite coordination polymer particles derived from a diarylethene photoswitch.
Hu, Xiao Guang; Li, XiaoLiang; Yang, Sung Ik
2015-07-01
A novel infinite coordination polymer (DAE-ICP) based on zinc nitrite and a diarylethene photoswitch, with reversible photochromic properties in solution and the solid state upon applying photostimuli, was synthesized and characterized by FT-IR, EDX, FE-SEM and FE-TEM. PMID:26041619
Elastic moduli of pyrope rich garnets
NASA Astrophysics Data System (ADS)
Pandey, B. K.; Pandey, A. K.; Singh, C. K.
2013-06-01
The elastic properties of minerals depend on its composition, crystal structure, temperature and level of defects. The elastic parameters are important for the interpretation of the structure and composition of the garnet rich family. In present work we have calculated the elastic moduli such as isothermal bulk modulus, Young's modulus and Shear modulus over a wide range of temperature from 300 K to 1000 K by using Birch EOS and Poirrier Tarantola equation of state. The obtained results are compared with the experimental results obtained by measuring the elastic moduli of single crystal. The calculated results show that the logarithmic isothermal EOS does not cooperate well with experimental results.
Faraday wave lattice as an elastic metamaterial
NASA Astrophysics Data System (ADS)
Domino, L.; Tarpin, M.; Patinet, S.; Eddi, A.
2016-05-01
Metamaterials enable the emergence of novel physical properties due to the existence of an underlying subwavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial.
Faraday wave lattice as an elastic metamaterial.
Domino, L; Tarpin, M; Patinet, S; Eddi, A
2016-05-01
Metamaterials enable the emergence of novel physical properties due to the existence of an underlying subwavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial. PMID:27300815
Elastic anomalies in Fe-Cr alloys.
Zhang, Hualei; Wang, Guisheng; Punkkinen, Marko P J; Hertzman, Staffan; Johansson, Börje; Vitos, Levente
2013-05-15
Using ab initio alloy theory, we determine the elastic parameters of ferromagnetic and paramagnetic Fe(1-c)Cr(c) (0 ≤ c ≤ 1) alloys in the body centered cubic crystallographic phase. Comparison with the experimental data demonstrates that the employed theoretical approach accurately describes the observed composition dependence of the polycrystalline elastic moduli. The predicted single-crystal elastic constants follow complex anomalous trends, which are shown to originate from the interplay between magnetic and chemical effects. The nonmonotonic composition dependence of the elastic parameters has marked implications on the micro-mechanical properties of ferrite stainless steels. PMID:23604218
Elastic properties of solids at high pressure
NASA Astrophysics Data System (ADS)
Vekilov, Yu Kh; Krasilnikov, O. M.; Lugovskoy, A. V.
2015-11-01
This review examines the elastic response of solids under load. The definitions of isothermal and adiabatic elastic constants of ( n≥2) for a loaded crystal are given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third-, and fourth-order elastic constants from the energy-strain and stress-strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0-600 GPa.
Numerical study of interfacial solitary waves propagating under an elastic sheet
Wang, Zhan; Părău, Emilian I.; Milewski, Paul A.; Vanden-Broeck, Jean-Marc
2014-01-01
Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field. PMID:25104909
Breathing mode vibrations and elastic properties of single-crystal and penta-twinned gold nanorods.
Gan, Yong; Sun, Zheng; Chen, Zhen
2016-08-10
The acoustic vibrations of individual single-crystal and penta-twinned gold nanorods with widths from ∼7 to ∼26 nm are studied using atomic-level simulations and finite element calculations. It is demonstrated that the continuum model in the limit of an infinite rod length could be used to describe the breathing periods of nanorods with an aspect ratio as small as ∼2.5, in combination with bulk material elastic constants. The elastic moduli of gold nanorods are determined via their atomistically simulated extensional periods and the dispersion relation based on long-wavelength approximation. The twinned nanorods become stiffer as the width is reduced, which is in contrast to the size dependence of the modulus in single-crystal nanorods. Further finite element calculations for the breathing periods of nanorods are performed using isotropic elastic constants of bulk gold. We find that the breathing vibrations of the penta-twinned nanorods are more affected by the crystal structure effect than those of single-crystal nanorods, because a smaller range of crystal directions perpendicular to the long axis is involved in the breathing vibrations of twinned nanorods. PMID:27476532
Numerical study of interfacial solitary waves propagating under an elastic sheet.
Wang, Zhan; Părău, Emilian I; Milewski, Paul A; Vanden-Broeck, Jean-Marc
2014-08-01
Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field. PMID:25104909
Argani, L P; Bigoni, D; Capuani, D; Movchan, N V
2014-09-01
The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney-Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing an ad hoc potential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup-cone rupture of ductile metal bars. PMID:25197258
NASA Astrophysics Data System (ADS)
Liang, Paul Nan-Jiune
1990-01-01
Three dimensional mode shapes for thermoelastic waves in a viscous, compressible, fluid-filled infinite annular elastic concentric cylinder are studied using the exact coupled three dimensional equations for the vibrations in the n = 0, 1 circumferential modes. These results are related to those which arise under circumstances where uncoupled shear modes in the wall and the fluid have similar axial phase velocities and therefore are in a state sometimes called "coincidence". Three dimensional dispersion curves and modal wave plots are presented for a range of parameters including a steel tube containing water, glycerin and air. The corresponding axial mode shapes and radial mode shapes and their three dimensional equivalents are plotted so that the types of wave motion can be identified. The thermal effect for wave propagation in a fluid -filled annular elastic steel tube is found to be very important. This effect can cause a 15% difference (the average for water and glycerin) with that neglecting the thermal effect with the system equations. However, for an elastic steel tube or a fluid line alone, the thermal effect is small (< 1%) under the conditions of room temperature and the radius ratio of inner to outer radii is 0.93. The mechanism for the importance of the thermal effect in the coupled fluid-solid problem is related to the relatively higher thermal conductivity at the solid wall which conducts away heat from the relatively insulated viscous liquid boundary layer.
