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.
NASA Astrophysics Data System (ADS)
Kochmann, D. M.; Drugan, W. J.
2016-06-01
An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.
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
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.
Linear Stability of Plane Poiseuille Flow in an Infinite Elastic Medium and Volcanic Tremors
NASA Astrophysics Data System (ADS)
Sakuraba, A.; Yamauchi, H.
2013-12-01
The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastically deformable media was investigated with the aim of presenting a general explanation for the excitation of volcanic tremors, which are characterized as long-period and long-lasting seismic events uniquely observed at active volcanoes. Results show that there are several regimes of instability and these primarily depend on the symmetry of the oscillatory fluid and solid motion, wavelength, and fluid viscosity. It is found that the antisymmetric (flexural) instability, involving two parallel Rayleigh waves traveling against the Poiseuille flow, occurs at a critical flow speed much slower than that of symmetric instability. Symmetric instability involves a slow Krauklis (crack) wave traveling with the Poiseuille flow, and it is unlikely that this is the cause of volcanic tremors. The critical flow speed for the antisymmetric instability decreases inversely proportional to the wavelength, and the asymptotic solution is derived when the wavelength is very long. The physical mechanism of this instability can be understood as a simple friction drag on the Rayleigh-wave particle motion caused by the main Poiseuille flow. Based on numerical calculations and analytical consideration, we conclude that the antisymmetric instability is possibly produced by a basaltic magma flow of 1 m/s through a dike of thickness 1 m and extending for several kilometers; this origin can explain some of the characteristics of volcanic tremors. A schematic explanation for the antisymmetric instability. A solid particle (open circle) at the boundary moves along an ellipse (dotted line). White arrows represent the perturbed fluid and solid velocities. The plane Poiseuille flow is represented by black arrows with its parabolic envelop.
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.
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.
Gaps in the essential spectrum of infinite periodic necklace-shaped elastic waveguide
NASA Astrophysics Data System (ADS)
Nazarov, Sergey A.; Ruotsalainen, Keijo; Taskinen, Jari
2009-03-01
We describe a periodic homogeneous elastic waveguide of a particular shape of beads connected by ligaments of diameter O(h) such that the essential spectrum contains gaps, the number of which grows unboundedly when h tends to +0. To cite this article: S.A. Nazarov et al., C. R. Mecanique 337 (2009).
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.
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
NASA Astrophysics Data System (ADS)
Pettit, J. R.; Walker, A.; Lowe, M. J. S.
2015-01-01
A common goal when using Finite Element (FE) modelling in time domain wave scattering problems is to minimise model size by only considering a region immediately surrounding a scatterer or feature of interest. The model boundaries must simulate infinite space by minimising the reflection of incident waves. This is a significant and long-standing challenge that has only achieved partial success. Industrial companies wishing to perform such modelling are keen to use established commercial FE packages that offer a thorough history of validation and testing. Unfortunately, this limits the flexibility available to modellers preventing the use of popular research tools such as Perfectly Matched Layers (PML). Unlike PML, Absorbing Layers by Increasing Damping (ALID) have proven successful offering practical implementation into any solver that has representation of material damping. Despite good performance further improvements are desirable. Here, a Stiffness Reduction Method (SRM) has been developed and optimised to operate within a significantly reduced spatial domain. The technique is applied by altering damping and stiffness matrices, inducing decay of incident waves. Variables are expressed as a function of known model constants, easing implementation for generic problems. Analytical and numerical solutions have shown that SRM out performs ALID, with results approaching those of PML.
Sound radiation from an infinite elastic cylinder with dual-wave propagation-intensity distributions
NASA Technical Reports Server (NTRS)
Fuller, C. R.
1988-01-01
The radiation of sound from an elastic cylindrical shell filled with fluid and supporting multiwave propagation is studied analytically. Combinations of supersonic and subsonic shell waves are considered. The radiated field is mapped by using acoustic intensity vectors evaluated at various locations. Both time averaged and instantaneous intensity are investigated. The acoustic intensity is seen to vary markedly with axial distance down the cylinder. The effect is shown to be associated with cross terms in the intensity relations, and its magnitude and location to depend upon the relative phase and amplitudes of individual waves. Subsonic shell waves are demonstrated to interact strongly with supersonic shell waves to cause a large modification in the radiated intensity distributions near the shell surface.
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.
Flow in Tubes of Non-Circular Cross-Sections
NASA Astrophysics Data System (ADS)
Quadir, Raushan Ara
In this thesis steady, laminar, viscous, incompressible flow in tubes of non-circular cross sections is investigated. The specific aims of the investigation are (a) to look at the problems of both developing flow and fully developed flow, (b) to consider non-circular cross sections in a more systematic manner than has been done in the past, and (c) to develop a relatively simple finite element technique for producing accurate numerical solutions of flow in tubes of fairly arbitrary cross sections. Fully developed flow in tubes is governed by a Poisson type equation for the mainstream velocity. Both analytical and numerical solutions are considered. The cross sections studied include elliptic and rectangular cross sections of different aspect ratios, some triangular cross sections, and a series of crescent-shaped cross sections. The physical characteristics of the flow are examined in a systematic manner in order to determine how these characteristics are affected by certain geometrical features of the cross section. Solutions fall into three basic categories depending on the shape of the cross section. In the first category, which includes circular and elliptic cross sections, solutions are possible in closed form. In the second, including rectangular and some triangular cross sections, solutions are in the form of infinite series. In the third, including cross sections of more complicated or irregular shapes, only numerical solutions are possible. Results of calculations of velocity profiles, flow rate, pumping power, and friction factor are presented in a way which can be useful for engineering applications. In numerical studies of both developing and fully developed flow finite element techniques are used. Results are obtained for tubes of rectangular and elliptic cross sections of different aspect ratios, for tubes of crescent -shaped cross sections and a tube whose cross section is an oval of Cassini. For fully developed flow, results are compared with the
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.
EFFECTS OF NON-CIRCULAR MOTIONS ON AZIMUTHAL COLOR GRADIENTS
Martinez-Garcia, Eric E.; Gonzalez-Lopezlira, Rosa A.; Gomez, Gilberto C. E-mail: r.gonzalez@crya.unam.m
2009-12-20
Assuming that density waves trigger star formation, and that young stars preserve the velocity components of the molecular gas where they are born, we analyze the effects that non-circular gas orbits have on color gradients across spiral arms. We try two approaches, one involving semianalytical solutions for spiral shocks, and another with magnetohydrodynamic (MHD) numerical simulation data. We find that, if non-circular motions are ignored, the comparison between observed color gradients and stellar population synthesis models would in principle yield pattern speed values that are systematically too high for regions inside corotation, with the difference between the real and the measured pattern speeds increasing with decreasing radius. On the other hand, image processing and pixel averaging result in systematically lower measured spiral pattern speed values, regardless of the kinematics of stellar orbits. The net effect is that roughly the correct pattern speeds are recovered, although the trend of higher measured OMEGA{sub p} at lower radii (as expected when non-circular motions exist but are neglected) should still be observed. We examine the MartInez-GarcIa et al. photometric data and confirm that this is indeed the case. The comparison of the size of the systematic pattern speed offset in the data with the predictions of the semianalytical and MHD models corroborates that spirals are more likely to end at outer Lindblad resonance, as these authors had already found.
DOE R&D Accomplishments Database
Nambu, Y.
1967-01-01
The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.
Effects of a Non-Circular Chainring on Sprint Performance During a Cycle Ergometer Test.
Hintzy, Frédérique; Grappe, Frédéric; Belli, Alain
2016-06-01
Non-circular chainrings have been reported to alter the crank angular velocity profile over a pedal revolution so that more time is spent in the effective power phase. The purpose of this study was to determine whether sprint cycling performance could be improved using a non-circular chainring (Osymetric: ellipticity 1.25 and crank lever mounted nearly perpendicular to the major axis), in comparison with a circular chainring. Twenty sprint cyclists performed an 8 s sprint on a cycle ergometer against a 0.5 N/kg(-1) friction force in four crossing conditions (non-circular or circular chainring with or without clipless pedal). Instantaneous force, velocity and power were continuously measured during each sprint. Three main characteristic pedal downstrokes were selected: maximal force (in the beginning of the sprint), maximal power (towards the middle), and maximal velocity (at the end of the sprint). Both average and instantaneous force, velocity and power were calculated during the three selected pedal downstrokes. The important finding of this study was that the maximal power output was significantly higher (+ 4.3%, p < 0.05) when using the non-circular chainring independent from the shoe-pedal linkage condition. This improvement is mainly explained by a significantly higher instantaneous external force that occurs during the downstroke. Non-circular chainring can have potential benefits on sprint cycling performance. Key pointsThe Osymetric non-circular chainring significantly maximized crank power by 4.3% during sprint cycling, in comparison with a circular chainring.This maximal power output improvement was due to significant higher force developed when the crank was in the effective power phase.This maximal power output improvement was independent from the shoe-pedal linkage condition.Present benefits provided by the non-circular chainring on pedalling kinetics occurred only at high cadences. PMID:27274658
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.
Flow in tubes of non-circular cross-sections
NASA Astrophysics Data System (ADS)
Quadir, Raushan Ara
Laminar, viscous, incompressible flow in tubes of noncircular cross sections is investigated. The specific aims of the investigation are (1) to look at the problems of both developing flow and fully developed flow, (2) to consider noncircular cross sections in a more systematic manner than has been done in the past, and (3) to develop a relatively simple finite element technique for producing accurate numerical solutions of flow in tubes of fairly arbitrary cross sections. Fully developed flow in tubes is governed by a Poisson type equation for the mainstream velocity. Both analytical and numerical solutions are considered. The cross sections studied include elliptic and rectangular cross sections of different aspect ratios, some triangular cross sections, and a series of crescent-shaped cross sections. The physical characteristics of the flow are examined in a systematic manner in order to determine how these characteristics are affected by certain geometrical features of the cross section. Solutions fall into three basic categories depending on the shape of the cross section. In the first category, which includes circular and elliptic cross sections, solutions are possible in closed form. In the second, including rectangular and some triangular cross sections, solutions are in the form of infinite series. In the third, including cross sections of more complicated or irregular shapes, only numerical solutions are possible. Results of calculations of velocity profiles, flow rate, pumping power, and friction factor are presented in a way which can be useful for engineering applications. In numerical studies of both developing and fully developed flow finite element techniques are used. Results are obtained for tubes of rectangular and elliptic cross sections of different aspect ratios, for tubes of crescent-shaped cross sections, and a tube whose cross section is an oval of Cassini. For fully developed flow, results are compared with the corresponding exact
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.
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
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
Exploring the GalMer database: bar properties and non-circular motions
NASA Astrophysics Data System (ADS)
Randriamampandry, T. H.; Deg, N.; Carignan, C.; Combes, F.; Spekkens, K.
2016-10-01
Context. We use Tree-SPH simulations from the GalMer database to characterize and quantify the non-circular motions induced by the presence of bar-like structures on the observed rotation curve of barred galaxies derived from empirical models of their line-of-sight velocity maps. The GalMer database consists of SPH simulations of galaxies spanning a wide range of morphological types and sizes. Aims: The aim is to compare the intrinsic velocities and bar properties from the simulations with those derived from pseudo-observations. This allows us to estimate the amount of non-circularity and to test the various methods used to derive the bar properties and rotation curves. Methods: The intrinsic velocities in the simulations are calculated from the gravitational forces whereas the observed rotation velocities are derived by applying the ROTCUR and DiskFit algorithms to well-resolved observations of intermediate-inclination, strongly barred galaxies. Results: Our results confirm that the tilted ring method implemented in ROTCUR systematically underestimates or overestimates the rotational velocities by up to 40 percent in the inner part of the galaxy when the bar is aligned with one of the symmetry axes for all the models. For the DiskFit analysis, we find that it produces unrealistic values for all the models used in this work when the bar is within approximately ten degrees of the major or minor axis.
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".
Experiments in dilution jet mixing effects of multiple rows and non-circular orifices
NASA Technical Reports Server (NTRS)
Holdeman, J. D.; Srinivasan, R.; Coleman, E. B.; Meyers, G. D.; White, C. D.
1985-01-01
Experimental and empirical model results are presented that extend previous studies of the mixing of single-sided and opposed rows of jets in a confined duct flow to include effects of non-circular orifices and double rows of jets. Analysis of the mean temperature data obtained in this investigation showed that the effects of orifice shape and double rows are significant only in the region close to the injection plane, provided that the orifices are symmetric with respect to the main flow direction. The penetration and mixing of jets from 45-degree slanted slots is slightly less than that from equivalent-area symmetric orifices. The penetration from 2-dimensional slots is similar to that from equivalent-area closely-spaced rows of holes, but the mixing is slower for the 2-D slots. Calculated mean temperature profiles downstream of jets from non-circular and double rows of orifices, made using an extension developed for a previous empirical model, are shown to be in good agreement with the measured distributions.
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.
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…
Zheng, Zhen; Chang, Long; Nekrashevich, Ivan; Ruchhoeft, Paul; Khizroev, Sakhrat; Litvinov, Dmitri
2013-01-01
We describe a low-energy glow-discharge process using reactive ion etching system that enables non-circular device patterns, such as squares or hexagons, to be formed from a precursor array of uniform circular openings in polymethyl methacrylate, PMMA, defined by electron beam lithography. This technique is of a particular interest for bit-patterned magnetic recording medium fabrication, where close packed square magnetic bits may improve its recording performance. The process and results of generating close packed square patterns by self-limiting low-energy glow-discharge are investigated. Dense magnetic arrays formed by electrochemical deposition of nickel over self-limiting formed molds are demonstrated.
Infinitely coloured black holes
NASA Astrophysics Data System (ADS)
Mavromatos, Nick E.; Winstanley, Elizabeth
2000-04-01
We formulate the field equations for SU (icons/Journals/Common/infty" ALT="infty" ALIGN="TOP"/> ) Einstein-Yang-Mills theory, and use an analytic approximation to elucidate the properties of spherically symmetric black hole solutions. This model may be motivated by string theory considerations, given the enormous gauge symmetries which characterize string theory. The solutions simplify considerably in the presence of a negative cosmological constant, particularly for the limiting cases of a very large cosmological constant or very small gauge field. The black holes possess infinite amounts of gauge field hair, and we speculate on possible consequences of this for quantum decoherence, which, however, we do not tackle here.
NASA Technical Reports Server (NTRS)
Bhat, Thonse R. S.; Baty, Roy S.; Morris, Philip J.
1990-01-01
The shock structure in non-circular supersonic jets is predicted using a linear model. This model includes the effects of the finite thickness of the mixing layer and the turbulence in the jet shear layer. A numerical solution is obtained using a conformal mapping grid generation scheme with a hybrid pseudo-spectral discretization method. The uniform pressure perturbation at the jet exit is approximated by a Fourier-Mathieu series. The pressure at downstream locations is obtained from an eigenfunction expansion that is matched to the pressure perturbation at the jet exit. Results are presented for a circular jet and for an elliptic jet of aspect ratio 2.0. Comparisons are made with experimental data.
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)
Wang, Xu; Zhou, Kun
2015-04-01
Within the framework of the Kirchhoff-Love isotropic and homogeneous plate theory, we obtain, in a unified manner, the analytic solutions to the Eshelby's problem of an inclusion of arbitrary shape with uniform eigencurvatures in an infinite plate, a semi-infinite plate, one of two bonded semi-infinite plates or a circular plate by means of conformal mapping and analytical continuation. The edge of the semi-infinite plate can be rigidly clamped, free or simply supported, while that of the circular plate can be rigidly clamped, free or perfectly bonded to the surrounding infinite plate. Several examples of practical and theoretical interests are presented to demonstrate the general method. In particular, the elementary expressions of the internal elastic fields of bending moments and deflections within an ( n + 1)-fold rotational symmetric inclusion described by a five-term mapping function, a symmetric airfoil cusp inclusion, a symmetric lip cusp inclusion and an inclusion described by a rational mapping function in an infinite plate are derived.
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
2000-01-24
We construct intersecting brane configurations in anitde Sitter (AdS) space which localize gravity to the intersection region, generalizing the trapping of gravity to any number n of infinite extra dimensions. Since the 4D Planck scale M{sub Pl} is determined by the fundamental Planck scale M{sub *} and the AdS radius L via the familiar relation M{sup 2}{sub Pl}{approx}M{sup 2+n}{sub *}L{sup n} , we get two kinds of theories with TeV scale quantum gravity and submillimeter deviations from Newton's law. With M{sub *}{approx}TeV and L{approx}submillimeter , we recover the phenomenology of theories with large extra dimensions. Alternatively, if M{sub *}{approx}L{sup -1}{approx}M{sub Pl} , and our 3-brane is at a distance of {approx}100M{sup -1}{sub Pl} from the intersection, we obtain a theory with an exponential determination of the weak/Planck hierarchy. (c) 2000 The American Physical Society.
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.
Ferromagnetic of nanowires of infinite length and infinite thin films
NASA Astrophysics Data System (ADS)
Chacouche, Khaled; Hadiji, Rejeb
2015-12-01
The aim of the work described in this paper is to determine, via an asymptotic analysis, the limiting form of the free energy governing in the first case 3D ferromagnetic nanowires of infinite length in the limit and in the second case 3D thin films which become infinite when their thickness is vanished. A 1D limit problem on the nanowires and a 2D limit problem on the thin films are obtained.
Adjective with Infinitive in English and Polish
ERIC Educational Resources Information Center
Arabski, Janusz
1975-01-01
Deals with infinitives that occur with predicate adjectives. Syntactic relations occuring between Infinitive and Copula plus Adjective are examined with the aim of showing the Polish counterparts of English infinitives. (Author/RM)
Infinite swapping in curved spaces
NASA Astrophysics Data System (ADS)
Curotto, E.; Mella, Massimo
2014-01-01
We develop an extension of the infinite swapping and partial infinite swapping techniques [N. Plattner, J. D. Doll, P. Dupuis, H. Wang, Y. Liu, and J. E. Gubernatis, J. Chem. Phys. 135, 134111 (2011)] to curved spaces. Furthermore, we test the performance of infinite swapping and partial infinite swapping in a series of flat spaces characterized by the same potential energy surface model. We develop a second order variational algorithm for general curved spaces without the extended Lagrangian formalism to include holonomic constraints. We test the new methods by carrying out NVT classical ensemble simulations on a set of multidimensional toroids mapped by stereographic projections and characterized by a potential energy surface built from a linear combination of decoupled double wells shaped purposely to create rare events over a range of temperatures.
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.
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
Infinite resources: the ultimate strategy.
Goeller, H E; Zucker, A
1984-02-01
By projecting global population growth and demand for nonrenewable materials over the next century, it appears unlikely that the world will run short of any element before about 2050. This provides considerable time to develop new technology to economically exploit lower grade and alternative ores to bring some 30 elements into essentially infinite supply, and to use these elements in developing substitutes to satisfy the requirements of modern civilized societies. PMID:17781431
Calculators to Motivate Infinite Composition of Functions.
