NASA Astrophysics Data System (ADS)
Stojanovi?, Vladimir
2015-11-01
Geometrically nonlinear vibrations of a Timoshenko beam resting on a nonlinear Winkler and Pasternak elastic foundation with variable discontinuity are investigated in this paper. A p-version finite element method is developed for geometric nonlinear vibrations of a shear deformable beam resting on a nonlinear foundation with discontinuity. The elastic foundation has cubic nonlinearity with the shearing layer. In the study the p-element which comes from the use of explored special displacement shape functions for damaged beams is used and applied to a model with nonlinear foundation. The novelty of the present study lies in the easy generalisation of the approach of natural frequencies, general mode shapes (transverse and rotations of cross sections), and maximal deflections in nonlinear steady state vibrations of the shear deformable beam for any size and location of discontinuity of the nonlinear elastic support. A new set of nonlinear partial differential equations is developed, and they are solved in the time domain using the Newmark method for obtaining the amplitudes and deformed shapes of a beam in the steady state forced vibration regime. The present work consists of the comparison of the results with various stiffnesses of nonlinear elastic supports of the Winkler and Pasternak type.
NASA Astrophysics Data System (ADS)
Rahmouni, A.; Beidouri, Z.; Benamar, R.
2013-09-01
The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, co
System level simulation of a micro resonant accelerometer with geometric nonlinear beams
NASA Astrophysics Data System (ADS)
Wenlong, Jiao; Weizheng, Yuan; Honglong, Chang
2015-10-01
Geometric nonlinear behaviors of micro resonators have attracted extensive attention of MEMS (micro-electro-mechanical systems) researchers, and MEMS transducers utilizing these behaviors have been widely researched and used due to the advantages of essentially digital output. Currently, the design of transducers with nonlinear behaviors is mainly performed by numerical method and rarely by system level design method. In this paper, the geometric nonlinear beam structure was modeled and established as a reusable library component by system level modeling and simulation method MuPEN (multi port element network). A resonant accelerometer was constructed and simulated using this model together with MuPEN reusable library. The AC (alternating current) analysis results of MuPEN model agreed well with the results of architect model and the experiment results shown in the existing reference. Therefore, we are convinced that the beam component based on MuPEN method is valid, and MEMS system level design method and related libraries can effectively model and simulate transducers with geometric nonlinear behaviors if appropriate system level components are available.
NASA Astrophysics Data System (ADS)
Torabizadeh, Mohammad Amin
2013-07-01
A new method is developed to derive equilibrium equations of Metal-Ceramic beams based on first order shear deformation plate theory which is named first order shear deformation beam theory2(FSDBT2). Equilibrium equations obtained from conventional method (FSDBT1) is compared with FSDBT2 and the case of cylindrical bending of Metal-Ceramic composite plates for non-linear thermomechanical deformations and various loadings and boundary conditions. These equations are solved by using three different methods (analytical, perturbation technique and finite element solution). The through-thickness variation of the volume fraction of the ceramic phase in a Metal-Ceramic beam is assumed to be given by a power-law type function. The non-linear strain-displacement relations in the von-Kármán sense are used to study the effect of geometric non-linearity. Also, four other representative averaging estimation methods, the linear rule, Mori-Tanaka, Self-Consistent and Wakashima-Tsukamoto schemes, by comparing with the power-law type function are also investigated. Temperature distribution through the thickness of the beams in thermal loadings is obtained by solving the one-dimensional heat transfer equation. Finally it is concluded that for Metal-Ceramic composites, these two theories result in identical static responses. Also the displacement field and equilibrium equations in the case of cylindrical bending of Metal-Ceramic plates are the same as those supposed in FSDBT2.
Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.
Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor
2013-08-01
The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation. PMID:23927186
Mahaffey, Patrick Brian
2013-08-07
theory and analysis that considers the nonlinear effects on the buckling response of beams. This thesis contains three new developments: (1) the conventional beam theories are generalized by accounting for nonlinear terms arising from ?zz and ?xz...
Nonlinear combining of laser beams
Lushnikov, Pavel M
2014-01-01
We propose to combine multiple laser beams into a single diffraction-limited beam by the beam self-focusing (collapse) in the Kerr medium. The beams with the total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with the Kerr nonlinearity. Random fluctuations during propagation eventually trigger strong self-focusing event and produce diffraction-limited beam carrying the critical power.
Nonlinear combining of laser beams.
Lushnikov, Pavel M; Vladimirova, Natalia
2014-06-15
We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-limited beam carrying the critical power. PMID:24978503
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations
Hunter, John K.
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometri- cal optics theories for variational wave equations. c 2000 Wiley Periodicals, Inc. 1 Introduction Geometrical optics1
A Geometrically Exact Active Beam Theory for Multibody Dynamics Simulation
Yu, Wenbin
A Geometrically Exact Active Beam Theory for Multibody Dynamics Simulation Dong Han, Wenbin Yu.); +1-435-7972417 (fax) #12;A Geometrically Exact Active Beam Theory for Multibody Dynamics Simulation 2-4130, USA E-mail: wenbin.yu@usu.edu Abstract. A geometrically exact beam theory suitable for dynamic
On simple and accurate finite element models for nonlinear bending analysis of beams and plates
Urthaler Lapeira, Yetzirah Yksya
2007-09-17
This study is concerned with the development of simple and accurate alternative finite element models to displacement finite element models for geometrically nonlinear bending analysis of beams and plates. First, a unified corotational beam finite...
Geometrical approach to gaussian beam propagation.
Laures, P
1967-04-01
The curvature of the wavefront and the spot size of a propagating Gaussian beam may be determined from simple geometrical transformations of the lateral foci. The analysis starts from the construction of the lateral foci in the case of a spherical Fabry-Perot. Then the cases of Gaussian beam propagation through media with different refractive indices, lenses, and simple optical systems are treated. Constructions show how propagation in the image space is readily determined in each case. This analysis is the generalization of the technique outlined by Deschamps and Mast. The geometrical constructions developed for simple cases are applied to the design of some special cases of interest in laser optics: cavities by a lens, laser zoom telescope, and ring cavity. PMID:20057839
NASA Astrophysics Data System (ADS)
Fu, Yiming; Chen, Yang; Zhong, Jun
2014-10-01
The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-? method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.
Large Deviations for Stochastic Nonlinear Beam Equations
Sidorov, Nikita
equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations). Key, and the nonlinear operator B(u) = 1 0 |xu|2 dx 2 xu. The mathematical model for the nonlinear penal vibrationLarge Deviations for Stochastic Nonlinear Beam Equations Tusheng Zhang First version: 31 December
Nonlinear Geometric Effects in Bioinspired Multistable Structures
NASA Astrophysics Data System (ADS)
Chen, Zi; Guo, Qiaohang; Chu, Kevin; Shillig, Steven; Li, Chi; Chen, Wenzhe; Taber, Larry; Holmes, Douglas
2013-03-01
Nature features many thin shell structures with spontaneous curvatures, where mechanical instabilities play important roles in the morphogenesis and functioning of the organisms. However, the large deformation and instability phenomena of shells due to geometric nonlinearity, which often arise in morphogenesis and nanofabrication, remain incompletely understood. Here, we create spontaneously curved shapes with pre-strains in tabletop experiments, and study their instabilities with a minimal theory based on linear elasticity. The development of such theoretical and experimental approaches will promote quantitative understanding of the morphogenesis of growing soft tissues, and meet the emergent needs of designing stretchable electronics, artificial muscles and bio-inspired robots. Zi Chen and Qiaohang Guo contributed equally. This work was supported by National Science Foundation of China (No. 11102040), American Academy of Mechanics Founder's Award, and Society in Science - Branco Weiss fellowship, administered by ETH.
Nonlinear Geometric Optics for Short Pulses Deborah ALTERMAN \\Lambda
Rauch, Jeffrey
Nonlinear Geometric Optics for Short Pulses Deborah ALTERMAN \\Lambda Department of Applied geometric optics it is proved that there is a family of exact solutions u ffl exact such that u ffl approx effects are important before diffractive effects. This scaling is called the scaling of geometric optics
GEOMETRIC-OPTICS FOR NONLINEAR CONCENTRATING WAVES IN FOCUSING AND
Ibrahim, Slim
GEOMETRIC-OPTICS FOR NONLINEAR CONCENTRATING WAVES IN FOCUSING AND NON-FOCUSING TWO GEOMETRIES SLIM geometrical optics of the critical wave equa- tion with variable coefficients, is reduced to linear geometrical optics combined with wave operators for the critical wave equation with coef- ficients fixed
NASA Technical Reports Server (NTRS)
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Gain scheduling for geometrically nonlinear flexible space structures
Yung, Jeremy Hoyt, 1971-
2002-01-01
A gain-scheduling approach for the control of geometrically nonlinear structures is developed. The objective is to improve performance over current linear design techniques that are applied to the same control problem. The ...
Laws of wave processes in a geometrically nonlinear elastic body
NASA Astrophysics Data System (ADS)
Chertova, Nadezhda V.
2015-10-01
Within the approximate model of a geometrically nonlinear elastic body accurate analytical solutions have been obtained in the plane harmonic wave form. These solutions describe the interaction between longitudinal and transversal waves propagating in the considered body and show that the character of wave processes depends on the mode of an excited wave. Laws of wave reflection on the free surface of the geometrically nonlinear elastic body are investigated for the case of normal incidence of a primary wave polarized in different ways.
GEOMETRIC OPTIMIZATION OF RADIATIVE ENCLOSURES THROUGH NONLINEAR PROGRAMMING
Morton, David
GEOMETRIC OPTIMIZATION OF RADIATIVE ENCLOSURES THROUGH NONLINEAR PROGRAMMING K. J. Daun, J. R, Texas, USA This article introduces a methodology for designing the geometry of diffuse-walled radiant enclosures through nonlinear programming. In this application, the enclosure is re- presented parametrically
Supercritical geometric optics for nonlinear Schrodinger equations
Thomas Alazard; Rémi Carles
2007-04-27
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.
Multiphase weakly nonlinear geometric optics for Schrodinger equations
Rémi Carles; Eric Dumas; Christof Sparber
2009-02-17
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation on the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrodinger equation on the torus in negative order Sobolev spaces.
User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1984-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.
Nonlinear geometric effects in mechanical bistable morphing structures.
Chen, Zi; Guo, Qiaohang; Majidi, Carmel; Chen, Wenzhe; Srolovitz, David J; Haataja, Mikko P
2012-09-14
Bistable structures associated with nonlinear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects on bistability remain elusive. We demonstrate, through both theoretical analysis and tabletop experiments, that two dimensionless parameters control bistability. Our work classifies the conditions for bistability, and extends the large deformation theory of plates and shells. PMID:23005634
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
NASA Technical Reports Server (NTRS)
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
Nonlinear normal modes in an intrinsic theory of anisotropic beams
NASA Astrophysics Data System (ADS)
Palacios, Rafael
2011-04-01
Nonlinear normal modes in nonlinear oscillations of beams are derived from intrinsic equations, that is, using velocities and strains as primary degrees of freedom. Displacements and rotations are thus not system states but are instead obtained using the propagation of the local beam material reference frames, as in rigid-body dynamics. It is shown that the intrinsic variables suffice to describe the free vibrations of the beam. The approach does not need assumptions in the material properties, i.e., it is valid for general anisotropic behavior, or the beam kinematics, i.e., it is based on Cosserat's exact geometrical description of the deformable curve. Furthermore, the nonlinear modal equations in intrinsic coordinates are obtained from integrals involving only products of the mode shapes and known coefficients. Using this description, the nonlinear normal modes are sought through an asymptotic approximation to the invariant manifolds that define them in the space of intrinsic modal coordinates. Particular cases of homogeneous isotropic and composite cantilever beams are finally used to exemplify the approach.
Nonlinear flap-lag axial equations of a rotating beam
NASA Technical Reports Server (NTRS)
Kaza, K. R. V.; Kvaternik, R. G.
1977-01-01
It is possible to identify essentially four approaches by which analysts have established either the linear or nonlinear governing equations of motion for a particular problem related to the dynamics of rotating elastic bodies. The approaches include the effective applied load artifice in combination with a variational principle and the use of Newton's second law, written as D'Alembert's principle, applied to the deformed configuration. A third approach is a variational method in which nonlinear strain-displacement relations and a first-degree displacement field are used. The method introduced by Vigneron (1975) for deriving the linear flap-lag equations of a rotating beam constitutes the fourth approach. The reported investigation shows that all four approaches make use of the geometric nonlinear theory of elasticity. An alternative method for deriving the nonlinear coupled flap-lag-axial equations of motion is also discussed.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.
1993-01-01
This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited.
Weakly Nonlinear Geometric Optics for Hyperbolic Systems of Conservation Laws
Gui-Qiang Chen; Wei Xiang; Yongqian Zhang
2012-12-22
We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and corresponding characteristic fields to be linearly degenerate. The approach is based on our careful construction of more accurate auxiliary approximation to weakly nonlinear geometric optics, the properties of wave front-tracking approximate solutions, the behavior of solutions to the approximate asymptotic equations, and the standard semigroup estimates. To illustrate this approach more clearly, we focus first on the Cauchy problem for the hyperbolic systems with compact support initial data of small bounded variation and establish that the $L^1-$estimate between the entropy solution and the geometric optics expansion function is bounded by $O(\\varepsilon^2)$, {\\it independent of} the time variable. This implies that the simpler geometric optics expansion functions can be employed to study the behavior of general entropy solutions to hyperbolic systems of conservation laws. Finally, we extend the results to the case with non-compact support initial data of bounded variation.
VALIDITY OF NONLINEAR GEOMETRIC OPTICS FOR ENTROPY SOLUTIONS OF MULTIDIMENSIONAL SCALAR
Rascle, Michel
VALIDITY OF NONLINEAR GEOMETRIC OPTICS FOR ENTROPY SOLUTIONS OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS GUIÂQIANG CHEN ST â?? EPHANE JUNCA MICHEL RASCLE Abstract. Nonlinear geometric optics is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation
VALIDITY OF NONLINEAR GEOMETRIC OPTICS FOR ENTROPY SOLUTIONS OF MULTIDIMENSIONAL SCALAR
Junca, StĂ©phane
VALIDITY OF NONLINEAR GEOMETRIC OPTICS FOR ENTROPY SOLUTIONS OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS GUI-QIANG CHEN STÂ´EPHANE JUNCA MICHEL RASCLE Abstract. Nonlinear geometric optics is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation
Nonlinear analysis of a simply-supported composite beam under random excitations
Eslami, H.; Gudmundson, S.
1994-12-31
Nonlinear analysis of composite laminated beams subjected-to random excitation is studied here. The forcing function is a stationary Gaussian type random excitation. The governing partial differential equations of motion are obtained by considering the Von Karman type geometrical nonlinearity. These partial differential equations are transformed into nonlinear Ordinary differential equations of Duffing type by applying the Galerkin`s method. The resulting nonlinear ODE are first solved by using the equivalent linearization method and the numerical integration (Runge Kutta) method. The equations are reduced to that of isotropic beam and results are also compared with the previously published ones.
Nonlinear Bessel vortex beams for applications
NASA Astrophysics Data System (ADS)
Arnold, C. L.; Akturk, S.; Mysyrowicz, A.; Jukna, V.; Couairon, A.; Itina, T.; Stoian, R.; Xie, C.; Dudley, J. M.; Courvoisier, F.; Bonanomi, S.; Jedrkiewicz, O.; Di Trapani, P.
2015-05-01
We investigate experimentally and numerically the nonlinear propagation of intense Bessel-Gauss vortices in transparent solids. We show that nonlinear Bessel-Gauss vortices preserve all properties of nonlinear Bessel-Gauss beams while their helicity provides an additional control parameter for single-shot precision micro structuring of transparent solids. For sufficiently large cone angle, a stable hollow tube of intense light is formed, generating a plasma channel whose radius and density are increasing with helicity and cone angle, respectively. We assess the potential of intense Bessel vortices for applications based on the generation of hollow plasma channels.
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Nonlinear evolution of the auroral electron beam
NASA Technical Reports Server (NTRS)
Maggs, James E.
1989-01-01
The nonlinear spatial evolution, from the source to the atmosphere, of the auroral electron beam and the beam-generated electrostatic whistler noise was studied, calculating changes in beam parameters from equations for the conservation of total particle and wave energy and momentum flux density. Wave power fluxes were calculated by numerically integrating the wave kinetic equations, and the levels of beam-generated noise were determined by using thermal levels of Cerenkov radiation as a source. It was found that beam parameters evolve on ionospheric scale lengths, and their positive slope feature in velocity space is maintained over altitudes measured in thousands of kilometers of altitude, even though they can generate wave energy density fluxes sufficient to modify the ionospheric density profile.
Spiraling elliptic beam in nonlocal nonlinear media.
Liang, Guo; Guo, Qi; Cheng, Wenjing; Yin, Naiqiang; Wu, Ping; Cao, Hongmin
2015-09-21
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams. PMID:26406663
Beams on nonlinear elastic foundation
Lukkassen, Dag; Meidell, Annette
2014-12-10
In order to determination vertical deflections and rail bending moments the Winkler model (1867) is often used. This linear model neglects several conditions. For example, by using experimental results, it has been observed that there is a substantial increase in the maximum rail deflection and rail bending moment when considering the nonlinearity of the track support system. A deeper mathematical analysis of the models is necessary in order to obtain better methods for more accurate numerical solutions in the determination of deflections and rail bending moments. This paper is intended to be a small step in this direction.
Geometrically nonlinear analysis of layered composite plates and shells
NASA Technical Reports Server (NTRS)
Chao, W. C.; Reddy, J. N.
1983-01-01
A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.
NASA Astrophysics Data System (ADS)
Wang, Dongwei
Recent research and development of adaptive materials, smart structures and structronic systems have opened a new era to aerospace and structural engineering. Effective control of these intelligent structures and systems using piezoelectric materials can enhance operation precision, accuracy and reliability. This research is to investigate the dynamics, vibration sensing and control of the geometrically nonlinear distributed piezothermoelastic structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Based on the layerwise constant shear angle theory, the curved hexahedral and triangular piezothermoelastic shell elements are proposed. The generic finite element formulations for vibration sensing and control analysis of nonlinear piezothermoelastic shell structures are derived based on the total Lagrangian virtual work principle. Dynamic system equations, equations of electric potential outputs, and feedback control forces are derived and discussed. The modified Newton-Raphson method is used for efficient dynamic analysis of the nonlinear piezothermoelastic structural systems. Different control algorithms are implemented. The feedback control forces generated from the distributed actuator can effectively enhance system damping and suppress system vibration via proper feedback control techniques. Comprehensive case studies are performed to evaluate the accuracy of the newly developed piezothermoelastic shell elements and to validate the finite element code. Dynamics and vibration sensing/control of nonlinear piezothermoelastic beam and plate systems are analyzed. Distributed piezoelectric films placed on the beam and plate structures respectively serving as sensor and actuators are discussed. The effect of geometric nonlinearity is to stiffen the beam and plate structures and the control effect becomes worse when geometric nonlinearity becomes significant. It shows that negative velocity control scheme is effective to dynamically and electrically induced oscillations. However, it is not effective to the vibrations induced by the steady-state thermal field. Accordingly, one additional control voltage is required to control thermally induced offset. The non-constant curvature structures such as conical shells and toroidal shells are also investigated in linear analysis. Various actuator layouts for these shell structures are proposed and the control effectiveness of the actuators is evaluated. It is suggested that an in-depth understanding of shell dynamics and dominating modes is a must in the effective design and layout of distributed actuators to maximize the distributed control effects.
Temperature modes for nonlinear Gaussian beams.
Myers, Matthew R; Soneson, Joshua E
2009-07-01
In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions. PMID:19603899
Active suppression of nonlinear composite beam vibrations by selected control algorithms
NASA Astrophysics Data System (ADS)
Warminski, Jerzy; Bochenski, Marcin; Jarzyna, Wojciech; Filipek, Piotr; Augustyniak, Michal
2011-05-01
This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab-Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric " L-shape" beam system.
Geometric Nonlinear Finite Element Analysis of Active Fibre Composite Bimorphs
NASA Astrophysics Data System (ADS)
Kernaghan, Robert
Active fibre composite-actuated bimorphic actuators were studied in order to measure deflection performance. The deflection of the actuators was a function of the actuating electric potential applied to the active material as well as the magnitude of the axial preload applied to the bimorphic structure. This problem required the use of geometric nonlinear modeling techniques. Geometric nonlinear finite element analysis was undertaken to determine the deflection performance of Macro Fibre Composite (MFC)- and Hollow Active Fibre (HAFC)-actuated bimorphic structures. A physical prototype MFC-actuated bimorphic structure was manufactured in order to verify the results obtained by the finite element analysis. Theses analyses determined that the bimorphic actuators were capable of significant deflection. The analyses determined that the axial preload of the bimorphic actuators significantly amplified the deflection performance of the bimorphic actuators. The deflection performance of the bimorphic actuators suggest that they could be candidates to act as actuators for the morphing wing of a micro unmanned air vehicle.
Nonlinear wave scattering and electron beam relaxation
NASA Technical Reports Server (NTRS)
Muschietti, L.; Dum, C. T.
1991-01-01
The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated through a numerical code based on kinetic equations. The code encompasses the quasi-linear wave-electron interaction and wave-wave scattering off ion clouds. Ions with velocities 2 nu sub i (nu sub i being the ion thermal velocity) are found to be the most efficient for scattering the Langmuir waves off their polarization clouds. The transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to usual estimates. The changes produced in the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum. In a late phase the classic condensate K of about 0 is depleted, with the formation of a new condensate in resonance with the flat-topped beam distribution, which follows from the fact that the mere presence of the beam electrons creates a minimum in the frequency-wave-number relation. For strong and slow beams, the predictions of the code are found to be in excellent agreement with the results of the particle simulation if a dispersion relation that includes the beam is used.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.; Turner, Travis L.; Robinson, Jay H.; Rizzi, Stephen A.
1999-01-01
In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear sti ness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures.
Nonlinear bending models for beams and plates
Antipov, Y. A.
2014-01-01
A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960
Nonlinear bending models for beams and plates.
Antipov, Y A
2014-10-01
A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler-Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960
NASA Astrophysics Data System (ADS)
Song, Pengchao
Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software. The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.
Galvez, Enrique J. "Kiko"
Geometric Phase Associated with Mode Transformations of Optical Beams Bearing Orbital Angular measurements of a new geometric phase acquired by optical beams carrying orbital angular momentum. This phase identified as a potential means of doing quantum computation [6,7]. A geometric phase acquired by an optical
FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS) FOR GEOMETRICALLY NONLINEAR ELASTICITY
McCormick, Steve
FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS) FOR GEOMETRICALLY NONLINEAR ELASTICITY T. A. MANTEUFFEL, S-squares (FOSLS) method to approximate the solution to the equations of geometrically nonlinear elasticity in two. The primary goal in the study of elasticity is to model the deformation of an elastic body under applied
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations
Giuseppe Ali; John K. Hunter
2005-11-02
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly nonlinear geometrical optics for the Einstein equations with nonlinear geometrical optics theories for variational wave equations.
Beam stability and nonlinear dynamics. Summary report
Parsa, Z.
1996-12-31
A {open_quotes}Beam Stability and Nonlinear Dynamics{close_quotes} Symposium was held October 3-5, 1996 at the Institute for Theoretical Physics (ITP) in Santa Barbara. This was one of the 3 symposia hosted by the ITP and supported by its sponsor, the National Science Foundation, as part of our {open_quotes}New Ideas for Particle Accelerators{close_quotes} program. The symposia was organized and chaired by Dr. Zohreh Parsa of ITP/ Brookhaven National Laboratory. The purpose of this symposium was to deal with some of the fundamental theoretical problems of accelerator physics by bringing together leaders from accelerator physics communities, mathematics, and other fields of physics. The focus was on nonlinear dynamics and beam stability. The symposium began with some defining talks on relevant mathematical topics such as single-particle Hamiltonian dynamics, chaos, and new ideas in symplectic integrators. The physics topics included single-particle and many-particle dynamics. These topics concern circular accelerators in which particles circulate for a very large number of turns as well as linear accelerators where space charge and wakefields induced in accelerating cavities play a strong role. A major question is to determine the best model for numerical simulations in order to accurately reproduce behavior of beams in real accelerators and to predict long-term or long distance stability. Comparison with experiment is recognized as an important tool in improving models.
Beam stability & nonlinear dynamics. Formal report
Parsa, Z.
1996-12-31
his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.
Necklace Beam Generation in Nonlinear Colloidal Engineered Media
Silahli, Salih Z; Litchinitser, Natalia M
2015-01-01
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes as supercontinuum generation, light filamentation, and rogue waves. However, practical realization of these phenomena in the majority of available nonlinear media still relies on high-intensity optical beams. Here, we analytically and numerically show the possibility of necklace beam generation originating from low-intensity spatial modulational instability of vortex beams in engineered soft-matter nonlinear media.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.
NASA Astrophysics Data System (ADS)
Capiez-Lernout, E.; Soize, C.; Mbaye, M.
2015-11-01
This paper deals with the dynamical analysis and uncertainty quantification of a mistuned industrial rotating integrally bladed disk, for which the operating regime under consideration takes into account the nonlinear geometrical effects induced by large displacements and deformations. First, a dedicated mean nonlinear reduced-order model of the tuned structure is explicitly constructed using the finite element method. The random nature of the mistuning is then modeled by using the nonparametric probabilistic approach extended to the nonlinear geometric context. Secondly, a detailed dynamic analysis and uncertainty propagation are conducted in order to quantify the impact of the nonlinear geometrical effects on the mistuned structure. The results show that the dynamic amplification in the frequency band is significant outside the frequency band of excitation due to the presence of geometric nonlinearities combined with mistuning effects.
Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions
NASA Astrophysics Data System (ADS)
Ma, NiuJing; Wang, RongHui; Han, Qiang; Lu, YiGang
2014-08-01
An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.
Nonlinear diffraction from high-order Hermite-Gauss beams.
Kalinowski, Ksawery; Shapira, Asia; Libster-Hershko, Ana; Arie, Ady
2015-01-01
We investigate experimentally and theoretically the nonlinearly diffracted second harmonic light from the first-order Hermite-Gauss beam. We investigate the cases of loosely and tightly focused beams in a periodically poled lithium niobate crystal in the temperature range near the birefringent phase matching. Unlike the case of fundamental Gaussian beam, the nonlinear diffracted beam is spatially structured. Its shape depends on the focusing conditions and on the crystal temperature. Furthermore, for the case of tight focusing, the diffracted beam structure depends on the beam's position with respect to the domain wall. PMID:25531596
Anti-diffracting beams through the diffusive optical nonlinearity.
Di Mei, F; Parravicini, J; Pierangeli, D; Conti, C; Agranat, A J; DelRe, E
2014-12-15
Anti-diffraction is a theoretically predicted nonlinear optical phenomenon that occurs when a light beam spontaneously focalizes independently of its intensity. We observe anti-diffracting beams supported by the peak-intensity-independent diffusive nonlinearity that are able to shrink below their diffraction-limited size in photorefractive lithium-enriched potassium-tantalate-niobate (KTN:Li). PMID:25607093
Geometric studies on variable radius spiral cone-beam scanning Yangbo Yea)
Ye, Yangbo
spiral cone-beam scanning is given in the context of electron-beam CT/micro-CT. Then, necessary Most distinctively, electron-beam CT scan- ners allow scan times down to 50 ms. In the EBCT designGeometric studies on variable radius spiral cone-beam scanning Yangbo Yea) and Jiehua Zhu
A Differential Geometric Approach to Nonlinear Filtering : the Projection Filter \\Lambda
LeGland, François
A Differential Geometric Approach to Nonlinear Filtering : the Projection Filter \\Lambda Damiano filters with finite di mensional filters, using the differential geometric ap proach to statistics. We define rigorously the projection filter in the case of exponential families. We propose a convenient
NASA Astrophysics Data System (ADS)
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to the continual generation of the assembled internal load vector, tangent stiffness matrix, and deformation-dependent external load vectors. Rather, for small deformations, the appropriate deformation-independent stiffness matrices and load vectors to be used for all times can be determined once at the start of the analysis. Of course, the time-dependent viscoelastic effects need to be correctly taken into account in both types of analyses. The present work details both geometrically-linear and nonlinear triangular flat shell formulations for linear viscoelastic composites. The accuracy and capability of the formulations are shown through a range of numerical examples involving beams, rings, plates, and shells.