Impact of a vortex dipole with a semi-infinite plate
NASA Astrophysics Data System (ADS)
Peterson, Sean D.; Porfiri, Maurizio
2012-11-01
Recently, several studies have been published on small-scale energy harvesting from fluids using electro-active polymers strips. Specifically, the feasibility of harvesting energy from vortex rings via impact with a cantilevered electro-active strip has recently been demonstrated. As a first step towards developing predictive models of the energy harvesting capacity of this modality, we develop a simplified two-dimensional representation of the vortex ring-deformable structure interaction, in which the vortex ring is modeled as a Lamb dipole, and the cantilevered deformable strip is replaced with a semi-infinite rigid plate. The interaction is explored numerically for a range of dipole Reynolds numbers from 500 to 3000, based upon the convection speed and dipole radius. The initial dipole trajectory results in an impact with the semi-infinite plate at its tip. As the dipole approaches, vorticity is induced in the boundary layer along the wall, which eventually separates and joins with half of the original dipole to form a secondary dipole. This interaction is similar to that of a dipole impacting an infinite wall. The other half of the original dipole merges with vorticity shed from the tip of the plate to produce another secondary dipole. The stagnation point is shifted away from the centerline of the original dipole, which differs from the case with an infinite wall. Of particular interest for the energy harvesting is the differential pressure across the semi-infinite plate, as it relates to the energy transferred to the wall in the event of a deformable, as opposed to rigid, structure, which will be discussed as well as the general flow features.
The elastic constants of the human lens
Fisher, R. F.
1971-01-01
1. When the lens is spun around its antero-posterior polar axis in an apparatus designed for the purpose, high speed photography can be used to record its changing profile. By this method a variable radial centrifugal force can be applied to the lens which mimics the pull of the zonule. 2. If the lens is not stressed at its centre beyond 100 Nm-2 it behaves as a truly elastic body. When stressed beyond this limit visco-elastic strain is produced at its poles. 3. The human lens has isotropic elastic properties at the extremes of life, but at the other times Young's Modulus of Elasticity varies with the direction in which it is measured. 4. Young's Modulus of Elasticity of the lens varies with age, polar elasticity and equatorial elasticity, at birth being 0·75 × 103 and 0·85 × 103 Nm-2 respectively, while at 63 years of age both are equal to 3 × 103 Nm-2. 5. A comparison of Young's Modulus of the young human lens with that of the rabbit and cat shows that the polar elasticity of the lenses of these animals was 5 times greater in the young rabbit, and 21 times greater in the adult cat. Equatorial elasticities of the rabbit and human lens were equal, while in the cat the equatorial elasticity was four times greater. 6. A mathematical model showing the lens substance possessing a nucleus of lower isotropic elasticity than that of the isotropic elastic cortex surrounding it, accounts for the difference between polar and equatorial elasticity of the intact adult lens. 7. The implications of these findings are discussed in relation to: (i) accommodation and the rheological properties of the lens; (ii) possible differences in the physical state of the lenticular proteins in the cortex and nucleus which may account for the senile variations in Young's Modulus of Elasticity in these regions of the lens; (iii) the loss of accommodation due solely to an increase in Young's Modulus of Elasticity of the lens between the ages of 15 and 60. This would amount to 44% of the
Deriving capture and reaction cross sections from observed quasi-elastic and elastic backscattering
NASA Astrophysics Data System (ADS)
Sargsyan, V. V.; Adamian, G. G.; Antonenko, N. V.; Diaz-Torres, A.; Gomes, P. R. S.; Lenske, H.
2014-12-01
Based on reaction theory, we suggest a useful method for extracting total and partial reaction and capture (complete fusion) cross sections from the experimental elastic and quasi-elastic backscattering excitation functions taken at a single angle. We also propose a method to predict the differential reaction cross section from the observed elastic-scattering angular distribution.
Elastic effects in superposed fluids
NASA Astrophysics Data System (ADS)
Joshi, Amey
2014-02-01
A non-uniform electric field of suitable gradient can make specific weights of two superposed dielectric fluids identical. If the fluids are Newtonian, this choice of electric field makes the interface resilient to small perturbations, even if the fluid on the top is heavier than the one at bottom. On the other hand, if the fluids are viscoelastic, the interface continues to remain unstable. We point out that although the right choice of electric field succeeds in overcoming the effects of gravity, the fluids' elasticity makes the interface unstable. The same effect can be achieved in the case of paramagnetic or ferro-fluids in presence of a non-uniform magnetic field.
Elasticity of polymeric nanocolloidal particles
NASA Astrophysics Data System (ADS)
Riest, Jonas; Athanasopoulou, Labrini; Egorov, Sergei A.; Likos, Christos N.; Ziherl, Primož
2015-11-01
Softness is an essential mechanical feature of macromolecular particles such as polymer-grafted nanocolloids, polyelectrolyte networks, cross-linked microgels as well as block copolymer and dendrimer micelles. Elasticity of individual particles directly controls their swelling, wetting, and adsorption behaviour, their aggregation and self-assembly as well as structural and rheological properties of suspensions. Here we use numerical simulations and self-consistent field theory to study the deformation behaviour of a single spherical polymer brush upon diametral compression. We observe a universal response, which is rationalised using scaling arguments and interpreted in terms of two coarse-grained models. At small and intermediate compressions the deformation can be accurately reproduced by modelling the brush as a liquid drop, whereas at large compressions the brush behaves as a soft ball. Applicable far beyond the pairwise-additive small-strain regime, the models may be used to describe microelasticity of nanocolloids in severe confinement including dense disordered and crystalline phases.
High elastic modulus polymer electrolytes
Balsara, Nitash Pervez; Singh, Mohit; Eitouni, Hany Basam; Gomez, Enrique Daniel
2013-10-22
A polymer that combines high ionic conductivity with the structural properties required for Li electrode stability is useful as a solid phase electrolyte for high energy density, high cycle life batteries that do not suffer from failures due to side reactions and dendrite growth on the Li electrodes, and other potential applications. The polymer electrolyte includes a linear block copolymer having a conductive linear polymer block with a molecular weight of at least 5000 Daltons, a structural linear polymer block with an elastic modulus in excess of 1.times.10.sup.7 Pa and an ionic conductivity of at least 1.times.10.sup.-5 Scm.sup.-1. The electrolyte is made under dry conditions to achieve the noted characteristics.