ERIC Educational Resources Information Center
McCune, E. D.; And Others
1980-01-01
This paper demonstrates how calculators may be used to motivate a concept called infinite composition of functions. Several mathematical topics, such as continued square roots, continued fractions, and infinite products are treated and discussed as special cases. (Author/MK)
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.
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.
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.
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…
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…
Scalable L-infinite coding of meshes.
Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter
2010-01-01
The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec. PMID:20224144
Orthogonality preserving infinite dimensional quadratic stochastic operators
Akın, Hasan; Mukhamedov, Farrukh
2015-09-18
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.
Envisioning the Infinite by Projecting Finite Properties
ERIC Educational Resources Information Center
Ely, Robert
2011-01-01
We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…
Quantum walks with infinite hitting times
Krovi, Hari; Brun, Todd A.
2006-10-15
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well.
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
Dual range infinitely variable transmission
Eichenberger, P.
1989-10-31
This patent describes in a transaxle assembly comprising an infinitely variably belt and sheave assembly driving sheave portions and driven sheave portions, a housing assembly enclosing the sheave portions. It includes a torque input shaft coaxially disposed with respect to the driving sheave portions, means for drivably connecting the driving sheave portions and the input shaft; a secondary shaft having an axis in spaced parallel relationship with respect to the torque input shaft. The driven sheave portions being mounted for rotation on the axis of the secondary shaft; a flexible drive member driveable connected to the input sheave portions and the output sheave portions. The flexible drive member engaging the input and output sheave portions at an effective pitch diameter for each sheave portion; fluid pressure servo means for adjustable positioning the sheave portions to effect variations in the effective pitch diameters of the driving sheave portions and the driven sheave portions; a countershaft mounted in spaced parallel dispositions with respect to the secondary shaft, a bearing assembly means for journalling the countershaft in the housing assembly, a high speed range gear train connecting the secondary shaft with the countershaft; fluid pressure operated clutch means for activating and deactivating selectively the high speed range gear train and the low speed range gear train; and planetary forward and reverse means disposed concentrically with respect to the countershaft including clutch means.
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.
Infinite resources: the ultimate strategy
Goeller, H.E.; Zucker, A.
1984-02-03
If the author's projections of world demand for nonrenewable materials prove to be reasonably correct, then it seems highly likely that currently economic resources of many important elements will be in inadequate supply by 2100. At the same time, the prospects appear good that resources of more than 30 elements can be made virtually unlimited if sufficient R and D is invested. Eventually a number of elements will undoubtedly become too scarce and expensive to use except for a few vital purposes. However, there is plenty of time before resources of any limited material become completely economically depleted in which to develop adequate substitutes by using more plentiful materials. The ability to tailor new materials to set specifications is advancing rapidly, and our capabilities in this direction should grow with time if R and D in this area is adequately supported. Although a strategy of infinite resources may be difficult to pursue in the face of global political uncertainties, success would mean that future shortages will be at most only transient events and that a stable population of 8.5 billion people will not be imperiled or impoverished by the lack of materials required for civilized life. 20 references, 3 tables.
Subdivisions with infinitely supported mask
NASA Astrophysics Data System (ADS)
Li, Song; Pan, Yali
2008-04-01
In this paper we investigate the convergence of subdivision schemes associated with masks being polynomially decay sequences. Two-scale vector refinement equations are the formwhere the vector of functions [phi]=([phi]1,E..,[phi]r)T is in and is polynomially decay sequence of rxr matrices called refinement mask. Associated with the mask a is a linear operator on given byBy using same methods in [B. Han, R. Q. Jia, Characterization of Riesz bases of wavelets generated from multiresolution analysis, manuscript]; [BE Han, Refinable functions and cascade algorithms in weighted spaces with infinitely supported masks, manuscript]; [R.Q. Jia, Q.T. Jiang, Z.W. Shen, Convergence of cascade algorithms associated with nonhomogeneous refinement equations, Proc. Amer. Math. Soc. 129 (2001) 415-427]; [R.Q. Jia, Convergence of vector subdivision schemes and construction of biorthogonal multiple wavelets, in: Advances in Wavelet, Hong Kong,1997, Springer, Singapore, 1998, pp. 199-227], a characterization of convergence of the sequences in the L2-norm is given, which extends the main results in [R.Q. Jia, S.D. Riemenschneider, D.X. Zhou, Vector subdivision schemes and multiple wavelets, Math. Comp. 67 (1998) 1533-1563] on convergence of the subdivision schemes associated with a finitely supported mask to the case in which mask a is polynomially decay sequence. As an application, we also obtain a characterization of smoothness of solutions of the refinement equation mentioned above for the case r=1.
NASA Astrophysics Data System (ADS)
Cronin, V. S.
2012-12-01
First generation ideas of the kinematic stability of triple junctions lead to the common belief that the geometry of ridge-ridge-ridge (RRR) triple junctions remains constant over time under conditions of symmetric spreading. Given constant relative motion between each plate pair -- that is, the pole of plate relative motion is fixed to both plates in each pair during finite motion, as assumed in many accounts of plate kinematics -- there would be no boundary mismatch at the triple junction and no apparent kinematic reason why a microplate might develop there. But if, in a given RRR triple junction, the finite motion of one plate as observed from the other plate is not circular (as is generally the case, given the three-plate problem of plate kinematics), the geometry of the ridges and the triple junction will vary with time (Cronin, 1992, Tectonophys 207, 287-301). To explore the possible consequences of non-circular finite motion between plates at an RRR triple junction, a simple model was coded based on the cycloid finite-motion model (e.g., Cronin, 1987, Geology 15, 1006-1009) using NNR-MORVEL56 velocities for individual plates (Argus et al., 2011, G3 12, doi: 10.1029/2011GC003751). Initial assumptions include a spherical Earth, symmetric spreading, and constant angular velocities during the modeled finite time interval. The assumed-constant angular velocity vectors constitute a reference frame for observing finite plate motion. Typical results are [1] that the triple junction migrates relative to a coordinate system fixed to the angular-velocity vectors, [2] ridge axes rotates relative to each other, and [3] a boundary mismatch develops at the synthetic triple junction that might result in microplate nucleation. In a model simulating the Galapagos triple junction between the Cocos, Nazca and Pacific plates whose initial state did not include the Galapagos microplate, the mismatch gap was as much as ~3.4 km during 3 Myr of model displacement (see figure). The
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}.
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.
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.
NASA Astrophysics Data System (ADS)
Spagnolie, Saverio E.; Lauga, Eric
2010-03-01
Motile eukaryotic cells propel themselves in viscous fluids by passing waves of bending deformation down their flagella. An infinitely long flagellum achieves a hydrodynamically optimal low-Reynolds number locomotion when the angle between its local tangent and the swimming direction remains constant along its length. Optimal flagella therefore adopt the shape of a helix in three dimensions (smooth) and that of a sawtooth in two dimensions (nonsmooth). Physically, biological organisms (or engineered microswimmers) must expend internal energy in order to produce the waves of deformation responsible for the motion. Here we propose a physically motivated derivation of the optimal flagellum shape. We determine analytically and numerically the shape of the flagellar wave which leads to the fastest swimming for a given appropriately defined energetic expenditure. Our novel approach is to define an energy which includes not only the work against the surrounding fluid, but also (1) the energy stored elastically in the bending of the flagellum, (2) the energy stored elastically in the internal sliding of the polymeric filaments which are responsible for the generation of the bending waves (microtubules), and (3) the viscous dissipation due to the presence of an internal fluid. This approach regularizes the optimal sawtooth shape for two-dimensional deformation at the expense of a small loss in hydrodynamic efficiency. The optimal waveforms of finite-size flagella are shown to depend on a competition between rotational motions and bending costs, and we observe a surprising bias toward half-integer wave numbers. Their final hydrodynamic efficiencies are above 6%, significantly larger than those of swimming cells, therefore indicating available room for further biological tuning.
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.
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.
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.
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
Contact problem for an elastic reinforcement bonded to an elastic plate
NASA Technical Reports Server (NTRS)
Erdogan, F.; Civelek, M. B.
1974-01-01
The contact problem for a thin elastic reinforcement bonded to an elastic plate is considered. 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 or 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.
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.
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.
Gauge fields and infinite chains of dualities
NASA Astrophysics Data System (ADS)
Boulanger, Nicolas; Sundell, Per; West, Peter
2015-09-01
We show that the particle states of Maxwell's theory, in D dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E 11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincaré group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.
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.
The infinite hidden Markov random field model.
Chatzis, Sotirios P; Tsechpenakis, Gabriel
2010-06-01
Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.
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
A motif for infinite metal atom wires.
Yin, Xi; Warren, Steven A; Pan, Yung-Tin; Tsao, Kai-Chieh; Gray, Danielle L; Bertke, Jeffery; Yang, Hong
2014-12-15
A new motif for infinite metal atom wires with tunable compositions and properties is developed based on the connection between metal paddlewheel and square planar complex moieties. Two infinite Pd chain compounds, [Pd4(CO)4(OAc)4Pd(acac)2] 1 and [Pd4(CO)4(TFA)4Pd(acac)2] 2, and an infinite Pd-Pt heterometallic chain compound, [Pd4(CO)4(OAc)4Pt(acac)2] 3, are identified by single-crystal X-ray diffraction analysis. In these new structures, the paddlewheel moiety is a Pd four-membered ring coordinated by bridging carboxylic ligands and μ2 carbonyl ligands. The planar moiety is either Pd(acac)2 or Pt(acac)2 (acac = acetylacetonate). These moieties are connected by metallophilic interactions. The results showed that these one-dimensional metal wire compounds have photoluminescent properties that are tunable by changing ligands and metal ions. 3 can also serve as a single source precursor for making Pd4Pt bimetallic nanostructures with precise control of metal composition.
Supersolids: Solids Having Finite Volume and Infinite Surfaces.
ERIC Educational Resources Information Center
Love, William P.
1989-01-01
Supersolids furnish an ideal introduction to the calculus topic of infinite series, and are useful for combining that topic with integration. Five examples of supersolids are presented, four requiring only a few basic properties of infinite series and one requiring a number of integration principles as well as infinite series. (MNS)
Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.
Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K
2016-02-01
This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices.
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.
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
Triton,... electron,... cosmon,...: An infinite regression?
Dehmelt, H
1989-11-01
I propose an elementary particle model in which the simplest near-Dirac particles triton, proton, and electron are members of the three top layers of a bottomless stack. Each particle is a composite of three particles from the next layer below in an infinite regression approaching Dirac point particles. The cosmon, an immensely heavy lower layer subquark, is the elementary particle. The world-atom, a tightly bound cosmon/anticosmon pair of zero relativistic total mass, arose from the nothing state in a quantum jump. Rapid decay of the pair launched the big bang and created the universe. PMID:16594084
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 infinite sites model of genome evolution
Ma, Jian; Ratan, Aakrosh; Raney, Brian J.; Suh, Bernard B.; Miller, Webb; Haussler, David
2008-01-01
We formalize the problem of recovering the evolutionary history of a set of genomes that are related to an unseen common ancestor genome by operations of speciation, deletion, insertion, duplication, and rearrangement of segments of bases. The problem is examined in the limit as the number of bases in each genome goes to infinity. In this limit, the chromosomes are represented by continuous circles or line segments. For such an infinite-sites model, we present a polynomial-time algorithm to find the most parsimonious evolutionary history of any set of related present-day genomes. PMID:18787111
Infinite densities for Lévy walks.
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 q(c) exhibit diffusive scaling while for q>q(c) 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 K(α). 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. PMID:25615072
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.
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.
Dynamics for QCD on an Infinite Lattice
NASA Astrophysics Data System (ADS)
Grundling, Hendrik; Rudolph, Gerd
2016-08-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796-1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.
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.
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
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.
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…
Equations of gas dynamics admitting an infinite number of symmetries
Meshkov, A.G.; Mikhalyaev, B.B.
1988-02-01
All the equations of state for which the equations of one-dimensional gas dynamics have an infinite Lie-Baecklund algebra are found. In all these cases, the gas-dynamic equations can either be integrated directly or represented in Lax form. A method for constructing an infinite set of conservation laws is indicated.
Hamel's Formalism for Infinite-Dimensional Mechanical Systems
NASA Astrophysics Data System (ADS)
Shi, Donghua; Berchenko-Kogan, Yakov; Zenkov, Dmitry V.; Bloch, Anthony M.
2016-09-01
In this paper, we introduce Hamel's formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.
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.
Scatter of elastic waves by a thin flat elliptical inhomogeneity
NASA Technical Reports Server (NTRS)
Fu, L. S.
1983-01-01
Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.
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.
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.
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.
Numerical solution of acoustic scattering by finite perforated elastic plates
NASA Astrophysics Data System (ADS)
Cavalieri, A. V. G.; Wolf, W. R.; Jaworski, J. W.
2016-04-01
We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k0 based on the plate length. However, at low k0, finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k0. The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k0 for perforated elastic plates.
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.
Parabosons, parafermions, and explicit representations of infinite-dimensional algebras
NASA Astrophysics Data System (ADS)
Stoilova, N. I.; van der Jeugt, J.
2010-03-01
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(∞) and of the Lie superalgebra osp(1|∞). 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.
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.
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.
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
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.
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.
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.
Packing Infinite Number of Cubes in a Finite Volume Box
ERIC Educational Resources Information Center
Yao, Haishen; Wajngurt, Clara
2006-01-01
Packing an infinite number of cubes into a box of finite volume is the focus of this article. The results and diagrams suggest two ways of packing these cubes. Specifically suppose an infinite number of cubes; the side length of the first one is 1; the side length of the second one is 1/2 , and the side length of the nth one is 1/n. Let n approach…
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.
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.
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
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.
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…
Planetary Rings: Circular and Non-circular
NASA Astrophysics Data System (ADS)
French, R. G.; Nicholson, P. D.; Colwell, J.; Marouf, E. A.; Rappaport, N. J.; Hedman, M. M.; McGhee, C.; Lonergan, K.; Sepersky, T.
2011-12-01
Although Saturn's rings appear at first glance to be axisymmetric, more precise measurements reveal that many of the gap edges and narrow ringlets within the rings are noncircular, a characteristic they share with the narrow uranian rings. A careful study of these features is of interest for several reasons: (i) resonantly-forced perturbations are believed to prevent the rings from spreading under the influence of collisions, (ii) unforced distortions, mostly eccentricities, can lead to estimates of the surface mass density and viscosity of the rings, and (iii) accurately-measured apsidal precession rates provide information on Saturn's zonal gravity harmonics. We present preliminary results from a comprehensive study of noncircular features in the Cassini Division and in the C ring. The data used in this study come from three Cassini experiments, and cover the period from May 2005 to September 2010. Over 120 stellar occultations have been observed by the Ultraviolet Imaging Spectrometer (UVIS) and by the Visual and Infrared Imaging Spectrometer (VIMS). In addition, we include 12 occultations of the spacecraft's radio Radio Science Subsystem (RSS) by the rings observed on Earth in May-September 2005. The simplest noncircular features can be modeled as inclined Keplerian ellipses, freely precessing under the influence of Saturn's oblate gravity field. In agreement with similar fits to the VIMS occultation data alone, we find that the inner edges of 7 of the 8 gaps within the Cassini Division are eccentric, with amplitudes ranging from 0.9 km to 28.3 km. In contrast, most of the outer gap edges are near-circular. We also find a rich assortment of normal modes on the edges of both ringlets and gaps. We have searched for modes with wavenumber m as high as 8, and find convincing evidence for modes with m = 0, 2, 3, 4 and 5, all with amplitudes of 1 km or greater. In some cases, as many as 3 or 4 normal modes coexist at a single edge with comparable amplitudes. Our fits also reveal the pervasive effects of the strong Mimas 2:1 inner Lindblad resonance (ILR), which has long been recognized to define the outer edge of the B ring. We find that almost all sharp-edged features in the Cassini Division exhibit a small but detectable m = 2 variation whose apoapse is locked to Mimas. The amplitudes of these distortions decrease with distance from the resonance, and conform to a simple analytical model for isolated test particles perturbed by the resonance. We confirm that the Colombo (or Titan) ringlet precesses at virtually the same rate as Titan's mean motion, 22.5770 deg d-1, with an apoapse oriented to within 4 deg of Titan's mean longitude. Both edges of this ringlet also exhibit what appear to be free normal modes, with m = 0 on the inner edge and m = 2, 3 and 4 on the outer edge. In contrast, the Maxwell ringlet is a freely precessing ellipse, and we see no evidence for additional normal modes on either edge. We also find clear evidence for normal modes on the edges of the Bond ringlet and Dawes gap.
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.
NASA Astrophysics Data System (ADS)
Davis, R. O.; Selvadurai, A. P. S.
1996-04-01
This book concisely examines the use of elasticity in solving geotechnical engineering problems. In a highly illustrated and user-friendly format, it provides a thorough grounding in the linear theory of elasticity and an understanding of the applications. The first two chapters present a basic framework of the theory of elasticity and describe test procedures for the determination of elastic parameters for soils. Chapters 3 and 4 present the fundamental solutions of Boussinesque, Kelvin, and Mindlin, and use these to formulate solutions to problems of practical interest in geotechnical engineering. The book concludes with a sequence of appendices designed to provide the interested student with details of elasticity theory that are peripheral to the main text. Each chapter concludes with a set of questions for the student to answer. The book is appropriate for upper level students in civil engineering and engineering geology.
Elastic fields due to centers of dilatation and thermal inhomogeneities in plane-layered solids
NASA Astrophysics Data System (ADS)
Yu, H. Y.; Sanday, S. C.
1993-02-01
A N IMAGE METHOD for obtaining the solution for a center of dilatation in a three-layer elastic solid with planar interfaces is presented. The three-layered elastic solid consists of an elastic slab sandwiched between two semi-infinite elastic solids. The three elastic solids are perfectly bonded together at the two planar interfaces. The solution is given in terms of Galerkin vectors which are in terms of an infinite series of the Newtonian potential function of a mass point at the center of dilatation, its mirror images and their derivatives. As an application, the solution for the center of dilatation is used to obtain the elastic solution due to thermal inhomogeneities. The thermoelastic solution is obtained by a method which is based on the integration of properly weighted centers of dilatation over the volume occupied by the inhomogeneity. The potential functions for the problem solved are the harmonic potential functions of attracting matter filling the volume of the thermal inhomogeneity and its mirror images. The solution for the thermal elastic stresses due to an expanding (or contracting) thermal inhomogeneity (inclusion) of any shape embedded in one of the solids is given as an example. Numerical results for a spherical inclusion with pure dilatation eigenstrain are also presented and discussed.
Proton Nucleus Elastic Scattering Data.
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.
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.
Representations of Canonical Commutation Relations Describing Infinite Coherent States
NASA Astrophysics Data System (ADS)
Joye, Alain; Merkli, Marco
2016-10-01
We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.
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.
Elastic properties of nanowires
NASA Astrophysics Data System (ADS)
da Fonseca, Alexandre F.; Malta, C. P.; Galva~O, Douglas S.