NASA Astrophysics Data System (ADS)
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide ef?cient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Nonlinear system identification of frictional effects in a beam with a bolted joint connection
NASA Astrophysics Data System (ADS)
Eriten, Melih; Kurt, Mehmet; Luo, Guanyang; Michael McFarland, D.; Bergman, Lawrence A.; Vakakis, Alexander F.
2013-08-01
We perform nonlinear system identification (NSI) of the effects of frictional connections in the dynamics of a bolted beam assembly. The methodology utilized in this work combines experimental measurements with slow-flow dynamic analysis and empirical mode decomposition, and reconstructs the dynamics through reduced-order models. These are in the form of single-degree-of-freedom linear oscillators (termed intrinsic modal oscillators—IMOs) with forcing terms derived directly from the experimental measurements through slow-flow analysis. The derived reduced order models are capable of reproducing the measured dynamics, whereas the forcing terms provide important information about nonlinear damping effects. The NSI methodology is applied to model nonlinear friction effects in a bolted beam assembly. A 'monolithic' beam with identical geometric and material properties is also tested for comparison. Three different forcing (energy) levels were considered in the tests in order to study the energy-dependencies of the damping nonlinearities induced in the beam from the bolted joint. In all cases, the NSI methodology employed was successful in identifying the damping nonlinearities, their spatial distributions and their effects of the vibration modes of the structural component.
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.; Hodges, Dewey H.
1987-01-01
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.; Hodges, Dewey H.
1987-01-01
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyze the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformation. The correlation is excellent in all cases.
Hybrid Analytical Technique for Nonlinear Vibration Analysis of Thin-Walled Beams
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Hadian, Jafar M.; Andersen, Carl M.
1993-01-01
A two-step hybrid analytical technique is presented for the nonlinear vibration analysis of thin-walled beams. The first step involves the generation of various-order perturbation functions using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation functions as coordinate (or approximation) functions and then computing both the amplitudes of these functions and the nonlinear frequency of vibration via a direct variational procedure. The analytical formulation is based on a form of the geometrically nonlinear beam theory with the effects of in-plane inertia, rotatory inertia, and transverse shear deformation included. The effectiveness of the proposed technique is demonstrated by means of a numerical example of thin-walled beam with a doubly symmetric I-section. The solutions obtained using a single-spatial mode were compared with those obtained using multiple-spatial modes. The standard of comparison was taken to be the frequencies obtained by the direct integration/fast Fourier transform (FFT) technique. The nonlinear frequencies obtained by the hybrid technique were shown to converge to the corresponding ones obtained by the direct integration/fast Fourier transform (FFT) technique well beyond the range of applicability of the perturbation technique. The frequencies and total strain energy of the beam were overestimated by using a single-spatial mode.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
Wave representation of geometrical laser beam trajectories in a hemiconfocal cavity
Chen, Y.F.; Jiang, C.H.; Lan, Y.P.; Huang, K.F.
2004-05-01
We use quantum-mechanics formalism to explore the formation of geometrical laser beam trajectories in a hemiconfocal cavity. Theoretical analysis reveals that laser modes localized on geometrical trajectories are formed by a frequency locking of nondegenerate transverse modes with different longitudinal orders. An experiment is performed to validate the theoretical analysis.
Limiting effects of geometrical and optical nonlinearities on the squeezing in optomechanics
P. Djorwé; S. G. Nana Engo; J. H. Talla Mbé; P. Woafo
2013-04-05
In recent experiments, the re-thermalization time of the mechanical resonator is stated as the limiting factor for quantum applications of optomechanical systems. To explain the origin of this limitation, an analytical nonlinear investigation supported by the recent successful experimental laser cooling parameters is carried out in this work. To this end, the effects of geometrical and the optical nonlinearities on the squeezing are studied and are in a good agreement with the experimental results. It appears that highly squeezed state are generated where these nonlinearities are minimized and that high nonlinearities are limiting factors to reach the quantum ground state.
Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations
NASA Astrophysics Data System (ADS)
Sotoudeh, Zahra
2011-07-01
Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.
Geometric manipulation of light : from nonlinear optics to invisibility cloaks
Hashemi, Hila
2012-01-01
In this work, we study two different manipulations of electromagnetic waves governed by macroscopic Maxwell's equations. One is frequency conversion of such waves using small intrinsic material nonlinearities. We study ...
MULTIPHASE WEAKLY NONLINEAR GEOMETRIC OPTICS FOR SCHRODINGER EQUATIONS
Sparber, Christof
-evolution of the (complex-valued) electric field amplitude of an optical pulse, it is known that the dominant nonlinear. SPARBER auto-resonant solutions of NLS given in [11] where again wave mixing phenomena are used
Nonlinear Shape Prior from Kernel Space for Geometric Active Contours
The Geometric Active Contour (GAC) framework, which utilizes image information, has proven to be quite valuable the steps for using Kernel PCA to in the GAC framework to introduce prior shape knowledge. Several framework11 (GAC) involves a parameter free representation of contours, i.e., a contour is represented
Shape Reconstruction Incorporating Multiple Non-linear Geometric Constraints
Fisher, Bob
Academic Publishers. Printed in the Netherlands. revisedpaper.tex; 6/04/2000; 15:35; p.1 #12;2 3D scanning), for instance a 3D laser scanner. In this deals with the reconstruction of 3D geometric shapes based on observed noisy 3D measurements
Geometrical Nonlinear Analysis of Composite Structures by Zigzag Theory—A Review
NASA Astrophysics Data System (ADS)
Shirbhate, N. J.; Tungikar, V. B.
2010-10-01
Advances in manufacturing technologies of composites leads to its uses as main load carrying structures which essentially need to be thick structures. Thus it is becoming increasingly important to predict accurately interlaminar variations of stresses and displacements along thickness of the composites. A review of the recent development of finite element methods for geometrical nonlinear analysis of composite structures specifically using zigzag theory is presented in this paper. The literature review is devoted to the recently developed finite elements, theories based on zigzag function for carrying out geometrical nonlinear analysis of composite structures. The future research is summarized finally.
Non-Linear Vibration of Beams with Internal Resonance by the Hierarchical Finite-Element Method
NASA Astrophysics Data System (ADS)
RIBEIRO, P.; PETYT, M.
1999-07-01
The hierarchical finite-element (HFEM) and the harmonic balance methods (HBM) are used to investigate the geometrically non-linear free and steady-state forced vibrations of uniform, slender beams. The beam analogue of von Kármán's non-linear strain-displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method, 1:3 and 1:5 internal resonances are discovered and their consequences are discussed. The convergence properties of the HFEM are analyzed and it is demonstrated that the HFEM model requires far fewer degrees of freedom than theh-version of the FEM models presented in the literature.
Geometric nonlinear analysis of microbeam under electrostatic loading
Murgude, Nikhil C.
2001-01-01
This study investigates the behavior of a microbeam subjected to electrostatic loading. Two devices, namely, a tungsten microtweezer and a clamped-clamped beam which is part of a micro-electromechanical system (MEMS), are ...
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2002-01-01
Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.
NASA Technical Reports Server (NTRS)
Raju, K. K.; Rao, G. V.; Raju, I. S.
1978-01-01
The effect of geometric nonlinearity on the free flexural vibrations of moderately thick rectangular plates is studied in this paper. Finite element formulation is employed to obtain the non-linear to linear period ratios for some rectangular plates. A conforming finite element of rectangular shape wherein the effects of shear deformation and rotatory inertia are included, is developed and used for the analysis. Results are presented for both simply supported and clamped boundary conditions.
Control and controllability of nonlinear dynamical networks: a geometrical approach
Le-Zhi Wang; Ri-Qi Su; Zi-Gang Huang; Xiao Wang; Wenxu Wang; Celso Grebogi; Ying-Cheng Lai
2015-09-23
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.
Soliton beam dynamics in parity-time symmetric nonlinear coupler
NASA Astrophysics Data System (ADS)
Aysha Muhsina, K.; Subha, P. A.
2015-07-01
This work analyzes the propagation of soliton beam in (1 + 1) D dimensional Parity-Time symmetric linear and nonlinear coupled systems. The beam dynamics in the coupled systems has been studied variationally and numerically. The beam propagation is stable when the gain/loss coefficient is less than or equal to the coupling constant. Above the phase transition point, the eigen modes become complex, which result in unstable beam propagation. The stability of the solution against small perturbation has been analyzed using linear stability analysis.
NASA Astrophysics Data System (ADS)
Neto, Alfredo Gay; Martins, Clóvis A.; Pimenta, Paulo M.
2014-01-01
In offshore applications there are elements that can be modeled as long beams, such as umbilical cables, flexible and rigid pipes and hoses, immersed in the sea water, suspended from the floating unit to the seabed. The suspended part of these elements is named "riser" and is subjected to the ocean environment loads, such as waves and sea current. This work presents a structural geometrically-exact 3D beam model, discretized using the finite element method for riser modeling. An updated Lagrangian framework for the rotation parameterization has been used for the description of the exact kinematics. The goal is to perform a complete static analysis, considering the oceanic loads and the unilateral contact with the seabed, extending the current standard analysis for situations in which very large rotations occurs, in particular, large torsion. Details of the nonlinear 3D model and loads from oceanic environment are discussed, including the contact unilateral constraint.
Linear and nonlinear methods for detecting cracks in beams
Prime, M.B.; Shevitz, D.W.
1995-12-31
This paper presents experimental results from the vibration of a polycarbonate beam containing a crack that opens and closes during vibration. Several techniques were employed to detect and locate the crack making use of the nonlinearity. ``Harmonic mode shapes`` proved to be more sensitive to damage than conventional mode shapes. Instantaneous frequency and time-frequency methods also showed clear signatures for the crack. The results indicate that nonlinearities may provide increased capabilities for structural damage detection and location.
A nonlinear theory for spinning anisotropic beams using restrained warping functions
NASA Technical Reports Server (NTRS)
Ie, C. A.; Kosmatka, J. B.
1993-01-01
A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
A nonlinear theory for spinning anisotropic beams using restrained warping functions
NASA Astrophysics Data System (ADS)
Ie, C. A.; Kosmatka, J. B.
1993-04-01
A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Li, Nianbei; Ren, Jie
2014-01-01
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668
Propagation of anomalous vortex beams in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Dai, Zhiping; Yang, Zhenjun; Zhang, Shumin; Pang, Zhaoguang
2015-09-01
The propagation properties of anomalous vortex beams in strongly nonlocal nonlinear media are investigated. Two equivalent analytical expressions for the evolution of anomalous vortex beams are obtained. It is found that the input power plays a key role in the beam evolutions. Selecting a proper input power, the beam width can be broadened or be compressed periodically, even it can keep invariant during propagation. The beam order and the topological charge mainly influence the intensity evolution and the phase evolution, respectively. The evolution period, the beam width, the phase distribution and the intensity distribution are discussed in detail. The results can also be generalized to other equivalent physical systems, such as an optical fractional Fourier transform system or a medium with a quadratic graded refractive index distribution.
Finite rotation and nonlinear beam kinematics
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.
1987-01-01
Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.
Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion
NASA Astrophysics Data System (ADS)
McBride, A. T.; Javili, A.; Steinmann, P.; Bargmann, S.
2011-10-01
Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.
Geometric Nonlinear Computation of Thin Rods and Shells
NASA Astrophysics Data System (ADS)
Grinspun, Eitan
2011-03-01
We develop simple, fast numerical codes for the dynamics of thin elastic rods and shells, by exploiting the connection between physics, geometry, and computation. By building a discrete mechanical picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting, we produce numerical codes that not only are consistent in a classical sense, but also reproduce qualitative, characteristic behavior of a physical system----such as exact preservation of conservation laws----even for very coarse discretizations. As two recent examples, we present discrete computational models of elastic rods and shells, with straightforward extensions to the viscous setting. Even at coarse discretizations, the resulting simulations capture characteristic geometric instabilities. The numerical codes we describe are used in experimental mechanics, cinema, and consumer software products. This is joint work with Miklós Bergou, Basile Audoly, Max Wardetzky, and Etienne Vouga. This research is supported in part by the Sloan Foundation, the NSF, Adobe, Autodesk, Intel, the Walt Disney Company, and Weta Digital.
A shear-shear torsional beam model for nonlinear aeroelastic analysis of tower buildings
NASA Astrophysics Data System (ADS)
Piccardo, G.; Tubino, F.; Luongo, A.
2015-08-01
In this paper, an equivalent one-dimensional beam model immersed in a three-dimensional space is proposed to study the aeroelastic behavior of tower buildings: linear and nonlinear dynamics are analyzed through a simple but realistic physical modeling of the structure and of the load. The beam is internally constrained, so that it is capable to experience shear strains and torsion only. The elasto-geometric and inertial characteristics of the beam are identified from a discrete model of three-dimensional frame, via a homogenization process. The model accounts for the torsional effect induced by the rotation of the floors around the tower axis; the macroscopic shear strain is produced by bending of the columns, accompanied by negligible rotation of the floors. Nonlinear aerodynamic forces are evaluated through the quasi-steady theory. The first aim is to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions. Furthermore, the role of aerodynamic nonlinearities on the galloping post-critical behavior is analyzed through a perturbation solution which permits to obtain a reduced one-dimensional dynamical system, capable of capturing the essential dynamics of the problem.
NASA Astrophysics Data System (ADS)
Liu, Chien-Sheng; Jiang, Sheng-Hong
2013-10-01
The measuring accuracy of conventional laser displacement sensors reduces over time as a result of geometrical fluctuations of the laser beam. Accordingly, the present study proposes a new laser displacement sensor in which the effects of geometrical fluctuations of the laser beam are minimized by means of a high-speed rotating optical diffuser. The performance of the proposed sensor is evaluated experimentally using a laboratory-built prototype. The experimental results show that the sensor achieves a higher measuring accuracy than a conventional laser displacement sensor based on a triangulation method. As a result, the proposed sensor provides an ideal solution for a wide range of automatic optical inspection and industrial applications.
NASA Astrophysics Data System (ADS)
Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan
2014-07-01
The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.
Nonlinear formation of holographic images of obscurations in laser beams
Kurapov, Alexander
the intensity and fluence of the beam at each component in the laser chain. Dam- age threats to the system can words: Nonlinear optics, self-focusing, optical damage, fusion lasers. 1. Introduction In high-peak-power with nonlin- ear properties similar to those of our high-power solid-state lasers. The computer models
Nonlinear optical catastrophe from a smooth initial beam.
Deykoon, A M; Soskin, M S; Swartzlander, G A
1999-09-01
We observed an optical cusp diffraction catastrophe with an initially smooth but elongated Gaussian beam with an aspect ratio of 2:1. Nonlinear and linear diffraction regimes account for the near-field elliptical annulus and the far-field spatially complex astroid. PMID:18073991
Heidari, Mohammad; Heidari, Ali; Homaei, Hadi
2014-01-01
The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602
Nonlinear transient neutralization theory of ion beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1975-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions. The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasi-neutral beam results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams, if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.
Anisotropic bending-torsion coupling for warping in a non-linear beam
NASA Astrophysics Data System (ADS)
Klinkel, S.; Govindjee, S.
MEMS devices made from single crystal silicon often contain rod-like structures that are operated in bending and/or torsion. The design of these devices usually relies upon simple mechanical theories that ignore the coupling between these two modes of operation. In this paper, we develop a theory that is capable of accounting for the material coupling in the bending and twisting of single crystal beams which arises from anisotropic elastic properties and apply it in selected examples to the case of silicon. The generalized Saint-Venant torsion theory, which is valid for isotropic materials, is extended to arbitrary anisotropic linear elastic materials. The anisotropic material behavior couples the bending and torsion behavior. Thus, for the geometrically linear case, we find two warping functions associated with the bending moments and one warping function which is associated with the torsion moment. These warping patterns or functions are then taken as inputs to a geometrically non-linear formulation. Due to the presence of the additional warping functions, we find the existence of non-standard bi-moment and bi-shears which play an important role under certain conditions of extreme deformations. The final complexity of the non-linear formulation dictates the usage of a numerical solution procedure for practical computations. Here we employ a finite element scheme to solve the governing equations. Example computations elucidate the importance of the coupling effects by examining beams cut from (1 0 0) type silicon wafers.
Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals
Arie, Ady
Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals to the highly asymmetric shape of nonlinear crystal in the Fourier space, these noncollinear interactions space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process
NASA Technical Reports Server (NTRS)
Hasanyan, Davresh; Librescu, Liviu; Qin, Zhanming; Ambur, Damodar R.
2006-01-01
A fully coupled magneto-thermo-elastokinetic model of laminated composite, finitely electroconductive plates incorporating geometrical nonlinearities and subjected to a combination of magnetic and thermal fields, as well as carrying an electrical current is developed, In this context. the first-order transversely shearable plate theory in conjunction with von-Karman geometrically nonlinear strain concept is adopted. Related to the distribution of electric and magnetic field disturbances within the plate, the assumptions proposed by Ambartsumyan and his collaborators are adopted. Based on the electromagnetic equations (i.e. the ones by Faraday, Ampere, Ohm, Maxwell and Lorentz), the modified Fourier's law of heat conduction and on the elastokinetic field equations, the 3-D coupled problem is reduced to an equivalent 2- D one. The theory developed herein provides a foundation for the investigation, both analytical and numerical, of the interacting effects among the magnetic, thermal and elastic fields in multi-layered thin plates made of anisotropic materials.
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don; Allen-Flowers, Jordan
2012-12-15
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.
Nonlinear analysis of a relativistic beam-plasma cyclotron instability
NASA Technical Reports Server (NTRS)
Sprangle, P.; Vlahos, L.
1986-01-01
A self-consistent set of nonlinear and relativistic wave-particle equations are derived for a magnetized beam-plasma system interacting with electromagnetic cyclotron waves. In particular, the high-frequency cyclotron mode interacting with a streaming and gyrating electron beam within a background plasma is considered in some detail. This interaction mode may possibly find application as a high-power source of coherent short-wavelength radiation for laboratory devices. The background plasma, although passive, plays a central role in this mechanism by modifying the dielectric properties in which the magnetized electron beam propagates. For a particular choice of the transverse beam velocity (i.e., the speed of light divided by the relativistic mass factor), the interaction frequency equals the nonrelativistic electron cyclotron frequency times the relativistic mass factor. For this choice of transverse beam velocity the detrimental effects of a longitudinal beam velocity spread is virtually removed. Power conversion efficiencies in excess of 18 percent are both analytically calculated and obtained through numerical simulations of the wave-particle equations. The quality of the electron beam, degree of energy and pitch angle spread, and its effect on the beam-plasma cyclotron instability is studied.
A geometrical model for the Monte Carlo simulation of the TrueBeam linac
NASA Astrophysics Data System (ADS)
Rodriguez, M.; Sempau, J.; Fogliata, A.; Cozzi, L.; Sauerwein, W.; Brualla, L.
2015-06-01
Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3??×??3 to 40??×??40 cm2 at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40??×??40 cm2 field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown.
NASA Astrophysics Data System (ADS)
Bekhoucha, Ferhat; Rechak, Said; Duigou, Laëtitia; Cadou, Jean-Marc
2015-05-01
This paper deals with the computation of backbone curves bifurcated from a Hopf bifurcation point in the framework of nonlinear free vibrations of a rotating flexible beams. The intrinsic and geometrical equations of motion for anisotropic beams subjected to large displacements are used and transformed with Galerkin and harmonic balance methods to one quadratic algebraic equation involving one parameter, the pulsation. The latter is treated with the asymptotic numerical method using Padé approximants. An algorithm, equivalent to the Lyapunov-Schmidt reduction is proposed, to compute the bifurcated branches accurately from a Hopf bifurcation point, with singularity of co-rank 2, related to a conservative and gyroscopic dynamical system steady state, toward a nonlinear periodic state. Numerical tests dealing with clamped, isotropic and composite, rotating beams show the reliability of the proposed method reinforced by accurate results.
Manipulating nonlinear optical processes with accelerating light beams
Bahabad, Alon; Murnane, Margaret M.; Kapteyn, Henry C.
2011-09-15
We show theoretically that accelerating light beams can be used to manipulate nonlinear optical processes through spatiotemporal quasi-phase-matching, allowing for unprecedented temporal and spectral shaping of the generated light. As a proof of principle, we demonstrate exquisite control over the high-order harmonic frequency conversion process, showing efficient enhancement of an extremely broad range of harmonics emitted during a selected quarter-cycle of the driving laser pulse.
NASA Astrophysics Data System (ADS)
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Douglas, David R. (York County, VA)
2012-01-10
A method of using off-axis particle beam injection in energy-recovering linear accelerators that increases operational efficiency while eliminating the need to merge the high energy re-circulating beam with an injected low energy beam. In this arrangement, the high energy re-circulating beam and the low energy beam are manipulated such that they are within a predetermined distance from one another and then the two immerged beams are injected into the linac and propagated through the system. The configuration permits injection without geometric beam merging as well as decelerated beam extraction without the use of typical beamline elements.
NASA Technical Reports Server (NTRS)
Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.
1991-01-01
A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.
Modeling of Gaussian-to-annular beam shaping by geometrical optics for optical trepanning
NASA Astrophysics Data System (ADS)
Zeng, Danyong; Latham, William P.; Kar, Aravinda
2004-09-01
Laser drilling is very important in many industries such as automotive, aerospace, electronics and materials processing. It can be used to produce critical components with novel hole geometry for advanced systems. Percussion drilling and trepanning are two laser drilling methods. In the conventional trepanning method, a laser beam in scanned along a circular or spiral orbit to remove material to achieve a desired hole shape. These orbits generally trace a circular path at the inner wall of the holes. This suggests that an annular beam can be used to accomplish trepanning, which we referred to as optical trepanning. The ray tracing technique of geometrical optics will be employed in this paper to design the necessary optics to transform a Gaussian laser beam into an annular beam of different intensity profiles. Such profiles include half Gaussian with maximum intensities at the inner and outer surfaces of the annulus, respectively, and full Gaussian with maximum intensity within the annulus.
Computing the laser beam path in optical cavities: a geometric Newton's method based approach
Cuccato, Davide; Ortolan, Antonello; Beghi, Alessandro
2015-01-01
In the last decade, increasing attention has been drawn to high precision optical experiments, which push resolution and accuracy of the measured quantities beyond their current limits. This challenge requires to place optical elements (e.g. mirrors, lenses, etc.) and to steer light beams with sub-nanometer precision. Existing methods for beam direction computing in resonators, e.g. iterative ray tracing or generalized ray transfer matrices, are either computationally expensive or rely on overparametrized models of optical elements. By exploiting Fermat's principle, we develop a novel method to compute the steady-state beam configurations in resonant optical cavities formed by spherical mirrors, as a function of mirror positions and curvature radii. The proposed procedure is based on the geometric Newton method on matrix manifold, a tool with second order convergence rate that relies on a second order model of the cavity optical length. As we avoid coordinates to parametrize the beam position on mirror surfac...
ON NONLINEAR VIBRATION OF NONUNIFORM BEAM WITH RECTANGULAR CROSS-SECTION AND PARABOLIC THICKNESS
Caruntu, Dumitru I. - Mechanical Engineering Department, University of Texas
ON NONLINEAR VIBRATION OF NONUNIFORM BEAM WITH RECTANGULAR CROSS-SECTION AND PARABOLIC THICKNESS tooth profile. It permits a nonlinear bending vibrations study (moderately large curvatures) of the gear results with Shaw and Pierre method. In this paper we study the nonlinear vibrations of nonuniform beam
Yang, Guang; Lin, Qingyu; Ding, Yu; Tian, Di; Duan, Yixiang
2015-01-01
A new laser induced breakdown spectroscopy (LIBS) based on single-beam-splitting (SBS) and proper optical geometric configuration has been initially explored in this work for effective signal enhancement. In order to improve the interaction efficiency of laser energy with the ablated material, a laser beam operated in pulse mode was divided into two streams to ablate/excite the target sample in different directions instead of the conventional one beam excitation in single pulse LIBS (SP-LIBS). In spatial configuration, the laser beam geometry plays an important role in the emission signal enhancement. Thus, an adjustable geometric configuration with variable incident angle between the two splitted laser beams was constructed for achieving maximum signal enhancement. With the optimized angles of 60° and 70° for Al and Cu atomic emission lines at 396.15?nm and 324.75?nm respectively, about 5.6- and 4.8-folds signal enhancements were achieved for aluminum alloy and copper alloy samples compared to SP-LIBS. Furthermore, the temporal analysis, in which the intensity of atomic lines in SP-LIBS decayed at least ten times faster than the SBS-LIBS, proved that the energy coupling efficiency of SBS-LIBS was significantly higher than that of SP-LIBS. PMID:25557721
Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates
Birsan, Mircea
2012-01-01
In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.
Geometrical and Dynamical Aspects of Nonlinear Higher-Order Riccati Systems
José F. Carińena; Partha Guha; Manuel F. Rańada
2015-07-02
We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on $S^1$, whichn in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method we obtain the first-integral of SORE and the results are applied to the study of its Lagrangian and Hamiltonian description. We unveil the relation between the Darboux polynomials and master symmetries associated to second-order Riccati. Using these results we show the existence of a Lagrangian description for the related system, and the Painlev\\'e II equation is analysed.
Geredeli, Pelin G.; Webster, Justin T.
2013-12-15
We analyze the convergence to equilibrium of solutions to the nonlinear Berger plate evolution equation in the presence of localized interior damping (also referred to as geometrically constrained damping). Utilizing the results in (Geredeli et al. in J. Differ. Equ. 254:1193–1229, 2013), we have that any trajectory converges to the set of stationary points N . Employing standard assumptions from the theory of nonlinear unstable dynamics on the set N , we obtain the rate of convergence to an equilibrium. The critical issue in the proof of convergence to equilibria is a unique continuation property (which we prove for the Berger evolution) that provides a gradient structure for the dynamics. We also consider the more involved von Karman evolution, and show that the same results hold assuming a unique continuation property for solutions, which is presently a challenging open problem.
Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
Seyed Hossein Hendi; Shahram Panahiyan; Behzad Eslam Panah
2015-09-16
In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.
NASA Astrophysics Data System (ADS)
Gautesen, A. K.; Morris, J. R.
We develop a geometric optics series expansion approximation to a model of phase-compensated whole-beam thermal blooming of high-power laser beams. The model consists of a nonlinear medium whose thermal blooming coupling coefficient decreases exponentially with the propagation distance from the laser and whose motion relative to the laser beam is taken to be unidirectional, a Gaussian high-power intensity profile at the laser, and a collimated beam boundary condition at an exit plane that is many e-folding scale lengths from the laser. The series expansion parameter is directly proportional to Smith's geometric optics distortion parameter. Expansion formulas are derived for both the intensity and phase at all propagation distances. The exit plane intensity profiles obtained from these formulas qualitatively agree with numerical results obtained from the wave-optics thermal blooming code FOURD, except when the FOURD results indicate that caustics are forming; quantitative agreement is also excellent, except for small differences in fine structure near the downwind edge of the beam. FOURD's return-wave phase-compensation iteration provides an estimate that the rms error in the initial phase obtained from our series approximation truncated at third-order is approximately 0.5 percent over the range of values we investigated.
On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics
NASA Astrophysics Data System (ADS)
Gay-Balmaz, François; Putkaradze, Vakhtang
2015-08-01
We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.
NASA Astrophysics Data System (ADS)
Konoshonkin, Alexander V.; Kustova, Natalia V.; Borovoi, Anatoli G.
2015-10-01
The open-source beam-splitting code is described which implements the geometric-optics approximation to light scattering by convex faceted particles. This code is written in C++ as a library which can be easy applied to a particular light scattering problem. The code uses only standard components, that makes it to be a cross-platform solution and provides its compatibility to popular Integrated Development Environments (IDE's). The included example of solving the light scattering by a randomly oriented ice crystal is written using Qt 5.1, consequently it is a cross-platform solution, too. Both physical and computational aspects of the beam-splitting algorithm are discussed. Computational speed of the beam-splitting code is obviously higher compared to the conventional ray-tracing codes. A comparison of the phase matrix as computed by our code with the ray-tracing code by A. Macke shows excellent agreement.