Elastic wave turbulence and intermittency
NASA Astrophysics Data System (ADS)
Chibbaro, Sergio; Josserand, Christophe
2016-07-01
We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by d cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only.
Elastic wave turbulence and intermittency.
Chibbaro, Sergio; Josserand, Christophe
2016-07-01
We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by d cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only. PMID:27575068
Elastic Torques about Membrane Edges
Lorenzen, Silke; Servuss, Rolf-M.; Helfrich, Wolfgang
1986-01-01
The shape of mechanically pierced giant vesicles is studied to obtain the elastic modulus of Gaussian curvature of egg lecithin bilayers. It is argued that such experiments are governed by an apparent modulus, ¯κapp, not the true modulus of Gaussian curvature, ¯κ. A theory of ¯κapp is proposed, regarding the pierced bilayer vesicle as a closed monolayer vesicle. The quantity measured, i.e. ¯κapp/κ, where κ is the rigidity, agrees satisfactorily with the theory. We find ¯κapp = -(1.9 ± 0.3) · 10-12 erg (on the basis of κ = (2.3 ± 0.3) · 10-12 erg). The result may have implications for bilayer fusion. ImagesFIGURE 4FIGURE 5 PMID:19431686
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 DEVICES GENERAL HOSPITAL AND PERSONAL USE DEVICES General Hospital and Personal Use Therapeutic Devices § 880.5075 Elastic bandage. (a)...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Elasticity. 29.3516 Section 29.3516 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Type 95) § 29.3516 Elasticity. The flexible, springy nature of the tobacco leaf to...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Elasticity. 29.6013 Section 29.6013 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... INSPECTION Standards Definitions § 29.6013 Elasticity. The flexible, springy nature of the tobacco leaf...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Elasticity. 29.3516 Section 29.3516 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Type 95) § 29.3516 Elasticity. The flexible, springy nature of the tobacco leaf to...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Elasticity. 29.1014 Section 29.1014 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Type 92) § 29.1014 Elasticity. The flexible, springy nature of the tobacco leaf to...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Elasticity. 29.2265 Section 29.2265 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Elasticity. The flexible, springy nature of the tobacco leaf to recover approximately its original size...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Elasticity. 29.2265 Section 29.2265 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Elasticity. The flexible, springy nature of the tobacco leaf to recover approximately its original size...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Elasticity. 29.2515 Section 29.2515 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing...-Cured Tobacco (u.s. Types 22, 23, and Foreign Type 96) § 29.2515 Elasticity. The flexible,...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Elasticity. 29.6013 Section 29.6013 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... INSPECTION Standards Definitions § 29.6013 Elasticity. The flexible, springy nature of the tobacco leaf...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Elasticity. 29.1014 Section 29.1014 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Type 92) § 29.1014 Elasticity. The flexible, springy nature of the tobacco leaf to...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Elasticity. 29.2515 Section 29.2515 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing...-Cured Tobacco (u.s. Types 22, 23, and Foreign Type 96) § 29.2515 Elasticity. The flexible,...
Wetting of Elastic Solids on Nanopillars
NASA Astrophysics Data System (ADS)
Ignacio, M.; Saito, Y.; Smereka, P.; Pierre-Louis, O.
2014-04-01
Solids and liquids are both known to exhibit Cassie-Baxter states, where a drop or a solid nanoparticle is maintained on top of pillars due to wetting forces. We point out that due to elastic strain, solid nanocrystals exhibit a behavior different from that of liquids. First, the equilibrium Cassie-Baxter state on a single pillar exhibits a spontaneous symmetry breaking due to elastic effects. The second consequence of elasticity is the existence of stable partially impaled states, resulting from a compromise between wetting forces which favor impalement and elastic strain which resists impalement. Based on kinetic Monte Carlo simulations which include elastic strain, we discuss these effects and we propose a global phase diagram for the stability of nanocrystals on nanopillars.
Decoherence due to Elastic Rayleigh Scattering
NASA Astrophysics Data System (ADS)
Uys, H.; Biercuk, M. J.; Vandevender, A. P.; Ospelkaus, C.; Meiser, D.; Ozeri, R.; Bollinger, J. J.
2010-11-01
We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of Be+9 in a 4.5 T magnetic field.
Decoherence due to elastic Rayleigh scattering.
Uys, H; Biercuk, M J; Vandevender, A P; Ospelkaus, C; Meiser, D; Ozeri, R; Bollinger, J J
2010-11-12
We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9Be+ in a 4.5 T magnetic field. PMID:21231210
3D Elastic Wavefield Tomography
NASA Astrophysics Data System (ADS)
Guasch, L.; Warner, M.; Stekl, I.; Umpleby, A.; Shah, N.
2010-12-01
Wavefield tomography, or waveform inversion, aims to extract the maximum information from seismic data by matching trace by trace the response of the solid earth to seismic waves using numerical modelling tools. Its first formulation dates from the early 80's, when Albert Tarantola developed a solid theoretical basis that is still used today with little change. Due to computational limitations, the application of the method to 3D problems has been unaffordable until a few years ago, and then only under the acoustic approximation. Although acoustic wavefield tomography is widely used, a complete solution of the seismic inversion problem requires that we account properly for the physics of wave propagation, and so must include elastic effects. We have developed a 3D tomographic wavefield inversion code that incorporates the full elastic wave equation. The bottle neck of the different implementations is the forward modelling algorithm that generates the synthetic data to be compared with the field seismograms as well as the backpropagation of the residuals needed to form the direction update of the model parameters. Furthermore, one or two extra modelling runs are needed in order to calculate the step-length. Our approach uses a FD scheme explicit time-stepping by finite differences that are 4th order in space and 2nd order in time, which is a 3D version of the one developed by Jean Virieux in 1986. We chose the time domain because an explicit time scheme is much less demanding in terms of memory than its frequency domain analogue, although the discussion of wich domain is more efficient still remains open. We calculate the parameter gradients for Vp and Vs by correlating the normal and shear stress wavefields respectively. A straightforward application would lead to the storage of the wavefield at all grid points at each time-step. We tackled this problem using two different approaches. The first one makes better use of resources for small models of dimension equal
Remarks on the elastic axis of shell wings
NASA Technical Reports Server (NTRS)
Kuhn, Paul
1936-01-01
The definitions of flexural center, torsional center, elastic center, and elastic axis are discussed. The calculation of elastic centers is dealt with in principle and a suggestion is made for the design of shear webs.