2006-05-01
We present a model to study Young's modulus and Poisson's ratio of the composite material of amorphous nanowires. It is an extension of the model derived by two of us [da Fonseca and Galva~o, Phys. Rev. Lett. 92, 175502 (2004)] to study the elastic properties of amorphous nanosprings. The model is based on twisting and tensioning a straight nanowire and we propose an experimental setup to obtain the elastic parameters of the nanowire. We used the Kirchhoff rod model to obtain the expressions for the elastic constants of the nanowire.
Permittivity and permeability of semi-infinite metamaterial
NASA Astrophysics Data System (ADS)
Porvatkina, O. V.; Tishchenko, A. A.; Strikhanov, M. N.
2016-08-01
In our work we investigate dielectric and magnetic properties of semi-infinite metamaterial consisting of particles of different possible nature: atoms, molecules, nanoparticles, etc. It is important that these particles would have magnetic properties. Polarization of a near-surface layer is known to differ from its bulk value for non-magnetic materials; for magnetic materials, including metamaterials, the situation should be similar, which is the subject of our research. We obtain analogues of the Clausius-Mossotti relation both for permittivity and permeability taking into account the local field effects in the longwave approximation for semi-infinite metamaterial. These relations describe the connection between macroscopic characteristics of the semi-infinite metamaterial (permittivity and permeability) and characteristics of constituent particles (dielectric polarizability and magnetic polarizability), which is a bright example of multi-scale approach - method very popular today in physical and computer simulating.
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.
Surface optical Bloch oscillations in semi-infinite waveguide arrays.
Chremmos, I D; Efremidis, N K
2012-06-01
We predict that surface optical Bloch oscillations can exist in semi-infinite waveguide arrays with a linear index variation, if the array parameters close to the boundary are appropriately perturbed. The perturbation is such that the surface states obtain the Wannier-Stark ladder eigenvalues of the unperturbed infinite array. The number of waveguides, whose parameters need to be controlled, decreases with increasing ratio of index gradient over coupling. The configuration can find applications as a "matched" termination of waveguide arrays to eliminate the distortion of Bloch oscillations due to reflection on the boundaries.
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.
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.
Extending NEC to model wire objects in infinite chiral media
Burke, G.J.; Miller, E.K.; Bhattachryya, A.K.
1992-03-01
The development of a moment-method model for wire objects in an infinite chiral medium is described. In this work, the Numerical Electromagnetics Code (NEC) was extended by including a new integral-equation kernel obtained from the dyadic Green`s function for an infinite chiral medium. The NEC moment-method treatment using point matching and a three-term sinusoidal current expansion was adapted to the case of a chiral medium. Examples of current distributions and radiation patterns for simple antennas are presented, and the validation of the code is discussed. 15 refs.
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.
Mechanism of Resilin Elasticity
Qin, Guokui; Hu, Xiao; Cebe, Peggy; Kaplan, David L.
2012-01-01
Resilin is critical in the flight and jumping systems of insects as a polymeric rubber-like protein with outstanding elasticity. However, insight into the underlying molecular mechanisms responsible for resilin elasticity remains undefined. Here we report the structure and function of resilin from Drosophila CG15920. A reversible beta-turn transition was identified in the peptide encoded by exon III and for full length resilin during energy input and release, features that correlate to the rapid deformation of resilin during functions in vivo. Micellar structures and nano-porous patterns formed after beta-turn structures were present via changes in either the thermal or mechanical inputs. A model is proposed to explain the super elasticity and energy conversion mechanisms of resilin, providing important insight into structure-function relationships for this protein. Further, this model offers a view of elastomeric proteins in general where beta-turn related structures serve as fundamental units of the structure and elasticity. PMID:22893127
NASA Astrophysics Data System (ADS)
Quilliet, Catherine; Quemeneur, François; Marmottant, Philippe; Imhof, Arnout; Pépin-Donat, Brigitte; van Blaaderen, Alfons
2010-03-01
The deflation of elastic spherical surfaces has been numerically investigated, and show very different types of deformations according the range of elastic parameters, some of them being quantitatively explained through simple calculations. This allows to retrieve various shapes observed on hollow shells (from colloidal to centimeter scale), on lipid vesicles, or on some biological objects. The extension of this process to other geometries allows to modelize vegetal objects such as the ultrafast trap of carnivorous plants.
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.
Elastic medium equivalent to Fresnel's double-refraction crystal.
Carcione, José M; Helbig, Klaus
2008-10-01
In 1821, Fresnel obtained the wave surface of an optically biaxial crystal, assuming that light waves are vibrations of the ether in which longitudinal vibrations (P waves) do not propagate. An anisotropic elastic medium mathematically analogous to Fresnel's crystal exists. The medium has four elastic constants: a P-wave modulus, associated with a spherical P wave surface, and three elastic constants, c(44), c(55), and c(66), associated with the shear waves, which are mathematically equivalent to the three dielectric permittivity constants epsilon(11), epsilon(22), and epsilon(33) as follows: mu(0)epsilon(11)<==>rho/c(44), mu(0)epsilon(22)<==>rho/c(55), mu(0)epsilon(33)<==>rho/c(66), where mu(0) is the magnetic permeability of vacuum and rho is the mass density. These relations also represent the equivalence between the elastic and electromagnetic wave velocities along the principal axes of the medium. A complete mathematical equivalence can be obtained by setting the P-wave modulus equal to zero, but this yields an unstable elastic medium (the hypothetical ether). To obtain stability the P-wave velocity has to be assumed infinite (incompressibility). Another equivalent Fresnel's wave surface corresponds to a medium with anomalous polarization. This medium is physically unstable even for a nonzero P-wave modulus.
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.
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…
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…
How Fragile Is Consolidated Knowledge? Ben's Comparisons of Infinite Sets
ERIC Educational Resources Information Center
Tsamir, Pessia; Dreyfus, Tommy
2005-01-01
This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…
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 ?
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…
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.
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.
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…
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.
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.
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.
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.
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
Elastic anisotropy of crystals
NASA Astrophysics Data System (ADS)
Kube, Christopher M.
2016-09-01
An anisotropy index seeks to quantify how directionally dependent the properties of a system are. In this article, the focus is on quantifying the elastic anisotropy of crystalline materials. Previous elastic anisotropy indices are reviewed and their shortcomings discussed. A new scalar log-Euclidean anisotropy measure AL is proposed, which overcomes these deficiencies. It is based on a distance measure in a log-Euclidean space applied to fourth-rank elastic tensors. AL is an absolute measure of anisotropy where the limiting case of perfect isotropy yields zero. It is a universal measure of anisotropy applicable to all crystalline materials. Specific examples of strong anisotropy are highlighted. A supplementary material (ftp://ftp.aip.org/epaps/aip_advances/E-AAIDBI-6-041609) provides an anisotropy table giving the values of AL for 2,176 crystallite compounds.
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.
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.
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
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
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
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.
Mechanics of elastic networks.
Norris, Andrew N
2014-12-01
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. A470, 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.
Acquired disorders of elastic tissue: Part II. decreased elastic tissue.
Lewis, Kevan G; Bercovitch, Lionel; Dill, Sara W; Robinson-Bostom, Leslie
2004-08-01
Elastic fibers in the extracellular matrix are integral components of dermal connective tissue. The resilience and elasticity required for normal structure and function of the skin are attributable to the network of elastic tissue. Advances in our understanding of elastic tissue physiology provide a foundation for studying the pathogenesis of elastic tissue disorders. Many acquired disorders are nevertheless poorly understood owing to the paucity of reported cases. Several acquired disorders in which loss of dermal elastic tissue produces prominent clinical and histopathologic features have recently been described, including middermal elastolysis, papular elastorrhexis, and pseudoxanthoma-like papillary dermal elastolysis, which must be differentiated from more well-known disorders such as anetoderma, acquired cutis laxa, and acrokeratoelastoidosis. Learning objective At the conclusion of this learning activity, participants should have an understanding of the similarities and differences between acquired disorders of elastic tissue that are characterized by a loss of elastic tissue.
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.
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.
Polygons in restricted geometries subjected to infinite forces
NASA Astrophysics Data System (ADS)
Beaton, N. R.; Eng, J. W.; Soteros, C. E.
2016-10-01
We consider self-avoiding polygons in a restricted geometry, namely an infinite L × M tube in {{{Z}}}3. These polygons are subjected to a force f, parallel to the infinite axis of the tube. When f\\gt 0 the force stretches the polygons, while when f\\lt 0 the force is compressive. We obtain and prove the asymptotic form of the free energy in both limits f\\to +/- ∞ . We conjecture that the f\\to -∞ asymptote is the same as the limiting free energy of ‘Hamiltonian’ polygons, polygons which visit every vertex in a L× M× N box. We investigate such polygons, and in particular use a transfer-matrix methodology to establish that the conjecture is true for some small tube sizes. Dedicated to Anthony J Guttmann on the occasion of his 70th birthday.
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.
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
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…
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
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…
Hydrodynamic Elastic Magneto Plastic
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.
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}.
Analysis of Multiple Cracks in an Infinite Functionally Graded Plate
NASA Technical Reports Server (NTRS)
Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.
1999-01-01
A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.
Infinite Simple 3d Cubic Network of Identical Capacitors
NASA Astrophysics Data System (ADS)
Asad, Jihad H.
2013-06-01
In this paper, the effective capacitance between the origin (0, 0, 0) and any other lattice site (l1, l2, l3), in an infinite simple cubic (SC) network consisting of identical capacitors each of capacitance C, has been expressed rationally in terms of the known value go and π. The asymptotic behavior is also investigated, and some numerical values for the effective capacitance are presented.
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.
Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D
2015-01-01
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
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.
Single file diffusion into a semi-infinite tube.
Farrell, Spencer G; Brown, Aidan I; Rutenberg, Andrew D
2015-11-23
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
Single file diffusion into a semi-infinite tube
NASA Astrophysics Data System (ADS)
Farrell, Spencer G.; Brown, Aidan I.; Rutenberg, Andrew D.
2015-12-01
We investigate single file diffusion (SFD) of large particles entering a semi-infinite tube, such as luminal diffusion of proteins into microtubules or flagella. While single-file effects have no impact on the evolution of particle density, we report significant single-file effects for individually tracked tracer particle motion. Both exact and approximate ordering statistics of particles entering semi-infinite tubes agree well with our stochastic simulations. Considering initially empty semi-infinite tubes, with particles entering at one end starting from an initial time t = 0, tracked particles are initially super-diffusive after entering the system, but asymptotically diffusive at later times. For finite time intervals, the ratio of the net displacement of individual single-file particles to the average displacement of untracked particles is reduced at early times and enhanced at later times. When each particle is numbered, from the first to enter (n = 1) to the most recent (n = N), we find good scaling collapse of this distance ratio for all n. Experimental techniques that track individual particles, or local groups of particles, such as photo-activation or photobleaching of fluorescently tagged proteins, should be able to observe these single-file effects. However, biological phenomena that depend on local concentration, such as flagellar extension or luminal enzymatic activity, should not exhibit single-file effects.
Infinitely dilute partial molar properties of proteins from computer simulation.
Ploetz, Elizabeth A; Smith, Paul E
2014-11-13
A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.
Infinite slope stability under steady unsaturated seepage conditions
Lu, N.; Godt, J.
2008-01-01
[1] We present a generalized framework for the stability of infinite slopes under steady unsaturated seepage conditions. The analytical framework allows the water table to be located at any depth below the ground surface and variation of soil suction and moisture content above the water table under steady infiltration conditions. The framework also explicitly considers the effect of weathering and porosity increase near the ground surface on changes in the friction angle of the soil. The factor of safety is conceptualized as a function of the depth within the vadose zone and can be reduced to the classical analytical solution for subaerial infinite slopes in the saturated zone. Slope stability analyses with hypothetical sandy and silty soils are conducted to illustrate the effectiveness of the framework. These analyses indicate that for hillslopes of both sandy and silty soils, failure can occur above the water table under steady infiltration conditions, which is consistent with some field observations that cannot be predicted by the classical infinite slope theory. A case study of shallow slope failures of sandy colluvium on steep coastal hillslopes near Seattle, Washington, is presented to examine the predictive utility of the proposed framework. Copyright 2008 by the American Geophysical Union.
Infinite variance in fermion quantum Monte Carlo calculations.
Shi, Hao; Zhang, Shiwei
2016-03-01
For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling. PMID:27078480
Fuhrman, Marco Hu, Ying
2007-09-15
In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.
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 .
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.
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.
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.
Yong, Ee Hou; Nelson, David R; Mahadevan, L
2013-10-25
On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.
Asare-Asher, Samuel; Connor, Jason N; Sedev, Rossen
2015-07-01
Liquid marbles are liquid droplets covered densely with small particles. They exhibit hydrophobic properties even on hydrophilic surfaces and this behaviour is closely related to the Cassie wetting state and the phenomenon of superhydrophobicity. Typical liquid marbles are of millimetre size but their properties are analogous to smaller capsules and droplets of Pickering emulsions. We study water marbles covered with an uneven multilayer of polyethylene particles. Their elastic properties were assessed under quasi-static conditions. The liquid marbles are highly elastic and can sustain a reversible deformation of up to 30%. The spring constant is of the same order of magnitude as that for bare water droplets. Therefore the elasticity of the liquid marble is provided mainly by the liquid menisci between the particles. Upon further compression, the spring constant increases up to the point of breakage. This increase may be due to capillary attraction acting across the emerging cracks in the particle coating. The stress-strain curve for liquid marbles is similar to that obtained with liquid-filled microcapsules. A mechanical scaling description proposed for capsules is qualitatively applicable for liquid marbles. The exact mechanical role of the multilayer particle network remains elusive.
NASA Astrophysics Data System (ADS)
Dremin, I. M.
2013-01-01
Colliding high-energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features can be seen that provide information on the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law decrease. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
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.
Convex aggregative modelling of infinite memory nonlinear systems
NASA Astrophysics Data System (ADS)
Wachel, Paweł
2016-08-01
The convex aggregation technique is applied for modelling general class of nonlinear systems with unknown structure and infinite memory. The finite sample size properties of the algorithm are formally established and compared to the standard least-squares counterpart of the method. The proposed algorithm demonstrates its advantages when the a-priori knowledge and the measurement data are both scarce, that is, when the information about the actual system structure is unknown or uncertain and the measurement set is small and disturbed by a noise. Numerical experiments illustrate application and practical benefits of the method for various nonlinear systems.
Approximate Controllability of Fractional Neutral Stochastic System with Infinite Delay
NASA Astrophysics Data System (ADS)
Sakthivel, R.; Ganesh, R.; Suganya, S.
2012-12-01
The concept of controllability plays an important role in analysis and design of linear and nonlinear control systems. Further, fractional differential equations have wide applications in engineering and science. In this paper, the approximate controllability of neutral stochastic fractional integro-differential equation with infinite delay in a Hilbert space is studied. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
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.
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.
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.
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.
Conformal field theories with infinitely many conservation laws
NASA Astrophysics Data System (ADS)
Todorov, Ivan
2013-02-01
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Unitary positive energy representations of scalar bilocal fields," Commun. Math. Phys. 271, 223-246 (2007), 10.1007/s00220-006-0182-2; e-print arXiv:math-ph/0604069v3; B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, "Infinite dimensional Lie algebras in 4D conformal quantum field theory," J. Phys. A Math Theor. 41, 194002 (2008), 10.1088/1751-8113/41/19/194002; e-print arXiv:0711.0627v2 [hep-th
Infinite 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
Spectra of Semi-Infinite Quantum Graph Tubes
NASA Astrophysics Data System (ADS)
Shipman, Stephen P.; Tillay, Jeremy
2016-10-01
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half of the tube. The eigenfunctions associated to the spectrum of the half-tube involve all Floquet modes of the full tube. This requires solving the complex dispersion relation {D(λ,k_1,k_2)=0} with {(k_1,k_2)in({C}/2π{Z})^2} subject to the constraint {a k_1 + b k_2 ≡ 0} (mod {2π}), where a and b are integers. The number of Floquet modes for a given {λin{R}} is {2max{ a, b }}. Rightward and leftward modes are determined according to an indefinite energy flux form. The spectrum may contain eigenvalues that depend on the boundary conditions, and some eigenvalues may be embedded in the continuous spectrum.
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.
Continuum elastic theory of adsorbate vibrational relaxation
NASA Astrophysics Data System (ADS)
Lewis, Steven P.; Pykhtin, M. V.; Mele, E. J.; Rappe, Andrew M.
1998-01-01
An analytical theory is presented for the damping of low-frequency adsorbate vibrations via resonant coupling to the substrate phonons. The system is treated classically, with the substrate modeled as a semi-infinite elastic continuum and the adsorbate overlayer modeled as an array of point masses connected to the surface by harmonic springs. The theory provides a simple expression for the relaxation rate in terms of fundamental parameters of the system: γ=mω¯02/AcρcT, where m is the adsorbate mass, ω¯0 is the measured frequency, Ac is the overlayer unit-cell area, and ρ and cT are the substrate mass density and transverse speed of sound, respectively. This expression is strongly coverage dependent, and predicts relaxation rates in excellent quantitative agreement with available experiments. For a half-monolayer of carbon monoxide on the copper (100) surface, the predicted damping rate of in-plane frustrated translations is 0.50×1012s-1, as compared to the experimental value of (0.43±0.07)×1012s-1. Furthermore it is shown that, for all coverages presently accessible to experiment, adsorbate motions exhibit collective effects which cannot be treated as stemming from isolated oscillators.
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.
NASA Astrophysics Data System (ADS)
Wisdom, Jack; Meyer, Jennifer
2016-11-01
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.
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.
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.
Polysoaps: Configurations and Elasticity
NASA Astrophysics Data System (ADS)
Halperin, A.
1997-03-01
Simple polymers are very long, flexible, linear molecules. Amphiphiles, soaps, are small molecules comprising of a part that prefers water over oil and a part that prefers oil over water. By combining the two we arrive at an interesting, little explored, class of materials: Polysoaps. These comprise of a water soluble backbone incorporating, at intervals, covalently bound amphiphilic monomers. In water, the polymerised amphiphiles aggregate into self assembled units known as micelles. This induces a dramatic modification of the spatial configurations of the polymers. What were featureless random coils now exhibit intramolecular, hierachial self organisation. Due to this self organisation it is necessary to modify the paradigms describing the large scale behaviour of these polymers: Their configurations, dimensions and elasticity. Understanding the behaviour of these polymers is of practical interest because of their wide range of industrial applications, ranging from cosmetics to paper coating. It is of fundamental interest because polysoaps are characterised by a rugged free energy landscape that is reminiscent of complex systems such as proteins and glasses. The talk concerns theoretical arguments regarding the following issues: (i) The design parameters that govern the spatial configurations of the polysoaps, (ii) The interaction between polysoaps and free amphiphiles, (iii) The effect of the intramolecular self organisation on the elasticity of the chains.
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.
Mathematical Models for Elastic Structures
NASA Astrophysics Data System (ADS)
Villaggio, Piero
1997-10-01
During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear 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.
Casimir energy of a semi-circular infinite cylinder
NASA Astrophysics Data System (ADS)
Nesterenko, V. V.; Lambiase, G.; Scarpetta, G.