Investigation of the Geometric Accuracy of Proton Beam Irradiation in the Liver
Fukumitsu, Nobuyoshi; Hashimoto, Takayuki; Okumura, Toshiyuki; Mizumoto, Masashi; Tohno, Eriko; Fukuda, Kuniaki; Abei, Masato; Sakae, Takeji; Sakurai, Hideyuki
2012-02-01
Purpose: To investigate the geometric accuracy of proton beam irradiation to the liver by measuring the change in Hounsfield units (HUs) after irradiation. Methods and Materials: We examined 21 patients with liver tumors who were treated with respiratory-gated proton beam therapy (PBT). The radiation dose was 66 GyE in 12 patients and 72.6 GyE in 9 patients. Image registration and reslicing of the computed tomography (CT) results obtained within 1 month before and 3 months after PBT was performed, referring to the planning CT image. The resliced CT images obtained after PBT were subtracted from the images obtained before PBT. We investigated whether the area of the large HU change was consistent with the high-dose distribution area using the location of the largest change in HU around the tumor (peak) on the subtracted CT image and the 90% dose distribution area of the planning CT image. Results: The number of patients (n = 20) whose left-right peaks were within the 90% dose distribution area was significantly larger than the number of patients whose anterior-posterior peaks and superior-inferior peaks were within the 90% dose distribution area (n = 14, n = 13, p = 0.034, and p = 0.02, respectively). Twelve patients exhibited a peak within the 90% dose distribution area in all directions. Nine of the 11 patients with smaller 90% confidence intervals of the percent normalization of the beam cycle (BC; 90% BC) showed a peak within the 90% dose distribution area in six directions, and this percentage was higher than that among the patients with larger 90% BC (3/10, p = 0.03). Conclusion: The geometric accuracy of proton beam irradiation to the liver was higher in the left-right direction than in the other directions. Patients with an irregular respiratory rhythm have a greater risk of a reduced geometric accuracy of PBT in the liver.
Lin, Tai-Chia; Beli?, Milivoj R.; Petrovi?, Milan S.; Chen, Goong; Department of Mathematics and Institute for Quantum Science and Engineering, Texas A and M University, College Station, Texas 77843
2014-01-15
Counterpropagating optical beams in nonlinear media give rise to a host of interesting nonlinear phenomena such as the formation of spatial solitons, spatiotemporal instabilities, self-focusing and self-trapping, etc. Here we study the existence of ground state (the energy minimizer under the L{sup 2}-normalization condition) in two-dimensional (2D) nonlinear Schrödinger (NLS) systems with saturable nonlinearity, which describes paraxial counterpropagating beams in isotropic local media. The nonlinear coefficient of saturable nonlinearity exhibits a threshold which is crucial in determining whether the ground state exists. The threshold can be estimated by the Gagliardo-Nirenberg inequality and the ground state existence can be proved by the energy method, but not the concentration-compactness method. Our results also show the essential difference between 2D NLS equations with cubic and saturable nonlinearities.
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
M. Spata, T.L. Allison, K.E. Cole, J. Musson, J. Yan
2011-09-01
The beam position monitors at CEBAF have four antenna style pickups that are used to measure the location of the beam. There is a strong nonlinear response when the beam is far from the electrical center of the device. In order to conduct beam experiments at large orbit excitation we need to correct for this nonlinearity. The correction algorithm is presented and compared to measurements from our stretched wire BPM test stand.
Multi-direction vibration isolation with quasi-zero stiffness by employing geometrical nonlinearity
NASA Astrophysics Data System (ADS)
Sun, Xiuting; Jing, Xingjian
2015-10-01
The study proposes a novel vibration isolator with 3D quasi-zero-stiffness (QZS) property. The remarkable feature of the proposed system is to apply symmetrically scissor-like structures (SLS) in the horizontal directions, together with a traditional spring-mass-damper system assembled vertically with positive stiffness. With the mathematical modeling of the proposed system, it is shown that the stiffness and damping properties are nonlinear due to nonlinear geometric relations within the SLSs and both can be adjusted via structural parameters of the system. Theoretical analysis with the harmonic balance method reveals that the system can demonstrate QZS property in 3 directions, and can achieve much better 3D vibration isolation performance, including high-static and quasi-zero-dynamic stiffness, and much larger displacement range around equilibrium, compared with an existing QZS system in the literature. The results provide a novel and significant multi-direction vibration isolation method using structural nonlinearity with noticeable performance but using only passive elements.
The wave energy flux of high frequency diffracting beams in complex geometrical optics
Maj, Omar; Poli, Emanuele; Mariani, Alberto; Farina, Daniela
2013-04-15
We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow.
Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F
2014-11-21
Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane. PMID:25361057
Time domain simulation of the response of geometrically nonlinear panels subjected to random loading
NASA Technical Reports Server (NTRS)
Moyer, E. Thomas, Jr.
1988-01-01
The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.
Sotskii, A.B.; Khomchenko, A.V.; Sotskaya, L.I.
1995-03-01
The problem of the field of TE-polarized light beam reflected from the prism during excitation of an optical waveguide possessing cubic nonlinearity is solved. The effect of nonlinear switching is studied taking into account the amplitude distribution of the exciting beam and nonlinear absorption. New possibilities of determining the nonlinear constants of waveguide layers form the intensity distribution of the reflected beam are found. The results of experimental study of the As{sub 2}S{sub 3} film waveguide are presented. 20 refs., 4 figs.
Ronald C. Davidson; W. Wei-li Lee; Hong Qin; Edward Startsev
2001-11-08
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.
Nonlinear diffusion and beam self-trapping in diffraction-managed
. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguideNonlinear diffusion and beam self-trapping in diffraction-managed waveguide arrays Ivan L. Garanovich, Andrey A. Sukhorukov, and Yuri S. Kivshar Nonlinear Physics Centre and Centre for Ultra
Fast Calculations in Nonlinear Collective Models of Beam/Plasma Physics
Antonina N. Fedorova; Michael G. Zeitlin
2002-12-31
We consider an application of variational-wavelet approach to nonlinear collective models of beam/plasma physics: Vlasov/Boltzmann-like reduction from general BBGKY hierachy. We obtain fast convergent multiresolution representations for solutions which allow to consider polynomial and rational type of nonlinearities. The solutions are represented via the multiscale decomposition in nonlinear high-localized eigenmodes (waveletons).
Integrability and chaos in nonlinearly coupled optical beams
David, D.
1989-01-01
This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.
A higher-order theory for geometrically nonlinear analysis of composite laminates
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Liu, C. F.
1987-01-01
A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.
Geometric nonlinear analysis of self-anchored cable-stayed suspension bridges.
Hui-Li, Wang; Yan-Bin, Tan; Si-Feng, Qin; Zhe, Zhang
2013-01-01
Geometric nonlinearity of self-anchored cable-stayed suspension bridges is studied in this paper. The repercussion of shrinkage and creep of concrete, rise-to-span ratio, and girder camber on the system is discussed. A self-anchored cable-stayed suspension bridge with a main span of 800 m is analyzed with linear theory, second-order theory, and nonlinear theory, respectively. In the condition of various rise-to-span ratios and girder cambers, the moments and displacements of both the girder and the pylon under live load are acquired. Based on the results it is derived that the second-order theory can be adopted to analyze a self-anchored cable-stayed suspension bridge with a main span of 800 m, and the error is less than 6%. The shrinkage and creep of concrete impose a conspicuous impact on the structure. And it outmatches suspension bridges for system stiffness. As the rise-to-span ratio increases, the axial forces of the main cable and the girder decline. The system stiffness rises with the girder camber being employed. PMID:24282388
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
NASA Technical Reports Server (NTRS)
Crivelli, Luis A.; Felippa, Carlos A.
1992-01-01
A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.
Non-linear optical measurements using a scanned, Bessel beam
NASA Astrophysics Data System (ADS)
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-03-01
Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.
Light beams with general direction and polarization: Global description and geometric phase
Nityananda, R.; Sridhar, S.
2014-02-15
We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S{sup 2} of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S{sup 2}×C{sup 2}?(0), the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S{sup 2}×S{sup 2} which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP{sup 2}, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S{sup 2}×S{sup 2}. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework. -- Highlights: • We construct a polarization basis for light which is smooth in all directions. • Proof that the manifold of all polarizations and directions is S{sup 2}×S{sup 2}. • Formula for the geometric phase for paths in S{sup 2}×S{sup 2}, generalizing earlier work.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.
2002-01-01
The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.
NASA Astrophysics Data System (ADS)
Cesnik, C. E. S.; Opoku, D. G.; Nitzsche, F.; Cheng, T.
2004-06-01
An active aeroelastic and aeroacoustic analysis of helicopter rotor systems is presented in this paper. It is a tightly coupled computational aeroelastic code that interfaces a particle-wake panel method code with an active nonlinear mixed variational intrinsic beam element code. In addition, a Ffowcs-Williams-Hawkings equation-based acoustic component is incorporated to complete the numerical implementation. The theory behind each component is summarized here as well as the method for coupling the aerodynamic and structural components. Sample acoustic and aeroelastic results are given for different model-scale rotors. Comparisons with available (passive) results show very good agreement. Preliminary study with an active twist rotor is also shown.
NASA Astrophysics Data System (ADS)
Kuang, Zheng; Li, Jiangning; Edwardson, Stuart; Perrie, Walter; Liu, Dun; Dearden, Geoff
2015-07-01
We have demonstrated an original ultrafast laser beam shaping technique for material processing using a spatial light modulator (SLM). Complicated and time-consuming diffraction far-field phase hologram calculations based on Fourier transformations are avoided, while simple and direct geometric masks are used to shape the incident beam at diffraction near-field. Various beam intensity shapes, such as square, triangle, ring and star, are obtained and then reconstructed at the imaging plane of an f-theta lens. The size of the shaped beam is approximately 20 ?m, which is comparable to the beam waist at the focal plane. A polished stainless steel sample is machined by the shaped beam at the imaging plane. The shape of the ablation footprint well matches the beam shape.
NASA Astrophysics Data System (ADS)
Moroni, Giovanni; Syam, Wahyudin P.; Petrň, Stefano
2014-08-01
Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT
Zhao, Jintao; Hu, Xiaodong; Zou, Jing; Hu, Xiaotang
2015-01-01
The quality of Computed Tomography (CT) images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB) phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration. PMID:26371008
Geometric Parameters Estimation and Calibration in Cone-Beam Micro-CT.
Zhao, Jintao; Hu, Xiaodong; Zou, Jing; Hu, Xiaotang
2015-01-01
The quality of Computed Tomography (CT) images crucially depends on the precise knowledge of the scanner geometry. Therefore, it is necessary to estimate and calibrate the misalignments before image acquisition. In this paper, a Two-Piece-Ball (TPB) phantom is used to estimate a set of parameters that describe the geometry of a cone-beam CT system. Only multiple projections of the TPB phantom at one position are required, which can avoid the rotation errors when acquiring multi-angle projections. Also, a corresponding algorithm is derived. The performance of the method is evaluated through simulation and experimental data. The results demonstrated that the proposed method is valid and easy to implement. Furthermore, the experimental results from the Micro-CT system demonstrate the ability to reduce artifacts and improve image quality through geometric parameter calibration. PMID:26371008
Observation of Nonlinear Self-Trapping of Broad Beams in Defocusing Waveguide Arrays
Bennet, Francis H.; Haslinger, Franz; Neshev, Dragomir N.; Kivshar, Yuri S.; Alexander, Tristram J.; Mitchell, Arnan
2011-03-04
We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.; Nguyen, Duc T.
2008-01-01
A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.
NASA Astrophysics Data System (ADS)
He, Qizhi; Kang, Zhan; Wang, Yiqiang
2014-09-01
Based on the element-free Galerkin (EFG) method, an analysis-independent density variable approach is proposed for topology optimization of geometrically nonlinear structures. This method eliminates the mesh distortion problem often encountered in the finite element analysis of large deformations. The topology optimization problem is formulated on the basis of point-wise description of the material density field. This density field is constructed by a physical meaning-preserving interpolation with the density values of the design variable points, which can be freely positioned independently of the field points used in the displacement analysis. An energy criterion of convergence is used to resolve the well-known convergence difficulty, which would be usually encountered in low density regions, where displacements oscillate severely during the optimization process. Numerical examples are given to demonstrate the effectiveness of the developed approach. It is shown that relatively clear optimal solutions can be achieved, without exhibiting numerical instabilities like the so-called "layering" or "islanding" phenomena even in large deformation cases. This study not only confirms the potential of the EFG method in topology optimization involving large deformations, but also provides a novel topology optimization framework based on element-free discretization of displacement and density fields, which can also easily incorporate other meshless analysis methods for specific purposes.
Geometrically nonlinear deformation and the emergent behavior of polarons in soft matter.
Li, Xiaobao; Liu, Liping; Sharma, Pradeep
2015-10-14
Mechanical strain can alter the electronic structure of both bulk semiconductors as well as nanostructures such as quantum dots. This fact has been extensively researched and exploited for tailoring electronic properties. The strain mediated interaction between the charge carriers and the lattice is interpreted through the so-called deformation potential. In the case of soft materials or nanostructures, such as DNA, the deformation potential leads to the formation of polarons which largely determine the electronic characteristics of DNA and similar polymer entities. In addition, polarons are also speculated to be responsible for the mechanism of quantum actuation in carbon nanotubes. The deformation potential is usually taken to be a linear function of the lattice deformation (U ? ??) where ? is the deformation potential "constant" that determines the coupling strength and ? is the mechanical strain. In this letter, by carefully accounting for nonlinear geometric deformation that has been hitherto ignored so far in this context, we show that the deformation potential constant is renormalized in a non-trivial manner and is hardly a constant. It varies spatially within the material and with the size of the material. This effect, while negligible for hard materials, is found to be important for soft materials and critically impacts the interpretation of quantities such as polaron size, binding energy, and accordingly, electronic behavior. PMID:26345397
Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity
NASA Astrophysics Data System (ADS)
Sharma, Prerana
2015-07-01
This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel-Kramers-Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.
Davis, M. J.; Skodje, R. T.; Chemistry; Univ. of Colorado
2001-01-01
A geometric approach to the study of multiple-time-scale kinetics is taken here. The approach to equilibrium for kinetic systems is studied via low-dimensional manifolds, with an application to a nonlinear master equation for vibrational relaxation. One of our main concerns is the asymptotic (in time) behavior of the system and whether there is a well-defined rate of approach to equilibrium. One-dimensional slow manifolds provide a good means for studying such behavior in nonlinear systems, because they are the analogue of the eigenvector with least negative eigenvalue for linear kinetics.
Fedele, Renato; Jovanovic, Dusan
2004-12-01
Charged-particle beams are employed for a number of scientific and technological applications. The conventional description of their collective behavior is usually given in terms of the Vlasov equation. In the last 15 years some alternative descriptions have been developed in terms of a nonlinear Schroedinger equation governing the collective dynamics of the beam while interacting with the surrounding medium. This approach gives new insights, providing an alternative 'key of reading' of the charged-particle beam dynamics, and have been applied to a number of physical problems concerning conventional particle accelerating machines as well as plasma-based accelerator schemes. Remarkably, it is based on a mathematical formalism fully similar to those used for the propagation of e.m. radiation beams in nonlinear media a well as the nonlinear dynamics of the Bose-Einsten condensates.In this paper, a presentation of some significant nonlinear collective effects of a charged-particle beam in particle accelerators, that have been recently investigated in the framework of the above Schroedinger-like descriptions, is given.
NASA Astrophysics Data System (ADS)
Foxon, C. T.; Novikov, S. V.; Hall, J. L.; Campion, R. P.; Cherns, D.; Griffiths, I.; Khongphetsak, S.
2009-06-01
In this article, we propose a new complementary geometrical growth mechanism, which may partially explain some of the apparent anomalies in our understanding of the growth of GaN nanocolumns by plasma-assisted molecular beam epitaxy (PA-MBE). This geometrical addition to any complete model for nanocolumn growth is based on the fact that most samples are grown using substrate rotation and it predicts an enhanced growth rate in the plane normal to the surface, i.e. vertically compared with the lateral growth rate of the columns. It also suggests a mechanism for the enhanced diffusion of gallium on the sidewalls of the columns even under strongly nitrogen-rich conditions. Finally, geometrical considerations also predict the growth of non-(0 0 0 1) oriented samples from the same mechanism. Some experimental evidence supporting this complementary geometrical model is presented.
Davidson, Ronald C.; Qin, Hong
2015-09-21
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w . The average axial electric field is expressed as < E_{z} >=–(?/?z)=–e_{b}g???_{b}/?z – e_{b}g_{2}r^{2}_{w}?^{3}?_{b}/?z^{3}, where g_{0} and g_{2} are constant geometric factors, ?_{b}(z,t)=?dp_{z} F_{b} (z,p_{z},t) is the line density of beam particles, and F _{b} (z,p_{z},t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where F_{b} = const in a bounded region of p_{z}-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field.
Davidson, Ronald C.; Qin, Hong
2015-09-21
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w . The average axial electric field is expressed as z >=–(?/?z)=–ebg???b/?z – ebg2r2w?3?b/?z3, where g0 and g2 are constant geometric factors, ?b(z,t)=?dpz Fb (z,pz,t) is the line density of beam particles, and F b (z,pz,t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations ofmore »the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where Fb = const in a bounded region of pz-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field.« less
NASA Astrophysics Data System (ADS)
Davidson, Ronald C.; Qin, Hong
2015-09-01
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius rw. The average axial electric field is expressed as ?Ez?=-(?/?z )?? ?=-ebg0??b/?z -ebg2rw2?3?b/?z3, where g0 and g2 are constant geometric factors, ?b(z ,t )=?d pzFb(z ,pz,t ) is the line density of beam particles, and Fb(z ,pz,t ) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where Fb=const in a bounded region of pz-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field ?Ez?.
Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction
Van Stryland, Eric
that determines the beam position. Our application of the beam deflection method mea- sures the absolute magnitude tensor elements using different combina- tions of polarization of light. As an excite-probe tech- nique to study the dispersion of different tensor elements of the nonlinear suscep- tibility. This technique
Mode transition and nonlinear self-oscillations in the beam-driven collisional discharge plasma
Lee, Hae June
regions near the anode and the cathode, and the den- sity of the ionized plasma is much higher thanMode transition and nonlinear self-oscillations in the beam-driven collisional discharge plasma Hae in a beam-injected plasma system by experiments17 and simulation8 has received much attention during
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
Shen, Ming; Gao, Jinsong; Ge, Lijuan
2015-01-01
We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878
NASA Technical Reports Server (NTRS)
Rosen, A.; Friedmann, P.
1979-01-01
The nonlinear behavior of slender and initially straight beams is investigated. A set of equilibrium equations for a beam undergoing moderate rotations and small strains is derived. The derivation includes several assumptions which are clearly stated and explained. These equations are used to investigate the deformations of a cantilevered beam which is loaded by a concentrated transverse load at the free end. The numerical results are in very good agreement with the experimental results.
Linear and nonlinear analysis of a gyrotron traveling wave amplifier with misaligned electron beam
NASA Astrophysics Data System (ADS)
Jiao, Chongqing; Luo, Jirun
2006-11-01
This paper presents linear and self-consistent nonlinear theories to describe the beam-wave interaction in a gyrotron traveling wave amplifier (gyro-TWA) with a misaligned electron beam. A linear theory based on the linearized Vlasov equations is developed by using Laplace transforms. By setting appropriate initial values of the electron guiding center, the nonlinear theory without misalignment can be used to study the misalignment effect. The two theories are in good agreement in the small-signal region for the gyro-TWA. The effects of beam misalignment on the TE01 mode gyro-TWA operating at the fundamental are discussed and the corresponding physical mechanism is analyzed.
Labat; Remenieras; Matar; Ouahabi; Patat
2000-03-01
We propose a method to determine the nonlinearity parameter B/A of a liquid from the spatial evolution of harmonic components. We describe an analytical model, in the parabolic and quasi-linear approximations, that predicts the continuous finite amplitude sound beam propagation radiated by a plane piston source. This model takes into consideration attenuation, diffraction and nonlinear effects. The fundamental and second harmonic ultrasonic fields are expressed as the superposition of Gaussian beams. Axial propagation curves are then compared with those obtained by direct numerical solution of the transformed beam equation using the finite difference method, and with experimental results. Accurate measurements of pressure levels for the nonlinearly generated harmonics in water are performed along and across the propagation axis for different pressure values delivered at the piston surface. Experimental results, for water and ethanol, are in agreement with those of our model, which allows us to obtain the expected value of the nonlinearity parameter B/A. PMID:10829676
NASA Astrophysics Data System (ADS)
Rafiee, M.; Liu, X. F.; He, X. Q.; Kitipornchai, S.
2014-07-01
The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin-Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.
Underlying conservation and stability laws in nonlinear propagation of axicon-generated Bessel beams
Porras, Miguel A; Losada, Juan Carlos
2015-01-01
In light filamentation induced by axicon-generated, powerful Bessel beams, the spatial propagation dynamics in the nonlinear medium determines the geometry of the filament channel and hence its potential applications. We show that the observed steady and unsteady Bessel beam propagation regimes can be understood in a unified way from the existence of an attractor and its stability properties. The attractor is identified as the nonlinear unbalanced Bessel beam (NL-UBB) whose inward H\\"ankel beam amplitude equals the amplitude of the linear Bessel beam that the axicon would generate in linear propagation. A simple analytical formula that determines de NL-UBB attractor is given. Steady or unsteady propagation depends on whether the attracting NL-UBB has a small, exponentially growing, unstable mode. In case of unsteady propagation, periodic, quasi-periodic or chaotic dynamics after the axicon reproduces similar dynamics after the development of the small unstable mode into the large perturbation regime.
Nonlinear beam-based vibration energy harvesters and load cells
Kluger, Jocelyn Maxine
2014-01-01
This thesis studies a novel nonlinear spring mechanism that is comprised of a cantilever wrapping around a curved surface as it deflects. Static force versus displacement tests and dynamic "initial displacement" tests ...
Refraction of nonlinear light beams in nematic liquid crystals
Xia, Wenjun
2013-07-01
Optical spatial solitons in nematic liquid crystals, termed nematicons, have become an excellent test bed for nonlinear optics, ranging from fundamental effects to potential uses, such as designing and demonstrating ...
Farr, J. B.; Schoenenberg, D.; Dessy, F.; De Wilde, O.; Bietzer, O.
2013-07-15
Purpose: The purpose of this investigation was to compare and contrast the measured fundamental properties of two new types of modulated proton scanning systems. This provides a basis for clinical expectations based on the scanned beam quality and a benchmark for computational models. Because the relatively small beam and fast scanning gave challenges to the characterization, a secondary purpose was to develop and apply new approaches where necessary to do so.Methods: The following performances of the proton scanning systems were investigated: beamlet alignment, static in-air beamlet size and shape, scanned in-air penumbra, scanned fluence map accuracy, geometric alignment of scanning system to isocenter, maximum field size, lateral and longitudinal field uniformity of a 1 l cubic uniform field, output stability over time, gantry angle invariance, monitoring system linearity, and reproducibility. A range of detectors was used: film, ionization chambers, lateral multielement and longitudinal multilayer ionization chambers, and a scintillation screen combined with a digital video camera. Characterization of the scanned fluence maps was performed with a software analysis tool.Results: The resulting measurements and analysis indicated that the two types of delivery systems performed within specification for those aspects investigated. The significant differences were observed between the two types of scanning systems where one type exhibits a smaller spot size and associated penumbra than the other. The differential is minimum at maximum energy and increases inversely with decreasing energy. Additionally, the large spot system showed an increase in dose precision to a static target with layer rescanning whereas the small spot system did not.Conclusions: The measured results from the two types of modulated scanning types of system were consistent with their designs under the conditions tested. The most significant difference between the types of system was their proton spot size and associated resolution, factors of magnetic optics, and vacuum length. The need and benefit of mutielement detectors and high-resolution sensors was also shown. The use of a fluence map analytical software tool was particularly effective in characterizing the dynamic proton energy-layer scanning.
Horizontal geometrical reaction time model for two-beam nacelle LiDARs
NASA Astrophysics Data System (ADS)
Beuth, Thorsten; Fox, Maik; Stork, Wilhelm
2015-06-01
Wind energy is one of the leading sustainable energies. To attract further private and state investment in this technology, a broad scaled drop of the cost of energy has to be enforced. There is a trend towards using Laser Doppler Velocimetry LiDAR systems for enhancing power output and minimizing downtimes, fatigue and extreme forces. Since most used LiDARs are horizontally setup on a nacelle and work with two beams, it is important to understand the geometrical configuration which is crucial to estimate reaction times for the actuators to compensate wind gusts. In the beginning of this article, the basic operating modes of wind turbines are explained and the literature on wind behavior is analyzed to derive specific wind speed and wind angle conditions in relation to the yaw angle of the hub. A short introduction to the requirements for the reconstruction of the wind vector length and wind angle leads to the problem of wind shear detection of angled but horizontal homogeneous wind fronts due to the spatial separation of the measuring points. A distance is defined in which the wind shear of such homogeneous wind fronts is not present which is used as a base to estimate further distance calculations. The reaction time of the controller and the actuators are having a negative effect on the effective overall reaction time for wind regulation as well. In the end, exemplary calculations estimate benefits and disadvantages of system parameters for wind gust regulating LiDARs for a wind turbine of typical size. An outlook shows possible future improvements concerning the vertical wind behavior.
Vibrations in an elastic beam with nonlinear supports at both ends
NASA Astrophysics Data System (ADS)
Wang, Yi-Ren; Fang, Zhi-Wei
2015-03-01
Vibrations in an elastic beam supported by nonlinear supports at both ends under the influence of harmonic forces are analyzed in this study. It is hypothesized that the elastic Bernoulli-Euler beam is supported by cubic springs to simulate nonlinear boundary conditions. The dynamic behavior of the beam is described by using the Fourier expansion and the Bessel functions. The Hankel transform is then applied to obtain particular (nonhomogeneous) solutions. This study succeeds in describing the "jump" phenomenon (instantaneous transition of the system from one position to another) of the vibrating system at certain frequencies. Models based on linear boundary conditions are unable to capture this phenomenon. A larger modulus of elasticity in nonlinear supports increases the frequency of unstable vibrations in the first mode and also widens the frequency region of system instability. This influence is less prominent in the second mode, in which the largest amplitude is smaller than those observed in the first mode.
Nonlinear energy flow in a beam-plasma system
NASA Technical Reports Server (NTRS)
Whelan, D. A.; Stenzel, R. L.
1983-01-01
The three-dimensional character of the beam-plasma instability is investigated. The true beam-electron distribution function is resolved with a novel directional energy analyzer. The electron plasma waves are observed to develop a large spread in perpendicular wave numbers and damp in a relatively short distance producing an energetic electron tail on the background distribution. The damping is believed to be due to strong ion fluctuations which produce an anomalous resistivity.
Beam propagation method for wide-field nonlinear wave mixing microscope
NASA Astrophysics Data System (ADS)
Lv, Yong-Gang; Ji, Zi-Heng; Yu, Wen-Tao; Shi, Ke-Bin
2015-09-01
We develop a nonlinear beam propagation method for signal generation in inhomogeneous medium for wide-field nonlinear wave mixing microscope. Experimental results performed in wide-field coherent anti-Stokes Raman imaging have shown good agreement with the developed theory. Project supported by the National Natural Science Foundation of China (Grant Nos. 11174019, 61322509 and 11121091) and the National Basic Research Program of China (Grant No. 2013CB921904).
Nonlinear beam kinematics by decomposition of the rotation tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion, extension, shear deformation, and warping of an initially curved and twisted beam.
Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor
NASA Technical Reports Server (NTRS)
Danielson, D. A.; Hodges, D. H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the displacements and rotations are large. The only restrictions are on the magnitudes of the strain and of the local rotation, a newly-identified kinematical quantity. The local rotation is defined as the change of orientation of material elements relative to the change of orientation of the beam reference triad. The vectors and tensors in the theory are resolved along orthogonal triads of base vectors centered along the undeformed and deformed beam reference axes, so Cartesian tensor notation is used. Although a curvilinear coordinate system is natural to the beam problem, the complications usually associated with its use are circumvented. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of beams with both open and closed cross sections in applications of the theory. The theory is used to obtain the kinematical relations for coupled bending, torsion extension, shear deformation, and warping of an initially curved and twisted beam.
Nonlinear beam kinematics for small strains and finite rotations
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.
1987-01-01
A simple matrix expression is obtained for the strain components of a beam in which the magnitudes of neither beam displacements nor rotations are explicitly restricted. The only kinematical restrictions are that: (1) strains are small compared to unity and (2) components of local rotation, a newly identified kinematical quantity, are of the order of the strains to a fractional power equal to at least one half. Local rotations are defined as the change of orientation of material elements off the beam reference axis relative to those on the beam reference axis. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of both open- and closed-section beams in applications of the theory. The resulting strain components are expressed in a local Cartesian coordinate system and can be calculated directly in that way. Thus, one can use a curvilinear coordinate system that is natural to the beam problem without the complications that usually surround such an approach. Examples show the simplicity and the generality of the present approach as well as why previously published results differ among themselves concerning tension-torsion coupling.
Numerical simulation of nonlinear processes in a beam-plasma system
NASA Astrophysics Data System (ADS)
Efimova, A. A.; Berendeev, E. A.; Dudnikova, G. I.; Vshivkov, V. A.
2015-10-01
In the present paper we consider the efficiency of the electromagnetic radiation generation due to various nonlinear processes in the beam-plasma system. The beam and plasma parameters were chosen close to the parameters in the experiment on the GOL-3 facility (BINP SB RAS). The model of the collisionless plasma is described by system of the Vlasov-Maxwell equations with periodic boundary conditions. The parallel numerical algorithm is based on the particles-in-cell method (PIC) with mixed Euler-Lagrangian domain decomposition. Various scenarios of nonlinear evolution in the beam-plasma system under the influence of an external magnetic field in case of a low density beam were studied. The energy transfer from one unstable mode to the others modes was observed.
NASA Astrophysics Data System (ADS)
Rauter, N.; Lammering, R.
2015-04-01
In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1-S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1-S2 and S2-S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo-Hooke and Mooney-Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.
Nonlinear delta(f) Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qin
2003-01-21
A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, et al., in Proc. of the Particle Accelerator Conference, Chicago, 2001 (IEEE, Piscataway, NJ, 2001), Vol. 1, p. 688.] at the Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very-high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles.
Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D
NASA Astrophysics Data System (ADS)
Shen, Wei; Fu, G. Y.; Tobias, Benjamin; Van Zeeland, Michael; Wang, Feng; Sheng, Zheng-Mao
2015-04-01
In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.
Enhanced sensitivity beam emission spectroscopy system for nonlinear turbulence measurements
Gupta, Deepak K.; Fonck, Raymond J.; McKee, George R.; Schlossberg, David J.; Shafer, Morgan W.
2004-10-01
An upgraded beam emission spectroscopy (BES) system has been deployed to access low amplitude turbulence regions near internal transport barriers on the DIII-D tokamak. Sixteen high sensitivity channels are being installed. A significant increase in total signal to noise is achieved by: (1) Increased spatial volume sampling tailored to known turbulence characteristics; (2) An increased throughput spectrometer assembly to isolate the local beam fluorescence, coupled to new large area photoconductive photodiodes; (3) A new sharp edge interference filter designed to optimize detection of the beam emission plus a significant fraction of the thermal deuterium charge exchange. A new data acquisition system has been installed, providing an eight times increase in integration time or an increased sample rate. Preliminary results from the upgraded system show a signal enhancement of greater than an order of magnitude. A clear broadband density fluctuation signal is observed in H-mode discharges with the upgraded BES system, demonstrating the significant performance enhancement.
Geometrically nonlinear static and dynamic analysis of functionally graded skew plates
NASA Astrophysics Data System (ADS)
Upadhyay, A. K.; Shukla, K. K.
2013-08-01
The present paper deals with nonlinear static and dynamic behavior of functionally graded skew plates. The equations of motion are derived using higher order shear deformation theory in conjunction with von-Karman's nonlinear kinematics. The physical domain is mapped into computational domain using linear mapping and chain rule of differentiation. The spatial and temporal discretization is based on fast converging finite double Chebyshev series and Houbolt's method. Quadratic extrapolation technique is employed to linearize the governing nonlinear equations. The spatial and temporal convergence and validation studies have been carried out to establish the efficacy of the present solution methodology. In case of dynamic analysis, the results are obtained for uniform step, sine, half sine, triangular and exponential type of loadings. The effect of volume fraction index, skew angle and boundary conditions on nonlinear displacement and moment response are presented.
Concatenated beam splitters, optical feed-forward and the nonlinear sign gate
Kurt Jacobs; Jonathan P. Dowling
2006-06-26
We consider a nonlinear sign gate implemented using a sequence of two beam splitters, and consider the use of further sequences of beam splitters to implement feed-forward so as to correct an error resulting from the first beam splitter. We obtain similar results to Scheel et al. [Scheel et al., Phys. Rev. A 73, 034301 (2006)], in that we also find that our feed-forward procedure is only able to produce a very minor improvement in the success probability of the original gate.
Magnetic design and measurement of nonlinear multipole magnets for the APT beam expander system
Barlow, D.B.; Shafer, R.E.; Martinez, R.P.; Walstrom, P.L.; Kahn, S.; Jain, A.; Wanderer, P.
1997-10-01
Two prototype nonlinear multipole magnets have been designed for use in the 800-MeV beam test of the APT beam-expansion concept at LANSCE. The iron-dominated magnets each consist of three independent coils, two for producing a predominantly octupole field with a tunable duodecapole component, and one for canceling the residual quadrupole field. Two such magnets, one for shaping each transverse plane, are required to produce a rectangular, uniform beam current density distribution with sharp edges on the APT target. This report will describe the magnetic design of these magnets, along with field measurements, and a comparison to the magnetic design.
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2012-08-15
In the present study, the dissipation processes of circularly polarized Alfven waves in solar wind plasmas including beam components are numerically discussed by using a 2-D hybrid simulation code. Numerical results suggest that the parent Alfven waves are rapidly dissipated due to the presence of the beam-induced obliquely propagating waves, such as kinetic Alfven waves. The nonlinear wave-wave coupling is directly evaluated by using the induction equation for the parent wave. It is also observed both in the 1-D and 2-D simulations that the presence of large amplitude Alfven waves strongly suppresses the beam instabilities.
Stancari, Giulio
2014-01-01
Electron lenses are pulsed, magnetically confined electron beams whose current-density profile is shaped to obtain the desired effect on the circulating beam. Electron lenses were used in the Fermilab Tevatron collider for bunch-by-bunch compensation of long-range beam-beam tune shifts, for removal of uncaptured particles in the abort gap, for preliminary experiments on head-on beam-beam compensation, and for the demonstration of halo scraping with hollow electron beams. Electron lenses for beam-beam compensation are being commissioned in the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL). Hollow electron beam collimation and halo control were studied as an option to complement the collimation system for the upgrades of the Large Hadron Collider (LHC) at CERN; a conceptual design was recently completed. Because of their electric charge and the absence of materials close to the proton beam, electron lenses may also provide an alternative to wires for long-range beam-beam compens...
Saffman, Mark
.65.Hw I. INTRODUCTION Propagation and spatial evolution of light beams in non- linear media is a central evolution of solitary-wave solutions of nonlinear propagation equations is one of the most crucial parts in defocusing media are subject to a snake instability 5 and decay into a line of optical vortices 10,11 . When
Michael Spata
2012-08-01
An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a beam-based technique for characterizing the extent of the nonlinearity of the magnetic fields of a beam transport system. Horizontally and vertically oriented pairs of air-core kicker magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the beam orbit relative to the unperturbed reference orbit. Fourier decomposition of the position data at eight different points along the beamline was then used to measure the amplitude of these frequencies. For a purely linear transport system one expects to find solely the frequencies that were applied to the kickers with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was then applied to a pair of Arc 1 dipoles and then to the magnets in the Transport Recombiner beamline to measure their multipole content as a function of transverse position within the magnets.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Chang, Philip; Lamberts, Astrid; Broderick, Avery E.; Shalaby, Mohamad; Pfrommer, Christoph; Puchwein, Ewald
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Thermodynamic Bounds on Nonlinear Electrostatic Perturbations in Intense Charged Particle Beams
Nikolas C. Logan and Ronald C. Davidson
2012-07-18
This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (TllT? < 1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in accelerated particle beams, including Harris-type electrostatic instabilities, known to limit the luminosity and minimum spot size attainable in experiments. The thermodynamic bound on the field perturbation energy of the instabilities is obtained from the nonlinear Vlasov-Poisson equations for an arbitrary initial distribution function, including the effects of intense self-fields, finite geometry and nonlinear processes. This paper also includes analytical estimates of the nonlinear bounds for space-charge-dominated and emittance-dominated anisotropic bi-Maxwellian distributions.
High Current Electron Beam Emission Driven by a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
French, David; Hoff, Brad; Heidger, Susan
2014-10-01
Simulations of an electron beam diode driven by a modulated voltage pulse provided by a nonlinear transmission line (NLTL) will be presented. Based on a previous low voltage experiment the new design operates at 250 kV and provides a multi-kA modulated electron beam based on the modulated drive signal from a ferrite based NLTL. The NLTL driver has been demonstrated experimentally and is tunable from 900-1400 MHz with pulse durations from 4-17 ns. Particle-In-Cell simulations in ICEPIC show the modulated voltage signal results in a modulated electron beam current emitted directly from the cathode in a few cm annular beam. Expected results and the experimental design for the electron beam diode and diagnostics will also be presented.
Beam-Shape Effects in Nonlinear Compton and Thomson Scattering
Heinzl, T; Kämpfer, B
2009-01-01
We discuss intensity effects in collisions between beams of optical photons from a high-power laser and relativistic electrons. Our main focus are the modifications of the emission spectra due to realistic finite-beam geometries. By carefully analyzing the classical limit we precisely quantify the distinction between strong-field QED Compton scattering and classical Thomson scattering. A purely classical, but fully covariant, calculation of the bremsstrahlung emitted by an electron in a plane wave laser field yields radiation into harmonics, as expected. This result is generalized to pulses of finite duration and explains the appearance of line broadening and harmonic substructure as an interference phenomenon. The ensuing numerical treatment confirms that strong focussing of the laser leads to a broad continuum while higher harmonics become visible only at moderate focussing, hence lower intensity. We present a scaling law for the backscattered photon spectral density which facilitates averaging over electro...
Energy harvesting of cantilever beam system with linear and nonlinear piezoelectric model
NASA Astrophysics Data System (ADS)
Borowiec, Marek
2015-11-01
The nonlinear beam with vertical combined excitations is proposed as an energy harvester. The nonlinearities are included both, in the beam model and also in the electrical subsystem. The system is modelled as a cantilever beam with included a tip mass and piezoelectric patches which convert the bending strains induced by both, the harmonic and the additive stochastic forces. The excitation affects in vertical directions by kinematic forcing into electrical charge. The first main goal is to analyse the dynamics of the electro-mechanical beam system and the influence of the mixed excitation forces into an effectiveness of the energy harvesting. Overcoming the potential barrier by the beam system is also analysed, where large output amplitudes occur. Such region of the vibration affects more power generation, which is crucial in terms of load resistors sensitivities. By increasing the additive noise level with fixed harmonic force it is observed the transition from single well oscillations to inter-well stochastic jumps. The second mail goal is analysing the influence of the piezoelectric nonlinear characteristic and compare the results to the linear piezoelectric cases. The output power is measured during different system behaviours provided by different piezoelectric characteristic as well as introduced stochastic components by modulated tip mass of the system.
Huang, J. L.; Chen, S. H.; Su, R. K. L.; Lee, Y. Y.
2010-05-21
This paper analyzes nonlinear vibration of an axially moving beam subject to periodic lateral forces by Incremental Harmonic Balance (IHB) method. Attention is paid to the fundamental resonance as the force frequency is close to the first frequencies omega{sub 1} of the system. Galerkin method is used to discretize the governing equations and the IHB method is used to illustrate the nonlinear dynamic behavior of the axially moving beam. The stable and unstable periodic solutions for given parameters are determined by the multivariable Floquet theory. Hsu's method is applied for computing the transition matrix at the end of one period. The effects of internal resonance on the beam responses are discussed. The periodic solutions obtained from the IHB method are in good agreement with the results obtained from numerical integration.
Nonlinear modes of an intense laser beam interacting with a periodic lattice of nanoparticle
NASA Astrophysics Data System (ADS)
Sepehri Javan, N.; Homami, S. H. H.
2015-08-01
Self-guided nonlinear propagation of an intense laser beam through a periodic lattice of nanoparticle is studied. Using a perturbative method, a cubic nonlinear wave equation describing the laser-nanoparticle interaction in the weakly relativistic regime is derived. Transverse Eigen modes of the laser, nonlinear dispersion relation and its related group velocity are obtained. It is shown that the best fitted function to the transverse profile is Gaussian. Effect of the laser amplitude and also the ratio of nanoparticles radius to their separation on the nonlinear dispersion and amplitude profiles are investigated. It is found that the increase in the just mentioned parameters leads to the localization of transverse profile around the propagation axis.
White-Noise and Geometrical Optics Limits of Wigner-Moyal Equation for Wave Beams in Turbulent Media
Albert C. Fannjiang
2004-03-05
Starting with the Wigner distribution formulation for beam wave propagation in H\\"{o}lder continuous non-Gaussian random refractive index fields we show that the wave beam regime naturally leads to the white-noise scaling limit and converges to a Gaussian white-noise model which is characterized by the martingale problem associated to a stochastic differential-integral equation of the It\\^o type. In the simultaneous geometrical optics the convergence to the Gaussian white-noise model for the Liouville equation is also established if the ultraviolet cutoff or the Fresnel number vanishes sufficiently slowly. The advantage of the Gaussian white-noise model is that its $n$-point correlation functions are governed by closed form equations.
Patil, Mayuresh
-Aspect-Ratio Wings Mayuresh J. Patil, Dewey H. Hodges Georgia Institute of Technology, Atlanta, Georgia and Carlos E. S. Cesnik Massachusetts Institute of Technology, Cambridge, Massachusetts This paper presents the results of nonlinear aeroelastic analysis of a representative large-aspect-ratio wing. The effects
Effect of Geometric Azimuthal Asymmetrics of PPM Stack on Electron Beam Characteristics
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2000-01-01
A three-dimensional (3D) beam optics model has been developed using the electromagnetic particle-in-cell (PIC) code MAFIA. The model includes an electron beam with initial transverse velocity distribution focused by a periodic permanent magnet (PPM) stack. All components of the model are simulated in three dimensions allowing several azimuthally asymmetric traveling wave tube (TWT) characteristics to be investigated for the first time. These include C-magnets, shunts and magnet misalignment and their effects on electron beam behavior. The development of the model is presented and 3D TWT electron beam characteristics are compared in the absence of and under the influence of the azimuthally asymmetric characteristics described.
NASA Astrophysics Data System (ADS)
Müller, Kei W.; Meier, Christoph; Wall, Wolfgang A.
2015-12-01
Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers (? 5 nm) govern the mechanics of the entire network (? 10 ?m). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
NASA Astrophysics Data System (ADS)
Carlevaro, Nakia; Falessi, Matteo V.; Montani, Giovanni; Zonca, Fulvio
2015-10-01
> In this paper we study transport features of a one-dimensional beam-plasma system in the presence of multiple resonances. As a model description of the general problem of a warm energetic particle beam, we assume cold supra-thermal beams and investigate the self-consistent evolution in the presence of the complete spectrum of nearly degenerate Langmuir modes. A qualitative transport estimation is obtained by computing the Lagrangian Coherent Structures of the system on given temporal scales. This leads to the splitting of the phase space into regions where the local transport processes are relatively faster. The general theoretical framework is applied to the case of the nonlinear dynamics of two cold beams, for which numerical simulation results are illustrated and analysed.
Lee, S. Y.
2014-04-07
We had carried out a design of an ultimate storage ring with beam emittance less than 10 picometer for the feasibility of coherent light source at X-ray wavelength. The accelerator has an inherent small dynamic aperture. We study method to improve the dynamic aperture and collective instability for an ultimate storage ring. Beam measurement and accelerator modeling are an integral part of accelerator physics. We develop the independent component analysis (ICA) and the orbit response matrix method for improving accelerator reliability and performance. In collaboration with scientists in National Laboratories, we also carry out experimental and theoretical studies on beam dynamics. Our proposed research topics are relevant to nuclear and particle physics using high brightness particle and photon beams.
Geometrically nonlinear design sensitivity analysis on parallel-vector high-performance computers
NASA Technical Reports Server (NTRS)
Baddourah, Majdi A.; Nguyen, Duc T.
1993-01-01
Parallel-vector solution strategies for generation and assembly of element matrices, solution of the resulted system of linear equations, calculations of the unbalanced loads, displacements, stresses, and design sensitivity analysis (DSA) are all incorporated into the Newton Raphson (NR) procedure for nonlinear finite element analysis and DSA. Numerical results are included to show the performance of the proposed method for structural analysis and DSA in a parallel-vector computer environment.
Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven
2014-01-01
Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding the potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619
Reichert, Matthew; Zhao, Peng; Reed, Jennifer M; Ensley, Trenton R; Hagan, David J; Van Stryland, Eric W
2015-08-24
A polarization-resolved beam deflection technique is used to separate the bound-electronic and molecular rotational components of nonlinear refractive transients of molecular gases. Coherent rotational revivals from N(2), O(2), and two isotopologues of carbon disulfide (CS(2)), are identified in gaseous mixtures. Dephasing rates, rotational and centrifugal distortion constants of each species are measured. Polarization at the magic angle allows unambiguous measurement of the bound-electronic nonlinear refractive index of air and second hyperpolarizability of CS(2). Agreement between gas and liquid phase second hyperpolarizability measurements is found using the Lorentz-Lorenz local field correction. PMID:26368195
NASA Astrophysics Data System (ADS)
Sahmani, S.; Bahrami, M.; Ansari, R.
2014-12-01
This investigation deals with the free vibration characteristics of circular higher-order shear deformable nanoplates around the postbuckling configuration incorporating surface effects. Using the Gurtin-Murdoch elasticity theory, a size-dependent higher-order shear deformable plate model is developed which takes account all surface effects including surface elasticity, surface stress and surface density. Geometrical nonlinearity is considered based on the von Karman type nonlinear strain-displacement relationships. Also, in order to satisfy the balance conditions between bulk and surfaces of nanoplate, it is assumed that the normal stress is distributed cubically through the thickness of nanoplate. Hamilton's principle is utilized to derive non-classical governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based on a generalized differential quadrature (GDQ) method is employed to solve numerically the problem so as to discretize the governing partial differential equations along various edge supports using Chebyshev-Gauss-Lobatto grid points and pseudo arc-length continuation technique. A comparison between the results of present non-classical model and those of the classical plate theory is conducted. It is demonstrated that in contrast to the prebuckling domain, for a specified value of axial load in the postbuckling domain, increasing the plate thickness leads to higher frequencies.
Linear and nonlinear properties of the ULF waves driven by ring-beam distribution functions
NASA Technical Reports Server (NTRS)
Killen, K.; Omidi, N.; Krauss-Varban, D.; Karimabadi, H.
1995-01-01
The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.
Influence of non-linear index on coherent passive beam combining of fiber lasers
NASA Astrophysics Data System (ADS)
Napartovich, A. P.; Elkin, N. N.; Vysotsky, D. V.
2011-02-01
Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts in this case rather low efficiency of beam combining even for an array of 8 lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for up to 20 lasers in an array. Possible explanation of this discrepancy may be associated with a number of factors. These factors are: gain saturation, intensity-dependent index, laser wavelength self-adjustment within the gain bandwidth. Besides, high degree of phase-locking can be established in self-sustained pulse periodic or spiky regime. Our approach takes injection controlled laser as a base unit of an ensemble. Beams from the neighboring lasers are injected into the reference laser in the array. Then a relationship between reference laser characteristics and whole wave field parameters can be found. As an example, fiber laser array with global coupling is numerically simulated with laser wavelength scanned within the gain bandwidth. Non-linear index is found to improve essentially passive phasing efficiency independent of the non-linearity sign.
Feng, Zexin; Froese, Brittany D; Huang, Chih-Yu; Ma, Donglin; Liang, Rongguang
2015-07-10
We consider here creation of an unconventional flattop beam with a large depth of field by employing double freeform optical surfaces. The output beam is designed with continuous variations from the flattop to almost zero near the edges to resist the influence of diffraction on its propagation. We solve this challenging problem by naturally incorporating an optimal transport map computation scheme for unconventional boundary conditions with a simultaneous point-by-point double surface construction procedure. We demonstrate experimentally the generation of a long-range propagated triangular beam through a plano-freeform lens pair fabricated by a diamond-tuning machine. PMID:26193404
NASA Astrophysics Data System (ADS)
Egorov, E. N.; Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-01
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
Multiple beam two-plasmon decay: linear threshold to nonlinear saturation in three dimensions.
Zhang, J; Myatt, J F; Short, R W; Maximov, A V; Vu, H X; DuBois, D F; Russell, D A
2014-09-01
The linear stability of multiple coherent laser beams with respect to two-plasmon-decay instability in an inhomogeneous plasma in three dimensions has been determined. Cooperation between beams leads to absolute instability of long-wavelength decays, while shorter-wavelength shared waves are shown to saturate convectively. The multibeam, in its absolutely unstable form, has the lowest threshold for most cases considered. Nonlinear calculations using a three-dimensional extended Zakharov model show that Langmuir turbulence created by the absolute instability modifies the convective saturation of the shorter-wavelength modes, which are seen to dominate at late times. PMID:25238364
Egorov, E. N. Koronovskii, A. A.; Kurkin, S. A.; Hramov, A. E.
2013-11-15
Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.
Omar Maj
2008-02-12
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \\emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \\emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.
Nonlinear dust-plasma interactions of a cross-beam system in interplanetary space
Jammalamadaka, S.; Araneda, J.; McKenzie, J. F.; Gruenwaldt, H.
1998-10-21
Dust plasma interaction has been considered. The present work is an extension of the paper of Mann and McKenzie [Mann and McKenzie, 1997]. Using the cross-beam configuration we investigate the dust plasma interaction taking into account the inhomogeneity of density. The dust interacts in our case with an inhomogeneous collisionless multi-ion plasma. Linear and nonlinear behaviour of the system has been examined and its impact on the dust dynamics is pointed out.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Judkins, J.B.
1992-12-31
A modified finite-difference time-domain method for solving Maxwell`s equations in nonlinear media is presented. This method allows for a finite response time to be incorporated in the medium, physically creating dispersion and absorption mechanisms. The technique models electromagnetic fields in two space dimensions and time and encompasses both the TE{sub z} and TM{sub z} set of decoupled field equations. Aspects of an ultra-short pulsed Gaussian beam are studied in a variety of linear and nonlinear environments to demonstrate that the methods developed here can be used efficaciously in the modeling of pulses in complex problem space geometries even when nonlinearities are present.
Stimulated Raman scattering and nonlinear focusing of high-power laser beams propagating in water.
Hafizi, B; Palastro, J P; Peńano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-04-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown, and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. The phenomenon of gain-focusing discussed here for propagation in water is expected to be of general occurrence applicable to any medium supporting nonlinear focusing and stimulated Raman scattering. PMID:25831383
Nonlinear gyrofluid models of shear Alfven instabilities in ignited and beam heated toroidal plasmas
Spong, D.A.; Hedrick, C.L.; Carreras, B.A.
1993-07-01
Shear Alfven instabilities driven by energetic beams and alpha populations are investigated using a reduced MHD-gyrofluid model with Landau closure. The moment equations for the fast ions are truncated in a way which incorporates the wave particle resonances that are required to destabilize the shear Alfven mode. These are coupled to an Ohm`s law and vorticity equations which have been generalized to include ion FLR, electron and ion Landau damping. This model has been applied to experimentally observed regimes in a number of tokamak and stellarator devices. Both linearized growth rates and the nonlinear evolution are obtained. The saturated nonlinear regimes indicate mode number and frequency spectra which are generally consistent with experiment. A detailed examination of one typical nonlinear state has allowed identification of the dominant saturation mechanisms. This indicates that generation of n = 0, m = 0 sheared poloidal velocity flows and quasi linear modification of the q(r) profile can be important factors in reaching saturation.
Stimulated Raman Scattering and Nonlinear Focusing of High-Power Laser Beams Propagating in Water
Hafizi, B; Penano, J R; Gordon, D F; Jones, T G; Helle, M H; Kaganovich, D
2015-01-01
The physical processes associated with propagation of a high-power (power > critical power for self-focusing) laser beam in water include nonlinear focusing, stimulated Raman scattering (SRS), optical breakdown and plasma formation. The interplay between nonlinear focusing and SRS is analyzed for cases where a significant portion of the pump power is channeled into the Stokes wave. Propagation simulations and an analytical model demonstrate that the Stokes wave can re-focus the pump wave after the power in the latter falls below the critical power. It is shown that this novel focusing mechanism is distinct from cross-phase focusing. While discussed here in the context of propagation in water, the gain-focusing phenomenon is general to any medium supporting nonlinear focusing and stimulated forward Raman scattering.
Olarte, Omar E; Licea-Rodriguez, Jacob; Palero, Jonathan A; Gualda, Emilio J; Artigas, David; Mayer, Jürgen; Swoger, Jim; Sharpe, James; Rocha-Mendoza, Israel; Rangel-Rojo, Raul; Loza-Alvarez, Pablo
2012-07-01
We present the implementation of a combined digital scanned light-sheet microscope (DSLM) able to work in the linear and nonlinear regimes under either Gaussian or Bessel beam excitation schemes. A complete characterization of the setup is performed and a comparison of the performance of each DSLM imaging modality is presented using in vivoCaenorhabditis elegans samples. We found that the use of Bessel beam nonlinear excitation results in better image contrast over a wider field of view. PMID:22808423
NASA Astrophysics Data System (ADS)
Andreaus, Ugo; Baragatti, Paolo
2011-02-01
Numerical evaluation of the flexural forced vibration of a cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed to relate the nonlinear resonances to the crack presence, location, and depth. To this end, the qualitative characteristics, namely phase portrait distortions, sub- and super-harmonic components in the Fourier spectrum, and curved shape of the modal line were considered. Furthermore, quantitative parameters, such as the eccentricity and the excursion of the orbit, and the harmonic amplitude in the spectrum were measured. Then, an identification procedure was proposed which was based on the intersection of constructed surfaces which allowed to identify the structural damage. The acceleration record of the beam tip was sufficient to detect the existence of the crack and to identify crack depth and site.
Nonlinear control of an experimental beam by IMSC. [Independent Modal-Space Control
NASA Technical Reports Server (NTRS)
Meirovitch, L.; Baruh, H.; Montgomery, R. C.; Williams, J. P.
1983-01-01
Results are reported from an experiment designed to control the vibratory motion of a beam at NASA, Langley Research Center. The experimental setup consists of a free-free uniform beam acted upon by four electromagnetic force actuators, with the motion being measured by nine displacement sensors. The entire assembly is linked to a CDC Cyber 175 computer which permits on-line real-time computation of the control forces. The control scheme is based on Independent Modal-Space Control (IMSC), whereby the modal forces are computed using a nonlinear, on-off control law. The actuator forces are then synthesized using a linear transformation, resulting in quantized forces. The sensors data is processed by modal filters. It is observed that the controls designed on the basis of the IMSC method are very effective in suppressing the vibratory motion of the beam, even though there is about a 50 percent differene between the actual and the analytically computed frequencies.
On the Nonlinear Effects in Focused Ultrasound Beams with Frequency Power Law Attenuation
NASA Astrophysics Data System (ADS)
Jiménez, N.; Redondo, J.; Sánchez-Morcillo, V.; Iglesias, P. C.; Camarena, F.