A remark on the infinite-volume Gibbs measures of spin glasses
NASA Astrophysics Data System (ADS)
Arguin, Louis-Pierre
2008-12-01
In this note, we point out that infinite-volume Gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a Hilbert space. This simple observation follows from a result of Dovbysh and Sudakov on weakly exchangeable random matrices. Limiting Gibbs measures can then be studied as single well-defined objects. This approach naturally extends the space of random overlap structures as defined by Aizenman et al. We discuss the Ruelle probability cascades and the stochastic stability within this framework. As an application, we use an idea of Parisi and Talagrand to prove that if a sequence of finite-volume Gibbs measures satisfies the Ghirlanda-Guerra identities, then the infinite-volume measure must be singular as a measure on a Hilbert space.
Analysis of monotectic growth: infinite diffusion in the L 2 phase
NASA Astrophysics Data System (ADS)
Coriell, S. R.; Mitchell, W. F.; Murray, B. T.; Andrews, J. B.; Arikawa, Y.
1997-08-01
The Jackson-Hunt model of eutectic solidification is applied to monotectic solidification in which a liquid (L 1) transforms into rods of a different liquid (L 2) in a solid matrix. Limiting cases of no diffusion and infinite diffusion (complete mixing) in the L 2 phase are considered. An adaptive refinement and multigrid algorithm (MGGHAT) is used to obtain numerical solutions for the concentration field in the L 1 phase; this allows consideration of a general phase diagram. Density differences between the three phases, which cause fluid flow, are treated approximately. Specific calculations are carried out for aluminum-indium alloys. Infinite diffusion in the L 2 phase has only a small effect on the relationship between interface undercooling and rod spacing.
Calculating alpha Eigenvalues in a Continuous-Energy Infinite Medium with Monte Carlo
Betzler, Benjamin R.; Kiedrowski, Brian C.; Brown, Forrest B.; Martin, William R.
2012-09-04
The {alpha} eigenvalue has implications for time-dependent problems where the system is sub- or supercritical. We present methods and results from calculating the {alpha}-eigenvalue spectrum for a continuous-energy infinite medium with a simplified Monte Carlo transport code. We formulate the {alpha}-eigenvalue problem, detail the Monte Carlo code physics, and provide verification and results. We have a method for calculating the {alpha}-eigenvalue spectrum in a continuous-energy infinite-medium. The continuous-time Markov process described by the transition rate matrix provides a way of obtaining the {alpha}-eigenvalue spectrum and kinetic modes. These are useful for the approximation of the time dependence of the system.
Langlands, T A M; Henry, B I; Wearne, S L
2009-12-01
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models. PMID:19221755
Direct observation of infinite NiO2 planes in LaNiO2 films
NASA Astrophysics Data System (ADS)
Ikeda, Ai; Krockenberger, Yoshiharu; Irie, Hiroshi; Naito, Michio; Yamamoto, Hideki
2016-06-01
Epitaxial thin films of LaNiO2, which is an oxygen-deficient perovskite with “infinite layers” of Ni1+O2, were prepared by a low-temperature reduction of LaNiO3 single-crystal films on NdGaO3 substrates. We report the high-angle annular dark-field and bright-field scanning transmission electron microscopy observations of infinite NiO2 planes of c-axis-oriented LaNiO2 epitaxial thin films with a layer stacking sequence of NiO2/La/NiO2. Resistivity measurements on the films show T 2 dependence between 400 and 150 K and a negative Hall coefficient.
Z2 gauge theory description of the Mott transition in infinite dimensions
NASA Astrophysics Data System (ADS)
Žitko, Rok; Fabrizio, Michele
2015-06-01
The infinite-dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a Z2 gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local Z2 gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.
NASA Astrophysics Data System (ADS)
Guo, Gang; Chen, Bin; Zhao, Xinjun; Zhao, Fang; Wang, Quanmin
2015-09-01
We investigate the first passage time (FPT) distribution for accelerating subdiffusion governed by the modified fractional diffusion equation which has a secondary fractional time derivative acting on a diffusion operator. For the FPT problem subject to absorbing barrier condition, we obtain exact analytical expressions for the FPT distribution as well as its Laplace transform in the semi-infinite interval. Most of the results have been derived by using the Laplace transform, the Fourier Cosine transform, the Mellin transform and the properties of the Fox H-function. In contrast to the Laplace transform of the FPT distribution which can be expressed elegantly and neatly, the exact solution for the FPT distribution requires an infinite series of Fox H-functions instead of a single Fox H-function. Numerical result reveals that the crossover between the two distinct scaling regimes is apparent only when the discrepancy between the two diffusion exponents becomes more pronounced.
Option pricing for stochastic volatility model with infinite activity Lévy jumps
NASA Astrophysics Data System (ADS)
Gong, Xiaoli; Zhuang, Xintian
2016-08-01
The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.
Lévy flights in an infinite potential well as a hypersingular Fredholm problem
NASA Astrophysics Data System (ADS)
Kirichenko, Elena V.; Garbaczewski, Piotr; Stephanovich, Vladimir; Żaba, Mariusz
2016-05-01
We study Lévy flights with arbitrary index 0 <μ ≤2 inside a potential well of infinite depth. Such a problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schrödinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain D , reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numerically with some analytical results regarding the structure of the spectrum.
Nonlinear and Quantum Origin of Doubly Infinite Family of Modified Addition Laws for Fourmomenta
NASA Astrophysics Data System (ADS)
Lukierski, J.; Nowicki, A.
2002-11-01
We show that infinite variety of Poincaré bialgebras with nontrivial classical r-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition law in any order of dimensionfull deformation parameter λ (from physical reasons we can put λ= λ p where λ p is the Planck length). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct. In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can help to resolve the problem of consistent passage to macroscopic classical limit.