2001-05-01
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for the electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions.
Multilocus models in the infinite island model of population structure.
Roze, Denis; Rousset, François
2008-06-01
Different methods have been developed to consider the effects of statistical associations among genes that arise in population genetics models: kin selection models deal with associations among genes present in different interacting individuals, while multilocus models deal with associations among genes at different loci. It was pointed out recently that these two types of models are very similar in essence. In this paper, we present a method to construct multilocus models in the infinite island model of population structure (where deme size may be arbitrarily small). This method allows one to compute recursions on allele frequencies, and different types of genetic associations (including associations between different individuals from the same deme), and incorporates selection. Recursions can be simplified using quasi-equilibrium approximations; however, we show that quasi-equilibrium calculations for associations that are different from zero under neutrality must include a term that has not been previously considered. The method is illustrated using simple examples.
Eisenstein series for infinite-dimensional U-duality groups
NASA Astrophysics Data System (ADS)
Fleig, Philipp; Kleinschmidt, Axel
2012-06-01
We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E 9, E 10 and E 11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D < 3 space-time dimensions.
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.
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.
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.
Predictive optimized adaptive PSS in a single machine infinite bus.
Milla, Freddy; Duarte-Mermoud, Manuel A
2016-07-01
Power System Stabilizer (PSS) devices are responsible for providing a damping torque component to generators for reducing fluctuations in the system caused by small perturbations. A Predictive Optimized Adaptive PSS (POA-PSS) to improve the oscillations in a Single Machine Infinite Bus (SMIB) power system is discussed in this paper. POA-PSS provides the optimal design parameters for the classic PSS using an optimization predictive algorithm, which adapts to changes in the inputs of the system. This approach is part of small signal stability analysis, which uses equations in an incremental form around an operating point. Simulation studies on the SMIB power system illustrate that the proposed POA-PSS approach has better performance than the classical PSS. In addition, the effort in the control action of the POA-PSS is much less than that of other approaches considered for comparison.
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
LETTERS AND COMMENTS: Noninteracting fermions in infinite dimensions
NASA Astrophysics Data System (ADS)
Acharyya, Muktish
2010-11-01
Usually, we study the statistical behaviour of noninteracting fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions, and it becomes equal to 50% and 60% of the Fermi energy respectively. However, in higher dimensions this percentage increases as the dimensionality increases, and in infinite dimensions it becomes 100%. This is an interesting result, at least pedagogically, which implies that all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. Here this fact is discussed and explained. I hope that this letter will be helpful for graduate students to study the behaviours of free fermions in generalized dimensionality.
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.
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.
Infinite dilution conductimetry of plasma and urine: correlation with osmolality.
Genain, C; Tellier, P; Syrota, A; Pocidalo, J J; Hans, M
1978-08-15
The infinite dilution conductivity (IDC) of plasma and urine allows a measurement of the electrolyte content in small samples (5 to 15 microliter). The method was compared to the corrected osmolality (II'p) measured by the freezing-point depression. A linear correlation existed between II'p and the IDC: for plasma: II'p = 13.10 sigma o,p + 37.00 (n = 46 and r = 0.9949) for urine: II'u = 12.75 sigma o,u + 16.56 (n = 85 and r = 0.9504). The measurement of the IDC does not depend on protein concentration and can be used instead of the osmometer methods to determine the total plasma and urine electrolyte content.
Broadband computation of the scattering coefficients of infinite arbitrary cylinders.
Blanchard, Cédric; Guizal, Brahim; Felbacq, Didier
2012-07-01
We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.
Solutions of evolution equations associated to infinite-dimensional Laplacian
NASA Astrophysics Data System (ADS)
Ouerdiane, Habib
2016-05-01
We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).
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.
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.
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
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.
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
Elasticity of ``Fuzzy'' Biomembranes
NASA Astrophysics Data System (ADS)
Evans, E.; Rawicz, W.
1997-09-01
Sensitive micropipet methods have been used to measure the elastic stretch modulus and bending rigidity of biomembranes studded with water-soluble polymers. The fully extended lengths of the chemically grafted chains ranged from 10-50× the length of the embedding membrane lipid. Concentrations of the polymer were varied from 1-10× the surface density needed for isolated chains to touch, nominally satisfying the scaling theory requirement for semidilute brushes. Over this range, the membrane stretch modulus was unchanged by the polymer layers, but the bending rigidity increased by as much as 10kBT. Surprisingly, the increase in rigidity deviated significantly from scaling theory predictions, revealing a large marginal brush regime between dilute mushrooms and a semidilute brush.
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.
Larkin, A. I.; Khmelnitskii, D. E.
2013-09-15
Friction of elastic bodies is connected with the passing through the metastable states that arise at the contact of surfaces rubbing against each other. Three models are considered that give rise to the metastable states. Friction forces and their dependence on the pressure are calculated. In Appendix A, the contact problem of elasticity theory is solved with adhesion taken into account.
ERIC Educational Resources Information Center
Girill, T. R.
1972-01-01
The Boyle-Mariotte gas law was formulated in terms of pneumatic springs," subsumed by Hooke under his own stress-strain relation, and generally regarded as a law of elasticity. The subsequent development of Boyle's principle and elasticity provide thought-provoking test cases for Kuhn's notations of paradigm and puzzle solving in physics.…
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.
On the mechanism of bandgap formation in locally resonant finite elastic metamaterials
NASA Astrophysics Data System (ADS)
Sugino, Christopher; Leadenham, Stephen; Ruzzene, Massimo; Erturk, Alper
2016-10-01
Elastic/acoustic metamaterials made from locally resonant arrays can exhibit bandgaps at wavelengths much longer than the lattice size for various applications spanning from low-frequency vibration/sound attenuation to wave guiding and filtering in mechanical and electromechanical devices. For an effective use of such locally resonant metamaterial concepts in finite structures, it is required to bridge the gap between the lattice dispersion characteristics and modal behavior of the host structure with its resonators. To this end, we develop a novel argument for bandgap formation in finite-length elastic metamaterial beams, relying on the modal analysis and the assumption of infinitely many resonators. We show that the dual problem to wave propagation through an infinite periodic beam is the modal analysis of a finite beam with an infinite number of resonators. A simple formula that depends only on the resonator natural frequency and total mass ratio is derived for placing the bandgap in a desired frequency range, yielding an analytical insight and a rule of thumb for design purposes. A method for understanding the importance of a resonator location and mass is discussed in the context of a Riemann sum approximation of an integral, and a method for determining the optimal number of resonators for a given set of boundary conditions and target frequency is introduced. The simulations of the theoretical framework are validated by experiments for bending vibrations of a locally resonant cantilever beam.
Sulcus formation in a compressed elastic half space
NASA Astrophysics Data System (ADS)
Biggins, John; Mahadevan, L.
2012-02-01
When a block of rubber, biological tissue or other soft material is subject to substantial compression, its surfaces undergo a folding instability. Rather than having a smooth profile, these folds contain cusps and hence have been called creases or sulcii rather than wrinkles. The stability of a compressed surface was first investigated by Biot (1965), assuming the strains associated with the instability were small. However, the compression threshold predicted with this approach is substantially too high. I will introduce a family of analytic area preserving maps that contain cusps (and hence points of infinite strain) that save energy before the linear stability threshold even at vanishing amplitude. This establishes that there is a region before the linear stability threshold is reached where the system is unstable to infinitesimal perturbations, but that this instability is quintessentially non-linear and cannot be found with linear strain elasticity.
NASA Technical Reports Server (NTRS)
Hardrath, Herbert F; Ohman, Lachlan
1953-01-01
Six large 24s-t3 aluminum-alloy-sheet specimens containing various notches or fillets were tested in tension to determine their stress concentration factors in both the elastic and plastic ranges. The elastic stress concentration factors were found to be slightly higher than those calculated by Neuber's method and those obtained photoelastically by Frocht. The results showed further that the stress concentration factor decreases as strains at the discontinuity enter the plastic range. A generalization of Stowell's relation for the plastic stress concentration factor at a circular hole in an infinite plate was applied to the specimen shapes tested and gave good agreement with test results.
Elasticity theory of smectic and canonic mesophases
Stallinga, S.; Vertogen, G. )
1995-01-01
The general theory of elasticity for smectic and canonic mesophases is formulated, starting from the assumption that the equilibrium state is spatially periodic. The various surface terms appearing in the deformation free energy density are considered as well. The effective description of the elastic behavior of a general nonchiral smectic mesophase involves one positional elastic constant, 16 bulk orientational elastic constants, and six surface orientational elastic constants. One additional bulk orientational elastic constant is required for the description of a general chiral smectic mesophase. The effective description of the elastic behavior of a general nonchiral canonic mesophase involves six positional elastic constants and three bulk orientational elastic constants. In this case the property of chirality does not introduce additional orientational elastic constants. The elastic constants for some relevant smectic and canonic mesophases are given, including the elastic constants for the antiferroelectric Sm-[ital C][sub [ital A
Maxwell-Higgs self-dual solitons on an infinite cylinder
NASA Astrophysics Data System (ADS)
Casana, Rodolfo; Sourrouille, Lucas
2015-07-01
We have studied the Maxwell-Higgs model on the surface of an infinite cylinder. In particular, we show that this model supports self-dual topological soliton solutions on the infinite tube. Finally, the Bogomol’nyi-type equations are studied from theoretical and numerical point of view.
ERIC Educational Resources Information Center
Tsamir, Pessia
1999-01-01
Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…
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
Masiero, Federica
2007-05-15
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
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…
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.
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
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
Partition Theory for Periodic and Semi-Infinite Systems
NASA Astrophysics Data System (ADS)
Niffenegger, Kelsie; Wasserman, Adam
Standard approximations to the exchange-correlation (XC) functional of Kohn-Sham Density-Functional Theory are insufficiently accurate to describe charge transfer at metal-atom interfaces and other systems requiring proper treatment of fractional electron charges. The root of the problem is connected to the lack of derivative discontinuities in the approximate XC functionals at integer numbers of electrons. Partition Theory (PT) is a promising, formally exact method to correct this issue. We study the simplest model for an atom adsorbed at a metal surface: A one-dimensional step potential separated a fixed distance from an attractive well that admits only one bound state when isolated. The semi-infinite metal is populated with non-interacting electrons up to the Fermi energy. We derive the PT-equations for this problem and indicate how the associated partition potential can be calculated. PT is also a promising method for improving the computational scaling of other large and/or periodic systems. We study the partition potential for periodic 1-D chains of identical attractive wells and comment on the uniqueness of the partition potential when going from finite to periodic systems.
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.
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.
Superposition, Transition Probabilities and Primitive Observables in Infinite Quantum Systems
NASA Astrophysics Data System (ADS)
Buchholz, Detlev; Størmer, Erling
2015-10-01
The concepts of superposition and of transition probability, familiar from pure states in quantum physics, are extended to locally normal states on funnels of type I∞ factors. Such funnels are used in the description of infinite systems, appearing for example in quantum field theory or in quantum statistical mechanics; their respective constituents are interpreted as algebras of observables localized in an increasing family of nested spacetime regions. Given a generic reference state (expectation functional) on a funnel, e.g. a ground state or a thermal equilibrium state, it is shown that irrespective of the global type of this state all of its excitations, generated by the adjoint action of elements of the funnel, can coherently be superimposed in a meaningful manner. Moreover, these states are the extreme points of their convex hull and as such are analogues of pure states. As further support of this analogy, transition probabilities are defined, complete families of orthogonal states are exhibited and a one-to-one correspondence between the states and families of minimal projections on a Hilbert space is established. The physical interpretation of these quantities relies on a concept of primitive observables. It extends the familiar framework of observable algebras and avoids some counter intuitive features of that setting. Primitive observables admit a consistent statistical interpretation of corresponding measurements and their impact on states is described by a variant of the von Neumann-Lüders projection postulate.
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
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
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.
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.
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)
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)
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.
Calcification of medial elastic fibers and aortic elasticity.
Niederhoffer, N; Lartaud-Idjouadiene, I; Giummelly, P; Duvivier, C; Peslin, R; Atkinson, J
1997-04-01
We tested the hypothesis that a simple change in wall composition (medial calcium overload of elastic fibers) can decrease aortic elasticity. Calcium overload was produced by hypervitaminosis D plus nicotine (VDN) in the young rat. Two months later, measurement of central aortic mean blood pressure in the unanesthetized, unrestrained rat showed that the VDN rat suffered from isolated systolic hypertension but that mean blood pressure was normal. Wall thickness and internal diameter determined after in situ pressurized fixation were unchanged, as was calculated wall stress. Wall stiffness was estimated from (1) elastic modulus (determined with the Moens-Korteweg equation and values for aortic pulse wave velocity in the unanesthetized, unrestrained rat and arterial dimensions) and (2) isobaric elasticity (= slope relating pulse wave velocity to mean intraluminal pressure in the phenylephrine-infused, pithed rat preparation). Both increased after VDN, and both were significantly correlated to the wall content of calcium and the elastin-specific amino acids desmosine and isodesmosine. Left ventricular hypertrophy occurred in the VDN model, and left ventricular mass was related to isobaric elasticity. In conclusion, elastocalcinosis induces destruction of elastic fibers, which leads to arterial stiffness, and the latter may be involved in the development of left ventricular hypertrophy in a normotensive model.
Hoover, Jill R.; Storkel, Holly L.; Rice, Mabel L.
2011-01-01
The effect of neighborhood density on optional infinitives was evaluated for typically developing (TD) children and children with Specific Language Impairment (SLI). Forty children, 20 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 half presented a sparse verb. Children’s third person singular accuracy was compared across dense and sparse verbs. Results showed that the TD group was significantly less likely to use optional infinitives with dense, rather than sparse verbs. In contrast, the distribution of optional infinitives for the SLI group was independent of verb neighborhood density. Follow-up analyses showed that the lack of neighborhood density effect for the SLI group could not be attributed to heterogeneous neighborhood density effects or floor effects. Results were interpreted within the Optional Infinitive/Extended Optional Infinitive accounts for typical language development and SLI for English speaking children. PMID:22123500
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
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.
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)
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.
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
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.
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
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.
Wave vector modification of the infinite order sudden approximation
NASA Astrophysics Data System (ADS)
Sachs, Judith Grobe; Bowman, Joel M.
1980-10-01
A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities Pn1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=‖nf-ni‖ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.
Commutative law for products of infinitely large isotropic random matrices
NASA Astrophysics Data System (ADS)
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 An of a single matrix drawn from the underlying matrix ensemble. For example, the eigenvalue density of ABCCABC is the same as that of A2B2C3. 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 s∈(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.
Axial gravitational perturbations of an infinite static line source
NASA Astrophysics Data System (ADS)
Gleiser, Reinaldo J.
2015-03-01
The Levi-Civita metric, which contains a naked singularity that has been interpreted as an infinite static line source, appears, for instance, as the possible end point in the collapse of cylindrically symmetric objects such as shells of dust. The analysis of its gravitational stability should therefore be relevant in the contexts of the cosmic censorship and hoop conjectures. In this paper we study axial gravitational perturbations of the Levi-Civita metric. The perturbations are restricted to axial symmetry but break the cylindrical symmetry of the background metric. We analyze the gauge issues that arise in setting up the appropriate form of the perturbed metric and show that it is possible to restrict the perturbations to diagonal terms but that this does not fix the gauge completely. We derive and solve the perturbation equations. The solutions contain gauge-trivial parts, and we show how to extract the gauge-nontrivial components. We impose appropriate boundary conditions on the solutions and show that these lead to a boundary value problem that determines the allowed functional forms of the perturbation modes. The associated eigenvalues determine a sort of ‘dispersion relation’ for the frequencies and corresponding ‘wave vector’ components. The central result of this analysis is that the spectrum of allowed frequencies contains one unstable (imaginary frequency) mode for every possible choice of the background metric. The completeness of the mode expansion in relation to the initial value problem and to the gauge problem is discussed in detail, and we show that the perturbations contain an unstable component for generic initial data and therefore that the Levi-Civita space times are gravitationally unstable. We also include, for completeness, a set of approximate eigenvalues and examples of the functional form of the solutions.
Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates
NASA Astrophysics Data System (ADS)
Destrade, Michel; Fu, Yibin; Nobili, Andrea
2016-09-01
The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
Interactions between a spherical elastic shell and acoustic waves from a water-entry moving source
NASA Astrophysics Data System (ADS)
Lee, M.
2004-05-01
A possible interaction between the acoustic waves, which are generated from a water-entry body (moving source), and a submerged elastic shell is investigated theoretically within the scope of linear theory. The incident wave is defined from the ballistic wave model. The transient interaction is solved through extension of a method formulated for the excitation from a stationary source in an infinite domain. Numerical examples for the incident wave forms and corresponding shell responses are given to illustrate the effect of a moving source on the structure response.
The DPG methodology applied to different variational formulations of linear elasticity
NASA Astrophysics Data System (ADS)
Keith, Brendan; Fuentes, Federico; Demkowicz, Leszek
2016-09-01
The flexibility of the DPG methodology is exposed by solving the linear elasticity equations under different variational formulations, including some with non-symmetric functional settings (different infinite-dimensional trial and test spaces). The family of formulations presented are proved to be mutually ill or well-posed when using traditional energy spaces on the whole domain. Moreover, they are shown to remain well-posed when using broken energy spaces and interface variables. Four variational formulations are solved in 3D using the DPG methodology. Numerical evidence is given for both smooth and singular solutions and the expected convergence rates are observed.
Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity
Arzhantsev, Ivan V; Zaidenberg, M G; Kuyumzhiyan, Karine G
2012-07-31
We say that a group G acts infinitely transitively on a set X if for every m element of N the induced diagonal action of G is transitive on the cartesian mth power X{sup m} backslash {Delta} with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of normal affine cones over flag varieties, the second of nondegenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups. Bibliography: 42 titles.
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:
Buckling modes of elastic thin films on elastic substrates
NASA Astrophysics Data System (ADS)
Mei, Haixia; Huang, Rui; Chung, Jun Young; Stafford, Christopher M.; Yu, Hong-Hui
2007-04-01
Two buckling modes have been observed in thin films: buckle delamination and wrinkling. This letter identifies the conditions for selecting the favored buckling modes for elastic films on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or is predicted for variation of the stiffness ratio between the substrate and the film or variation of theinterfacial defect size. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.