When finite amplitude ultrasound propagation is considered, changes in spatial features of focused ultrasound beams can be observed. These nonlinear effects typically appear in thermoviscous fluids as focal displacements, beam-width variations or gain changes. However, in soft-tissue media, the frequency dependence of the attenuation doesn't obey a squared law. In this way, these complex media response leads to weak dispersion that prevents the cumulative processes of energy transfer to higher harmonics. In this work we explore the influence of different frequency power law attenuation responses and its influence on the self-defocusing effects in focused ultrasound beams. Thus, we numerically explore the spatial field distributions produced by low-Fresnel number devices and High Intensity Focused Ultrasound (HIFU) radiating trough different soft-tissue media.
A geometrically exact finite beam element formulation for thin film adhesion and debonding
to study the peeling behavior of a gecko spatula. It is shown that the beam model is capable of capturing methods, gecko adhesion, van der Waals interaction 1 Introduction The adhesion, debonding, and peeling and coatings, adhesive tapes, liquid films, and adhesive pads of insects and lizards like the gecko spatula pad
Explicit nonlinear finite element geometric analysis of parabolic leaf springs under various loads.
Kong, Y S; Omar, M Z; Chua, L B; Abdullah, S
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
HAMMERAND,DANIEL C.; KAPANIA,RAKESH K.
2000-05-01
A triangular flat shell element for large deformation analysis of linear viscoelastic laminated composites is presented. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Recurrence relations are developed and implemented for the evaluation of the viscoelastic memory loads. The nonlinear deformation process is computed using an incremental/iterative approach with the Newton-Raphson Method used to find the incremental displacements in each step. The presented numerical examples consider the large deformation and stability of linear viscoelastic structures under deformation-independent mechanical loads, deformation-dependent pressure loads, and thermal loads. Unlike elastic structures that have a single critical load value associated with a given snapping of buckling instability phenomenon, viscoelastic structures will usually exhibit a particular instability for a range of applied loads over a range of critical times. Both creep buckling and snap-through examples are presented here. In some cases, viscoelastic results are also obtained using the quasielastic method in which load-history effects are ignored, and time-varying viscoelastic properties are simply used in a series of elastic problems. The presented numerical examples demonstrate the capability and accuracy of the formulation.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
Electron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion
Arie, Ady
to achieve noncollinear second-harmonic generation. The sample was fabricated using an electron-beam indirectElectron-beam-induced domain poling in LiNbO3 for two-dimensional nonlinear frequency conversion Yinnon Glickman, Emil Winebrand, Ady Arie,a and Gil Rosenman Department of Physical Electronics, School
Yin, L.; Albright, B. J.; Rose, H. A.; Bowers, K. J.; Bergen, B.; Montgomery, D. S.; Kline, J. L.; Kirkwood, R. K.; Hinkel, D. E.; Langdon, A. B.; Michel, P.
2012-05-15
In inertial confinement fusion experiments, stimulated Raman scattering (SRS) occurs when electron density fluctuations are amplified resonantly by the incident laser beams and scattered light. These beams comprise several thousands of individual laser speckles. We have found in single-speckle studies that electron trapping lowers the threshold intensity for SRS onset to a value below that from linear theory and enhances scattering. The trapping-induced plasma-wave frequency shift leads to wave-front bowing and filamentation processes that saturate SRS and limit scattering within a speckle. With large-scale simulations, we have now examined how laser speckles interact with one another through three-dimensional (3D) particle-in-cell (PIC) simulations of two interacting speckles and 2D PIC simulations of ensembles of laser speckles (hundreds of speckles). Our work shows that kinetic trapping physics also governs the onset and saturation of SRS in ensembles of speckles. Speckles interact in a manner that is nonlinear and nonlocal: An intense speckle can destabilize its neighbors through transport of hot electrons and SRS waves, resulting in enhanced emission of particles and waves that, in turn, act upon the original speckle. In this manner, speckles below threshold when in isolation can be above the threshold in multi-speckled beams under conditions for laser-driven fusion experiments at the National Ignition Facility (NIF) and ensembles of speckles are thus found to collectively lower the SRS onset threshold. Simulations of the hohlraum interior where laser beams overlap show that multi-speckled laser beams at low average intensity (a few times 10{sup 14} W/cm{sup 2}) have correspondingly lower thresholds for enhanced SRS and that the sub-ps bursts of SRS saturate through trapping induced nonlinearities. Because of electron trapping effects, SRS reflectivity grows slowly with average laser intensity. While SRS reflectivity saturates under NIF conditions, SRS hot electron energy increases with increasing laser intensity and may contribute to capsule preheat.
A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems
Yosibash, Zohar
to thickness for plate and shell-like structures, and with respect to the Poisson ratio for nearly and isotropic beams taking into account geometric nonlinearities were used to investigate the vibrations
Kong, Ling-Bao; Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 ; Wang, Hong-Yu; Hou, Zhi-Ling; Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 ; Jin, Hai-Bo; Du, Chao-Hai
2013-12-15
The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2014-10-01
The damping process of field-aligned, low-frequency right-handed polarized nonlinear Alfvén waves (NAWs) in solar wind plasmas with and without proton beams is studied by using a two-dimensional ion hybrid code. The numerical results show that the obliquely propagating kinetic Alfvén waves (KAWs) excited by beam protons affect the damping of the low-frequency NAW in low beta plasmas, while the nonlinear wave-wave interaction between parallel propagating waves and nonlinear Landau damping due to the envelope modulation are the dominant damping process in high beta plasmas. The nonlinear interaction between the NAWs and KAWs does not cause effective energy transfer to the perpendicular direction. Numerical results suggest that while the collisionless damping due to the compressibility of the envelope-modulated NAW plays an important role in the damping of the field-aligned NAW, the effect of the beam instabilities may not be negligible in low beta solar wind plasmas.
Nonlinear optics and liquid crystal light valve for laser beam control
NASA Astrophysics Data System (ADS)
Huignard, Jean Pierre; Brignon, Arnaud; Steinhausser, Bastien
2008-11-01
The recent advances in solid state laser technology now permit to achieve high energy and efficiency sources for a wide range of applications extending from laser physics to material processing, biophotonics, remote sensing and coherent lidar systems. In particular the progress of fibre laser exploiting the double clading diode pumping structure are impressive: they are compact and emit single mode beams. However optical damage and nonlinear effects limit the output peak power emitted by a single mode fiber laser. Also limitations arise in bulk laser materials due to the thermal loading which induces strong wavefront distortions on the beams. We develop in this paper original concepts adapted to power-energy scaling of bulk or fibre lasers. The final objective is to emit high brightness and high energy beams whose quality is close to the diffraction limit. For this purpose we present new technics to be inspired from from Fourier optics and allowing the wavefront processing either through nonlinear interactions or with adaptive optical components such as electro optic phase modulators or liquid crystal light valves.
NASA Astrophysics Data System (ADS)
Gupta, Naveen; Singh, Navpreet; Singh, Arvinder
2015-11-01
This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on a numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
NASA Astrophysics Data System (ADS)
Lajimi, S. A. M.; Friswell, M. I.
2015-04-01
For a nonlinear beam-mass system used to harvest vibratory energy, the two-mode approximation of the response is computed and compared to the single-mode approximation of the response. To this end, the discretized equations of generalized coordinates are developed and studied using a computational method. By obtaining phase-portraits and time-histories of the displacement and voltage, it is shown that the strong nonlinearity of the system affects the system dynamics considerably. By comparing the results of single- and two-mode approximations, it is shown that the number of mode shapes affects the dynamics of the response. Varying the tip-mass results in different structural configurations namely linear, pre-buckled nonlinear, and post-buckled nonlinear configurations. The nonlinear dynamics of the system response are investigated for vibrations about static equilibrium points arising from the buckling of the beam. Furthermore, it is demonstrated that the harvested power is affected by the system configuration.
Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.
2005-01-15
We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at {lambda}=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples.
Nonlinear theory of electron neutralization waves in ions beams with dissipation
NASA Technical Reports Server (NTRS)
Wilhelm, H. E.
1974-01-01
An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.
Sonnad, Kiran G.; Cary, John R.
2015-04-15
A procedure to obtain a near equilibrium phase space distribution function has been derived for beams with space charge effects in a generalized periodic focusing transport channel. The method utilizes the Lie transform perturbation theory to canonically transform to slowly oscillating phase space coordinates. The procedure results in transforming the periodic focusing system to a constant focusing one, where equilibrium distributions can be found. Transforming back to the original phase space coordinates yields an equilibrium distribution function corresponding to a constant focusing system along with perturbations resulting from the periodicity in the focusing. Examples used here include linear and nonlinear alternating gradient focusing systems. It is shown that the nonlinear focusing components can be chosen such that the system is close to integrability. The equilibrium distribution functions are numerically calculated, and their properties associated with the corresponding focusing system are discussed.
Yin, L.; Daughton, W.; Albright, B. J.; Bowers, K. J.; Montgomery, D. S.; Kline, J. L.; Fernandez, J. C.; Roper, Q.
2006-07-15
The backward stimulated Raman scattering (BSRS) of a laser from electron beam acoustic modes (BAM) in the presence of self-consistent non-Maxwellian velocity distributions is examined by linear theory and particle-in-cell (PIC) simulations in one and two dimensions (1D and 2D). The BAM evolve from Langmuir waves (LW) as electron trapping modifies the distribution to a non-Maxwellian form that exhibits a beam component. Linear dispersion relations using the nonlinearly modified distribution from simulations are solved for the electrostatic modes involved in the parametric coupling. Results from linear analysis agree well with electrostatic spectra from simulations. It is shown that the intersection of the Stokes root with BAM (instead of LW) determines the matching conditions for BSRS at a nonlinear stage. As the frequency of the unstable Stokes mode decreases with increasing wave number, the damping rate and the phase velocity of BAM decreases with the phase velocity of the Stokes mode, providing a self-consistently evolving plasma linear response that favors continuation of the nonlinear frequency shift. Coincident with the emergence of BAM is a rapid increase in BSRS reflectivity. The details of the wave-particle interaction region in the electron velocity distribution determine the growth/damping rate of these electrostatic modes and the nonlinear frequency shift; in modeling this behavior, the use of sufficiently large numbers of particles in the simulations is crucial. Both the reflectivity scaling with laser intensity and the spectral features from simulations are discussed and are consistent with recent Trident experiments.
NASA Astrophysics Data System (ADS)
Makov, Y. N.; Espinosa, V.; Sánchez-Morcillo, V. J.; Ramis, J.; Cruańes, J.; Camarena, F.
2006-05-01
On the basis of theoretical concepts, an accurate and complete experimental and numerical examination of the on-axis distribution and the corresponding temporal profiles for low-Fresnel-number focused ultrasound beams under increasing transducer input voltage has been performed. For a real focusing transducer with sufficiently small Fresnel number, a strong initial (linear) shift of the main on-axis pressure maximum from geometrical focal point towards the transducer, and its following displacement towards the focal point and backward motion as the driving transducer voltage increase until highly nonlinear regimes were fixed. The simultaneous monitoring of the temporal waveform modifications determines the real roles and interplay between different nonlinear effects (refraction and attenuation) in the observed dynamics of on-axis pressure maximum. The experimental results are in good agreement with numerical solutions of KZK equation, confirming that the observed dynamic shift of the maximum pressure point is related only to the interplay between diffraction, dissipation and nonlinearity of the acoustic wave.
Nonlinear Elastic J-Integral Measurements in Mode I Using a Tapered Double Cantilever Beam Geometry
NASA Technical Reports Server (NTRS)
Macon, David J.
2006-01-01
An expression for the J-integral of a nonlinear elastic material is derived for an advancing crack in a tapered double cantilever beam fracture specimen. The elastic and plastic fracture energies related to the test geometry and how these energies correlates to the crack position are discussed. The dimensionless shape factors eta(sub el and eta(sub p) are shown to be equivalent and the deformation J-integral is analyzed in terms of the eta(sub el) function. The fracture results from a structural epoxy are interpreted using the discussed approach. The magnitude of the plastic dissipation is found to strongly depend upon the initial crack shape.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
NASA Astrophysics Data System (ADS)
Romanchenko, I. V.; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-01
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
Non-Linear Optical Flow Cytometry Using a Scanned, Bessel Beam Light-Sheet
Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.
2015-01-01
Modern flow cytometry instruments have become vital tools for high-throughput analysis of single cells. However, as issues with the cellular labeling techniques often used in flow cytometry have become more of a concern, the development of label-free modalities for cellular analysis is increasingly desired. Non-linear optical phenomena (NLO) are of growing interest for label-free analysis because of the ability to measure the intrinsic optical response of biomolecules found in cells. We demonstrate that a light-sheet consisting of a scanned Bessel beam is an optimal excitation geometry for efficiently generating NLO signals in a microfluidic environment. The balance of photon density and cross-sectional area provided by the light-sheet allowed significantly larger two-photon fluorescence intensities to be measured in a model polystyrene microparticle system compared to measurements made using other excitation focal geometries, including a relaxed Gaussian excitation beam often used in conventional flow cytometers. PMID:26021750
Nonlinear effects in optical pumping of a cold and slow atomic beam
NASA Astrophysics Data System (ADS)
Porfido, N.; Bezuglov, N. N.; Bruvelis, M.; Shayeganrad, G.; Birindelli, S.; Tantussi, F.; Guerri, I.; Viteau, M.; Fioretti, A.; Ciampini, D.; Allegrini, M.; Comparat, D.; Arimondo, E.; Ekers, A.; Fuso, F.
2015-10-01
By photoionizing hyperfine (HF) levels of the Cs state 6 2P3 /2 in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around 180 ? s ) spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of "dark" and "bright" resonances leading to power-dependent branching coefficients.
Beam quality from self and ionization induced trapping in the nonlinear LWFA regime
NASA Astrophysics Data System (ADS)
Davidson, Asher; Lu, Wei; Joshi, Chan; Silva, Luis; Martins, Joana; Fonseca, Ricardo; Mori, Warren
2011-10-01
In plasma based accelerators (LWFA and PWFA), the methods of injecting high quality electron bunches into the accelerating wakefield is of utmost importance for various applications. Understanding how injection occurs in both self and controlled scenarios is therefore important. We present results from high fidelity OSIRIS simulations on the beam quality that can be obtained from self and ionized induced trapping in the nonlinear LWFA regime. We compare trapping thresholds from the simulations to analytical expressions. We also quantify how the beam quality of 1.5-5 GeV beams can be improved through angle and energy selection as well as quantify the slice energy spread and emittance. We also study the effect of ion motion and the axial density profile. Preliminary results on inputting beams from OSIRS into the FEL code GENESIS will be presented. This work was supported by UC Lab Fees Research Award No. 09-LR-05-118764-DOUW, DOE grants DOE DE-FC02-07ER41500 and DE-FG02-92ER40727 and by NSF grants NSF PHY-0904039 and NSF PHY-0936266. The simulations were performed on Jaguar under an INCITE award.
NASA Astrophysics Data System (ADS)
Reaungamornrat, S.; Otake, Y.; Uneri, A.; Schafer, S.; Mirota, D. J.; Nithiananthan, S.; Stayman, J. W.; Khanna, A. J.; Reh, D. D.; Gallia, G. L.; Taylor, R. H.; Siewerdsen, J. H.
2012-02-01
Conventional surgical tracking configurations carry a variety of limitations in line-of-sight, geometric accuracy, and mismatch with the surgeon's perspective (for video augmentation). With increasing utilization of mobile C-arms, particularly those allowing cone-beam CT (CBCT), there is opportunity to better integrate surgical trackers at bedside to address such limitations. This paper describes a tracker configuration in which the tracker is mounted directly on the Carm. To maintain registration within a dynamic coordinate system, a reference marker visible across the full C-arm rotation is implemented, and the "Tracker-on-C" configuration is shown to provide improved target registration error (TRE) over a conventional in-room setup - (0.9+/-0.4) mm vs (1.9+/-0.7) mm, respectively. The system also can generate digitally reconstructed radiographs (DRRs) from the perspective of a tracked tool ("x-ray flashlight"), the tracker, or the C-arm ("virtual fluoroscopy"), with geometric accuracy in virtual fluoroscopy of (0.4+/-0.2) mm. Using a video-based tracker, planning data and DRRs can be superimposed on the video scene from a natural perspective over the surgical field, with geometric accuracy (0.8+/-0.3) pixels for planning data overlay and (0.6+/-0.4) pixels for DRR overlay across all C-arm angles. The field-of-view of fluoroscopy or CBCT can also be overlaid on real-time video ("Virtual Field Light") to assist C-arm positioning. The fixed transformation between the x-ray image and tracker facilitated quick, accurate intraoperative registration. The workflow and precision associated with a variety of realistic surgical tasks were significantly improved using the Tracker-on-C - for example, nearly a factor of 2 reduction in time required for C-arm positioning, reduction or elimination of dose in "hunting" for a specific fluoroscopic view, and confident placement of the x-ray FOV on the surgical target. The proposed configuration streamlines the integration of C-arm CBCT with realtime tracking and demonstrated utility in a spectrum of image-guided interventions (e.g., spine surgery) benefiting from improved accuracy, enhanced visualization, and reduced radiation exposure.
NASA Technical Reports Server (NTRS)
Dowell, E. H.; Traybar, J.; Hodges, D. H.
1977-01-01
An experimental study of the large deformation of a cantilevered beam under a gravity tip load has been made. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies have been measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed non-linear structural theory. Agreement is reasonably good when bending deflections are small compared to the beam span, but systematic differences occur for larger deflections.
Vibration of vehicle-pavement coupled system based on a Timoshenko beam on a nonlinear foundation
NASA Astrophysics Data System (ADS)
Ding, Hu; Yang, Yan; Chen, Li-Qun; Yang, Shao-Pu
2014-12-01
This paper focuses on the coupled nonlinear vibration of vehicle-pavement system. The pavement is modeled as a Timoshenko beam resting on a six-parameter foundation. The vehicle is simplified as a spring-mass-damper oscillator. For the first time, the dynamic response of vehicle-pavement coupled system is studied by modeling the pavement as a Timoshenko beam resting on a nonlinear foundation. Consequently, the shear effects and the rotational inertia of the pavement are included in the modeling process. The pavement model is assumed to be a linear-plus-cubic Pasternak-type foundation. Furthermore, the convergent Galerkin truncation is used to obtain approximate solutions to the coupled vibratory response of the vehicle-pavement coupled system. The dynamic responses of the vehicle-pavement system with the asphalt pavement on soft soil foundation are investigated via the numerical examples. The numerical results show that the calculation for the coupled vibratory response needs high-order modes. Moreover, the coupling effects between the pavement and the vehicle are numerically examined by using the convergent modal truncation. The physical parameters of the vehicle-pavement system such as the shear modulus are compared for determining their influences on the coupled vibratory response.
Nonlinear Interaction of the Beat-Photon Beams with the Brain Neurocenters: Laser Neurophysics
NASA Astrophysics Data System (ADS)
Stefan, V. Alexander
2010-03-01
I propose a novel mechanism for laser-brain interaction: Nonlinear interaction of ultrashort pulses of beat-photon, (?1-- ?2), or double-photon, (?1+?2), footnotetextMaria Goeppert-Mayer, "Uber Elementarakte mit zwei Quantenspr"ungen, Ann Phys 9, 273, 95. (1931). beams with the corrupted brain neurocenters, causing a particular neurological disease. The open-scull cerebral tissue can be irradiated with the beat-photon pulses in the range of several 100s fs, with the laser irradiances in the range of a few mW/cm^2, repetition rate of a few 100s Hz, and in the frequency range of 700-1300nm generated in the beat-wave driven free electron laser.footnotetextV. Alexander Stefan, The Interaction of Photon Beams with the DNA Molecules: Genomic Medical Physics. American Physical Society, 2009 APS March Meeting, March 16-20, 2009, abstract #K1.276; V. Stefan, B. I. Cohen, and C. Joshi, Nonlinear Mixing of Electromagnetic Waves in Plasmas Science 27 January 1989:Vol. 243. no. 4890, pp. 494 -- 500 (January 1989). This method may prove to be an effective mechanism in the treatment of neurological diseases: Parkinson's, Lou Gehrig's, and others.
NASA Technical Reports Server (NTRS)
Noor, A. K.; Peters, J. M.
1981-01-01
Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.
He, Qingbo Xu, Yanyan; Lu, Siliang; Dai, Daoyi
2014-04-28
This Letter reports an out-of-resonance vibro-acoustic modulation (VAM) effect in nonlinear ultrasonic evaluation of a microcracked cantilever beam. We design a model to involve the microcracked cantilever beam in a nonlinear oscillator system whose dynamics is introduced to extend the operating vibration excitation band of the VAM out of resonance. The prototype model exhibits an effective bandwidth four times that of the traditional linear model. The reported VAM effect allows efficiently enhancing the detection, localization, and imaging of various types of microcracks in solid materials at out-of-resonance vibration excitation frequencies.
NASA Astrophysics Data System (ADS)
Sasmal, Saptarshi; Kalidoss, S.
2015-05-01
In the present study, investigations on fiber-reinforced plastic (FRP) plated-reinforced concrete (RC) beam are carried out. Numerical investigations are performed by using a nonlinear finite element analysis by incorporating cracking and crushing of concrete. The numerical models developed in the present study are validated with the results obtained from the experiment under monotonic load using the servo-hydraulic actuator in displacement control mode. Further, the validated numerical models are used to evaluate the influence of different parameters. It is found from the investigations that increase in the elastic modulus of adhesive layer and CFRP laminate increases the interfacial stresses whereas increase in laminate modulus decreases the displacement and reinforcement strain of the beam. It is also observed that increase in the adhesive layer can largely reduce the interfacial stresses, whereas increase in laminate thickness increases it. However, increase in laminate thickness decreases the displacement and reinforcement strain of the beam significantly. It is mention worthy that increase in laminate length reduces the interfacial stresses, whereas CFRP width change does not affect the interfacial stresses. The study will be useful for the design and practicing engineers for arriving at the FRP-based strengthening schemes for RC structures judiciously.
Korte, Dorota; Franko, Mladen
2015-01-01
In this work, complex geometrical optics is, for what we believe is the first time, applied instead of geometrical or wave optics to describe the probe beam interaction with the field of the thermal wave in photothermal beam deflection (photothermal deflection spectroscopy) experiments on thin films. On the basis of this approach the thermal (thermal diffusivity and conductivity), optical (energy band gap), and transport (carrier lifetime) parameters of the semiconductor thin films (pure TiO_{2}, N- and C-doped TiO_{2}, or TiO_{2}/SiO_{2} composites deposited on a glass or aluminum support) were determined with better accuracy and simultaneously during one measurement. The results are in good agreement with results obtained by the use of other methods and reported in the literature. PMID:26366490
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.
2014-03-21
We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with ?{sub eff}{sup (2)}???0.6?pm V{sup ?1}) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired.
Fast spatial beam shaping by acousto-optic diffraction for 3D non-linear microscopy.
Akemann, Walther; Léger, Jean-François; Ventalon, Cathie; Mathieu, Benjamin; Dieudonné, Stéphane; Bourdieu, Laurent
2015-11-01
Acousto-optic deflection (AOD) devices offer unprecedented fast control of the entire spatial structure of light beams, most notably their phase. AOD light modulation of ultra-short laser pulses, however, is not straightforward to implement because of intrinsic chromatic dispersion and non-stationarity of acousto-optic diffraction. While schemes exist to compensate chromatic dispersion, non-stationarity remains an obstacle. In this work we demonstrate an efficient AOD light modulator for stable phase modulation using time-locked generation of frequency-modulated acoustic waves at the full repetition rate of a high power laser pulse amplifier of 80 kHz. We establish the non-local relationship between the optical phase and the generating acoustic frequency function and verify the system for temporal stability, phase accuracy and generation of non-linear two-dimensional phase functions. PMID:26561090
Lagrange-type formulation for finite element analysis of non-linear beam vibrations
NASA Astrophysics Data System (ADS)
Sarma, B. S.; Varadan, T. K.
1983-01-01
A Lagrange-type formulation for finite element analysis of non-linear vibrations of immovably supported beams is presented. Two equations of motion coupled in axial and transverse displacements are derived by using Lagrange's equations. By neglecting the in-plane inertial effects, these equations are written in terms of the transverse displacement alone. Upon defining certain properties for the non-linear oscillatory behaviour of the transverse displacement, the governing equation is reduced to an equation in space alone from which the eigenvalue-like quantity is computed. The governing equation is solved in two ways. A direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency. A Rayleigh quotient type of formulation, similar to linear vibration analysis, is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear FEM model and is maintained constant at all amplitudes. Numerical results are compared with available results and they corroborate the observations of earlier research workers.
Time-domain modeling of nonlinear distortion of pulsed finite amplitude sound beams.
Remenieras, J P; Bou Matar, O; Labat, V; Patat, F
2000-03-01
This work aims to validate a time domain numerical model for the nonlinear propagation of a short pulse of finite amplitude sound beam propagation in a tissue-mimicking liquid. The complete evolution equation is simply derived by a superposition of elementary operators corresponding to the 'one effect equation'. Diffraction LD, absorption and dispersion LAD, and nonlinear distortion LNL effects are treated independently using a first order operator-splitting algorithm. Using the method of fractional steps, the normal particle velocity and the acoustical pressure are calculated plane by plane, at each point of a two-dimensional spatial grid, from the surface of the plane circular transducer to a specified distance. The LA operator is a time convolution between the particle velocity and the causal attenuation filter built after the Kramers-Kroning relations. The LNL operator is a time-based transformation obtained by following an implicit Poisson analytic solution. The LD operator is the usual Rayleigh integral. We present a comparison between theoretical and experimental temporal pressure waveform and axial pressure curves for fundamental (2.25 MHz), second, third and fourth harmonics, obtained after spectral analysis. PMID:10829679
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790 nm
NASA Astrophysics Data System (ADS)
Serna, J.; Rueda, E.; García, H.
2014-11-01
The two-photon absorption (TPA) coefficient ? and the nonlinear index of refraction n2 for bulk cuprous oxide (Cu2O) direct gap semiconductor single crystal have been measured by using a balance-detection Z-scan single beam technique, with an excellent signal to noise ratio. Both coefficients were measured at 790 nm using a 65 fs laser pulse at a repetition rate of 90.9 MHz, generated by a Ti:Sapphire laser oscillator. The experimental values for ? were explained by using a model that includes allowed-allowed, forbidden-allowed, and forbidden-forbidden transitions. It was found that the forbidden-forbidden transition is the dominant mechanism, which is consistent with the band structure of Cu2O. The low value for ? found in bulk, as compared with respect to thin film, is explained in terms of the structural change in thin films that result in opposite parities of the conduction and valence band. The n2 is also theoretically calculated by using the TPA dispersion curve and the Kramers-Kronig relations for nonlinear optics.
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790?nm
Serna, J.; Rueda, E.; García, H.
2014-11-10
The two-photon absorption (TPA) coefficient ? and the nonlinear index of refraction n{sub 2} for bulk cuprous oxide (Cu{sub 2}O) direct gap semiconductor single crystal have been measured by using a balance-detection Z-scan single beam technique, with an excellent signal to noise ratio. Both coefficients were measured at 790?nm using a 65 fs laser pulse at a repetition rate of 90.9?MHz, generated by a Ti:Sapphire laser oscillator. The experimental values for ? were explained by using a model that includes allowed-allowed, forbidden-allowed, and forbidden-forbidden transitions. It was found that the forbidden-forbidden transition is the dominant mechanism, which is consistent with the band structure of Cu{sub 2}O. The low value for ? found in bulk, as compared with respect to thin film, is explained in terms of the structural change in thin films that result in opposite parities of the conduction and valence band. The n{sub 2} is also theoretically calculated by using the TPA dispersion curve and the Kramers-Kronig relations for nonlinear optics.
NASA Astrophysics Data System (ADS)
Chrysochoidis, Nikolaos A.; Barouni, Antigoni K.; Saravanos, Dimitris A.