Semi-infinite jellium: Thermodynamic potential, chemical potential, and surface energy
NASA Astrophysics Data System (ADS)
Kostrobij, P. P.; Markovych, B. M.
2015-08-01
A general expression for the thermodynamic potential of the model of semi-infinite jellium is obtained. By using this expression, the surface energy for the infinite barrier model is calculated. The behavior of the surface energy and of the chemical potential as functions of the Wigner-Seitz radius and the influence of the Coulomb interaction between electrons on the calculated values is studied. It is shown that taking into account the Coulomb interaction between electrons leads to growth of the surface energy. The surface energy is positive in the entire area of the Wigner-Seitz radius. It is shown that taking into account the Coulomb interaction between electrons leads to a decrease of the chemical potential.
NASA Astrophysics Data System (ADS)
Taylor, Emma A.; Kay, Laurie; Shrine, Nick R. G.
Hypervelocity impact on brittle materials produces features not observed on ductile targets. Low fracture toughness and high yield strength produce a range of fracture morphologies including cracking, spallation and shatter. For sub-mm diameter projectiles, impact features are characterised by petaloid spallation separated by radial cracks. The conchoidal or spallation diameter is a parameter in current cratering equations. An alternative method for interpreting hypervelocity impacts on glass targets of semi-infinite thickness is tested against impact data produced using the Light Gas Gun (LGG) facility at the University of Kent at Canterbury (UKC), U.K. Spherical projectiles of glass and other materials with diameters 30-300 μm were fired at ~5 km s^-1 at a glass target of semi-infinite thickness. The data is used to test a power law relationship between projectile diameter and crack length. The results of this work are compared with published cratering/spallation equations for brittle materials.
On Implicit Active Constraints in Linear Semi-Infinite Programs with Unbounded Coefficients
Goberna, M. A.; Lancho, G. A.; Todorov, M. I.; Vera de Serio, V. N.
2011-04-15
The concept of implicit active constraints at a given point provides useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming provided the set of gradient vectors of the constraints is bounded, commonly under the additional assumption that there exists some strong Slater point. This paper shows that the mentioned global boundedness condition can be replaced by a weaker local condition (LUB) based on locally active constraints (active in a ball of small radius whose center is some nominal point), providing geometric information about the solution set and Karush-Kuhn-Tucker type conditions for the optimal solution to be strongly unique. The maintaining of the latter property under sufficiently small perturbations of all the data is also analyzed, giving a characterization of its stability with respect to these perturbations in terms of the strong Slater condition, the so-called Extended-Nuernberger condition, and the LUB condition.
MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes
Williams, B.K.
1988-01-01
Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.
Numerical Solution of a Plane Jet Impingement on an Infinite Flat Surface
NASA Astrophysics Data System (ADS)
Arora, S.; Irfan, Nagma
2015-03-01
In this paper numerical solution of the unsteady plane incompressible viscous jet impinging on to an infinite flat surface are presented for Re=450. In the present study, all calculations have been done by using Dufort Frankel scheme and over relaxation scheme. Result and graphs have been obtained by using MATLAB programming. The obtained results explain the flow of water after exhaling from nozzle and the streamlines and vorticity of flow ofwater after striking with flat infinite surface. The solutions obtained by proposed method indicate that this approach is easy to implement and computationally very attractive and the results of our investigation are in qualitative agreement with those available in the literature [1, 9]. This method is capable of greatly reducing the size of calculations while still maintaining high accuracy of the numerical solution.
The axisymmetric elasticity problem for a laminated plate containing a circular hole
NASA Technical Reports Server (NTRS)
Delale, F.; Erdogan, F.
1981-01-01
The elasticity problem for a laminated thick plate which consists of two bonded dissimilar layers and which contains a circular hole is considered. The problem is formulated for arbitrary axisymmetric tractions on the hole surface by using the Love strain function. Through the expansion of the boundary conditions into Fourier series the problem is reduced to an infinite system of algebraic equations which is solved by the method of reduction. Of particular interest in the problem are the stresses along the interface as they relate to the question of delamination failure of the composite plate. These stresses are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singular behavior of the stress state is presented and the stress intensity factors are calculated.
Thermal stresses in chemically hardening elastic media with application to the molding process
NASA Technical Reports Server (NTRS)
Levitsky, M.; Shaffer, B. W.
1974-01-01
A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2004-01-01
An approach for synthesizing buckling results for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexural anisotropic plates that are subjected to combined mechanical loads. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. Many results are presented for some common laminates that are intended to facilitate a structural designer s transition to the use of the generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves.
Improvement of finite element meshes - Heat transfer in an infinite cylinder
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.
1989-01-01
An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffnes matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.
NASA Astrophysics Data System (ADS)
Kaplan, C. Nadir; Hinczewski, Michael; Berker, A. Nihat
2009-06-01
For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.
Improvement in finite element meshes: Heat transfer in an infinite cylinder
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.
1988-01-01
An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffness matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.
On the existence of infinitely many universal tree-based networks.
Hayamizu, Momoko
2016-05-01
A tree-based network on a set X of n leaves is said to be universal if any rooted binary phylogenetic tree on X can be its base tree. Francis and Steel showed that there is a universal tree-based network on X in the case of n = 3, and asked whether such a network exists in general. We settle this problem by proving that there are infinitely many universal tree-based networks for any n>1. PMID:26921465
Linear vs nonlinear and infinite vs finite: An interpretation of chaos
Protopopescu, V.
1990-10-01
An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.
Solutions of Boltzmann`s Equation for Mono-energetic Neutrons in an Infinite Homogeneous Medium
DOE R&D Accomplishments Database
Wigner, E. P.
1943-11-30
Boltzman's equation is solved for the case of monoenergetic neutrons created by a plane or point source in an infinite medium which has spherically symmetric scattering. The customary solution of the diffusion equation appears to be multiplied by a constant factor which is smaller than 1. In addition to this term the total neutron density contains another term which is important in the neighborhood of the source. It varies as 1/r{sup 2} in the neighborhood of a point source. (auth)
A note on the interpretation of magnetic anomalies of infinite thin sheets by using relation figures
Rama Rao, Ch.; Rao, M.B.S.V.; Vijayakumar, V.; Virupakshi, G.