The influence of gravity on the steady propagation of a semi-infinite bubble into a flexible channel
NASA Astrophysics Data System (ADS)
Hazel, Andrew L.; Heil, Matthias
2008-09-01
Motivated by discrepancies between recent bench-top experiments [A. Juel and A. Heap, J. Fluid Mech. 572, 287 (2007)] and numerical simulations [A. L. Hazel and M. Heil, ASME J. Biomech. Eng. 128, 573 (2006)] we employ computational methods to examine the effects of transverse gravity on the steady propagation of a semi-infinite, inviscid air finger into a two-dimensional elastic channel filled with a Newtonian fluid. The special case of propagation in a rigid channel is also discussed in Appendix B. The coupled free-surface, fluid-structure-interaction problem is solved numerically using the object-oriented multiphysics finite-element library OOMPH-LIB. In the absence of gravity the relationship between the applied pressure and the propagation speed of the finger is nonmonotonic, with a turning point at small values of the propagation speed. We demonstrate that the turning point disappears when a modest gravitational force is applied and conjecture that it is this effect of gravity rather than any instability of the zero-gravity solution, as postulated in previous studies, that explains why the turning point has never been observed in experiments. At large propagation speeds, the presence of transverse gravity is shown to increase the pressure required to drive the air finger at a given speed, which is consistent with the observed discrepancies between previous zero-gravity simulations and the experimental results. Finally, we briefly discuss the possible implications of our results for the physiological problem of pulmonary airway reopening.
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.
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)
Biodegradable stents with elastic memory.
Venkatraman, Subbu S; Tan, Lay Poh; Joso, Joe Ferry D; Boey, Yin Chiang Freddy; Wang, Xintong
2006-03-01
This work reports, for the first time, the development of a fully biodegradable polymeric stent that can self-expand at body temperatures (approximately 37 degrees C), using the concept of elastic memory. This self-expansion is necessary in fully polymeric stents, to overcome the problem of elastic recoil following balloon expansion in a body vessel. Bi-layered biodegradable stent prototypes were produced from poly-L-lactic acid (PLLA) and poly glycolic acid (PLGA) polymers. Elastic memory was imparted to the stents by temperature conditioning. The thickness and composition of each layer in the stents are critical parameters that affect the rate of self-expansion at 37 degrees C, as well as the collapse strengths of the stents. The rate of self-expansion of the stents, as measured at 37 degrees C, exhibits a maximum with layer thickness. The Tg of the outer layer is another significant parameter that affects the overall rate of expansion.
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.
The correlation length in thin film and semi-infinite medium
NASA Astrophysics Data System (ADS)
Korneta, W.; Pytel, Z.
1983-03-01
Correlation lengths in directions parallel and perpendicular to a surface of a thin ferromagnetic film and a semi-infinite ferromagnet are calculated. Their dependences both on temperature and distance to a surface are discussed.
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.
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.
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.
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 Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.
1983-01-01
The accuracy of the finite difference method in the solution of linear elasticity problems that involve either a stress discontinuity or a stress singularity is considered. Solutions to three elasticity problems are discussed in detail: a semi-infinite plane subjected to a uniform load over a portion of its boundary; a bimetallic plate under uniform tensile stress; and a long, midplane symmetric, fiber reinforced laminate subjected to uniform axial strain. Finite difference solutions to the three problems are compared with finite element solutions to corresponding problems. For the first problem a comparison with the exact solution is also made. The finite difference formulations for the three problems are based on second order finite difference formulas that provide for variable spacings in two perpendicular directions. Forward and backward difference formulas are used near boundaries where their use eliminates the need for fictitious grid points.
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.
Thermal fluctuations and rubber elasticity.
Xing, Xiangjun; Goldbart, Paul M; Radzihovsky, Leo
2007-02-16
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation. PMID:17359034
Thermal Fluctuations and Rubber Elasticity
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Goldbart, Paul M.; Radzihovsky, Leo
2007-02-01
The effects of thermal elastic fluctuations in rubbery materials are examined. It is shown that, due to their interplay with the incompressibility constraint, these fluctuations qualitatively modify the large-deformation stress-strain relation, compared to that of classical rubber elasticity. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the external deformation.
Cellular Uptake of Elastic Nanoparticles
NASA Astrophysics Data System (ADS)
Yi, Xin; Shi, Xinghua; Gao, Huajian
2011-08-01
A fundamental understanding of cell-nanomaterial interaction is of essential importance to nanomedicine and safe applications of nanotechnology. Here we investigate the adhesive wrapping of a soft elastic vesicle by a lipid membrane. We show that there exist a maximum of five distinct wrapping phases based on the stability of full wrapping, partial wrapping, and no wrapping states. The wrapping phases depend on the vesicle size, adhesion energy, surface tension of membrane, and bending rigidity ratio between vesicle and membrane. These results are of immediate interest to the study of vesicular transport and endocytosis or phagocytosis of elastic particles into cells.
NASA Astrophysics Data System (ADS)
Czechowski, Grzegorz; Zywucki, B.; Jadzyn, Jan
1993-10-01
The Frederiks transitions for the n-octyloxycyanobiphenyl (8-OCB) placed in the external magnetic and electric field as a function of the temperature have been studied. On the basis of threshold values Bc and Uc, the elastic constants for splay, bend and twist modes are determined. The magnetic anisotropy of 8-OCB as a function of temperature has been determined. The K11 and K33 elastic constants show the pretransitional nematic- smectic A effect. The values of critical exponents obtained from the temperature dependence of K11 and K33 in the vicinity of N-SA phase transition 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.
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.
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
George, Jineesh; Ebenezer, D D; Bhattacharyya, S K
2010-10-01
A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.
Harding, R.M.; Martinson, J.J.; Flint, J.; Clegg, J.B.; Boyce, A.J. )
1993-11-01
Extensive allelic diversity in variable numbers of tandem repeats (VNTRs) has been discovered in the human genome. For population genetic studies of VNTRs, such as forensic applications, it is important to know whether a neutral mutation-drift balance of VNTR polymorphism can be represented by the infinite alleles model. The assumption of the infinite alleles model that each new mutant is unique is very likely to be violated by unequal sister chromatid exchange (USCE), the primary process believed to generate VNTR mutants. The authors show that increasing both mutation rates and misalignment constraint for intrachromosomal recombination in a computer simulation model reduces simulated VNTR diversity below the expectations of the infinite alleles model. Maximal constraint, represented as slippage of single repeats, reduces simulated VNTR diversity to levels expected from the stepwise mutation model. Although misalignment rule is the more important variable, mutation rate also has an effect. At moderate rates of USCE, simulated VNTR diversity fluctuates around infinite alleles expectation. However, if rates of USCE are high, as for hypervariable VNTRs, simulated VNTR diversity is consistently lower than predicted by the infinite alleles model. This has been observed for many VNTRs and accounted for by technical problems in distinguishing alleles of neighboring size classes. The authors use sampling theory to confirm the intrinsically poor fit to the infinite model of both simulated VNTR diversity and observed VNTR polymorphisms sampled from two Papua New Guinean populations. 25 refs., 20 figs., 4 tabs.
NASA Astrophysics Data System (ADS)
Camacho, Miguel; Boix, Rafael R.; Medina, Francisco
2016-06-01
The authors present a computationally efficient technique for the analysis of extraordinary transmission through both infinite and truncated periodic arrays of slots in perfect conductor screens of negligible thickness. An integral equation is obtained for the tangential electric field in the slots both in the infinite case and in the truncated case. The unknown functions are expressed as linear combinations of known basis functions, and the unknown weight coefficients are determined by means of Galerkin's method. The coefficients of Galerkin's matrix are obtained in the spatial domain in terms of double finite integrals containing the Green's functions (which, in the infinite case, is efficiently computed by means of Ewald's method) times cross-correlations between both the basis functions and their divergences. The computation in the spatial domain is an efficient alternative to the direct computation in the spectral domain since this latter approach involves the determination of either slowly convergent double infinite summations (infinite case) or slowly convergent double infinite integrals (truncated case). The results obtained are validated by means of commercial software, and it is found that the integral equation technique presented in this paper is at least two orders of magnitude faster than commercial software for a similar accuracy. It is also shown that the phenomena related to periodicity such as extraordinary transmission and Wood's anomaly start to appear in the truncated case for arrays with more than 100 (10 ×10 ) slots.
Stiffness and Mass Matrices of FEM-Applicable Dynamic Infinite Element with Unified Shape Basis
NASA Astrophysics Data System (ADS)
Kazakov, Konstantin
2009-05-01
This paper is devoted to the construction and evaluation of mass and stiffness matrices of elastodynamic four and five node infinite elements with unified shape functions (EIEUSF), recently proposed by the author. Such elements can be treated as a family of elastodynamic infinite elements appropriate for multi-wave soil-structure interaction problems. The common characteristic of the proposed infinite elements is the so-called unified shape function, based on finite number of wave shape functions. The idea and the construction of the unified shape basis are described in brief. This element belongs to the decay class of infinite elements. It is shown that by appropriate mapping functions the formulation of such an element can be easily transformed to a mapped form. The results obtained using the proposed infinite elements are in a good agreement with the superposed results obtained by a series of standard computational models. The continuity along the finite/infinite element line (artificial boundary) in two-dimensional substructure models is also discussed in brief. In this type of computational models such a line marks the artificial boundary between the near and the far field of the model.
Elastic modes and their computation
Hedstrom, G.W.
1995-04-01
In this note we summarize the theory of modes in stratified elastic media, and we discuss some of the considerations necessary to achieve reliable numerical computations. We also point out the consequences of the fact that the corresponding eigenvalue problem is not selfadjoint. 14 refs.
Elastic forward scattering of gluons
NASA Astrophysics Data System (ADS)
Ermolaev, B. I.
1995-06-01
The colour octet and singlet parts of the elastic gg→ gg-scattering amplitude are evaluated in the Regge kinematical region s≫- t in the LLA, with iπ-terms taken into account, by constructing and solving a set of the infrared evolution equations.
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…
HEMP. Hydrodynamic Elastic Magneto Plastic
Wilkins, M.L.; Levatin, J.A.
1985-02-01
The HEMP code solves the conservation equations of two-dimensional elastic-plastic flow, in plane x-y coordinates or in cylindrical symmetry around the x-axis. Provisions for calculation of fixed boundaries, free surfaces, pistons, and boundary slide planes have been included, along with other special conditions.
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…
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.
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.
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2016-10-01
Stemming from the law of the conservation of energy in an elastic medium, this work extends the scope of the previous analysis for a scatterer immersed in a nonviscous liquid [F. G. Mitri, Ultrasonics 62, 20-26 (2015)] to the case of a (viscous) fluid circular cylinder cross-section encased in a homogeneous, isotropic, elastic matrix. Analytical expressions for the absorption, scattering, and extinction efficiencies (or cross-sections) are derived for "elastic-sheets" (i.e., finite beams in 2D propagating in elastic media) of arbitrary wavefront, in contrast to the ideal case of plane waves of infinite extent. The mathematical expressions are formulated in generalized partial-wave series expansions in cylindrical coordinates involving the beam-shape coefficients of finite elastic-sheet beams with arbitrary wavefront, and the scattering coefficients of the fluid cylinder encased in the elastic matrix. The analysis shows that in elastodynamic scattering, both the scattered L-wave as well as the scattered T-wave contribute to the time-averaged scattered efficiency (or power). However, the extinction efficiency only depends on the scattering coefficients characterizing the same type (L or T) as the incident wave. Numerical computations for the (non-dimensional energy) efficiency factors such as the absorption, scattering, and extinction efficiencies of a circular cylindrical viscous fluid cavity embedded in an elastic aluminum matrix are performed for nonparaxial focused Gaussian and Airy elastic-sheet beams with arbitrary longitudinal and transverse normally-polarized (shear) wave incidences in the Rayleigh and resonance regimes. A series of elastic resonances are manifested in the plots of the efficiencies as the non-dimensional size parameters for the L- and T-waves are varied. As the beam waist for the nonparaxial Gaussian beam increases, the plane wave result is recovered, while for a tightly focused wavefront, some of the elastic resonances can be suppressed
Nonlinear elastic properties of particulate composites
NASA Astrophysics Data System (ADS)
Chen, Yi-Chao; Jiang, Xiaohu
1993-07-01
A METHOD of computing effective elastic moduli of isotropic nonlinear composites is developed by using a perturbation scheme. It is demonstrated that only solutions from linear elasticity are needed in computing higher order moduli. As an application of the method, particulate composites of nonlinear elastic materials are analysed.
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.
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.
Elastic scattering in geometrical model
NASA Astrophysics Data System (ADS)
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Elastic modulus of viral nanotubes
NASA Astrophysics Data System (ADS)
Zhao, Yue; Ge, Zhibin; Fang, Jiyu
2008-09-01
We report an experimental and theoretical study of the radial elasticity of tobacco mosaic virus (TMV) nanotubes. An atomic force microscope tip is used to apply small radial indentations to deform TMV nanotubes. The initial elastic response of TMV nanotubes can be described by finite-element analysis in 5nm indentation depths and Hertz theory in 1.5nm indentation depths. The derived radial Young’s modulus of TMV nanotubes is 0.92±0.15GPa from finite-element analysis and 1.0±0.2GPa from the Hertz model, which are comparable with the reported axial Young’s modulus of 1.1GPa [Falvo , Biophys. J. 72, 1396 (1997)].
Elastic 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.
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.
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.
Limiting Motion for the Parabolic Ginzburg-Landau Equation with Infinite Energy Data
NASA Astrophysics Data System (ADS)
Côte, Delphine; Côte, Raphaël
2016-08-01
We study a class of solutions to the parabolic Ginzburg-Landau equation in dimension 2 or higher, with ill-prepared infinite energy initial data. We show that, asymptotically, the vorticity evolves according to motion by mean curvature in Brakke's weak formulation. Then, we prove that in the plane, point vortices do not move in the original time scale. These results extend the works of Bethuel, Orlandi and Smets (Ann Math (2) 163(1):37-163, 2006; Duke Math J 130(3):523-614, 2005) to infinite energy data; they allow us to consider point vortices on a lattice (in dimension 2), or filament vortices of infinite length (in dimension 3).
Elastic fibres in health and disease.
Kielty, Cay M
2006-08-08
Elastic fibres are a major class of extracellular matrix fibres that are abundant in dynamic connective tissues such as arteries, lungs, skin and ligaments. Their structural role is to endow tissues with elastic recoil and resilience. They also act as an important adhesion template for cells, and they regulate growth factor availability. Mutations in major structural components of elastic fibres, especially elastin, fibrillins and fibulin-5, cause severe, often life-threatening, heritable connective tissue diseases such as Marfan syndrome, supravalvular aortic stenosis and cutis laxa. Elastic-fibre function is also frequently compromised in damaged or aged elastic tissues. The ability to regenerate or engineer elastic fibres and tissues remains a significant challenge, requiring improved understanding of the molecular and cellular basis of elastic-fibre biology and pathology, and ability to regulate the spatiotemporal expression and assembly of its molecular components.
Elastic fibres in health and disease.
Baldwin, Andrew K; Simpson, Andreja; Steer, Ruth; Cain, Stuart A; Kielty, Cay M
2013-08-20
Elastic fibres are insoluble components of the extracellular matrix of dynamic connective tissues such as skin, arteries, lungs and ligaments. They are laid down during development, and comprise a cross-linked elastin core within a template of fibrillin-based microfibrils. Their function is to endow tissues with the property of elastic recoil, and they also regulate the bioavailability of transforming growth factor β. Severe heritable elastic fibre diseases are caused by mutations in elastic fibre components; for example, mutations in elastin cause supravalvular aortic stenosis and autosomal dominant cutis laxa, mutations in fibrillin-1 cause Marfan syndrome and Weill-Marchesani syndrome, and mutations in fibulins-4 and -5 cause autosomal recessive cutis laxa. Acquired elastic fibre defects include dermal elastosis, whereas inflammatory damage to fibres contributes to pathologies such as pulmonary emphysema and vascular disease. This review outlines the latest understanding of the composition and assembly of elastic fibres, and describes elastic fibre diseases and current therapeutic approaches.
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
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.
Analytical solution of the radiative transfer equation for infinite-space fluence
Liemert, Andre; Kienle, Alwin
2011-01-15
This Brief Report presents the derivation of analytical expressions for the fluence of the steady state radiative transfer equation in an infinitely extended and anisotropically scattering medium in arbitrary dimensions for different source types. The fluence, which is composed of an infinite sum of diffusion-like Green's functions, was compared to the Monte Carlo method. Within the stochastic nature of the Monte Carlo simulations, an exact agreement was found in the steady state and time domains. It is shown that the use of low-order approximations is sufficient for many relevant cases.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
1986-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
NASA Technical Reports Server (NTRS)
Gibson, J. S.; Rosen, I. G.
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.
Extending NEC to model wire objects in infinite chiral media. [Numerical electromagnetic code (NEC)
Burke, G.J. ); Miller, E.K. ); Bhattachryya, A.K. . Physical Science Lab.)
1992-01-01
The development of a moment-method model for wire objects in an infinite chiral medium is described. In this work, the Numerical Electromagnetics Code (NEC) was extended by including a new integral-equation kernel obtained from the dyadic Green's function for an infinite chiral medium. The NEC moment-method treatment using point matching and a three-term sinusoidal current expansion was adapted to the case of a chiral medium. Examples of current distributions and radiation patterns for simple antennas are presented, and the validation of the code is discussed. 15 refs.
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
Persistence and Permanence for a Class of Functional Differential Equations with Infinite Delay
NASA Astrophysics Data System (ADS)
Faria, Teresa
2016-09-01
The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with initial conditions that are positive, continuous and bounded. The present method applies to a very broad class of abstract systems of FDEs with infinite delay, both autonomous and non-autonomous, which include many important models used in mathematical biology. Moreover, the hypotheses imposed are in general very easy to check. The results are illustrated with some selected examples.
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.
Finding Limit Cycles in self-excited oscillators with infinite-series damping functions
NASA Astrophysics Data System (ADS)
Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.
2015-03-01
In this paper we present a simple method for finding the location of limit cycles of self excited oscillators whose damping functions can be represented by some infinite convergent series. We have used standard results of first-order perturbation theory to arrive at amplitude equations. The approach has been kept pedagogic by first working out the cases of finite polynomials using elementary algebra. Then the method has been extended to various infinite polynomials, where the fixed points of the corresponding amplitude equations cannot be found out. Hopf bifurcations for systems with nonlinear powers in velocities have also been discussed.
NASA Astrophysics Data System (ADS)
Titovich, Alexey S.; Norris, Andrew N.
2015-03-01
A thin infinitely long elastic shell is stiffened by J in number identical lengthwise ribs distributed uniformly around the circumference and joined to a rod in the center. The 2D model of the substructure is a rigid central mass supported by J axisymmetrically placed linear springs. The response of the shell-spring-mass system is quite different from a fluid filled shell or that of a solid cylinder due to the discrete number of contact points which couple the displacement of the shell at different locations. Exterior acoustic scattering due to normal plane wave incidence is solved in closed form for arbitrary J. The scattering matrix associated with the normal mode solution displays a simple structure, composed of distinct sub-matrices which decouple the incident and scattered fields into J families. The presence of a spring-mass substructure causes resonances which are shown to be related to the subsonic shell flexural waves, and an approximate analytic expression is derived for the quasi-flexural resonance frequencies. Numerical simulations indicate that the new solution for J ≥ 3 springs results in a complicated scattering response for plane wave incidence. As the number of springs becomes large enough, the total scattering cross-section is asymptotically zero at low frequencies and slightly increased compared to the empty shell at moderate frequencies due to the added stiffness and mass. It is also observed that the sensitivity to the angle of incidence diminishes as the number of springs is increased. This system can be tuned by selecting the shell thickness, spring stiffness and added mass to yield desired quasi-static effective properties making it a candidate element for graded index sonic crystals.