2009-03-01
This paper investigates the potential of a novel SHM method for the detection of delamination cracks in composites which exploits the nonlinear ultrasonic response with in-situ d31 piezoceramic actuators and sensors. Composite beam specimens with artificially created delamination cracks are tested, entailing two piezoceramic actuator patches, the first to generate a low frequency, high power modal excitation and the second a high frequency acoustical wave, as well as a piezoceramic sensor. Nonlinearities induced at the high-frequency signal, such as sidebands at the spectral components as long as modulations at the measured sensory voltage are evaluated as damage indicators. Experimental results quantify the potential of the method in detecting small delamination cracks through spectral sideband components. The influence of high-frequency on the effectiveness of the method is shown. Additionally, the effect of the magnitude of applied voltage on the low frequency actuator on the formation of spectral components is investigated. Finally, the obtained results of the present method are compared with a guided wave based pitch and catch SHM method using the same actuator-sensor pair to excite and monitor the propagation of the first symmetric and asymmetric Lamb waves.
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-? method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
Karaton, Muhammet
2014-01-01
A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-? method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched. PMID:24578667
NASA Technical Reports Server (NTRS)
Ball, R. E.
1972-01-01
A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.
NASA Astrophysics Data System (ADS)
Yan, Liping; Chen, Benyong; Zhang, Cen; Zhang, Enzheng; Yang, Ye
2015-08-01
In order to analyze and characterize the periodic nonlinear error resulting from the misalignment of a polarizing beam splitter (PBS) in a laser heterodyne interferometer more accurately, in this paper, starting from the light separating principle of thin-film PBS, we have found that the root cause of the periodic nonlinear error is the frequency mixing induced by the deviation from the Brewster angle of the incident angle or by the rotation of the incident plane when the PBS is misaligned. Moreover, we have established the direct function relationships between the periodic nonlinear error and different PBSs’ misalignment errors for the first time. The theoretical analysis shows that the periodic nonlinear error arising from the PBS’s yaw error is the largest and the maximal nonlinear errors are unequal even if the positive yaw angle is equal to the negative yaw angle. The nonlinear errors are much smaller under the PBS’s roll and pitch errors. The experiments of polarizing leakage and nonlinear error measurement under the PBS’s yaw error demonstrate that the experimental results are in agreement with the theoretical analysis.
Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam
NASA Astrophysics Data System (ADS)
Bar-Yoseph, P. Z.; Fisher, D.; Gottlieb, O.
1996-11-01
Spectral element methods are high order accurate methods which have been successfully utilized for solving ordinary and partial differential equations. In this paper the space-time spectral element (STSE) method is employed to solve a simply supported modified Euler-Bernoulli nonlinear beam undergoing forced lateral vibrations. This system was chosen for analysis due to the availability of a reference solution of the form of a forced Duffing's equation. Two formulations were examined: i) a generalized Galerkin method with Hermitian polynomials as interpolants both in spatial and temporal discretization (HHSE), ii) a mixed discontinuous Galerkin formulation with Hermitian cubic polynomials as interpolants for spatial discretization and Lagrangian spectral polynomials as interpolants for temporal discretization (HLSE). The first method revealed severe stability problems while the second method exhibited unconditional stability and was selected for detailed analysis. The spatial h-convergence rate of the HLSE method is of order ?= p s+1 (where p s is the spatial polynomial order). Temporal p-convergence of the HLSE method is exponential and the h-convergence rate based on the end points (the points corresponding to the final time of each element) is of order 2 p T-1 ???2 p T+1 (where p T is the temporal polynomial order). Due to the high accuracy of the HLSE method, good results were achieved for the cases considered using a relatively large spatial grid size (4 elements for first mode solutions) and a large integration time step (1/4 of the system period for first mode solutions, with p T=3). All the first mode solution features were detected including the onset of the first period doubling bifurcation, the onset of chaos and the return to periodic motion. Two examples of second mode excitation produced homogeneous second mode and coupled first and second mode periodic solutions. Consequently, the STSE method is shown to be an accurate numerical method for simulation of nonlinear spatio-temporal dynamical systems exhibiting chaotic response.
NASA Technical Reports Server (NTRS)
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
Arbind, Archana
2012-10-19
: : : : : : : : : : : : : : : : : : : : : : : : : : : : : 49 8.1. Micro-Structure Dependent FGM Beam . . . . . . . . . . . . . . . 49 8.1.1. Pin-pin connected beam . . . . . . . . . . . . . . . . . 49 8.1.2. Clamped beam . . . . . . . . . . . . . . . . . . . . . . 53 8.1.3. Numerical results for general... third order beam theory . 55 8.2. FGM Beams under Thermo-Mechanical Loads . . . . . . . . . . . 56 8.2.1. Temperature pro le and section properties . . . . . . . 56 8.2.2. Cantilever beam . . . . . . . . . . . . . . . . . . . . . . 61 8.2.3. Pinned...
NASA Astrophysics Data System (ADS)
Kienappel, K.
1982-02-01
The influence of various parameters such as tube length, change of diameter, tube shape, and tube material on the transfer function was investigated experimentally. In many cases there is a pronouncedly nonlinear behavior. A method is presented to estimate the transfer characteristics for such a nonlinear system. When unsteady pressures are measured on the end of a pressure tube instead of directly at the desired site, the pressure tube changes the unsteady signal. This characteristic is demonstrated to be frequency dependent. Pressure amplitude measurement results are used to determine real values for the transfer function. An empirical model of an estimated pressure control system is given. The possibility of approximating nonlinear pressure transfer from unsteady pressure measurement is shown.
NASA Astrophysics Data System (ADS)
Kienappel, K.
1980-07-01
The influence of various parameters such as tube length, change of diameter, tube shape and tube material on the transfer function was investigated experimentally. In many cases there is a pronouncedly nonlinear behavior. A method is presented to estimate the transfer characteristics for such a nonlinear system. When unsteady pressures are measured on the end of a pressure tube instead of directly at the desired site, the pressure tube changes the unsteady signal. This characteristic is demonstrated to be frequency dependent. Pressure amplitude measurement results are used to determine real values for the transfer function. An empirical model of an estimated pressure control system is given. The possibility of approximating nonlinear pressure transfer from unsteady pressure measurement is shown.
NASA Astrophysics Data System (ADS)
Lapsanska, Hana; Chmelickova, Hana; Hrabovsky, Miroslav
2010-10-01
Weld geometric characteristics in laser overlapping spot welding of 0.6-mm AISI 304 stainless steel sheets were investigated. A pulsed Nd:YAG laser with maximal average power of 150 W was used for welding experiments with different laser beam energies in the range of 3.5 J to 6.2 J, keeping all other processing parameters constant. The main objective of these experiments was to study the effect of energy changes and to identify the welding mode in dependency on the beam effective peak power density. Each weld surface and its cross section were analyzed using a laser scanning confocal microscope. The spot diameter on the specimen, weld width, and penetration depth were measured. Three-dimensional surface reconstruction was realized to describe the effect of energy changes on weld surface properties.
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel
2014-12-10
We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.
Umeda, Takayuki
2008-06-15
Nonlinear evolution of the electron two-stream instability in a current-carrying plasma is examined by using a two-dimensional electromagnetic particle-in-cell simulation. Formation of electron phase-space holes is observed as an early nonlinear consequence of electron-beam-plasma interactions. Lower-hybrid waves, electrostatic, and electromagnetic whistler mode waves are also excited by different mechanisms during the ensuing nonlinear wave-particle interactions. It is shown by the present computer simulation with a large simulation domain and a long simulation time that these low-frequency waves can disturb the electrostatic equilibrium of electron phase-space holes, suggesting that the lifetime of electron phase-space holes sometimes becomes shorter in a current-carrying plasma.
NASA Technical Reports Server (NTRS)
Moyer, E. T., Jr.
1984-01-01
The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.
NASA Astrophysics Data System (ADS)
Gao, Q. D.; Budny, R. V.
2015-03-01
By using gyro-Landau fluid transport model (GLF23), time-dependent integrated modeling is carried out using TRANSP to explore the dynamic process of internal transport barrier (ITB) formation in the neutral beam heating discharges. When the current profile is controlled by LHCD (lower hybrid current drive), with appropriate neutral beam injection, the nonlinear interplay between the transport determined gradients in the plasma temperature (Ti,e) and toroidal velocity (V?) and the E×B flow shear (including q-profile) produces transport bifurcations, generating spontaneously a stepwise growing ITB. In the discharge, the constraints imposed by the wave propagation condition causes interplay of the LH driven current distribution with the plasma configuration modification, which constitutes non-linearity in the LH wave deposition. The non-linear effects cause bifurcation in LHCD, generating two distinct quasi-stationary reversed magnetic shear configurations. The change of current profile during the transition period between the two quasi-stationary states results in increase of the E×B shearing flow arising from toroidal rotation. The turbulence transport suppression by sheared E×B flow during the ITB development is analysed, and the temporal evolution of some parameters characterized the plasma confinement is examined. Ample evidence shows that onset of the ITB development is correlated with the enhancement of E×B shearing rate caused by the bifurcation in LHCD. It is suggested that the ITB triggering is associated with the non-linear effects of the LH power deposition.
NASA Astrophysics Data System (ADS)
Zeng, Juan; Garg, Anurag; Kovacs, Andrew; Bajaj, Anil K.; Peroulis, Dimitrios
2015-05-01
Anchor supports in MEMS beams are often far from the ideally assumed built-in or step-up conditions. Practical fabrication processes often result in non-vertical anchoring supports (referred to as inclined supports in the following text) which significantly influence the post-release performance of the beam. This paper brings attention to the presence of the inclined supports in surface micromachined fixed-fixed beams and models the mechanical and electromechanical effects of inclined supports for the first time. Specifically, we calculate and validate the effects of residual stress and loading on the post-release beam behavior including their nonlinear large-displacement characteristics. In addition the model accounts for non-flat beam profiles caused by residual stress and/or a non-flat sacrificial layer profile. Inclined supports are modeled as cantilever beams connected to a horizontal beam. The Euler-Bernoulli equations for all beams are simultaneously solved to calculate the axial stress of the horizontal beam and the axial, translational, and rotational compliance of the supports. Nonlinear effects due to stretching and residual stress are also included. The calculated beam displacements agree with FEM models to within 1.1% in both the linear and nonlinear regimes. Furthermore, experimentally-obtained displacements of six fabricated beams with inclined supports agree to within 5.2% with the presented model.
NASA Astrophysics Data System (ADS)
Saccomandi, Giuseppe; Vitolo, Raffaele
2014-08-01
Using the theory of 1 + 1 hyperbolic systems we put in perspective the mathematical and geometrical structure of the celebrated circularly polarized waves solutions for isotropic hyperelastic materials determined by Carroll [Acta Mechanica 3, 167-181 (1967)]. We show that a natural generalization of this class of solutions yields an infinite family of linear solutions for the equations of isotropic elastodynamics. Moreover, we determine a huge class of hyperbolic partial differential equations having the same property of the shear wave system. Restricting the attention to the usual first order asymptotic approximation of the equations determining transverse waves we provide the complete integration of this system using generalized symmetries.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
NASA Astrophysics Data System (ADS)
Mojahedi, M.; Ahmadian, M. T.; Firoozbakhsh, K.
2013-12-01
The nonlinear dynamic and static deflection of a micro/nano gyroscope under DC voltages and base rotation are investigated. The gyroscope undertakes two coupled bending motions along the drive and sense directions and subjected to electrostatic actuations and intermolecular forces. The nonlinear governing equations of motion for the system with the effect of electrostatic force, intermolecular tractions and base rotation are derived using extended Hamilton principle. Under constant voltage, the gyroscope finds the preformed shape. First, the deflection of the micro/nano gyroscope under electrostatic forces is obtained by static and dynamic analyses. Furthermore, the static and dynamic instability of the system are investigated. Afterward the oscillatory behavior of the pre-deformed micro/nano gyroscope around equilibrium is studied. The effects of intermolecular and nonlinear parameters on the static and dynamic deflection, natural frequencies and instability of the micro/nano gyroscope are studied. The presented model can be used to exactly determine static and the dynamic behavior of vibratory micro/nano gyroscopes.
Edward A. Startsev; Ronald C. Davidson
2004-04-09
To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.
NASA Astrophysics Data System (ADS)
Munish, Aggarwal; Shivani, Vij; Niti, Kant
2015-11-01
The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode.
C. L. Bohn , P. Piot and B. Erdelyi
2008-05-31
According to its original Statement of Work (SOW), the overarching objective of this project is: 'To enhance substantially the understanding of the fundamental dynamics of nonequilibrium high-brightness beams with space charge.' Our work and results over the past three and half years have been both intense and fruitful. Inasmuch as this project is inextricably linked to a larger, growing research program - that of the Beam Physics and Astrophysics Group (BPAG) - the progress that it has made possible cannot easily be separated from the global picture. Thus, this summary report includes major sections on 'global' developments and on those that can be regarded as specific to this project.
Kanagawa, Tetsuya
2015-05-01
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set. PMID:25994696
Nonlinear combining of laser beams Pavel M. Lushnikov* and Natalia Vladimirova
Lushnikov, Pavel
and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation-focusing; (190.4370) Nonlinear optics, fibers; (140.3510) Lasers, fiber. http://dx.doi.org/10.1364/OL.39 of Mathematics and Statistics, University of New Mexico, New Mexico 87131, USA *Corresponding author: plushnik
Energy harvesting in a nonlinear piezomagnetoelastic beam subjected to random excitation
NASA Astrophysics Data System (ADS)
De Paula, Aline S.; Inman, Daniel J.; Savi, Marcelo A.
2015-03-01
This work addresses the influence of nonlinearities in energy harvesting from a piezomagnetoelastic structure subjected to random vibrations. Nonlinear equations of motion that describe the electromechanical system are given along with theoretical simulations. The numerical analysis presents a comparison between the voltage provided from a linear, nonlinear bistable and nonlinear monostable systems due to random vibration. Experimental performance of the generator exhibits qualitative agreement with the theory, showing an enhancement of piezoelectric power generation in a bistable system when it vibrates around both stable equilibrium points. A relationship between variations in the excitation and a bistable system response is established from numerical simulations, defining a region of enhanced power generation when compared to the linear and nonlinear monostable cases.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
NASA Astrophysics Data System (ADS)
Dou, Suguang; Jensen, Jakob Sřndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinear vibration analysis. An optimization procedure based on a gradient-based algorithm is developed and we use the adjoint method for efficient computation of design sensitivities. We consider several examples in which we find optimized beam width distributions that minimize or maximize fundamental or super-harmonic resonant responses.
The nonlinear OPC technique for laser beam control in turbulent atmosphere
NASA Astrophysics Data System (ADS)
Sprangle, P.; Penano, J. R.; Markov, Vladimir B.; Khizhnyak, Anatoliy; Ting, A.; Hafizi, Bahman; Davis, C. C.; DeSandre, L.
2012-10-01
This paper discusses a novel type of beam director for effective laser beacon formation in deep turbulence conditions. The concept of the proposed beam director is based on an innovative approach employing a Brillouin enhanced four-wave mixing (BEFWM) mechanism for generating a tight (small spot size) laser beacon on a remote image-resolved target. The BEFWM technique enables both amplification and total (phase and amplitude) conjugation of the beacon-forming beam without the need for wavefront sensors, deformable mirrors or predictive feedback algorithms. Total conjugation is critical for beam control in the presence of strong turbulence, whereas conventional adaptive optics methods do not have this capability. The phase information retrieved from the beacon beam can be used in conjunction with an AO system to propagate laser beams in deep turbulence.
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
NASA Astrophysics Data System (ADS)
Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.
2015-04-01
In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects could be readily achieved.
NASA Astrophysics Data System (ADS)
Sederberg, S.; Elezzabi, A. Y.
2015-10-01
Silicon-loaded nanoplasmonic waveguides were integrated onto a micron-scale characterization beam to allow for accurate and efficient nonlinear optical characterization. The waveguides consist of a 95 nm × 340 nm silicon core that is capped by a 60 nm thick gold film. The characterization beam is formed by precision cleaving one waveguide end facet and by deep silicon etching the substrate area adjacent to the other end facet. This configuration allows input radiation to be coupled directly to the waveguides using a microscope objective and output radiation to be out-coupled with a lensed single-mode optical fiber. The fabrication steps are characterized via scanning electron microscopy at various points throughout the process. The fabricated devices are optically characterized using an ultrafast nonlinear pump-probe time-domain spectroscopy setup. Ultrafast all-optical modulation is measured in the waveguides on two timescales: ?1 = 1.98 ± 0.40 ps and ?2 = 17.9 ± 6.8 ps.
Combination instabilities and non-linear vibratory interactions in beam systems
Cartmell, Matthew Phillip
combination instabilities are observed. In addition to the well-known sum-type combination instability existing between the fundamental out-of-plane bending and the torsional modes of the beam, investigation has revealed the occurrence of higher order...
NASA Technical Reports Server (NTRS)
Kvaternik, R. G.; Kaza, K. R. V.
1976-01-01
The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.
NASA Astrophysics Data System (ADS)
Shibata, A.; Ohishi, S.; Yabuno, H.
2015-08-01
In the present paper, we propose a simple method for controlling the nonlinear characteristics of the frequency response curve in a parametrically excited hinged-hinged beam with a movable end (changing from softening to hardening and decreasing the overhang in the frequency response curve). The proposed method is achieved simply by the attachment of a linear spring in the axial direction to the movable end and does not require any power. By applying the extended Hamilton's principle, the equation of motion of the beam in the lateral direction is derived, and the change in the nonlinear characteristics of the parametric resonance is theoretically analyzed while tuning the linear stiffness of the attached linear spring. The linear spring affects only the nonlinearity in the lateral vibration, but not the linear natural frequency of the beam. That is, the linear unstable region in the parametric resonance is not shifted, but only the frequency response curve can be changed. This is advantageous in applications to resonators, such as mass sensors and mechanical filters. It is shown experimentally that the nonlinear characteristics of the frequency response curve can be changed by tuning the stiffness of a linear spring. Furthermore, the experimental results reveal that quadratic damping plays a dominant role in determining the nonlinear characteristics of the steady-state amplitude for the case in which the nonlinearity in the system is modified to be relatively small.
NASA Astrophysics Data System (ADS)
Riabko, Alexander I.
1999-12-01
Profound understanding of nonlinear beam dynamics in accelerator has become critically important for successful operation of high brightness storage rings for nuclear and particle physics research. Combination of theoretical analysis, computer simulations and experimental measurements provide an effective way to understand complex problems of beam physics. This dissertation describes application of methods of nonlinear dynamics to analysis of three important problems in accelerator physics. First, the problem of particle motion in a double RF potential is studied both theoretically and experimentally. Development of Hamiltonian formalism for double RF system allows us to conduct a theoretical analysis of effects of time dependent harmonic RF phase and voltage modulation on a single particle dynamics. Parametric resonances, created by a weak time dependent perturbation, are analyzed in terms of action-angle variables of the unperturbed Hamiltonian, studied in numerical simulations and observed experimentally. Second, the dynamics of a test particle in a space charge dominated beam propagating through periodic focusing channel is studied. We show that a set of parametric resonances of the particle Hamiltonian call be excited by mismatched envelope oscillations in the transport channel. It is demonstrated that the onset of global chaos in the particle phase space exhibits a sharp transition when the amplitude of envelope oscillations is larger than a critical value. The relation between the critical envelope mismatch for the halo formation and the space charge perveance is obtained numerically. Finally, theoretical analysis of a single particle dynamics in quasi-isochronous (QI) storage rings is presented. We derive analytical solution for QI system, analyze its scaling properties and study effects of phase space damping and external harmonic modulation on a particle motion. We find that the RF phase modulation is particularly important in QI storage rings; this means that for successful operation of QI storage rings one should pay special attention to control of RF phase noise. In order to analyze the effect of stochastic excitations on QI system, we investigate effects of quantum fluctuation and quantum lifetime in QI system. The effects of harmonic RF phase modulation on equilibrium distribution function, quantum lifetime reduction and the occurrence of stochastic resonance are also studied.
NASA Astrophysics Data System (ADS)
Rashidian Vaziri, M. R.; Hajiesmaeilbaigi, F.; Maleki, M. H.
2013-03-01
Knowing the Gaussian beam parameters, such as its radius of curvature and spot size during propagation in nonlinear Kerr media, is of paramount importance in describing the observable far-field diffraction ring patterns as well as in design and stability analysis of Kerr-lens mode-locked resonators. Specifically, the sign of the beam radius of curvature after exiting these media has been proposed to be of assistance in recognizing their optical nonlinearity sign through determining the type of diffraction ring pattern in the far field. In order to be able to trace the evolution of the beam parameters in the Gaussian beam formalism, we have used the common aberration-free theory. We have shown that the nonlinear propagation problem of a fundamental Gaussian beam in a Kerr medium with an intensity-dependent index of refraction can be handled by assuming a ducting index profile along the propagation direction. Knowing the familiar ABCD matrix of a duct, the evolution of the mentioned beam parameters can be traced during propagation using the ABCD law in Gaussian beam theory. We have validated our ducting model by comparing its results with the outcomes of one widely used and accepted model which has been known to yield consistent results when electronic optical nonlinearity prevails. We have shown that when thermal optical nonlinearity is dominant, as in diffraction ring observation experiments, our ducting model yields sensible results and should be used. Our model predicts that when the sign of the thermal nonlinearity and the beam radius of curvature on the entrance plane of the medium are positive, the sign of the beam radius of curvature on the exit plane may have either sign, depending on the medium thickness used in the experiment. Hence, two types of diffraction ring pattern may be obtained using the same medium with two different thicknesses and this may cast doubt on the validity of the methods proposing the detection of the optical nonlinearity signs by observing these patterns. We have proposed a simple procedure for experimentally obtaining the two different types of diffraction pattern from the same medium.
Ali Shan, S.; National Centre For Physics , Shahdra Valley Road, 44000 Islamabad; Pakistan Institute of Engineering and Applied Sciences , Islamabad ; El-Tantawy, S. A.; Moslem, W. M.
2013-08-15
Arbitrary amplitude ion-acoustic waves in an unmagnetized plasma consisting of cold positive ions, superthermal electrons, and positrons beam are reported. The basic set of fluid equations is reduced to an energy-balance like equation. The latter is numerically analyzed to examine the existence regions for solitary and shock waves. It is found that only solitary waves can propagate, however, the model cannot support shocks. The effects of superthermality and beam parameters (via, positrons concentration and streaming velocity) on the existence region, as well as solitary wave profile have been discussed.
Progress on Optimization of the Nonlinear Beam Dynamics in the MEIC Collider Rings
Morozov, Vasiliy S.; Derbenev, Yaroslav S.; Lin, Fanglei; Pilat, Fulvia; Zhang, Yuhong; Cai, Y.; Nosochkov, Y. M.; Sullivan, Michael; Wang, M.-H.; Wienands, Uli
2015-09-01
One of the key design features of the Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is a small beta function at the interaction point (IP) allowing one to achieve a high luminosity of up to 1034 cm-2s-1. The required strong beam focusing unavoidably causes large chromatic effects such as chromatic tune spread and beam smear at the IP, which need to be compensated. This paper reports recent progress in our development of a chromaticity correction scheme for the ion ring including optimization of dynamic aperture and momentum acceptance.
NASA Astrophysics Data System (ADS)
Cammin, J.; Srivastava, S.; Tang, Q.; Barber, W. C.; Iwanczyk, J. S.; Hartsough, N. E.; Taguchi, K.
2012-03-01
Photon counting detectors are an emerging technology for spectral computed tomography. They have the potential to improve tissue contrast and specificity, reduce dose, and enable novel applications for K-edge and functional imaging. In this presentation various non-linear distortions were investigated that affect the image quality in photon-counting spectral CT: deadtime losses and spectral response, inherent to the new technology, and beam hardening artifacts that stem from the use of a polychromatic x-ray source. These effects were corrected or compensated for by performing calibration measurements. Techniques from material decomposition were applied to reconstruct images at a desired energy. Two methods were compared to synthesize a single monoenergetic image from photon counting data with multiple energy bins. The parameters were optimized to maximize a given image quality index. The procedures were evaluated on phantom data acquired on an experimental CT scanner with photon-counting detectors with two energy thresholds.
NASA Technical Reports Server (NTRS)
Hodges, D. H.; Ormiston, R. A.
1973-01-01
The nonlinear partial differential equations for the flapping and lead-lag degrees of freedom of a torisonally rigid, rotating cantilevered beam are derived. These equations are linearized about an equilibrium condition to study the flap-lag stability characteristics of hingeless helicopter rotor blades with zero twist and uniform mass and stiffness in the hovering flight condition. The results indicate that these configurations are stable because the effect of elastic coupling more than compensates for the destabilizing flap-lag Coriolis and aerodynamic coupling. The effect of higher bending modes on the lead-lag damping was found to be small and the common, centrally hinged, spring restrained, rigid blade approximation for elastic rotor blades was shown to be resonably satisfactory for determining flap-lag stability. The effect of pre-cone was generally stabilizing and the effects of rotary inertia were negligible.
Piezomagnetoelastic broadband energy harvester: Nonlinear modeling and characterization
NASA Astrophysics Data System (ADS)
Aravind Kumar, K.; Ali, S. F.; Arockiarajan, A.
2015-11-01
Piezomagnetoelastic energy harvesters are one among the widely explored configurations to improve the broadband characteristics of vibration energy harvesters. Such nonlinear harvesters follow a Moon beam model with two magnets at the base and one at the tip of the beam. The present article develops a geometric nonlinear mathematical model for the broadband piezomagnetoelastic energy harvester. The electromechanical coupling and the nonlinear magnetic potential equations are developed from the dimensional system parameters to describe the nonlinear dynamics exhibited by the system. The developed model is capable of characterizing the monostable, bistable and tristable operating regimes of the piezomagnetoelastic energy harvester, which are not explicit in the Duffing representation of the system. Bifurcations and attractor motions are analyzed as nonlinear functions of the distance between base magnets and the field strength of the tip magnet. The model is further used to characterize the potential wells and stable states, with due focus on the performance of the system in broadband energy harvesting.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
NASA Astrophysics Data System (ADS)
Kamiya, Keisuke; Yoshinaga, Terumitsu
This paper presents a method for analysis of steady-state vibration of a beam with breathing cracks, which open and close during vibration. There are several papers treating problems of vibration analysis of a beam with breathing cracks. However, due to their treatments of the condition which determines the switch between the open and closed states of the crack, it is difficult for one to obtain steady-state vibration efficiently by methods such as the incremental harmonic balance method. Since opening and closing of a breathing crack depends on the sign of the bending moment, or the curvature, of the beam, the key point to this problem is explicit treatment of the bending moment. The mixed variational principle allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper a governing equation of a beam with breathing cracks is derived by a finite element procedure based on the mixed variational principle. Then, the derived governing equations are solved by combining the iteration method and the harmonic balance method. Finally, examples of analysis by the presented method are given.
Kheifets, S.
1983-01-01
A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
NASA Astrophysics Data System (ADS)
Franchetti, G.; Schmidt, F.
2015-06-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom).
Wei, Jingsong; Yan, Hui
2014-08-14
Self-focusing is a well-researched phenomenon. Nanoscale spots can be achieved through self-focusing, which is an alternative method for achieving high-density data storage, high-resolution light imaging, and maskless nanolithography. Several research groups have observed that self-focusing spots can be reduced to nanoscale levels via incident laser power manipulation. Self-focusing spots can be analyzed by solving the nonlinear Schrödinger equation and the finite difference time domain method. However, both procedures are complex and time-consuming. In the present work, a multi-layer thin-lens self-focusing model that considers diffraction effects and changes of refractive index along the radial and film thickness directions is proposed to analyze the self-focusing behavior and traveling process of light beams intuitively. The self-focusing behaviors of As{sub 2}S{sub 3} are simulated, and results show that a nanoscale self-focusing spot with a radius of about 0.12??m can be formed at the bottom of nonlinear sample when the incident laser power exceeds 4.25?mW. Our findings are basically consistent with experimental reports and provide a good method for analyzing and understanding the self-focusing process. An appropriate application schematic design is also provided.
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines.