1985-08-01
The concept of relation figures is utilized in the case of a thin infinite sheet for identification and determination of the causative source geometry, and its various parameters. The plot of ..delta..T versus ..delta..V is a conic, the plots between the respective symmetric components and the respective asymmetric components are straight lines, and the resulting diagram between the first horizontal versus the first vertical derivative of either ..delta..T or ..delta..V is a cardioid.
Static properties of Bose-Einstein condensate mixtures in semi-infinite space
NASA Astrophysics Data System (ADS)
Thu, Nguyen Van
2016-08-01
Using double-parabola approximation (DPA) applied to Gross-Pitaevskii theory, the interfacial tension of Bose-Einstein condensate mixtures in semi-infinite system is obtained and shows that it is not vanishing at demix state K = 1, its value exactly coincides to wall tension of second component. A new kind of wetting phase transition (Antonov transition) is also considered within DPA and phase transition is first-order. Antonov line is thoroughly proved, too.
Second cluster integral from the spectrum of an infinite XXZ spin chain
NASA Astrophysics Data System (ADS)
Bibikov, P. N.
2015-03-01
First and second terms of the low-temperature cluster expansion for the free energy density of a magnetically polarized XXZ spin chain is obtained within the propagator approach suggested by E.W. Montroll and J.C. Ward. All the calculations employ only one- and two-magnon infinite-chain spectrums. In the XXX-point the result reproduces the well known S. Katsura's formula obtained 50 years ago by finite-chain calculations.
Amplification of current density modulation in a FEL with an infinite electron beam
Wang, G.; Litvinenko, V.N.; Webb, S.D.
2011-03-28
We show that the paraxial field equation for a free electron laser (FEL) in an infinitely wide electron beam with {kappa}-2 energy distribution can be reduced to a fourth ordinary differential equation (ODE). Its solution for arbitrary initial phase space density modulation has been derived in the wave-vector domain. For initial current modulation with Gaussian profile, close form solutions are obtained in space-time domain. In developing an analytical model for a FEL-based coherent electron cooling system, an infinite electron beam has been assumed for the modulation and correction processes. While the assumption has its limitation, it allows for an analytical close form solution to be obtained, which is essential for investigating the underlying scaling law, benchmarking the simulation codes and understanding the fundamental physics. 1D theory was previously applied to model a CeC FEL amplifier. However, the theory ignores diffraction effects and does not provide the transverse profile of the amplified electron density modulation. On the other hand, 3D theories developed for a finite electron beam usually have solutions expanded over infinite number of modes determined by the specific transverse boundary conditions. Unless the mode with the largest growth rate substantially dominates other modes, both evaluation and extracting scaling laws can be complicated. Furthermore, it is also preferable to have an analytical FEL model with assumptions consistent with the other two sections of a CeC system. Recently, we developed the FEL theory in an infinitely wide electron beam with {kappa}-1 (Lorentzian) energy distribution. Close form solutions have been obtained for the amplified current modulation initiated by an external electric field with various spatial-profiles. In this work, we extend the theory into {kappa}-2 energy distribution and study the evolution of current density induced by an initial density modulation.
Green's function for cracks of equal length from a circular hole in an infinite sheet
NASA Technical Reports Server (NTRS)
Shivakumar, V.; Forman, R. G.
1981-01-01
Stress-intensity factors are obtained for twin collinear cracks emanating from a hole in an infinite plate. Point forces that tend to make the crack surfaces separate and slide are applied to one of the cracks. A conformal mapping and the Muskelishvili formulation involving series representation of the Kolosov stress functions are used to derive the solutions. The variation of stress-intensity factor with crack length and with point of application of the loads is presented for both crack tips.
NASA Astrophysics Data System (ADS)
Chen, Jianyi; Zhang, Zhitao
2016-04-01
In this paper, we consider the periodic-Dirichlet problem for a forced nonlinear wave equation with resonance utt - Δu = μu + a (t , x)| u | p - 1 u in a n-dimensional ball. Under some suitable assumptions on μ, p and a (t , x), we prove the existence of infinitely many radially symmetric time-periodic solutions for the problem by variational methods.
Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process
Maslowski, Bohdan Pospisil, Jan
2008-06-15
Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise.
On the stability of an infinite swept attachment line boundary layer
NASA Technical Reports Server (NTRS)
Hall, P.; Mallik, M. R.; Poll, D. I. A.
1984-01-01
The instability of an infinite swept attachment line boundary layer is considered in the linear regime. The basic three dimensional flow is shown to be susceptible to travelling wave disturbances which propagate along the attachment line. The effect of suction on the instability is discussed and the results suggest that the attachment line boundary layer on a swept wing can be significantly stabilized by extremely small amounts of suction. The results obtained are in excellent agreement with the available experimental observations.
On the stability of an infinite swept attachment line boundary layer
NASA Technical Reports Server (NTRS)
Hall, P.; Malik, M. R.; Poll, D. I. A.
1984-01-01
The instability of an infinite swept attachment line boundary layer is considered in the linear regime. The basic three dimensional flow is shown to be susceptible to travelling wave disturbances which propagate along the attachment line. The effect of suction on the instability is discussed and the results suggest that the attachment in boundary layer on a swept wing can be significantly stabilized by extremely small amounts of suction. The results obtained are in excellent agreement with the available experimental observations.
Viscosity Solutions of an Infinite-Dimensional Black-Scholes-Barenblatt Equation
Kelome, D.; Swiech, A. swiech@math.gatech.edu
2003-05-21
We study an infinite-dimensional Black-Scholes-Barenblatt equation which is a Hamilton-Jacobi-Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black-Scholes-Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton-Jacobi-Bellman equations.
Friedberg, Richard; Manassah, Jamal T.
2011-08-15
We obtain in both the scalar and vector photon models the analytical expressions for the initial cooperative decay rate and the cooperative Lamb shift for an ensemble of resonant atoms distributed uniformly in an infinite cylindrical geometry for the case that the initial state of the system is prepared in a phased state modulated in the direction of the cylindrical axis. We find that qualitatively the scalar and vector theories give different results.