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%.
Flexural magneto-elastic vibrations of thin metal wires
NASA Astrophysics Data System (ADS)
Lukyanov, A.; Molokov, S.
2004-03-01
Flexural vibrations of thin metal wires owing to a high, pulsed electric current have been investigated. The current is sufficiently low to inhibit melting but sufficiently high to induce stresses, leading to the wire fragmentation. The problem is treated numerically on the basis of the theory of three-dimensional linear elasticity. The model has been verified on the well-known exact, eigenmode solution for the flexural vibrations of an infinite wire. The agreement is excellent. Further, the model has been used to study vibrations owing to two sources. The first one is perturbations of wires owing to the Lorentz force leading to a kink-type instability similar to that in plasmas. As the main cause of the wire fragmentation has been previously found to be the thermal expansion of material owing to Joule heating, this problem mainly serves to compare results between the three-dimensional and the one-dimensional, thin-rod models. Comparison of the growth rate of the instability obtained by the two models has shown an excellent agreement. The second source of vibrations is the magnetic fields induced in the external electric circuit. The results show that depending on the shape of the circuit, the induced stresses may exceed 20 MPa for the aluminium wires used in the low-current experiments. Although the external fields are not the main source of the wire fragmentation, these values alone may cause the fracture process at elevated temperatures.
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.
Variable Joint Elasticities in Running
NASA Astrophysics Data System (ADS)
Peter, Stephan; Grimmer, Sten; Lipfert, Susanne W.; Seyfarth, Andre
In this paper we investigate how spring-like leg behavior in human running is represented at joint level. We assume linear torsion springs in the joints and between the knee and the ankle joint. Using experimental data of the leg dynamics we compute how the spring parameters (stiffness and rest angles) change during gait cycle. We found that during contact the joints reveal elasticity with strongly changing parameters and compare the changes of different parameters for different spring arrangements. The results may help to design and improve biologically inspired spring mechanisms with adjustable parameters.
Bria, Pietro; Lombardi, Riccardo
2008-08-01
The idea of the infinite has its origins in the very beginnings of western philosophy and was developed significantly by modern philosophers such as Galileo and Leibniz. Freud discovered the Unconscious which does not respect the laws of classical logic, flouting its fundamental principle of non-contradiction. This opened the way to a new epistemology in which classical logic coexists with an aberrant logic of infinite affects. Matte Blanco reorganized this Freudian revolution in logic and introduced the concept of bi-logic, which is an intermingling of symmetric and Aristotelic logics. The authors explore some epistemological and clinical aspects of the functioning of the deep unconscious where the emergence of infinity threatens to overwhelm the containing function of thought, connecting this topic to some of Bion's propositions. They then suggest that bodily experiences can be considered a prime source of the logic of turmoil, and link a psychoanalytic consideration of the infinite to the mind-body relation. Emotional catastrophe is seen both as a defect-a breakdown of the unfolding function which translates unconscious material into conscious experience-and as the consequence of affective bodily pressures. These pressures function in turn as symmetrizing or infinitizing operators. Two clinical vignettes are presented to exemplify the hypotheses.
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…
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.
Variable Input: What Sarah Reveals about Nonagreeing "Don't" and Theories of Root Infinitives
ERIC Educational Resources Information Center
Miller, Karen
2013-01-01
Two recent proposals link the use of nonagreeing "don't" to the Root Infinitive (RI) Stage. Guasti & Rizzi (2002) argue for a misset parameter involving how agreement is spelled out. Schütze (2010) proposes that Infl is underspecified in child language and that "do" surfaces to support the contracted clitic/affix…
One-Dimensional Infinite Horizon Nonconcave Optimal Control Problems Arising in Economic Dynamics
Zaslavski, Alexander J.
2011-12-15
We study the existence of optimal solutions for a class of infinite horizon nonconvex autonomous discrete-time optimal control problems. This class contains optimal control problems without discounting arising in economic dynamics which describe a model with a nonconcave utility function.
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
Renner, R; Cirac, J I
2009-03-20
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks. PMID:19392183
Stochastic control of infinite dimensional systems in Hilbert space: A factorization perspective
NASA Technical Reports Server (NTRS)
Milman, Mark M.; Schumitzky, Alan
1987-01-01
A factorization perspective on problems of optimal causal estimation and optimal causal control of linear stochastic systems defined on an infinite-dimensional Hilbert space is presented. A separation principle is derived for the case in which the system input/output map is generated by an abstract evolution operator. The factorization formalism allows for an essentially algebraic approach to these problems.
Local density approximation results for bond length alternation in the infinite polyyne chain
NASA Astrophysics Data System (ADS)
Bylaska, Eric; Weare, John
1998-03-01
Calculations for large even numbered carbon ring molecules and band structure calculations for the infinite polyyne chain within the local density approximation are reported. We studied the alternation of bond lengths in this system as a function of size. Particular focus is on alternation in the infinite system. For intermediate and large sized Cn rings with n satisfying n=4N (doubly-antiaromatic rings) there is a substantial first order Jahn-Teller distortion which decreases for large N. On the other hand, for Cn rings satisfying n=4N+2 (doubly-aromatic rings) the second order Jahn-Teller distortion does not produce bond length alternation even by the large C_42 ring. The persistance of aromatic behavior in the very large carbon rings manifests itself in the band structure calculations by making the amount of bond length alternation predicted for the infinite polyyne chain extremely sensitive to the numerical treatment of the Brillouin zone. We have shown that the infinite polyyne has a finite amount of bond length alternation but the condensation energy is very small.
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…
“Infinite statistics” and its two-parameter q-deformation
NASA Astrophysics Data System (ADS)
Mishra, A. K.; Rajasekaran, G.
1994-05-01
We generalize Greenberg's q-mutator algebra for infinite statistics to the most general form invariant under unitary transformations in the indices and study its consequences. Constraints on the parameter space arising from the positivity of the metric in the underlying Fock space are obtained.
Wavenumbers for currents on infinite- and finite-length wires in a chiral medium
Bhattacharyya, A.K.; Burke, G.J.; Miller, E.K.
1992-03-01
There is increasing interest in determining the electromagnetic properties of material media differing from free space and the effects thereof on the radiation, propagation, and scattering of electromagnetic fields. A material property of special present interest is that of chirality. Chirality manifests itself as a ``handedness`` wherein a chiral medium does not support propagation of a linearly-polarized plane wave, but which instead decomposes into two circularly-polarized waves that propagate at different speeds. Initial work in this area was devoted to developing various analytical solutions to some basic problems such as the Green`s Dyadic for a point current source. Attention is now being increasingly devoted to using this early work for a variety of applications such as analyzing antennas in chiral media scattering from chiral objects; scattering from objects having chiral coatings; and reflection from planar chiral interfaces. The focus of the work described here is determining the wavenumbers (={minus}{alpha}{minus}j{beta}) of the current waves excited on wire antennas located in an infinite chiral medium using two complementary approaches. One is to use an extension of an existing computer model (NEC) that permits modeling of arbitrary wire objects located in an infinite chiral medium. The other is to develop a solution for an infinitely long cylindrical antenna also located in an infinite chiral medium. The latter canonical problem is of interest in its own right as well as providing a means for achieving mutual validation with the NEC model. 9 refs.
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…
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.
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…
Subsonic Euler Flows with Large Vorticity Through an Infinitely Long Axisymmetric Nozzle
NASA Astrophysics Data System (ADS)
Du, Lili; Duan, Ben
2016-09-01
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.
Wavenumbers for currents on infinite- and finite-length wires in a chiral medium
Bhattacharyya, A.K. ); Burke, G.J. ); Miller, E.K. )
1992-01-01
There is increasing interest in determining the electromagnetic properties of material media differing from free space and the effects thereof on the radiation, propagation, and scattering of electromagnetic fields. A material property of special present interest is that of chirality. Chirality manifests itself as a handedness'' wherein a chiral medium does not support propagation of a linearly-polarized plane wave, but which instead decomposes into two circularly-polarized waves that propagate at different speeds. Initial work in this area was devoted to developing various analytical solutions to some basic problems such as the Green's Dyadic for a point current source. Attention is now being increasingly devoted to using this early work for a variety of applications such as analyzing antennas in chiral media scattering from chiral objects; scattering from objects having chiral coatings; and reflection from planar chiral interfaces. The focus of the work described here is determining the wavenumbers (={minus}{alpha}{minus}j{beta}) of the current waves excited on wire antennas located in an infinite chiral medium using two complementary approaches. One is to use an extension of an existing computer model (NEC) that permits modeling of arbitrary wire objects located in an infinite chiral medium. The other is to develop a solution for an infinitely long cylindrical antenna also located in an infinite chiral medium. The latter canonical problem is of interest in its own right as well as providing a means for achieving mutual validation with the NEC model. 9 refs.
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…
Acoustic transmission through a 2-D orthotropic multi-layered infinite cylindrical shell
NASA Astrophysics Data System (ADS)
Blaise, A.; Lesueur, C.
1992-05-01
An investigation is presented of the transmission loss of two-dimensional orthotropic multilayered infinite cylindrical shells. Equations of motion are established by using a variational displacement formulation; these equations remain unchanged in form whatever the number of layers. Numerical results are presented illustrating the influence of acoustic and structural parameters on the transmission loss.
Infinite face-centered-cubic network of identical resistors: Application to lattice Green's function
NASA Astrophysics Data System (ADS)
Asad, J. H.; Diab, A. A.; Hijjawi, R. S.; Khalifeh, J. M.
2013-01-01
The equivalent resistance between the origin and any other lattice site, in an infinite face-centered-cubic network consisting of identical resistors, has been expressed rationally in terms of the known value f_o(3;0,0,0) and π . The asymptotic behavior is investigated, and some calculated values for the equivalent resistance are presented.
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…
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
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
Eulerian formulation of elastic rods
NASA Astrophysics Data System (ADS)
Huynen, Alexandre; Detournay, Emmanuel; Denoël, Vincent
2016-06-01
In numerous biological, medical and engineering applications, elastic rods are constrained to deform inside or around tube-like surfaces. To solve efficiently this class of problems, the equations governing the deflection of elastic rods are reformulated within the Eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface. This reformulation hinges on describing the rod-deformed configuration by means of its relative position with respect to a reference curve, defined as the axis or spine curve of the constraint, and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve. Associated with a segmentation strategy, which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact (except for their extremities), this re-parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two-points boundary-value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment.
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.
Effective elastic constants of polycrystalline aggregates
NASA Astrophysics Data System (ADS)
Bonilla, Luis L.
A METHOD is presented for the determination of the effective elastic constants of a transversely isotropic aggregate of weakly anisotropic crystallites with cubic symmetry. The results obtained generalize those given in the literature for the second and third order elastic constants. In addition, the second moments and the binary angular correlations of the second order stiffnesses are obtained. It is also explained how these moments can be used to find the two-point correlations of the elastic constants.
Multi-spectral photoacoustic elasticity tomography
Liu, Yubin; Yuan, Zhen
2016-01-01
The goal of this work was to develop and validate a spectrally resolved photoacoustic imaging method, namely multi-spectral photoacoustic elasticity tomography (PAET) for quantifying the physiological parameters and elastic modulus of biological tissues. We theoretically and experimentally examined the PAET imaging method using simulations and in vitro experimental tests. Our simulation and in vitro experimental results indicated that the reconstructions were quantitatively accurate in terms of sizes, the physiological and elastic properties of the targets. PMID:27699101
Multi-spectral photoacoustic elasticity tomography
Liu, Yubin; Yuan, Zhen
2016-01-01
The goal of this work was to develop and validate a spectrally resolved photoacoustic imaging method, namely multi-spectral photoacoustic elasticity tomography (PAET) for quantifying the physiological parameters and elastic modulus of biological tissues. We theoretically and experimentally examined the PAET imaging method using simulations and in vitro experimental tests. Our simulation and in vitro experimental results indicated that the reconstructions were quantitatively accurate in terms of sizes, the physiological and elastic properties of the targets.
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 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.
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.
Universal Elasticity and Fluctuations of Nematic Gels
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Radzihovsky, Leo
2003-04-01
We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to dlc<3.
Accounting for elastic bodies in multibody loops
NASA Astrophysics Data System (ADS)
Hiller, Manfred; Sokol, Peter
A technique for modeling multibody systems with closed kinematic loops containing elastic bodies is developed analytically. The elastic body is treated as a beam element, and its linear-elastic deformation is discretized using ansatz functions. The free elastic body is then integrated into the multibody loop with the help of coupling equations, as described by Woernle (1988), and the equations of motion are obtained in minimal form via the principle of D'Alembert. The applicability of the present approach to problems in large space structures and robotics is indicated.
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
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
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.
Argani, L. P.; Bigoni, D.; Capuani, D.; Movchan, N. V.
2014-01-01
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
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.
NASA Astrophysics Data System (ADS)
Lim, In Gweon; Park, Suhyun; Oh, Junghwan
2016-08-01
The theoretical development of a magnetic force and an induced motion while applying a magnetic field to magnetic nanoparticles in elastic media is described. An analytical expression for tissue-surface displacement derived from Mindlin's theory of elasticity in semi-infinite media was used to analyze the magneto-motive technique. The initial motion of the magnetic nanoparticles is driven by a constant magnetic force that displays a dampened transient motion before steady-state movement at twice the modulation frequency of the applied sinusoidal magnetic field. The motion of the nanoparticles at double the modulation frequency originated from the magnetic force being proportional to the product of the magnetic flux density and its gradient. Finally, we demonstrate the detection of iron-oxide nanoparticles taken up by liver parenchymal Kupffer cells and macrophages in atherosclerotic plaques by using a differential-phase optical coherence tomography (DP-OCT) system to compare simulation results with experimental data.
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 x 10(3) and 0.85 x 10(3) Nm(-2) respectively, while at 63 years of age both are equal to 3 x 10(3) 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 total
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
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.
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.
Nanometer thick elastic graphene engine.
Lee, Jong Hak; Tan, Jun You; Toh, Chee-Tat; Koenig, Steven P; Fedorov, V E; Castro Neto, Antonio H; Ozyilmaz, Barbaros
2014-05-14
Significant progress has been made in the construction and theoretical understanding of molecular motors because of their potential use. Here, we have demonstrated fabrication of a simple but powerful 1 nm thick graphene engine. The engine comprises a high elastic membrane-piston made of graphene and weakly chemisorbed ClF3 molecules as the high power volume changeable actuator, while a 532 nm LASER acts as the ignition plug. Rapid volume expansion of the ClF3 molecules leads to graphene blisters. The size of the blister is controllable by changing the ignition parameters. The estimated internal pressure per expansion cycle of the engine is about ∼10(6) Pa. The graphene engine presented here shows exceptional reliability, showing no degradation after 10,000 cycles. PMID:24773247
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
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.
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, 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. 29.1014 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,...
Simulation and control problems in elastic robots
NASA Technical Reports Server (NTRS)
Tadikonda, S. S. K.; Baruh, H.
1989-01-01
Computational issues associated with modeling and control of robots with revolute joints and elastic arms are considered. A manipulator with one arm and pinned at one end is considered to investigate various aspects of the modeling procedure and the model, and the effect of coupling between the rigid-body and the elastic motions. The rigid-body motion of a manipulator arm is described by means of a reference frame attached to the shadow beam, and the linear elastic operator denoting flexibility is defined with respect to this reference frame. The small elastic motion assumption coupled with the method of assumed modes is used to model the elasticity in the arm. It is shown that only terms up to quadratic in these model amplitudes need to be retained. An important aspect of the coupling between the rigid-body and the elastic motion is the centrifugal stiffening effect. This effect stiffens the elastic structure, as to be expected on physical grounds, gives rise to a time-varying inertia term for the rigid-body motion, and, in general, results in an effective inertia term smaller than the rigid-body inertia term. Simulation results are presented for an elastic beam pinned at one end and free at the other, and rotating in a horizontal plane, and control issues such as the order of the model, number of sensors, and modal extraction are examined within this context.
Cavitation, Elasticity and Fracture in Strong Hydrogels
NASA Astrophysics Data System (ADS)
Cui, Jun; Madkour, Ahmad; Tew, Gregory; Crosby, Alfred
2010-03-01
The interplay between the molecular network and material microstructure of a polymer-based hydrogel is critical for determining both the low strain elastic properties and fracture toughness. We present a novel complex hydrogel network developed by introducing polydimethylsiloxane (PDMS) into a polyethylene glycol (PEG)-based network. Using a combination of conventional characterization techniques, as well as the recently developed technique of cavitation rheology, we investigate the balance of elasticity and fracture in these complex networks. The polymer network maintains elasticity, with negligible hysteresis, at large strains over a wide range of swelling ratios. These properties are investigated across a continuum of length scales ranging from microns to centimeters by taking advantage of cavitation rheology, which uses the onset of an elastic instability to quantify local network mechanics. We compare our results with established scaling theories to describe both the elastic and fracture properties as a function of polymer volume fraction.
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.
Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems
NASA Astrophysics Data System (ADS)
Bambusi, Dario; Giorgilli, Antonio
1993-05-01
We develop canonical perturbation theory for a physically interesting class of infinite-dimensional systems. We prove stability up to exponentially large times for dynamical situations characterized by a finite number of frequencies. An application to two model problems is also made. For an arbitrarily large FPU-like system with alternate light and heavy masses we prove that the exchange of energy between the optical and the acoustical modes is frozen up to exponentially large times, provided the total energy is small enough. For an infinite chain of weakly coupled rotators we prove exponential stability for two kinds of initial data: (a) states with a finite number of excited rotators, and (b) states with the left part of the chain uniformly excited and the right part at rest.
NASA Astrophysics Data System (ADS)
Talaganis, Spyridon; Biswas, Tirthabir; Mazumdar, Anupam
2015-11-01
In this paper we will consider quantum aspects of a non-local, infinite-derivative scalar field theory—a toy model depiction of a covariant infinite-derivative, non-local extension of Einstein’s general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it asymptotically free, thus providing strong prospects of resolving various classical and quantum divergences. In particular, we will find that at one loop, the two-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet behavior of all other one-loop diagrams as well as the two-loop, two-point function remains well under control. We will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.
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.
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.
Weak coupling expansion of Yang-Mills theory on recursive infinite genus surfaces
NASA Astrophysics Data System (ADS)
Ghoshal, Debashis; Imbimbo, Camillo; Kumar, Dushyant
2014-10-01
We analyze the partition function of two dimensional Yang-Mills theory on a family of surfaces of infinite genus. These surfaces have a recursive structure, which was used by one of us to compute the partition function that results in a generalized Migdal formula. In this paper we study the `small area' (weak coupling) expansion of the partition function, by exploiting the fact that the generalized Migdal formula is analytic in the (complexification of the) Euler characteristic. The structure of the perturbative part of the weak coupling expansion suggests that the moduli space of flat connections (of the SU(2) and SO(3) theories) on these infinite genus surfaces are well defined, perhaps in an appropriate regularization.