Franchetti, G; Schmidt, F
2015-06-12
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1-3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called "Poincaré surface of section," which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century. We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phase space (two degrees of freedom). PMID:26196806
Bindoni, Luca . E-mail: lucabindoni@inwind.it
2005-06-15
A technique for geometric and dosimetric pretreatment verification of step-and-shoot intensity modulated radiotherapy treatments (IMRT) using a beam imaging system (BIS) made up of a charge-coupled device (CCD) digital camera optically coupled with a metal-plate/phosphor screen is described. Some physical properties of BIS were investigated in order to demonstrate its capability to perform measurements with a high spatial resolution and a high sampling rate. High-speed imaging, with a minimum charge integration time on the CCD of 120 ms, can be performed. The study of the signal-to-noise ratio as a function of sampling time is presented. In-plane and cross-line pixel size was measured to be 0.368{+-}0.004 mm/pixel, which agrees within 0.5% of the manufacturer value of 0.366 mm. Spatial linearity results are very good and there are no detectable image distortions on whole 30x30 cm{sup 2} detector area. A software routine was written to automatically extract positions of the collimator leaves from the images of the field shaped by the multileaf collimator (MLC) and also to compare them with the coordinates from the treatment planning system (TPS), thus directly testing both the MLC positioning and the treatment parameters transfer from TPS to the linear accelerator in a fast and precise way. The dosimetric capabilities (characteristics) of the imaging device for photon beams with energies of 6 and 15 MV were studied. Additional plexiglass buildup layers, depending on x-ray energy, were needed to reach maximum efficiency. The energy dependence of the BIS response versus dose and dose rate was found to be linear over a wide range. Relative output factors of BIS as a function of field size, compared with values measured with an ionization chamber, were in good accord for smaller field sizes {<=}10x10 cm{sup 2} but showed differences up to 4% for all the energies at the respective buildup depth for bigger fields. Square field profiles at water-equivalent buildup depths, extracted from BIS maps, are compared with the corresponding scans performed with a diode detector. Disagreement is always shown in the regions outside the field penumbra (tails) and near the field edges only for field sizes {>=}15x15 cm{sup 2} due to the metal/phosphor screen higher sensitivity to low energy scattering x-rays. A straightforward correction method for the 'tails effect' was developed and then generalized to MLC-shaped fields. In order to demonstrate the validity of this procedure, the comparison between the two-dimensional (2D) dose distributions of a triangle MLC-shaped field and of two simple IMRT fields created by the superimposition of five segments resulting from BIS images and the dose distribution of the same fields achieved by film, was measured and reported. The gamma index method, introduced by Low et al. (1998), was used for 2D dose distributions analysis. Agreements are good for both 6 and 15 MV energies. The described technique provides a lower time-expensive mean to verify geometric and dosimetric accuracy of the treatment delivered in IMRT with the use of a high resolution beam imaging system and homemade software tools.
Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system
NASA Technical Reports Server (NTRS)
Whelan, D. A.; Stenzel, R. L.
1985-01-01
It is shown that the unstable electron-plasma waves of a beam-plasma system can generate electromagnetic radiation in a uniform plasma. The generation mechanism is a scattering of the unstable electron plasma waves off ion-acoustic waves, producing electromagnetic waves whose frequency is near the local plasma frequency. The wave vector and frequency matching conditions of the three-wave mode coupling are experimentally verified. The electromagnetic radiation is observed to be polarized with the electric field parallel to the beam direction, and its source region is shown to be localized to the unstable plasma wave region. The frequency spectrum shows negligible intensity near the second harmonic of the plasma frequency. These results suggest that the observed electromagnetic radiation of type III solar bursts may be generated near the local plasma frequency and observed downstream where the wave frequency is near the harmonic of the plasma frequency.
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals
Assanto, Gaetano; Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.
2010-11-15
The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.
Refraction of nonlinear beams by localized refractive index changes in nematic liquid crystals
NASA Astrophysics Data System (ADS)
Assanto, Gaetano; Minzoni, Antonmaria A.; Smyth, Noel F.; Worthy, Annette L.
2010-11-01
The propagation of solitary waves in nematic liquid crystals in the presence of localized nonuniformities is studied. These nonuniformities can be caused by external electric fields, other light beams, or any other mechanism which results in a modified director orientation in a localized region of the liquid-crystal cell. The net effect is that the solitary wave undergoes refraction and trajectory bending. A general modulation theory for this refraction is developed, and particular cases of circular, elliptical, and rectangular perturbations are considered. The results are found to be in excellent agreement with numerical solutions.
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
NASA Technical Reports Server (NTRS)
Manning, Robert M.
2012-01-01
The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.
NASA Astrophysics Data System (ADS)
Tsysar, S. A.; Nikolaeva, A. V.; Svet, V. D.; Khokhlova, V. A.; Yuldashev, P. V.; Sapozhnikov, O. A.
2015-10-01
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
NASA Astrophysics Data System (ADS)
Belashov, Vasily
We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega
Three-Dimensional Postbuckling Analysis of Curved Beams
NASA Technical Reports Server (NTRS)
Pai, P. Frank; Lee, Seung-Yoon
2002-01-01
Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.
NASA Astrophysics Data System (ADS)
Liu, Yongqi; Qi, Xinyuan; Lu, Yang; Cao, Zheng; Li, Shasha; Bai, Jintao
2016-01-01
We numerically and experimentally investigated the deflection of a laser beam in a photo-induced one dimensional (1D) photonic lattice (PL) in a pure LiNbO3 crystal accompanied with self-focusing and self-defocusing nonlinearities, respectively. The results show that the probe beam will be self-focused or self-defocused when the sample temperature is increased or decreased. Moreover, the light beam deflects to the direction of heat flux if there exists an additional temperature difference between the two lateral sides of the sample. The probe beam forms a deflected discrete circle soliton in the PL when the sample temperature is increased from 25 °C to 45°C and the additional temperature difference is ±5 °C. Our simulation results are in agreement with the experimental observation.
SEVERAL RECENT RESULTS IN NON LINEAR GEOMETRIC OPTICS
Joly, Jean-Luc
SEVERAL RECENT RESULTS IN NON LINEAR GEOMETRIC OPTICS JeanÂLuc JOLY CEREMAB, Universitâ??ee de, and to nonlinear geometric optics. Typical questions are the existence, the propagation, the interaction to rescaling) for the validity of the nonlinear geometric optics approximations. For quasilinear first order
Influence of axial loads on the nonplanar vibrations of cantilever beams
NASA Astrophysics Data System (ADS)
Carvalho, Eulher C.; Gonçalves, Paulo B.; Del Prado, Zenón; Rega, Giuseppe
2012-11-01
The three-dimensional motions of cantilever beams have been extensively studied in the past. This structural element can be found in several applications, including MEMS and NEMS. In many applications the beam is subjected to axial loads which can play an important role in the dynamics of very slender beams. In this paper a cantilever inextensible beam subject to a concentrated axial load and a lateral harmonic excitation is investigated. Special attention is given to the effect of axial load on the frequency-amplitude relation, bifurcations and instabilities of the beam, a problem not tackled in the previous literature on this subject. To this aim, the nonlinear integro-differential equations describing the flexural-flexural-torsional couplings of the beam are used, together with the Galerkin method, to obtain a set of discretized equations of motion, which are in turn solved by numerical integration using the Runge-Kutta method. Both inertial and geometric nonlinearities are considered in the present analysis. Due to symmetries of the beam cross section, the beam exhibits a 1:1 internal resonance which has an important role on the nonlinear oscillations and bifurcation scenario. The results show that the axial load influences the stiffness of the beam changing its nonlinear behavior from hardening to softening. A detailed parametric analysis using several tools of nonlinear dynamics, unveils the complex dynamics of the beam in the parametric or external resonance regions. Bifurcations leading to multiple coexisting solutions are observed.
On a nonlinear theory of thin rods
NASA Astrophysics Data System (ADS)
Luo, Albert C. J.
2010-12-01
In this paper, a nonlinear theory for a straight rod is presented from the general theory of the three-dimensional deformable-body in the Cartesian coordinate frame. A set of nonlinear strains is presented, and the stretch on central curve exactly satisfies the deformation geometrical relations. The relations between the Euler angles and deformation are given from the curvatures and torsion curvatures of the central curves, which can easily explain the existing theories of rods and beams. Full nonlinear equations of motion for a nonlinear rod are developed via the vector form. Such a treatise is different from the traditional treatises of nonlinear rods, based on the Cosserat's theory (e.g., Cosserat and Cosserat [1] in 1896) or the Kirchhoff assumptions (e.g., Kirchhoff [18] in 1859; Love [3] in 1944). This paper extends the ideas of Galerkin [4] in 1915. The nonlinear theory of thin rods can reduce to the existing theories for thin rods and beams, such ideas presented in this paper can be applied for development of the nonlinear theory for plates and shells as well.
A case study of analysis methods for large deflections of a cantilever beam
NASA Technical Reports Server (NTRS)
Craig, L. D.
1994-01-01
A load case study of geometric nonlinear large deflections of a cantilever beam is presented. The bending strain must remain elastic. Closed form solution and finite element methods of analysis are illustrated and compared for three common load cases. A nondimensional nomogram for each case is presented in the summary.
Geometrical Bioelectrodynamics
Vladimir G. Ivancevic; Tijana T. Ivancevic
2008-09-26
This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism. Keywords: Bioelectrodynamics, exterior geometrical machinery, Dirac-Feynman quantum electrodynamics, functional electrical stimulation
Selvaraj, J
2014-06-15
Purpose: To determine required PTV margins for ?1% loss in mean population TCP using systematic (?) and random (?) errors calculated from daily cone-beam CT (CBCT) images of head and neck patients. Methods: Daily CBCT images were acquired for 50 head and neck patients. The CBCT image sets acquired at each fraction were registered with planning CT to obtain positional errors for each patient for each fraction. Systematic and random errors were calculated from data collected for 50 patients as described in IPEM On Target report. CTV delineation uncertainty of 2mm is added quadratically to systematic error. Assuming a spherical target volume, the dose in each voxel of target volume is summed for each fraction in the treatment by shifting the dose grid to calculate mean population TCP inclusive of geometric uncertainties using a Monte Carlo method. These simulations were repeated for the set of ? and ? in each axis for different PTV margins and drop in TCP for each margin are obtained. In order to study the effect of dose-response curve on PTV margins, two different ?? of 0.048 Gy-1 and 0.218 Gy-1 representing steep and shallow dose-response curves are studied. ? were 2.5, 2.5, 2.1 mm and ? were 0.3, 0.3 0.2 mm respectively in x, y and z axis respectively. Results: PTV margins based on tumor radiobiological characteristics are 4.8, 4.8 and 4 mm in x, y and z axis assuming 25 treatment fractions for ?? 0.048 Gy-1 (steep) and 4.2,4.2 and 2.2 for ?? of 0.218 Gy-1 (shallow). While the TCP-based margins did not differ much in x and y axis, it is considerably smaller in z axis for shallow DRC. Conclusion: TCP based margins are substantially smaller than physical dose-based margin recipes. This study also demonstrates the importance of considering tumor radiobiological characteristics while deriving margins.
NASA Astrophysics Data System (ADS)
Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak
2015-10-01
The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show that the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.
Structural optimization for nonlinear dynamic response.
Dou, Suguang; Strachan, B Scott; Shaw, Steven W; Jensen, Jakob S
2015-09-28
Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance condition, thereby providing a means for tailoring its nonlinear response. The method is applied to the fundamental nonlinear resonance of a clamped-clamped beam and to the coupled mode response of a frame structure, and the results show that one can modify essential normal form coefficients by an order of magnitude by relatively simple changes in the shape of these elements. We expect the proposed approach, and its extensions, to be useful for the design of systems used for fundamental studies of nonlinear behaviour as well as for the development of commercial devices that exploit nonlinear behaviour. PMID:26303922
NASA Astrophysics Data System (ADS)
Djomo Mbong, T. L. M.; Siewe Siewe, M.; Tchawoua, C.
2015-05-01
This research work is based on the study of the dynamic of one-degree-of freedom nonlinear oscillator representing a built-in clamped-clamped prestressed beam model with a nonlinear damping. First of all, we model this moving structure where we regard the perturbations as a combination of both low-frequency force and high-frequency force. Then, we analyze the occurrence of vibrational resonance, where the response consists of a slow motion and a fast motion respectively with low and high frequencies. Through this, we obtain an approximate analytical expression of the response amplitude and we determine the values of the low frequency and the amplitude of the high-frequency force at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. Moreover, for fixed parameters values of the system, as the nonlinear damping vary, we found appearance and the disappearance of resonance with or without cross-well motion. Secondly, we study the chaotic dynamic of the beam. In this case, critical values of perturbation parameters for the onset of the chaotic motion are specified using Melnikov's method. Hence, the global dynamical changes of the system have been examined by plotting phase portrait, bifurcation diagram and their corresponding Lyapunov exponent.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
Lajimi, Seyed Amir Mousavi
2014-01-01
The nonlinear dynamics of a microbeam-rigid body gyroscope are investigated by using a continuation method. To study the nonlinear dynamics of the system, the Lagrangian of the system is discretized and the reduced-order model is obtained. By using the continuation method, the frequency-response curves are computed and the stability of response is determined.
Niethammer, Marc; Hart, Gabriel L.; Pace, Danielle F.; Vespa, Paul M.; Irimia, Andrei; Van Horn, John D.; Aylward, Stephen R.
2013-01-01
Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient. PMID:21995083
Jafari Bahman, F.; Maraghechi, B.
2013-02-15
Efficiency enhancement in free-electron laser is studied by three-dimensional and nonlinear simulation using tapered helical wiggler magnetic field or tapered ion-channel density. In order to reduce the saturation length, prebunched electron beam is used. A set of nonlinear and coupled differential equations are derived that provides the self-consistent description of the evolution of both an ensemble of electrons and the electromagnetic radiation. These equations are solved numerically to show that the combined effect of tapering and prebunching results in significant enhancement of power and considerable reduction of the saturation length. To have a deeper insight into the problem, an analytical treatment is also presented that uses the small signal theory to derive a modified pendulum equation.
NASA Astrophysics Data System (ADS)
Maraghechi, B.; Jokar, M.; Bahman, F. Jafari; Naeimabadi, A.; Naeimabadi
2013-10-01
A nonlinear simulation of the E × B drifting electron laser (DEL) and the free-electron laser (FEL), in three dimensions, is presented for a prebunched electron beam to study efficiency enhancement. For the planar wiggler with flat pole faces, prebunching considerably shortens the saturation length, which favors the DEL compared to the FEL. Operation of the DEL with the planar wiggler with parabolic pole faces was not found to be possible due to the modulation of the E × B drift by the wiggler. However, simulation results of the FEL with this type of wiggler are reported.
Hramov, A. E.; Koronovskii, A. A.; Kurkin, S. A.; Filatova, A. E.
2012-11-15
The report is devoted to the results of the numerical study of the virtual cathode (VC) formation conditions in the relativistic electron beam (REB) under the influence of the self-magnetic and external axial magnetic fields. The azimuthal instability of the relativistic electron beam leading to the formation of the vortex electron structure in the system was found out. This instability is determined by the influence of the self-magnetic fields of the relativistic electron beam, and it leads to the decrease of the critical value of the electron beam current (current when the non-stationary virtual cathode is formed in the drift space). The typical dependencies of the critical current on the external uniform magnetic field value were discovered. The effect of the beam thickness on the virtual cathode formation conditions was also analyzed.
Experimental verification of a bridge-shaped, nonlinear vibration energy harvester
Gafforelli, Giacomo Corigliano, Alberto; Xu, Ruize; Kim, Sang-Gook
2014-11-17
This paper reports a comprehensive modeling and experimental characterization of a bridge shaped nonlinear energy harvester. A doubly clamped beam at large deflection requires stretching strain in addition to the bending strain to be geometrically compatible, which stiffens the beam as the beam deflects and transforms the dynamics to a nonlinear regime. The Duffing mode non-linear resonance widens the frequency bandwidth significantly at higher frequencies than the linear resonant frequency. The modeling includes a nonlinear measure of strain coupled with piezoelectric constitutive equations which end up in nonlinear coupling terms in the equations of motion. The main result supports that the power generation is bounded by the mechanical damping for both linear and nonlinear harvesters. Modeling also shows the power generation is over a wider bandwidth in the nonlinear case. A prototype is manufactured and tested to measure the power generation at different load resistances and acceleration amplitudes. The prototype shows a nonlinear behavior with well-matched experimental data to the modeling.
M. O. Katanaev
2005-12-05
A description of dislocations and disclinations defects in terms of Riemann--Cartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free energy expression describing the static distribution of defects is presented, and equations of nonlinear elasticity theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal chiral SO(3)-field. In the defect-free case, the geometric model reduces to elasticity theory for the displacement vector field and to a principal chiral SO(3)-field model for the spin structure. As illustrated by the example of a wedge dislocation, elasticity theory reproduces only the linear approximation of the geometric theory of defects. It is shown that the equations of asymmetric elasticity theory for the Cosserat media can also be naturally incorporated into the geometric theory as the gauge conditions. As an application of the theory, phonon scattering on a wedge dislocation is considered. The energy spectrum of impurity in the field of a wedge dislocation is also discussed.
Non-isothermal elastoviscoplastic analysis of planar curved beams
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Carlson, R. L.; Riff, R.
1988-01-01
The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.
Saberian, E.; Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M.
2013-03-15
The propagation of ion-acoustic (IA) solitons is studied in a plasma system, comprised of warm ions and superthermal (Kappa distributed) electrons in the presence of an electron-beam by using a hydrodynamic model. In the linear analysis, it is seen that increasing the superthermality lowers the phase speed of the IA waves. On the other hand, in a fully nonlinear investigation, the Mach number range and characteristics of IA solitons are analyzed, parametrically and numerically. It is found that the accessible region for the existence of IA solitons reduces with increasing the superthermality. However, IA solitons with both negative and positive polarities can coexist in the system. Additionally, solitary waves with both subsonic and supersonic speeds are predicted in the plasma, depending on the value of ion-temperature and the superthermality of electrons in the system. It is examined that there are upper critical values for beam parameters (i.e., density and velocity) after which, IA solitary waves could not propagate in the plasma. Furthermore, a typical interaction between IA waves and the electron-beam in the plasma is confirmed.
Analytical method for describing the paraxial region of finite amplitude sound beams.
Hamilton, M F; Khokhlova, V A; Rudenko, O V
1997-03-01
A special analytical method, which combines the parabolic approximation (KZ equation) with nonlinear geometrical acoustics, is developed to model nonlinear and diffraction effects near the axis of a finite amplitude sound beam. The corresponding system of nonlinear equations describing waveform evolution is derived. For the case of an initially sinusoidal wave radiated by a Gaussian source, an analytic solution of the coupled equations is obtained for the paraxial region of the beam. The axial solution is expressed in both the time and frequency domains, and is analyzed in detail for both unfocused and focused beams in their preshock regions. Harmonic propagation curves are compared with finite difference solutions of the KZ equation, and good agreement is obtained for a variety of parameter values. PMID:9069621
Abrikosov, A.A. . E-mail: persik@itep.ru; Gozzi, E. . E-mail: gozzi@ts.infn.it; Mauro, D. . E-mail: mauro@ts.infn.it
2005-05-01
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional 'supertime,' we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.
NASA Astrophysics Data System (ADS)
Abrikosov, A. A.; Gozzi, E.; Mauro, D.
2005-05-01
Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime," we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schrödinger, the momentum and the coherent states ones.
Geometric Phase for Adiabatic Evolutions of General Quantum States
Wu, Biao; Liu, Jie; Niu, Qian; Singh, David J
2005-01-01
The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.
Raut, Ameeta A.
2010-07-14
Stiffness (EA) e xxB Extensional-Bending Stiffness exxD Bending Stiffness (EI) e iQ Nodal Force e i? Nodal Displacement of the Element eA Cross Sectional Area eI Second Moment of Area of the Beam j? Lagrange..., the virtual work done by the internal and external forces to move through their virtual displacements is zero. Thus based on this principle the following can be concluded. 0e e eI EW W W...
Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2000-01-01
A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.
Active vibration isolation with a MEMS device. Effects of nonlinearities on control efficiency
NASA Astrophysics Data System (ADS)
Meyer, Y.; Cumunel, G.
2015-08-01
This paper investigates piezoelectric and geometrical nonlinear effects on an active vibration isolation MEMS device. The objective is to study the impact of these nonlinearities on the vibration control efficiency. By confirming the importance of an accurate modeling of the microstructure, which is a laminated piezocomposite clamped-clamped beam in our example, we aim to develop high-performance active vibration isolation control. In this paper, the control law is an integral force feedback. The co-location condition is assumed because of the low device dimensions. First, a mathematical modeling is described and implemented into COMSOL Multiphysics software, with the governing equations of the beam taking into account geometric nonlinearities as well as piezoelectric nonlinearities. Then, active vibration control architecture is introduced. The active vibration control of the MEMS device is numerically implemented for different types of nonlinearity. The control performances of the classical linear structure are presented as a reference result. The impact of these nonlinearities on the control efficiency is presented and discussed.
Geometrical resonance in spatiotemporal systems
J. A. Gonzalez; A. Bellorin; L. I. Reyes; C. Vasquez; L. E. Guerrero
2003-10-19
We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems.
Hinker, P.; Hansen, C.
1993-09-01
An algorithm is presented which describes an application independent method for reducing the number of polygonal primitives required to faithfully represent an object. Reducing polygon count without a corresponding reduction in object detail is important for: achieving interactive frame rates in scientific visualization, reducing mass storage requirements, and facilitating the transmission of large, multi-timestep geometric data sets. This paper shows how coplanar and nearly coplanar polygons can be merged into larger complex polygons and re-triangulated into fewer simple polygons than originally required. The notable contributions of this paper are: (1) a method for quickly grouping polygons into nearly coplanar sets, (2) a fast approach for merging coplanar polygon sets and, (3) a simple, robust triangulation method for polygons created by 1 and 2. The central idea of the algorithm is the notion of treating polygonal data as a collection of segments and removing redundant segments to quickly form polygon hulls which represent the merged coplanar sets.
Saffman, Mark
Stripe Beams in Nonlinear Media: Snake Instability and Creation of Optical Vortices A. V. Mamaev* and M, Boulder, Colorado 80309-0440 (Received 27 November 1995) We analyze the evolution of 111 dimensional dark starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay
Geometric phase in optics and angular momentum of light
S C Tiwari
2004-03-20
Physical mechanism for the geometric phase in terms of angular momentum exchange is elucidated. It is argued that the geometric phase arising out of the cyclic changes in the tranverse mode space of the Gaussian light beams is a manifestation of the cycles in the momentum space of the light. Nonconservation of angular momentum in the spontaneous parametric down-conversion for the classical light beams is proposed to be related with the geometric phase.
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
Parallel processors and nonlinear structural dynamics algorithms and software
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1989-01-01
A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.
Geometric and projection effects in Kramers-Moyal analysis Steven J. Lade*
Geometric and projection effects in Kramers-Moyal analysis Steven J. Lade* Nonlinear Physics Centre mechanism that can affect the estimation of the coefficients is geometric projection effects. For some
BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint
Wang, Q.; Sprague, M.; Jonkman, J.; Johnson, N.
2015-01-01
BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
Lenart, V M; Gómez, S L; Bechtold, I H; Figueiredo Neto, A M; Salinas, S R
2012-01-01
We use Z-scan technique to investigate the nonlinear optical response of the thermotropic liquid crystal E7 in the neighborhood of the nematic-isotropic phase transition. The analysis of the data for the nonlinear optical birefringence is compatible with an effective critical exponent of the order parameter, ? = 0.28 ± 0.03, which is close to the classical value, ? = 0.25 , for a tricritical point. The nonlinear optical absorption in the nematic range depends on the geometrical configuration of the nematic director with respect to the polarization beam, and vanishes in the isotropic phase. PMID:22270454
Akimoto, Tetsuo . E-mail: takimoto@showa.gunma-u.ac.jp; Katoh, Hiroyuki; Kitamoto, Yoshizumi; Shirai, Katsuyuki; Shioya, Mariko; Nakano, Takashi
2006-04-01
Purpose: To evaluate the advantages of anatomy-based inverse optimization (IO) in planning high-dose-rate (HDR) brachytherapy. Methods and Materials: A total of 114 patients who received HDR brachytherapy (9 Gy in two fractions) combined with hypofractionated external beam radiotherapy (EBRT) were analyzed. The dose distributions of HDR brachytherapy were optimized using geometric optimization (GO) in 70 patients and by anatomy-based IO in the remaining 44 patients. The correlation between the dose-volume histogram parameters, including the urethral dose and the incidence of acute genitourinary (GU) toxicity, was evaluated. Results: The averaged values of the percentage of volume receiving 80-150% of the prescribed minimal peripheral dose (V{sub 8}-V{sub 15}) of the urethra generated by anatomy-based IO were significantly lower than the corresponding values generated by GO. Similarly, the averaged values of the minimal dose received by 5-50% of the target volume (D{sub 5}-D{sub 5}) obtained using anatomy-based IO were significantly lower than those obtained using GO. Regarding acute toxicity, Grade 2 or worse acute GU toxicity developed in 23% of all patients, but was significantly lower in patients for whom anatomy-based IO (16%) was used than in those for whom GO was used (37%), consistent with the reduced urethral dose (p <0.01). Conclusion: The results of this study suggest that anatomy-based IO is superior to GO for dose optimization in HDR brachytherapy for prostate cancer.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2005-01-01
An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.
DISPERSIVE NONLINEAR GEOMETRIC OPTICS Phillipe DONNAT
Rauch, Jeffrey
the fact that white light is split into a rainbow of colors on passing through a prism. The shorter wavelength light, bluish in color, is bent more than the longer wavelengths which are redish in color. The reason is that the short wavelength light travels more slowly through glass than does the longer
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.
1984-01-01
Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.
A geometrically nonlinear theory of elastic plates
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Atilgan, Ali R.; Danielson, D. A.
1992-01-01
A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.
NASA Astrophysics Data System (ADS)
Popa, Alexandru
2015-04-01
In a previous paper we proved a periodicity property of the Liénard-Wiechert equation in the case of the relativistic interaction between electromagnetic field and electron. This property predicts the existence of harmonics of the nonlinear Thomson scattered radiations in head on collisions between very intense laser beams and relativistic electron bunches. In this paper we present the properties of these radiations and show that our method for the calculation of the angular and spectral distributions of the backscattered radiations is in good agreement with the existing experimental data from literature. In the case of incident radiations having relativistic parameters of the order of few units and electron energies up to 100 MeV, our calculations predict the possibility of producing hard X-rays, having relatively high intensities, which are comparable to the intensities of the first harmonics, and energies higher than 1 MeV, using the current technology. Our theoretical model uses only one approximation, that of the neglecting of the radiative corrections.
Columnar deformation of human red blood cell by highly localized fiber optic Bessel beam stretcher
Lee, Sungrae; Joo, Boram; Jeon, Pyo Jin; Im, Seongil; Oh, Kyunghwan
2015-01-01
A single human red blood cell was optically stretched along two counter-propagating fiber-optic Bessel-like beams in an integrated lab-on-a-chip structure. The beam enabled highly localized stretching of RBC, and it induced a nonlinear mechanical deformation to finally reach an irreversible columnar shape that has not been reported. We characterized and systematically quantified this optically induced mechanical deformation by the geometrical aspect ratio of stretched RBC and the irreversible stretching time. The proposed RBC mechanism can realize a versatile and compact opto-mechanical platform for optical diagnosis of biological substances in the single cell level. PMID:26601005
Random Geometric Series E. BenNaim
Ben-Naim, Eli
Random Geometric Series E. BenNaim Theoretical Division and Center for Nonlinear Studies, Los Fibonacci sequence x n = x n-1 ± x n-2 [2--4] has links with various topics in condensed matter physics by the stochastic recursion law. For the random Fibonacci sequence, the typical behav ior is x n # e #n
Random Geometric Series E. Ben-Naim
Ben-Naim, Eli
Random Geometric Series E. Ben-Naim Theoretical Division and Center for Nonlinear Studies, Los and their relevance to disordered or random systems. For example, the random Fibonacci sequence xn = xn-1 ± xn-2 [2 Fibonacci sequence, the typical behav- ior is xn en with the intriguing Lyapunov exponent = 0
The Mathematics of Nonlinear Optics
MĂ©tivier, Guy
The Mathematics of Nonlinear Optics Guy MÂ´etivier March 7, 2009 Contents 1 Introduction 4 2 Examples of equations arising in nonlinear optics 11 3 The framework of hyperbolic systems 18 3.1 Equations Optics 49 5.1 Linear geometric optics . . . . . . . . . . . . . . . . . . . . . . . . . 49 5
Transition from linear- to nonlinear-focusing regime in filamentation
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678
Transition from linear- to nonlinear-focusing regime in filamentation.