Wald Entropy for Ghost-Free, Infinite Derivative Theories of Gravity.
Conroy, Aindriú; Mazumdar, Anupam; Teimouri, Ali
2015-05-22
In this Letter, we demonstrate that the Wald entropy for any spherically symmetric black hole within an infinite derivative theory of gravity that is quadratic in curvature is determined solely by the area law. Thus, the infrared behavior of gravity is captured by the Einstein-Hilbert term, provided that the massless graviton remains the only propagating degree of freedom in the spacetime. PMID:26047217
Elastic metamaterial beam with remotely tunable stiffness
NASA Astrophysics Data System (ADS)
Qian, Wei; Yu, Zhengyue; Wang, Xiaole; Lai, Yun; Yellen, Benjamin B.
2016-02-01
We demonstrate a dynamically tunable elastic metamaterial, which employs remote magnetic force to adjust its vibration absorption properties. The 1D metamaterial is constructed from a flat aluminum beam milled with a linear array of cylindrical holes. The beam is backed by a thin elastic membrane, on which thin disk-shaped permanent magnets are mounted. When excited by a shaker, the beam motion is tracked by a Laser Doppler Vibrometer, which conducts point by point scanning of the vibrating element. Elastic waves are unable to propagate through the beam when the driving frequency excites the first elastic bending mode in the unit cell. At these frequencies, the effective mass density of the unit cell becomes negative, which induces an exponentially decaying evanescent wave. Due to the non-linear elastic properties of the membrane, the effective stiffness of the unit cell can be tuned with an external magnetic force from nearby solenoids. Measurements of the linear and cubic static stiffness terms of the membrane are in excellent agreement with experimental measurements of the bandgap shift as a function of the applied force. In this implementation, bandgap shifts by as much as 40% can be achieved with ˜30 mN of applied magnetic force. This structure has potential for extension in 2D and 3D, providing a general approach for building dynamically tunable elastic metamaterials for applications in lensing and guiding elastic waves.
Intramuscular pressures beneath elastic and inelastic leggings
NASA Technical Reports Server (NTRS)
Murthy, G.; Ballard, R. E.; Breit, G. A.; Watenpaugh, D. E.; Hargens, A. R.
1994-01-01
Leg compression devices have been used extensively by patients to combat chronic venous insufficiency and by astronauts to counteract orthostatic intolerance following spaceflight. However, the effects of elastic and inelastic leggings on the calf muscle pump have not been compared. The purpose of this study was to compare in normal subjects the effects of elastic and inelastic compression on leg intramuscular pressure (IMP), an objective index of calf muscle pump function. IMP in soleus and tibialis anterior muscles was measured with transducer-tipped catheters. Surface compression between each legging and the skin was recorded with an air bladder. Subjects were studied under three conditions: (1) control (no legging), (2) elastic legging, and (3) inelastic legging. Pressure data were recorded for each condition during recumbency, sitting, standing, walking, and running. Elastic leggings applied significantly greater surface compression during recumbency (20 +/- 1 mm Hg, mean +/- SE) than inelastic leggings (13 +/- 2 mm Hg). During recumbency, elastic leggings produced significantly higher soleus IMP of 25 +/- 1 mm Hg and tibialis anterior IMP of 28 +/- 1 mm Hg compared to 17 +/- 1 mm Hg and 20 +/- 2 mm Hg, respectively, generated by inelastic leggings and 8 +/- 1 mm Hg and 11 +/- 1 mm Hg, respectively, without leggings. During sitting, walking, and running, however, peak IMPs generated in the muscular compartments by elastic and inelastic leggings were similar. Our results suggest that elastic leg compression applied over a long period in the recumbent posture may impede microcirculation and jeopardize tissue viability.(ABSTRACT TRUNCATED AT 250 WORDS).
Application of numerical methods to elasticity imaging.
Castaneda, Benjamin; Ormachea, Juvenal; Rodríguez, Paul; Parker, Kevin J
2013-03-01
Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of clinical applications: cancer diagnosis (prostate, breast, liver), hepatic cirrhosis, renal disease, thyroiditis, arterial plaque evaluation, wall stiffness in arteries, evaluation of thrombosis in veins, and many others. In this context, numerical methods are applied to solve forward and inverse problems implicit in the algorithms in order to estimate viscoelastic linear and nonlinear parameters, especially for quantitative elasticity imaging modalities. In this work, an introduction to elasticity imaging modalities is presented. The working principle of qualitative modalities (sonoelasticity, strain elastography, acoustic radiation force impulse) and quantitative modalities (Crawling Waves Sonoelastography, Spatially Modulated Ultrasound Radiation Force (SMURF), Supersonic Imaging) will be explained. Subsequently, the areas in which numerical methods can be applied to elasticity imaging are highlighted and discussed. Finally, we present a detailed example of applying total variation and AM-FM techniques to the estimation of elasticity. PMID:24010245
Estimation of In vivo Cancellous Bone Elasticity
NASA Astrophysics Data System (ADS)
Otani, Takahiko; Mano, Isao; Tsujimoto, Toshiyuki; Yamamoto, Tadahito; Teshima, Ryota; Naka, Hiroshi
2009-07-01
The effect of decreasing bone density (a symptom of osteoporosis) is greater for cancellous bone than for dense cortical bone, because cancellous bone is metabolically more active. Therefore, the bone density or bone mineral density of cancellous bone is generally used to estimate the onset of osteoporosis. Elasticity or elastic constant is a fundamental mechanical parameter and is directly related to the mechanical strength of bone. Accordingly, elasticity is a preferable parameter for assessing fracture risk. A novel ultrasonic bone densitometer LD-100 has been developed to determine the mass density and elasticity of cancellous bone with a spatial resolution comparable to that of peripheral quantitative computed tomography. Bone density and bone elasticity are evaluated using ultrasonic parameters based on fast and slow waves in cancellous bone by modeling the ultrasonic wave propagation path. Elasticity is deduced from the measured bone density and the propagation speed of the fast wave. Thus, the elasticity of cancellous bone is approximately expressed by a cubic equation of bone density.
Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances
Ancey, S. Bazzali, E. Gabrielli, P. Mercier, M.