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.
Multiple scattering of polarized light in turbid infinite planes: Monte Carlo simulations.
Otsuki, Soichi
2016-05-01
Monte Carlo simulations were performed for infinite plane media containing spherical particles of different sizes. Most of the features of the surface plots for the elements of the effective scattering Mueller matrices are explained by the azimuthal dependence of the matrix predicted according to the theory of Raković et al. [Appl. Opt.38, 3399 (1999)10.1364/AO.38.003399APOPAI1559-128X]. The reduced effective scattering Mueller matrices calculated according to the theory have eight nonzero elements, which are only dependent on the distance from the illumination point. The reduced matrices are factorized approximately into products of a depolarizer and retarding diattenuators. The turbid infinite plane media nearly behave as a pure depolarizer at long distances and become more diattenuating and birefringent with decreasing distance.
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.
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.
Time regularity and long-time behavior of parabolic p-Laplace equations on infinite graphs
NASA Astrophysics Data System (ADS)
Hua, Bobo; Mugnolo, Delio
2015-12-01
We consider the so-called discrete p-Laplacian, a nonlinear difference operator that acts on functions defined on the nodes of a possibly infinite graph. We study the corresponding Cauchy problem and identify the generator of the associated nonlinear semigroups. We prove higher order time regularity of the solutions. We investigate the long-time behavior of the solutions and discuss in particular finite extinction time and conservation of mass. Namely, on one hand, for small p if an infinite graph satisfies some isoperimetric inequality, then the solution to the parabolic p-Laplace equation vanishes in finite time; on the other hand, for large p, these parabolic p-Laplace equations always enjoy conservation of mass.
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.
Critical behavior of models with infinite disorder at a star junction of chains
NASA Astrophysics Data System (ADS)
Juhász, Róbert
2014-08-01
We study two models having an infinite-disorder critical point—the zero temperature random transverse-field Ising model and the random contact process—on a star-like network composed of M semi-infinite chains connected to a common central site. By the strong disorder renormalization group method, the scaling dimension xM of the local order parameter at the junction is calculated. It is found to decrease rapidly with the number M of arms, but remains positive for any finite M. This means that, in contrast with the pure transverse-field Ising model, where the transition becomes of first order for M > 2, it remains continuous in the disordered models, although, for not too small M, it is hardly distinguishable from a discontinuous one owing to a close-to-zero xM. The scaling behavior of the order parameter in the Griffiths-McCoy phase is also analyzed.
Uniform and weak stability of Bresse system with two infinite memories
NASA Astrophysics Data System (ADS)
Guesmia, Aissa; Kirane, Mokhtar
2016-10-01
In this paper, we consider one-dimensional linear Bresse systems in a bounded open domain under Dirichlet-Neumann-Neumann boundary conditions with two infinite memories acting only on two equations. First, we establish the well-posedness in the sense of semigroup theory. Then, we prove two (uniform and weak) decay estimates depending on the speeds of wave propagations, the smoothness of initial data and the arbitrarily growth at infinity of the two relaxation functions.
A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2016-06-01
This paper is devoted to the proof of the infinite-dimensional Borsuk-Ulam theorem for odd completely continuous multivalued maps with convex images which are defined on level sets of even functions. The results obtained in the paper are new even for single-valued maps. In the final section some applications of the theorem to analysis and differential equations are discussed. Bibliography: 12 titles.
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)
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
Kokhanovsky, Alexander A
2002-05-01
A simple, approximate analytical formula is proposed for the reflection function of a semi-infinite, homogeneous particulate layer. It is assumed that the zenith angle of the viewing direction is equal to zero (thus corresponding to the case of nadir observations), whereas the light incidence direction is arbitrary. The formula yields accurate results for incidence-zenith angles less than approximately 85 degrees and can be useful in analyzing satellite nadir observations of optically thick clouds.
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.
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.
The local autocorrelation time in thin film and semi-infinite model
NASA Astrophysics Data System (ADS)
Korneta, W.; Pytel, Z.
1984-05-01
The nearest-neighbour Ising model of a film in which exchange couplings in surface layers can differ from exchange couplings in other layers is considered. The dependence of the local autocorrelation time on distances to surfaces of the film, temperature and surface exchange couplings is discussed. The behaviour of the local autocorrelation time in a three-dimensional semi-infinite model is obtained assuming that the thickness of the film tends to infinity.
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.
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.
Neutron Flux Perturbations due to Infinite Plane Absorbers IV: The Exponential Flux Revisited
Williams, M.M.R
2002-02-15
Flux depression factors and measures of asymmetry are presented for an absorbing and scattering slab in an infinite medium in which there is an overall exponential flux. One speed transport theory is employed. The effect of the slab on the exponential flux is determined and the necessary correction factors to recover the unperturbed flux from the activation of the slab are calculated. Although this is an old problem, we present here a new formalism which highlights clearly some important physical aspects.
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.
Analytical solution for unsteady thermal stresses in an infinite cylinder composed of two materials
Pardo, E.; Sanchez Sarmiento, G.; Laura, P.A.A.; Gutierrez, R.H.
1987-01-01
An exact analytical solution for unsteady thermal stresses in an infinitely long solid composite cylinder is presented. The unsteady temperature field is determined following Ozisik's (1980) treatment, but a more general solution is achieved by the present approach by considering a heat convection situation at the outer boundary. The plane stress and plane strain states are considered next, and the thermal stresses are evaluated. Results are provided as dimensionless plots for several combinations of thermal and mechanical parameters of practical interest. 6 references.
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.
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.
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.
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.
Transitions in a compressible finite elastic sheet on a fluid substrate
NASA Astrophysics Data System (ADS)
Oshri, Oz; Diamant, Haim
2014-03-01
A thin elastic sheet, supported on a fluid substrate and uniaxially compressed, exhibits two critical transitions: From a flat state to sinusoidal wrinkles and from wrinkles to a localized fold. Previous theoretical studies treated the system in the limits of incompressible and infinite sheets. Both assumptions are relaxed in the current work to obtain details of the transitions and the phase diagram. Deriving an amplitude equation and using a variational approach, we show that the flat-to-wrinkle transition is second-order, whereas the wrinkle-to-fold one is first-order. The pressure-displacement relation is linear above the first transition and becomes parabolic after the second one, in agreement with numerical results. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
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.
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.
Dynamical scaling in infinitely correlated many-body systems through a quantum phase transition
NASA Astrophysics Data System (ADS)
Acevedo, Oscar Leonardo; Quiroga, Luis; Rodriguez, Ferney Javier; Johnson, Neil
2013-03-01
We assess dynamical scaling of many two-level systems (TLSs) infinitely correlated, either through a mediating radiation mode as in the Dicke Model, or through a direct interaction between TLSs as in the Lipkin-Meshkov-Glick model. Those models are characterized by the presence of a Quantum Phase Transition (QPT) in the thermodynamic limit, and they belong to the same universality class. The assessment is done by means of exact computational simulations of finite-size systems under linear rampings of the interaction parameter crossing the quantum critical point. Our results exhibit significant differences with respect to previous works on dynamical scaling across QPTs in the near-adiabatic regime, which have focused on spin-chain models where correlation lengths can be defined. We have confirmed that in infinitely correlated models an effective system size can play the role of the correlation length in traditional scaling arguments. However, due to the infinite correlation among TLSs, the standard Kibble-Zurek mechanism is not realized as the system cannot fully enter an adiabatic evolution during the ordered phase. Also, in the two-level approximation, a suitable deviation from the standard Landau-Zener protocol must be performed in order to obtain scaling collapse.
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
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Mazilu, Traian; Dumitriu, Mădălina; Tudorache, Cristina
2011-07-01
The paper herein deals with the study of the dynamic behaviour generated by the instability of the vibration of a loaded mass, uniformly moving along an Euler-Bernoulli beam on a viscoelastic foundation, induced by the anomalous Doppler waves excited in the beam. This issue is relevant for the case of modern trains travelling along a track with soft soil when the trains speed exceeds the phase velocity of the waves induced in the track. The model corresponds to a railway vehicle reduced to a loaded wheel running along a (half) track. The beam takes account of the bending stiffness of the rail and the mass of the track, including the mass of the rail, semi-sleepers and half of the ballast layer, where the viscoelastic foundation represents the subgrade. The model includes the wheel/rail Hertzian contact and it allows the simulation of the possibility of contact loss. The nonlinear equations of motion are integrated using a numerical approach based on the Green's function method. When the vibration becomes unstable, the system evolution is a limit cycle characterised by a succession of shocks, due to the action of two opposite factors: the anomalous Doppler waves that pump energy at the interface between the moving mass and the beam, thus forcing the mass to take off, and the static load that push the mass downwards. The frequency of the shocks increases at higher velocity and the magnitude of the impact force decreases; the most dangerous velocity is the critical one, which represents the stability limit of the linear approximation of the motion equations. The transient behaviour that precedes the limit cycle appearance is being analysed. The Hertzian contact influences the time history of the limit cycle and the magnitude of the impact force and, therefore, it is essential to be included in the model. To the authors' knowledge, this problem has never been dealt with.
Baldo, M.; Lombardo, U.; Saperstein, E.E.; Zverev, M.V.
1995-09-01
The problem of pairing in semi-infinite nuclear matter is considered in the Brueckner approach. Equations for effective pairing interaction in semi-infinite matter are derived for the case of the separable representation of realistic NN interaction. The propagator of two noninteracting particles in a semi-infinite potential well is calculated numerically. The equation for effective interaction is solved for a model 8-shaped NN interaction, which correctly reproduces NN scattering in the low-energy limit. 15 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Viveros, U.; Sanchez-Sesma, F. J.; Luzon, F.
2001-12-01
The scattering of elastic waves by various types of cracks is an important engineering problem. From a physical point of view the question that arises is up to what degree will a local perturbation in a medium modifies the scattered wave field. For instance, in the seismic monitoring to enhance oil recovery (due to extensive presence of cracks and cavities) a crucial problem is to determine zones where there are physical property changes. Modelling such highly heterogeneous media is critical to increased production from oil and gas. In order to study scattering effects caused by arbitrary-shaped cracks a simplified indirect boundary element method (BEM) is used to compute the seismic response of a 3-D crack under incident elastic P and S waves. The method is based on the integral representation for scattered elastic waves using single layer boundary sources. This approach is called indirect BEM in the literature as the sources strengths should be obtained as an intermediate step. Scattered waves are constructed at the boundaries from which they radiate. Therefore, this method can be regarded as a numerical realization of Huygens' principle. Boundary conditions lead to a system of integral for boundary sources. A simplified discretization scheme is used. It is based on the approximate rectification of the surfaces involved using circles for the numerical and analytical integration of the exact Green's function for the unbounded elastic space. Radiation patterns for penny-shaped and croissant-shaped cracks are explored. The scattering effects of the elastic waves in a homogeneous isotropic infinite elastic medium with a 3-D crack are displayed in both frequency and time domains.
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).
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.
Rolling Wrinkles on Elastic Substrates
NASA Astrophysics Data System (ADS)
Imburgia, Michael; Crosby, Alfred
The mechanics of rolling contact between an elastomer layer and a thin film present unique opportunities for taking advantage of elastic instabilities, such as surface wrinkling, to create patterned surfaces. Here we present a plate-to-roll(P2R) geometry to laminate a thin film onto an elastomer layer in order to induce surface wrinkling. First, a poly(dimethylsiloxane)(PDMS) layer is draped around a roller and pressed into contact with a poly(styrene)(PS) film supported on a plate. Once rolling begins, the PS film preferentially laminates onto the PDMS layer. During this process, the deformation of the PDMS layer can induce wrinkling when the contact load exceeds a critical value. Wrinkle feature size consists of amplitudes of 0 . 2 - 4 μm and wavelengths of 15 - 20 μm . Wrinkle amplitude can be controlled by contact load and roller curvature, as well as the mechanical properties and thickness of the film and elastomer. We develop semi-empirical equations to describe the effect of contact load and roller curvature on the wrinkle aspect ratio. Finite-element modeling of an elastomer layer in rolling contact with a rigid plate is used to support experimental results. Using these models, wrinkle-based technologies such as optoelectronics and enhanced adhesives can be envisioned.
Structural basis of spectrin elasticity
Shen, B.W.; Stevens, F.J.; Luthi, U.; Goldin, S.B.
1991-10-17
A new model of human erythrocyte {alpha}-spectrin is proposed. The secondary structure of human erythrocyte {alpha}-spectrin and its folding into a condensed structure that can convert reversibly in situ, into an elongated configuration is predicted from its deduced protein sequence. Results from conformational and amphipathicity analyses suggest that {alpha}-spectrin consists mainly of short amphipathicity helices interconnected by flexible turns and/or coils. The distribution of charges and amphipathicity of the helices can facilitate their folding into stable domains of 4 and 3 helices surrounding a hydrophobic core. The association between adjacent four- and three-helix domains further organize them into recurring seven-helix motifs that might constitute the basic structural units of the extended {alpha}-spectrin. The elongated spectrin molecule packs, in a sinusoidal fashion, through interactions between neighboring motifs into a compact structure. We suggest that the reversible extension and contraction of this sigmoidally packed structure is the molecular basis of the mechanism by which spectrin contributes to the elasticity of the red cell membrane.
Highly elastic conductive polymeric MEMS
NASA Astrophysics Data System (ADS)
Ruhhammer, J.; Zens, M.; Goldschmidtboeing, F.; Seifert, A.; Woias, P.
2015-02-01
Polymeric structures with integrated, functional microelectrical mechanical systems (MEMS) elements are increasingly important in various applications such as biomedical systems or wearable smart devices. These applications require highly flexible and elastic polymers with good conductivity, which can be embedded into a matrix that undergoes large deformations. Conductive polydimethylsiloxane (PDMS) is a suitable candidate but is still challenging to fabricate. Conductivity is achieved by filling a nonconductive PDMS matrix with conductive particles. In this work, we present an approach that uses new mixing techniques to fabricate conductive PDMS with different fillers such as carbon black, silver particles, and multiwalled carbon nanotubes. Additionally, the electrical properties of all three composites are examined under continuous mechanical stress. Furthermore, we present a novel, low-cost, simple three-step molding process that transfers a micro patterned silicon master into a polystyrene (PS) polytetrafluoroethylene (PTFE) replica with improved release features. This PS/PTFE mold is used for subsequent structuring of conductive PDMS with high accuracy. The non sticking characteristics enable the fabrication of delicate structures using a very soft PDMS, which is usually hard to release from conventional molds. Moreover, the process can also be applied to polyurethanes and various other material combinations.
Elasticity of polymeric nanocolloidal particles
Riest, Jonas; Athanasopoulou, Labrini; Egorov, Sergei A.; Likos, Christos N.; Ziherl, Primož
2015-01-01
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. PMID:26522242
Role of elasticity in stagnant lid convection
NASA Astrophysics Data System (ADS)
Patocka, Vojtech; Tackley, Paul; Cadek, Ondrej
2016-04-01
A present limitation of global thermo-chemical convection models is that they assume a purely viscous or visco-plastic flow law for solid rock, i.e. elasticity is ignored. This may not be a good assumption in the cold, outer boundary layer known as the lithosphere, where elastic deformation may be important. Elasticity in the lithosphere plays at least two roles: It changes surface topography, which changes the relationship between topography and gravity, and it alters the stress distribution in the lithosphere, which may affect dynamical behaviour such as the formation of plate boundaries and other tectonics features. In the present work we study these effects in the context of stagnant lid convection. We use StagYY (Tackley, 2008) enhanced to include elasticity through adding advected elastic stresses to the momentum equation and replacing viscosity by the "effective" one (the method described in e.g. Moresi et al., 2002). First, a test example with a cylinder rising below the lithosphere (Crameri et al., 2012) is considered in various geometries and the effect of elasticity on the resulting topography and geoid is evaluated. Both free-slip and free-surface upper boundary condition is considered. Second, comparison of stagnant lid convection models with and without elasticity is performed. It is shown that global characteristics of the convection do not change when a realistic value of shear modulus is employed and that the stress pattern in the lithosphere is very similar. The most important effect is that stresses build up gradually when elasticity is considered and thus the stress picture is more stable in the time domain in the elastic than in the viscous case. Viscoelastic lithosphere thus filters internal dynamics more effectively than a purely viscous one, responding only to features which stay stable for times comparable to its relaxation time. This effect is clearly recognizable only when free-surface upper boundary condition is considered. The role of
Elastic turbulence in a curvilinear channel flow.
Jun, Yonggun; Steinberg, Victor
2011-11-01
We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.
NASA Astrophysics Data System (ADS)
Musa, A. B.
2015-05-01
The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.
Interpretation of elasticity of liquid marbles.
Whyman, Gene; Bormashenko, Edward
2015-11-01
Liquid marbles are non-stick droplets covered with micro-scaled particles. Liquid marbles demonstrate quasi-elastic properties when pressed. The interpretation of the phenomenon of elasticity of liquid marbles is proposed. The model considering the growth in the marble surface in the course of deformation under the conservation of marble's volume explains semi-quantitatively the elastic properties of marbles in satisfactory agreement with the reported experimental data. The estimation of the effective Young modulus of marbles and its dependence on the marble volume are reported.
Elastic activator for treatment of open bite.
Stellzig, A; Steegmayer-Gilde, G; Basdra, E K
1999-06-01
This article presents a modified activator for treatment of open bite cases. The intermaxillary acrylic of the lateral occlusal zones is replaced by elastic rubber tubes. By stimulating orthopaedic gymnastics (chewing gum effect), the elastic activator intrudes upper and lower posterior teeth. A noticeable counterclockwise rotation of the mandible was accomplished by a decrease of the gonial angle. Besides the simple fabrication of the device and uncomplicated replacement of the elastic rubber tubes, treatment can be started even in mixed dentition when affixing plates may be difficult. PMID:10420241
DAEs and PDEs in elastic multibody systems
NASA Astrophysics Data System (ADS)
Simeon, B.
1998-12-01
Elastic multibody systems arise in the simulation of vehicles, robots, air- and spacecrafts. They feature a mixed structure with differential-algebraic equations (DAEs) governing the gross motion and partial differential equations (PDEs) describing the elastic deformation of particular bodies. We introduce a general modelling framework for this new application field and discuss numerical simulation techniques from several points of view. Due to different time scales, singular perturbation theory and model reduction play an important role. A slider crank mechanism with a 2D FE grid for the elastic connecting rod illustrates the techniques.
Polycrystalline gamma plutonium's elastic moduli versus temperature
Migliori, Albert; Betts, J; Trugman, A; Mielke, C H; Mitchell, J N; Ramos, M; Stroe, I
2009-01-01
Resonant ultrasound spectroscopy was used to measure the elastic properties of pure polycrystalline {sup 239}Pu in the {gamma} phase. Shear and longitudinal elastic moduli were measured simultaneously and the bulk modulus was computed from them. A smooth, linear, and large decrease of all elastic moduli with increasing temperature was observed. They calculated the Poisson ratio and found that it increases from 0.242 at 519 K to 0.252 at 571 K. These measurements on extremely well characterized pure Pu are in agreement with other reported results where overlap occurs.