2014-05-21
The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.
A modified holographic dark energy model with infrared infinite extra dimension(s)
NASA Astrophysics Data System (ADS)
Gong, Yungui; Li, Tianjun
2010-01-01
We propose a modified holographic dark energy (MHDE) model with the Hubble scale as the infrared (IR) cutoff. Introducing the infinite extra dimension(s) at very large distance scale, we consider the black hole mass in higher dimensions as the ultraviolet cutoff. Thus, we can probe the effects of the IR infinite extra dimension(s). As a concrete example, we consider the Dvali-Gabadadze-Porrati (DGP) model and its generalization. We find that the DGP model is dual to the MHDE model in five dimensions, and the ΛCDM model is dual to the MHDE model in six dimensions. Fitting the MHDE model to the observational data, we obtain that Ωm0=0.269-0.027+0.030, Ωk0=0.003-0.012+0.011, and the number of the spatial dimensions is N=4.78-0.44+0.68. The best fit value of N implies that there might exist two IR infinite extra dimensions.
Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions
Gonzalez, Guillermo A.; Gutierrez-Pineres, Antonio C.; Vina-Cervantes, Viviana M.
2009-06-15
An infinite family of new exact solutions of the vacuum Einstein equations is presented. The solutions are static and axially symmetric and correspond to an infinite family of thin dust disks with a central inner edge. The metric functions of all the solutions can be explicitly computed, and can be expressed in a simple manner in terms of oblate spheroidal coordinates. The energy density of all the disks of the family is positive everywhere and well behaved, so that the corresponding energy-momentum tensor is in full agreement with all the energy conditions. Moreover, although the total mass of the disks is infinite, the solutions are asymptotically flat and the Riemann tensor is regular everywhere, as it is shown by computing the curvature scalars. Now, besides its importance as a new family of exact solutions of the vacuum Einstein equations, the main importance of this family of solutions is that it can be easily superposed with the Schwarzschild solution in order to describe thin disks surrounding a central black hole. Accordingly, a detailed analysis of this superposition will be presented in a subsequent paper.
Complete spectrum of the infinite-U Hubbard ring using group theory
Soncini, Alessandro Van den Heuvel, Willem
2014-05-14
We present a full analytical solution of the multiconfigurational strongly correlated mixed-valence problem corresponding to the N-Hubbard ring filled with N−1 electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Hückel-annulene problems for rings of variable size. The number and size of these effective Hückel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for N−1 beads and two colors, within each subgroup of the C{sub N−1} permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-U Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-U Hubbard problem for N−1 electrons is easily generalized to the case of arbitrary electron count L, by analyzing the permutation group C{sub L} and all its subgroups.
Entanglement and local extremes at an infinite-order quantum phase transition
Rulli, C. C.; Sarandy, M. S.
2010-03-15
The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, that is, the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the XXZ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both XXZ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.
Spatio-temporal learning with the online finite and infinite echo-state Gaussian processes.
Soh, Harold; Demiris, Yiannis
2015-03-01
Successful biological systems adapt to change. In this paper, we are principally concerned with adaptive systems that operate in environments where data arrives sequentially and is multivariate in nature, for example, sensory streams in robotic systems. We contribute two reservoir inspired methods: 1) the online echostate Gaussian process (OESGP) and 2) its infinite variant, the online infinite echostate Gaussian process (OIESGP) Both algorithms are iterative fixed-budget methods that learn from noisy time series. In particular, the OESGP combines the echo-state network with Bayesian online learning for Gaussian processes. Extending this to infinite reservoirs yields the OIESGP, which uses a novel recursive kernel with automatic relevance determination that enables spatial and temporal feature weighting. When fused with stochastic natural gradient descent, the kernel hyperparameters are iteratively adapted to better model the target system. Furthermore, insights into the underlying system can be gleamed from inspection of the resulting hyperparameters. Experiments on noisy benchmark problems (one-step prediction and system identification) demonstrate that our methods yield high accuracies relative to state-of-the-art methods, and standard kernels with sliding windows, particularly on problems with irrelevant dimensions. In addition, we describe two case studies in robotic learning-by-demonstration involving the Nao humanoid robot and the Assistive Robot Transport for Youngsters (ARTY) smart wheelchair. PMID:25720008
Lartillot, Nicolas; Rodrigue, Nicolas; Stubbs, Daniel; Richer, Jacques
2013-07-01
Modeling across site variation of the substitution process is increasingly recognized as important for obtaining more accurate phylogenetic reconstructions. Both finite and infinite mixture models have been proposed and have been shown to significantly improve on classical single-matrix models. Compared with their finite counterparts, infinite mixtures have a greater expressivity. However, they are computationally more challenging. This has resulted in practical compromises in the design of infinite mixture models. In particular, a fast but simplified version of a Dirichlet process model over equilibrium frequency profiles implemented in PhyloBayes has often been used in recent phylogenomics studies, while more refined model structures, more realistic and empirically more fit, have been practically out of reach. We introduce a message passing interface version of PhyloBayes, implementing the Dirichlet process mixture models as well as more classical empirical matrices and finite mixtures. The parallelization is made efficient thanks to the combination of two algorithmic strategies: a partial Gibbs sampling update of the tree topology and the use of a truncated stick-breaking representation for the Dirichlet process prior. The implementation shows close to linear gains in computational speed for up to 64 cores, thus allowing faster phylogenetic reconstruction under complex mixture models. PhyloBayes MPI is freely available from our website www.phylobayes.org. PMID:23564032
Complete spectrum of the infinite-U Hubbard ring using group theory
NASA Astrophysics Data System (ADS)
Soncini, Alessandro; Van den Heuvel, Willem
2014-05-01
We present a full analytical solution of the multiconfigurational strongly correlated mixed-valence problem corresponding to the N-Hubbard ring filled with N-1 electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Hückel-annulene problems for rings of variable size. The number and size of these effective Hückel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for N-1 beads and two colors, within each subgroup of the CN-1 permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-U Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-U Hubbard problem for N-1 electrons is easily generalized to the case of arbitrary electron count L, by analyzing the permutation group CL and all its subgroups.