Comparative structures and properties of elastic proteins.
Tatham, Arthur S; Shewry, Peter R
2002-01-01
Elastic proteins are characterized by being able to undergo significant deformation, without rupture, before returning to their original state when the stress is removed. The sequences of elastic proteins contain elastomeric domains, which comprise repeated sequences, which in many cases appear to form beta-turns. In addition, the majority also contain domains that form intermolecular cross-links, which may be covalent or non-covalent. The mechanism of elasticity varies between the different proteins and appears to be related to the biological role of the protein. PMID:11911780
Nonlinear model of elastic field sources
NASA Astrophysics Data System (ADS)
Lev, B. I.; Zagorodny, A. G.
2016-09-01
A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.
Elastic Stiffness of a Skyrmion Crystal
NASA Astrophysics Data System (ADS)
Nii, Y.; Kikkawa, A.; Taguchi, Y.; Tokura, Y.; Iwasa, Y.
2014-12-01
We observe the elastic stiffness and ultrasonic absorption of a Skyrmion crystal in the chiral-lattice magnet MnSi. The Skyrmion crystal lattice exhibits a stiffness 3 orders of magnitude smaller than that of the atomic lattice of MnSi, being as soft as the flux line lattice in type-II superconductors. The observed anisotropic elastic responses are consistent with the cylindrical shape of the Skyrmion spin texture. Phenomenological analysis reveals that the spin-orbit coupling is responsible for the emergence of anisotropic elasticity in the Skyrmion lattice.
Darinskii, A N; Weihnacht, M; Schmidt, H
2013-07-01
The paper studies numerically the bulk acoustic wave generation by the surface acoustic wave propagating across a grating created on the surface of an elastically anisotropic half-infinite substrate. The computations are fully based on the finite element method. Applying the discrete Fourier transformation to the displacement field found inside the substrate and using an orthogonality relation valid for plane modes we determine separately the spatial spectrum of the quasi longitudinal and the quasi transverse bulk waves, that is, the dependence of the amplitudes of these waves on the tangential component of the wave vector. The dependence is investigated of the central spectral peak height and shape on the frequency of the incident surface wave as well as on the thickness, the width, and the number of strips forming the grating. In particular, it is found that under certain conditions the central peak can be approximated fairly precisely by the central peak of a sinc-function describing the spectrum of the bounded acoustic beam of rectangular shape and of width equal to the length of the grating.
A staggered-grid convolutional differentiator for elastic wave modelling
NASA Astrophysics Data System (ADS)
Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun
2015-11-01
The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.
Statistical properties of a folded elastic rod
NASA Astrophysics Data System (ADS)
Bayart, Elsa; Deboeuf, Stéphanie; Boué, Laurent; Corson, Francis; Boudaoud, Arezki; Adda-Bedia, Mokhtar
2010-03-01
A large variety of elastic structures naturally seem to be confined into environments too small to accommodate them; the geometry of folded structures span a wide range of length-scales. The elastic properties of these confined systems are further constrained by self-avoidance as well as by the dimensionality of both structures and container. To mimic crumpled paper, we devised an experimental setup to study the packing of a dimensional elastic object in 2D geometries: an elastic rod is folded at the center of a circular Hele-Shaw cell by a centripetal force. The initial configuration of the rod and the acceleration of the rotating disk allow to span different final folded configurations while the final rotation speed controls the packing intensity. Using image analysis we measure geometrical and mechanical properties of the folded configurations, focusing on length, curvature and energy distributions.
Measuring Moduli Of Elasticity At High Temperatures
NASA Technical Reports Server (NTRS)
Wolfenden, Alan
1993-01-01
Shorter, squatter specimens and higher frequencies used in ultrasonic measurement technique. Improved version of piezo-electric ultrasonic composite oscillator technique used to measure moduli of elasticity of solid materials at high temperatures.
Elastic spheres can walk on water
NASA Astrophysics Data System (ADS)
Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.
2016-02-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys.
Elasticity and Broken Symmetry in Nematic Elastomers
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Ranjan; Lubensky, T. C.; Xing, Xiangjun; Radzihovsky, Leo
2002-03-01
In nematic elastomers, the coupling between the internal liquid crystalline degrees of freedom and elastic strains lead to novel thermodynamic and mechanical behavior. Their remarkable properties make them candidates for a number of applications including artificial muscles and actuators. Other than their technological importance, their behavior highlights a major theme of physics: the interplay between broken symmetries and long-wavelength elasticity and hydrodynamics. In this talk my primary focus will be to show how the elastic "softness" and the pronounced nonlinear stress-strain relations in these materials arise as a consequence of broken rotational symmetry. We will reproduce these properties using simple models in a way that highlights this interplay between broken rotational symmetry and elasticity.
Universal elasticity and fluctuations of nematic gels.
Xing, Xiangjun; Radzihovsky, Leo
2003-04-25
We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3. PMID:12732018
Universal elasticity and fluctuations of nematic gels
NASA Astrophysics Data System (ADS)
Xing, Xiangjun; Radzihovsky, Leo
2003-03-01
We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local hetergeneities down to d_lc < 3.
Nanomedicine: Elastic clues in cancer detection
NASA Astrophysics Data System (ADS)
Suresh, Subra
2007-12-01
In vitro nanomechanical studies have shown that cultured cancer cells are elastically softer than healthy ones, and new measurements on cells from cancer patients suggest that this mechanical signature may be a powerful way to detect cancer in the clinic.
Elastic spheres can walk on water
Belden, Jesse; Hurd, Randy C.; Jandron, Michael A.; Bower, Allan F.; Truscott, Tadd T.
2016-01-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860
Elastic spheres can walk on water.
Belden, Jesse; Hurd, Randy C; Jandron, Michael A; Bower, Allan F; Truscott, Tadd T
2016-01-01
Incited by public fascination and engineering application, water-skipping of rigid stones and spheres has received considerable study. While these objects can be coaxed to ricochet, elastic spheres demonstrate superior water-skipping ability, but little is known about the effect of large material compliance on water impact physics. Here we show that upon water impact, very compliant spheres naturally assume a disk-like geometry and dynamic orientation that are favourable for water-skipping. Experiments and numerical modelling reveal that the initial spherical shape evolves as elastic waves propagate through the material. We find that the skipping dynamics are governed by the wave propagation speed and by the ratio of material shear modulus to hydrodynamic pressure. With these insights, we explain why softer spheres skip more easily than stiffer ones. Our results advance understanding of fluid-elastic body interaction during water impact, which could benefit inflatable craft modelling and, more playfully, design of elastic aquatic toys. PMID:26842860
NASA Astrophysics Data System (ADS)
Wang, Jianyong; Hu, Hanwei; Yu, Jun
2011-10-01
Starting from the nonlinear version of bilinear negative Kadomtsev-Petviashvili system, a new (2+1)-dimensional generalization of the modified Korteweg-deVries equation is obtained. For this new system, a set of infinitely many generalized symmetries is found by applying a formal series symmetry approach. And these symmetries constitute a closed infinite-dimensional Lie algebra which is a generalization of w∞ type algebra.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang; Wang, Zhenghan
2008-06-01
The classification of complex wave functions of infinite variables is an important problem since it is related to the classification of possible quantum states of matter. In this paper, we propose a way to classify symmetric polynomials of infinite variables using the pattern of zeros of the polynomials. Such a classification leads to a construction of a class of simple non-Abelian quantum Hall states which are closely related to parafermion conformal field theories.
Fracture imaging with converted elastic waves
Nihei, K.T.; Nakagawa, S.; Myer, L.R.
2001-05-29
This paper examines the seismic signatures of discrete, finite-length fractures, and outlines an approach for elastic, prestack reverse-time imaging of discrete fractures. The results of this study highlight the importance of incorporating fracture-generated P-S converted waves into the imaging method, and presents an alternate imaging condition that can be used in elastic reverse-time imaging when a direct wave is recorded (e.g., for crosswell and VSP acquisition geometries).
A NONLINEAR MESOSCOPIC ELASTIC CLASS OF MATERIALS
P. JOHNSON; R. GUYER; L. OSTROVSKY
1999-09-01
It is becoming clear that the elastic properties of rock are shared by numerous other materials (sand, soil, some ceramics, concrete, etc.). These materials have one or more of the following properties in common strong nonlinearity, hysteresis in stress-strain relation, slow dynamics and discrete memory. Primarily, it is the material's compliance, the mesoscopic linkages between the rigid components, that give these materials their unusual elastic properties.
Elastic form factors at higher CEBAF energies
Petratos, G.G.
1994-04-01
The prospects for elastic scattering from few body systems with higher beam energies at CEBAF is presented. The deuteron and{sup 3}He elastic structure functions A(Q{sup 2}) can be measured at sufficiently high momentum transfers to study the transition between the conventional meson-nucleon and the constituent quark-gluon descriptions. Possible improvements in the proton magnetic form factor data are also presented.
NASA Astrophysics Data System (ADS)
Renaud, Guillaume; Talmant, Maryline; Marrelec, Guillaume
2016-10-01
The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10-7 to 10-5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10-4 and can reach 10-2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10-6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = -73 GPa ± 9%, m = -34 GPa ± 9%, and n = -61 GPa ± 10% for polymethyl methacrylate, and l = -17 000 GPa ± 20%, m = -11 000 GPa ± 10%, and n = -30 000 GPa ± 20% for dry Berea sandstone.
Tattersall, Wade; Chiari, Luca; Machacek, J R; Anderson, Emma; White, Ron D; Brunger, M J; Buckman, Stephen J; Garcia, Gustavo; Blanco, Francisco; Sullivan, James P
2014-01-28
Utilising a high-resolution, trap-based positron beam, we have measured both elastic and inelastic scattering of positrons from water vapour. The measurements comprise differential elastic, total elastic, and total inelastic (not including positronium formation) absolute cross sections. The energy range investigated is from 1 eV to 60 eV. Comparison with theory is made with both R-Matrix and distorted wave calculations, and with our own application of the Independent Atom Model for positron interactions.
Linear Lumbar Localized Lysis of Elastic Fibers
Tschen, Jaime A.
2013-01-01
Background: The absence or loss of elastic fibers in the skin is referred to as dermal elastolysis. Purpose: This paper describes a woman with a distinctive clinical presentation of mid-dermal elastolysis characterized morphologically by multiple horizontal raised bands on the lower back. Methods: A 20-year-old Filipino woman presented with multiple asymptomatic, flesh-colored, raised, firm, linear, cord-like bands on the lumbar area of her back. There were neither similar lesions elsewhere nor a family member with this condition. Results: Microscopic examination of the raised band showed nearly complete absence of elastic fibers in the mid dermis. In contrast, a biopsy of symmetrically located normal-appearing skin showed a uniform distribution of elastic fibers throughout the dermis. Linear lumbar localized elastolysis is a descriptive designation that accurately reflects a correlation of the clinical and pathological changes of this condition. Conclusion: The clinical differential of raised horizontal cord-like bands on the lower back (without a family history of an inherited elastic fiber disorder, a prior history of trauma, or a significant change in weight or exercise habit) includes linear focal elastosis and linear lumbar localized elastolysis. Microscopic evaluation of a Verhoeff-van Gieson stained lesion specimen (which may be accompanied by a biopsy of normal-appearing skin for comparison) will readily differentiate these conditions. The former is usually characterized by increased elastic fibers, whereas the latter, as in this patient, shows a paucity or absence of elastic fibers in the mid dermis. PMID:23882313
Elastic actuator for precise force control
Pratt, Gill A.; Williamson, Matthew M.
1997-07-22
The invention provides an elastic actuator consisting of a motor and a motor drive transmission connected at an output of the motor. An elastic element is connected in series with the motor drive transmission, and this elastic element is positioned to alone support the full weight of any load connected at an output of the actuator. A single force transducer is positioned at a point between a mount for the motor and an output of the actuator. This force transducer generates a force signal, based on deflection of the elastic element, that indicates force applied by the elastic element to an output of the actuator. An active feedback force control loop is connected between the force transducer and the motor for controlling the motor. This motor control is based on the force signal to deflect the elastic element an amount that produces a desired actuator output force. The produced output force is substantially independent of load motion. The invention also provides a torsional spring consisting of a flexible structure having at least three flat sections each connected integrally with and extending radially from a central section. Each flat section extends axially along the central section from a distal end of the central section to a proximal end of the central section.
Elastic actuator for precise force control
Pratt, G.A.; Williamson, M.M.
1997-07-22
The invention provides an elastic actuator consisting of a motor and a motor drive transmission connected at an output of the motor. An elastic element is connected in series with the motor drive transmission, and this elastic element is positioned to alone support the full weight of any load connected at an output of the actuator. A single force transducer is positioned at a point between a mount for the motor and an output of the actuator. This force transducer generates a force signal, based on deflection of the elastic element, that indicates force applied by the elastic element to an output of the actuator. An active feedback force control loop is connected between the force transducer and the motor for controlling the motor. This motor control is based on the force signal to deflect the elastic element an amount that produces a desired actuator output force. The produced output force is substantially independent of load motion. The invention also provides a torsional spring consisting of a flexible structure having at least three flat sections each connected integrally with and extending radially from a central section. Each flat section extends axially along the central section from a distal end of the central section to a proximal end of the central section. 30 figs.
TOPICAL REVIEW: Inverse problems in elasticity
NASA Astrophysics Data System (ADS)
Bonnet, Marc; Constantinescu, Andrei
2005-04-01
This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.
Effects of physical exercise on the elasticity and elastic components of the rat aorta.
Matsuda, M; Nosaka, T; Sato, M; Ohshima, N
1993-01-01
To evaluate the effects of exercise on aortic wall elasticity and elastic components, young male rats underwent various exercise regimes for 16 weeks. In the exercised rats, the aortic incremental elastic modulus decreased significantly when under physiological strain. The aortic content of elastin increased significantly and the calcium content of elastin decreased significantly in the exercised group. The accumulated data from the exercised and sedentary groups revealed that the elastin calcium content was related positively to the incremental elastic modulus. We concluded that physical exercise from an early age decreases the calcium deposit in aortic wall elastin and that this effect probably produced in the exercised rats a distensible aorta.
NASA Astrophysics Data System (ADS)
Ettouhami, A. M.; Saunders, Karl; Radzihovsky, L.; Toner, John
2005-06-01
We study the elasticity, fluctuations, and pinning of a putative spontaneous vortex solid in ferromagnetic superconductors. Using a rigorous thermodynamic argument, we show that in the idealized case of vanishing crystalline pinning anisotropy the long-wavelength tilt modulus of such a vortex solid vanishes identically, as guaranteed by the underlying rotational invariance. The vanishing of the tilt modulus means that, to lowest order, the associated tension elasticity is replaced by the softer, curvature elasticity. The effect of this is to make the spontaneous vortex solid qualitatively more susceptible to the disordering effects of thermal fluctuations and random pinning. We study these effects, taking into account the nonlinear elasticity, that, in three dimensions, is important at sufficiently long length scales, and showing that a “columnar elastic glass” phase of vortices results. This phase is controlled by a previously unstudied zero-temperature fixed point, and it is characterized by elastic moduli that have universal strong wave-vector dependence out to arbitrarily long length scales, leading to non-Hookean elasticity. We argue that, although translationally disordered for weak disorder, the columnar elastic glass is stable against the proliferation of dislocations and is, therefore, a topologically ordered elastic glass. As a result, the phenomenology of the spontaneous vortex state of isotropic magnetic superconductors differs qualitatively from a conventional, external-field-induced mixed state. For example, for weak external fields H , the magnetic induction scales universally like B(H)˜B(0)+cHα , with α≈0.72 .
Shapiro, A. )
1992-12-01
Vertically sheared airflow over semi-infinite barriers is investigated with a simple hydrodynamical model. The idealized flow is steady, two-dimensional, neutrally buoyant, and inviscid, bounded on the bottom by a semi-infinite impermeable barrier and on the top by a rigid tropopause lid. With attention further restricted to an exponentially decreasing wind shear, the equations of motion (Euler's equations) reduce, without approximation, to a modified Poisson equation for a pseudo streamfunction and a formula for the Exner function. The free parameters characterizing the model's environment are the tropopause height, the density scale height, the wind speed at ground level, and the wind speed at tropopause level. Additional parameters characterize the barrier geometry. Exact solutions of the equations of motion are obtained for semi-infinite plateau barriers and for a barrier qualitatively resembling the shallow density current associated with some thunderstorm outflows. These solutions are noteworthy in that the reduction of a certain nondimensional shear parameter (through negative values) results in greater vertical parcel displacements over the barrier despite a corresponding reduction in the vertical velocity. This steepening tendency culminates in overturning motions associated with both upstream and down-stream steering levels. In this latter case the low-level inflow impinging on the barrier participates in a mixed jump and overturning updraft reminiscent of updrafts simulated in numerical convective models. Conversely, for large values of the nondimensional shear parameter, parcels undergo small vertical parcel displacements over the barrier despite large vertical velocities. This latter behavior may account for the finding that strong convergence along the leading edge of storm outflows does not always trigger deep convection even in unstable environments.
Traveling waves for the FitzHugh-Nagumo system on an infinite channel
NASA Astrophysics Data System (ADS)
Chen, Chao-Nien; Chen, Chiun-Chuan; Huang, Chih-Chiang
2016-09-01
We are concerned with the traveling wave solutions for the FitzHugh-Nagumo system on an infinite channel. Based on a variational formulation in which a non-local term depends on a parameter, the speed of a traveling wave can be selected out. Furthermore, to show the existence of a traveling wave solution with such a speed, we seek a minimizer subject to a constraint. In the way of solving the variational problem, we apply a truncation technique to the nonlocal term to obtain a minimizer located in a bounded invariant region.
NASA Astrophysics Data System (ADS)
Miller, William H.; Shi, Shenghua
1981-09-01
It is shown how two popular approximate dynamical models—the semiclassical perturbation (SCP) approximation and the infinite order sudden (IOS) approximation—can be combined in a consistent way that includes the correct features of both. Application of this unified SCP-IOS approximation to the reaction path Hamiltonian model of Miller, Handy, and Adam [J. Chem. Phys. 72, 99 (1980)] leads to extremely simple, explicit formulas for the reactive S matrix, product state distrubutions, etc., which can be readily applied to polyatomic systems. Initial numerical tests on a simple model problem indicate that the model is of useful accuracy.
Electromagnetic interactions and the relativistic infinite-component wave equation for hydrogen
Gerry, C.C.; Inomata, A.
1981-01-15
We examine the problem of incorporating external electromagnetic interactions into the theory of the relativistic infinite-component SO(4,2) wave equation for the hydrogen atom proposed by Barut. We introduce the simplest set of covariant interaction terms modeled after the nonrelativistic SO(4,2) theory as an alternative to the complicated array of terms obtained from the formal replacement P/sub ..mu../..-->..P/sub ..mu../-eA/sub ..mu../. Using a covariant perturbation theory, we calculate the electric and magnetic polarizabilities of the ground state of the hydrogen atom in uniform fields and show that they have the correct nonrelativistic reductions.