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-01-01
Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature. PMID:25434678
Transition from linear- to nonlinear-focusing regime in filamentation
NASA Astrophysics Data System (ADS)
Lim, Khan; Durand, Magali; Baudelet, Matthieu; Richardson, Martin
2014-12-01
Laser filamentation in gases is often carried out in the laboratory with focusing optics to better stabilize the filament, whereas real-world applications of filaments frequently involve collimated or near-collimated beams. It is well documented that geometrical focusing can alter the properties of laser filaments and, consequently, a transition between a collimated and a strongly focused filament is expected. Nevertheless, this transition point has not been identified. Here, we propose an analytical method to determine the transition, and show that it corresponds to an actual shift in the balance of physical mechanisms governing filamentation. In high-NA conditions, filamentation is primarily governed by geometrical focusing and plasma effects, while the Kerr nonlinearity plays a more significant role as NA decreases. We find the transition between the two regimes to be relatively insensitive to the intrinsic laser parameters, and our analysis agrees well with a wide range of parameters found in published literature.
Multidimensional nonlinear systems
Savel'ev, M.V.
1987-06-01
The problem of the construction and of the integrability of systems of nonlinear partial differential equations in a multidimensional space is discussed. A proposed algebraic-geometric construction is illustrated for the example of completely integrable equations of the Bourlet type and their generalizations, for which, in particular, Baecklund transformations are obtained.
Analysis of nonlinear self-focusing phenomenon in high-power laser system based on ray-tracing
NASA Astrophysics Data System (ADS)
Wang, Weiwei; Li, Xiaotong; Cen, Zhaofeng; Zhang, Luwei
2014-11-01
In high power laser systems, nonlinear effect, one of the key factors of beam wavefront aberration and even irreversible damage to system, has always been one of the top considerations of researchers for decades. A hybrid ray-tracing method for both linear media and nonlinear media based on geometric optics is presented in this paper and realized by programming. In a simple optic system with KDP crystal, an obvious decline of beam quality is observed in high laser power density conditions and a method taking component intervals as compensation of beam quality is proved feasible. Considering the complexity of traditional modeling method based on surfaces, a modeling method based on components is established. Hopefully, the conclusions and flaws of this paper can shed light on relevant work and further research.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
2014-11-15
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, “Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry,” J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, “Geometric factor and directional response of single and multi-element particle telescopes,” Nucl. Instrum. Methods 95(1), 5–11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories. PMID:25430216
Beam halo in high-intensity beams
Wangler, T.P.
1993-06-01
In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.
Beam halo in high-intensity beams
Wangler, T.P.
1993-01-01
In space-charge dominated beams the nonlinear space-charge forces produce a filamentation pattern, which in projection to the 2-D phase spaces results in a 2-component beam consisting of an inner core and a diffuse outer halo. The beam-halo is of concern for a next generation of cw, high-power proton linacs that could be applied to intense neutron generators for nuclear materials processing. The author describes what has been learned about beam halo and the evolution of space-charge dominated beams using numerical simulations of initial laminar beams in uniform linear focusing channels. Initial results are presented from a study of beam entropy for an intense space-charge dominated beam.
Frénod, Emmanuel
The Geometrical Gyro-Kinetic Approximation Emmanuel Frénod Introduction : The two parameters Jiao Tong University The Geometrical Gyro-Kinetic Approximation Emmanuel Frénod1 May, 24th - 2013 Joint.frenod@univ-ubs.fr http://web.univ-ubs.fr/lmam/frenod/index.html Emmanuel Frénod The Geometrical Gyro-Kinetic
GEOMETRIC OPTICS AND INSTABILITY FOR NLS AND DAVEY-STEWARTSON MODELS
Sparber, Christof
GEOMETRIC OPTICS AND INSTABILITY FOR NLS AND DAVEY-STEWARTSON MODELS RÂ´EMI CARLES, ERIC DUMAS. Contents 1. Introduction 2 1.1. Motivation 2 1.2. Weakly nonlinear geometric optics 4 1.3. Instability and norm inflation 6 2. Interaction of high frequency waves in NLS type models 8 2.1. Geometric optics
Nonlinear springs with applications to flow regulation valves and mechanisms
Freeman, David Calvin
2008-01-01
This thesis focuses on the application of nonlinear springs for fluid flow control valves where geometric constraints, or fabrication technologies, limit the use of available solutions. Types of existing nonlinear springs ...
Filamentation with nonlinear Bessel vortices.
Jukna, V; Milián, C; Xie, C; Itina, T; Dudley, J; Courvoisier, F; Couairon, A
2014-10-20
We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics. PMID:25401574
NASA Astrophysics Data System (ADS)
Gunda, Jagadish Babu; Venkateswara Rao, Gundabathula
2015-11-01
Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged-hinged, clamped-clamped and clamped-hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.
Vibration energy harvesting by a Timoshenko beam model and piezoelectric transducer
NASA Astrophysics Data System (ADS)
Stoykov, S.; Litak, G.; Manoach, E.
2015-11-01
An electro-mechanical system of vibrational energy harvesting is studied. The beam is excited by external and kinematic periodic forces and damped by an electrical resistor through the coupled piezoelectric transducer. Nonlinearities are introduced by stoppers limiting the transverse displacements of the beam. The interaction between the beam and the stoppers is modeled as Winkler elastic foundation. The mechanical properties of the piezoelectric layer are taken into account and the beam is modeled as a composite structure. For the examined composite beam, the geometrically nonlinear version of the Timoshenko's beam theory is assumed. The equations of motion are derived by the principle of virtual work considering large deflections. An isogeometric approach is applied for space discretization and B-Splines are used as shape functions. Finally, the power output and the efficiency of the system due to harmonic excitations are discussed. The influence of the position of the stoppers and their length on the dynamics of the beam and consequently on the power output are analyzed and presented.
Nonlinear analysis and redesign of the mixed-mode bending delamination test
NASA Technical Reports Server (NTRS)
Reeder, J. R.; Crews, J. H., Jr.
1991-01-01
The Mixed Mode Bending (MMB) test uses a lever to simultaneously apply mode I and mode II loading to a split beam specimen. An iterative analysis that accounts for the geometric nonlinearity of the MMB test was developed. The analysis accurately predicted the measured load displacement response and the strain energy release rate, G, of an MMB test specimen made of APC2 (AS4/PEEK). The errors in G when calculated using linear theory were found to be as large as thirty percent in some cases. Because it would be inconvenient to use a nonlinear analysis to analyze MMB data, the MMB apparatus was redesigned to minimize the nonlinearity. The nonlinear analysis was used as a guide in redesigning the MMB apparatus. With the redesigned apparatus, loads were applied through a roller attached to the level and loaded just above the midplane of the test specimen. The redesigned apparatuus has geometric nonlinearity errors of less than three percent, even for materials substantially tougher than APC2. This apparatus was demonstrated by measuring the mixed mode delamination fracture toughness of APC2.
Nonlinear spin acceptance in electron storage rings
Kewisch, J.; Rossmanith, R.; Limberg, T.
1989-01-23
It is shown that the degree of polarization of a beam in electron storage rings can be limited by nonlinear effects. The strength of a nonlinear effect depends on the amplitude of the particles. Particles performing synchrotron and betatron oscillations with high amplitudes can contribute over proportionally to depolarization. As a result, the emittance of a beam is not allowed to exceed certain boundaries, otherwise the beam will become more and more depolarized. This limit is called nonlinear spin acceptance.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2004-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.
Energy harvesting from controlled buckling of piezoelectric beams
NASA Astrophysics Data System (ADS)
Ansari, M. H.; Karami, M. Amin
2015-11-01
A piezoelectric vibration energy harvester is presented that can generate electricity from the weight of passing cars or crowds. The energy harvester consists of a piezoelectric beam, which buckles when the device is stepped on. The energy harvester can have a horizontal or vertical configuration. In the vertical (direct) configuration, the piezoelectric beam is vertical and directly sustains the weight of the vehicles or people. In the horizontal (indirect) configuration, the vertical weight is transferred to a horizontal axial force through a scissor-like mechanism. Buckling of the beam results in significant stresses and, thus, large power production. However, if the beam’s buckling is not controlled, the beam will fracture. To prevent this, the axial deformation is constrained to limit the deformations of the beam. In this paper, the energy harvester is analytically modeled. The considered piezoelectric beam is a general non-uniform beam. The natural frequencies, mode shapes, and the critical buckling force corresponding to each mode shape are calculated. The electro-mechanical coupling and the geometric nonlinearities are included in the model. The design criteria for the device are discussed. It is demonstrated that a device, realized with commonly used piezoelectric patches, can generate tens of milliwatts of power from passing car traffic. The proposed device could also be implemented in the sidewalks or integrated in shoe soles for energy generation. One of the key features of the device is its frequency up-conversion characteristics. The piezoelectric beam undergoes free vibrations each time the weight is applied to or removed from the energy harvester. The frequency of the free vibrations is orders of magnitude larger than the frequency of the load. The device is, thus, both efficient and insensitive to the frequency of the force excitations.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES
Leonard, Naomi
MECHANICS AND NONLINEAR CONTROL: MAKING UNDERWATER VEHICLES RIDE AND GLIDE Naomi Ehrich Leonard \\Lambda \\Lambda Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544 naomi@princeton.edu Abstract: Methods from geometric mechanics and dynamical systems theory make
Pescara benchmarks: nonlinear identification
NASA Astrophysics Data System (ADS)
Gandino, E.; Garibaldi, L.; Marchesiello, S.
2011-07-01
Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
Geometrization of Quantum Mechanics
J. F. Carinena; J. Clemente-Gallardo; G. Marmo
2007-03-23
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified geometrical description for the different pictures of Quantum Mechanics. This construction provides an alternative to the usual GNS construction for pure states.
Reconciling Geometric Planners with
North Carolina at Chapel Hill, University of
Search #12;#12;Manipulation #12;Manipulation Perception Systems Navigation Learning Parallelism Control 3;#12;#12;#12;Physical Manipulation Geometric Search Manipulation Perception Systems Navigation Learning Parallelism-away Sweep #12;Physical Manipulation Geometric Search Manipulation Perception Systems Navigation Learning
Tuning piezoresistive transduction in nanomechanical resonators by geometrical asymmetries
NASA Astrophysics Data System (ADS)
Llobet, J.; Sansa, M.; Lorenzoni, M.; Borrisé, X.; San Paulo, A.; Pérez-Murano, F.
2015-08-01
The effect of geometrical asymmetries on the piezoresistive transduction in suspended double clamped beam nanomechanical resonators is investigated. Tapered silicon nano-beams, fabricated using a fast and flexible prototyping method, are employed to determine how the asymmetry affects the transduced piezoresistive signal for different mechanical resonant modes. This effect is attributed to the modulation of the strain in pre-strained double clamped beams, and it is confirmed by means of finite element simulations.
Hierarchies of Geometric Entanglement
Blasone, M; De Siena, S; Illuminati, F
2007-01-01
We introduce and discuss a class of generalized geometric measures of entanglement. For pure quantum states of N elementary subsystems, these extended measures are defined as the distances from the sets of K-separable states (K = 2,...,N). In principle, the entire set of these geometric measures provides a complete quantification and a hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied in the study of entanglement for different classes of N-qubit pure states, including W, GHZ, and cluster states. In all these cases we introduce a general method for the computation of the different geometric entanglement com- ponents. The entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between GHZ and W states, clarifying the original result...
Nonlinear competition in nematicon propagation.
Laudyn, Urszula A; Kwasny, Micha?; Piccardi, Armando; Karpierz, Miros?aw A; Dabrowski, Roman; Chojnowska, Olga; Alberucci, Alessandro; Assanto, Gaetano
2015-11-15
We investigate the role of competing nonlinear responses in the formation and propagation of bright spatial solitons. We use nematic liquid crystals (NLCs) exhibiting both thermo-optic and reorientational nonlinearities with continuous-wave beams. In a suitably prepared dye-doped sample and dual beam collinear geometry, thermal heating in the visible affects reorientational self-focusing in the near infrared, altering light propagation and self-trapping. PMID:26565843
Discontinuous Buckling of Wide Beams and Metabeams
Corentin Coulais; Johannes T. B. Overvelde; Luuk A. Lubbers; Katia Bertoldi; Martin van Hecke
2015-08-11
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams ---beams made from a mechanical metamaterial--- exhibit discontinuous buckling, an unstable form of buckling where the post-buckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit increasingly negative post-buckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as $1\\%$ numerically and $5\\%$ experimentally.
Discontinuous Buckling of Wide Beams and Metabeams
NASA Astrophysics Data System (ADS)
Coulais, Corentin; Overvelde, Johannes T. B.; Lubbers, Luuk A.; Bertoldi, Katia; van Hecke, Martin
2015-07-01
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams—beams made from a mechanical metamaterial—exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally.
Discontinuous Buckling of Wide Beams and Metabeams.
Coulais, Corentin; Overvelde, Johannes T B; Lubbers, Luuk A; Bertoldi, Katia; van Hecke, Martin
2015-07-24
We uncover how nonlinearities dramatically alter the buckling of elastic beams. First, we show experimentally that sufficiently wide ordinary elastic beams and specifically designed metabeams-beams made from a mechanical metamaterial-exhibit discontinuous buckling, an unstable form of buckling where the postbuckling stiffness is negative. Then we use simulations to uncover the crucial role of nonlinearities, and show that beams made from increasingly nonlinear materials exhibit an increasingly negative postbuckling slope. Finally, we demonstrate that for sufficiently strong nonlinearity, we can observe discontinuous buckling for metabeams as slender as 1% numerically and 5% experimentally. PMID:26252687
Astrometry without Geometric Distortion
NASA Astrophysics Data System (ADS)
Peng, Qingyu; Wang, Na; Peng, Huanwen; Zhang, Qingfeng; Li, Zhan
2015-08-01
Geometric distortion often exists in an astronomical CCD image even though a long focal length telescope is used. Two algorithms are developed to solve the pattern of geometric distortion and are tested based on many dithering CCD images observed at Yunnan Observatory using the 1 m telescope and 2.4 m telescope. Our results have shown that the astrometry for some moving targets such as an asteroid (Apophis) or a planetary natural satellite (Phoebe) is improved significantly after removing the geometric distortion in each CCD image. The algorithms can be also extended to applying to other telescopes for the purpose of precise astrometry or the check of positional propriety of a telescope.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
NASA Astrophysics Data System (ADS)
Karagiozis, K. N.; Paďdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
Morphing of Geometric Composites via Residual Swelling
Matteo Pezzulla; Steven A. Shillig; Paola Nardinocchi; Douglas P. Holmes
2015-05-30
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth--like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Hierarchies of Geometric Entanglement
M. Blasone; F. Dell'Anno; S. De Siena; F. Illuminati
2008-05-28
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of generalized geometric measures provides a quantification and hierarchical ordering of the different bipartite and multipartite components of the global geometric entanglement, and allows to discriminate among the different contributions. The extended measures are applied to the study of entanglement in different classes of $N$-qubit pure states. These classes include $W$ and $GHZ$ states, and their symmetric superpositions; symmetric multi-magnon states; cluster states; and, finally, asymmetric generalized $W$-like superposition states. We discuss in detail a general method for the explicit evaluation of the multipartite components of geometric entanglement, and we show that the entire set of geometric measures establishes an ordering among the different types of bipartite and multipartite entanglement. In particular, it determines a consistent hierarchy between $GHZ$ and $W$ states, clarifying the original result of Wei and Goldbart that $W$ states possess a larger global entanglement than $GHZ$ states. Furthermore, we show that all multipartite components of geometric entanglement in symmetric states obey a property of self-similarity and scale invariance with the total number of qubits and the number of qubits per party.
Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer
NASA Technical Reports Server (NTRS)
Pai, P. F.; Lee, S.-Y.
2003-01-01
This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.
Development of solution techniques for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Vos, R. G.; Andrews, J. S.
1974-01-01
Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.
Confined energy distribution for charged particle beams
Jason, Andrew J. (Los Alamos, NM); Blind, Barbara (Los Alamos, NM)
1990-01-01
A charged particle beam is formed to a relatively larger area beam which is well-contained and has a beam area which relatively uniformly deposits energy over a beam target. Linear optics receive an accelerator beam and output a first beam with a first waist defined by a relatively small size in a first dimension normal to a second dimension. Nonlinear optics, such as an octupole magnet, are located about the first waist and output a second beam having a phase-space distribution which folds the beam edges along the second dimension toward the beam core to develop a well-contained beam and a relatively uniform particle intensity across the beam core. The beam may then be expanded along the second dimension to form the uniform ribbon beam at a selected distance from the nonlinear optics. Alternately, the beam may be passed through a second set of nonlinear optics to fold the beam edges in the first dimension. The beam may then be uniformly expanded along the first and second dimensions to form a well-contained, two-dimensional beam for illuminating a two-dimensional target with a relatively uniform energy deposition.
NASA Technical Reports Server (NTRS)
Simitses, George J.; Carlson, Robert L.; Riff, Richard
1991-01-01
The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.
Wave function as geometric entity
B. I. Lev
2011-02-10
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any manifold. A solution of this equation is obtained in terms of geometric treatment. Interference of electrons whose wave functions are represented by geometric entities is considered. New experiments concerning the geometric nature of electrons are proposed.
Geometrical description of the onset of multi-pulsing in mode-locked laser cavities
Wai, Ping-kong Alexander
Geometrical description of the onset of multi- pulsing in mode-locked laser cavities Feng Li,1 P. K-locked laser cavity. The resulting geometrical description of the laser dynamics completely characterizes. The results suggest ways to engineer the nonlinear losses in the cavity in order to achieve an enhanced
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Complex geometric optics for symmetric hyperbolic systems I: linear theory
Omar Maj
2008-02-12
We obtain an asymptotic solution for $\\ep \\to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.
NASA Astrophysics Data System (ADS)
Tahani, Masoud; Askari, Amir R.
2014-09-01
In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.
Nonlinear dynamics of a support-excited flexible rotor with hydrodynamic journal bearings
NASA Astrophysics Data System (ADS)
Dakel, Mzaki; Baguet, Sébastien; Dufour, Régis
2014-05-01
The major purpose of this study is to predict the dynamic behavior of an on-board rotor mounted on hydrodynamic journal bearings in the presence of rigid support movements, the target application being turbochargers of vehicles or rotating machines subject to seismic excitation. The proposed on-board rotor model is based on Timoshenko beam finite elements. The dynamic modeling takes into account the geometric asymmetry of shaft and/or rigid disk as well as the six deterministic translations and rotations of the rotor rigid support. Depending on the type of analysis used for the bearing, the fluid film forces computed with the Reynolds equation are linear/nonlinear. Thus the application of Lagrange's equations yields the linear/nonlinear equations of motion of the rotating rotor in bending with respect to the moving rigid support which represents a non-inertial frame of reference. These equations are solved using the implicit Newmark time-step integration scheme. Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability. The influence of sinusoidal rotational or translational motions of the support, the accuracy of the linear 8-coefficient bearing model and the interest of the nonlinear model for a hydrodynamic journal bearing are examined and discussed by means of stability charts, orbits of the rotor, time history responses, fast Fourier transforms, bifurcation diagrams as well as Poincaré maps.
Nonlinear vibrational microscopy
Holtom, Gary R. (Richland, WA); Xie, Xiaoliang Sunney (Richland, WA); Zumbusch, Andreas (Munchen, DE)
2000-01-01
The present invention is a method and apparatus for microscopic vibrational imaging using coherent Anti-Stokes Raman Scattering or Sum Frequency Generation. Microscopic imaging with a vibrational spectroscopic contrast is achieved by generating signals in a nonlinear optical process and spatially resolved detection of the signals. The spatial resolution is attained by minimizing the spot size of the optical interrogation beams on the sample. Minimizing the spot size relies upon a. directing at least two substantially co-axial laser beams (interrogation beams) through a microscope objective providing a focal spot on the sample; b. collecting a signal beam together with a residual beam from the at least two co-axial laser beams after passing through the sample; c. removing the residual beam; and d. detecting the signal beam thereby creating said pixel. The method has significantly higher spatial resolution then IR microscopy and higher sensitivity than spontaneous Raman microscopy with much lower average excitation powers. CARS and SFG microscopy does not rely on the presence of fluorophores, but retains the resolution and three-dimensional sectioning capability of confocal and two-photon fluorescence microscopy. Complementary to these techniques, CARS and SFG microscopy provides a contrast mechanism based on vibrational spectroscopy. This vibrational contrast mechanism, combined with an unprecedented high sensitivity at a tolerable laser power level, provides a new approach for microscopic investigations of chemical and biological samples.
Gradient Nonlinear Pancharatnam-Berry Metasurfaces
NASA Astrophysics Data System (ADS)
Tymchenko, Mykhailo; Gomez-Diaz, J. Sebastian; Lee, Jongwon; Nookala, Nishant; Belkin, Mikhail A.; AlĂą, Andrea
2015-11-01
We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multiquantum-well substrates, establishing a platform to control the nonlinear wave front at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization manipulation. Our findings open a new direction for nonlinear optics, in which phase matching issues are relaxed, and an unprecedented level of local wave front control is achieved over thin devices with giant nonlinear responses.
Gradient Nonlinear Pancharatnam-Berry Metasurfaces.
Tymchenko, Mykhailo; Gomez-Diaz, J Sebastian; Lee, Jongwon; Nookala, Nishant; Belkin, Mikhail A; Alů, Andrea
2015-11-13
We apply the Pancharatnam-Berry phase approach to plasmonic metasurfaces loaded by highly nonlinear multiquantum-well substrates, establishing a platform to control the nonlinear wave front at will based on giant localized nonlinear effects. We apply this approach to design flat nonlinear metasurfaces for efficient second-harmonic radiation, including beam steering, focusing, and polarization manipulation. Our findings open a new direction for nonlinear optics, in which phase matching issues are relaxed, and an unprecedented level of local wave front control is achieved over thin devices with giant nonlinear responses. PMID:26613471
Polychromatic nonlinear surface modes generated by supercontinuum light
Dreischuh, Alexander
. N. Christodoulides, "Polychromatic partially spatially incoherent solitons in a noninstantaneous of a nonlinear waveguide array. We describe simultaneous spatial and spectral beam reshaping associated. © 2006 Optical Society of America OCIS codes: (190.4420) Nonlinear optics, transverse effects in; (190
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
Time and Geometric Quantization
NASA Astrophysics Data System (ADS)
Abrikosov, A. A.; Gozzi, E.; Mauro, D.
In this paper we briefly review the functional version of the Koopman-von Neumann operatorial approach to classical mechanics. We then show that its quantization can be achieved by freezing to zero two Grassmannian partners of time. This method of quantization presents many similarities with the one known as Geometric Quantization.
ERIC Educational Resources Information Center
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Lin, Ming C.
paths Delay of sound Uses distance of path Attenuation from distance Inverse distance d c c: speedGeometric Sound Propagation Micah Taylor #12;Sound propagation Given a sound source in a scene arrive at the listener #12;Sound propagation Sound travels slow 344 m/s Specular reflections Perfect
LABORATORY I: GEOMETRIC OPTICS
Minnesota, University of
Lab I - 1 LABORATORY I: GEOMETRIC OPTICS In this lab, you will solve several problems related to the formation of optical images. Most of us have a great deal of experience with the formation of optical images this laboratory, you should be able to: Â· Describe features of real optical systems in terms of ray diagrams
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
Acoustic nonlinearity in fluorinert FC-43
Pantea, Cristian; Sinha, Dipen N; Osterhoudt, Curtis F; Mombourquette, Paul C
2009-01-01
Fluorinert FC-43 nonlinearity was investigated using two approaches: (i) a finite amplitude method with harmonic production; and (ii) a nonlinear frequency mixing in the fluid with consequent beam profile measurement of the difference frequency. The finite amplitude method provides information on the coefficient of nonlinearity, {beta}, through the amplitudes of the fundamental and the second harmonic, at a certain transmitter-receiver distance. A calibrated hydrophone was used as a receiver, in order to obtain direct pressure measurements of the acoustic waves in the fluid. The role of transmitter-receiver distance in {beta} determination is investigated. In the second approach, a single transducer is used to provide two high-frequency beams. The collinear high-frequency beams mix nonlinearly in the fluid resulting in a difference frequency beam and higher order harmonics of the primaries. The difference frequency beam profite is investigated at lengths beyond the mixing distance. The experimental data are compured with the KZK theory.
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to calculate basically two model variations that can be seen as geometric extremes of all available input data. This does not lead to a probability distribution for the spatial position of geometric elements but it defines zones of major (or minor resp.) geometric variations due to data uncertainty. Both model evaluations are then analyzed together to give ranges of possible model outcomes in metric units.
Geometric phase in inhomogeneous optical nutation
NASA Astrophysics Data System (ADS)
Yu, Yanxia; Pan, Hui; Xue, Liyuan; Guo, Liping; Wang, Zisheng
2015-11-01
Optical nutation and its geometric phase are investigated in terms of an inhomogeneous Bloch equation with a constant term. The analytic solution of optical nutation is obtained by mapping it onto a Bloch sphere structure. We find that a constant, from the equilibrium value of the population inversion in the absence of the laser beam, trends to keep the quantum coherence and is helpful to preserve quantum message. We show that the Berry phase of optical nutation is related to the inner evolution in processing of the optical nutation under a quasicyclic evolution. Furthermore, we find that the Berry phases of two-state mixture change very slowly with its environment variable so as to be robust against the decoherent effect. Our results provide a guidance to implement fault-tolerant geometric quantum computation in the echo approach with an inhomogeneous Bloch equation.
COHERENT STRUCTURES AND CARRIER SHOCKS IN THE NONLINEAR PERIODIC MAXWELL EQUATIONS
Simpson, Gideon
.1. Nonlinear geometric optics expansion 14 4.2. Periodic Media and xNLCME 16 4.3. Conservation Laws2010 #12;periodic and nonlinear constituitive laws. This paper explores a class of nonlinear hyperbolicCOHERENT STRUCTURES AND CARRIER SHOCKS IN THE NONLINEAR PERIODIC MAXWELL EQUATIONS GIDEON SIMPSON
Geometrical aspects of quantum spaces
Ho, P.M.
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S{sub 1}{sup 2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
nonlinearity G-perfect nonlinearity
Poinsot, Laurent
G-perfect nonlinearity Laurent Poinsot Outline G-perfect nonlinearity Laurent Poinsot Universit´e du Sud Toulon-Var (France) Organized by Professor J. Davis University of Richmond #12;G correlation ; High algebraic degree ; Perfect nonlinearity (bentness). #12;G-perfect nonlinearity Laurent
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rřnnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: ?SR measurements on single crystals Oren Ofer, Amit Keren, Jess H Brewer, Tianheng H Han and Young S Lee Classical topological order in kagome ice Andrew J Macdonald, Peter C W Holdsworth and Roger G Melko Magnetic phase diagrams of classical triangular and kagome antiferromagnets M V Gvozdikova, P-E Melchy and M E Zhitomirsky The ordering of XY spin glasses Hikaru Kawamura Dynamic and thermodynamic properties of the generalized diamond chain model for azurite Andreas Honecker, Shijie Hu, Robert Peters and Johannes Richter Classical height models with topological order Christopher L Henley A search for disorder in the spin glass double perovskites Sr2CaReO6 and Sr2MgReO6 using neutron diffraction and neutron pair distribution function analysis J E Greedan, Shahab Derakhshan, F Ramezanipour, J Siewenie and Th Proffen Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7 Yu Jiang, Ashfia Huq, Corwin H Booth, Georg Ehlers, John E Greedan and Jason S Gardner The magnetic phase diagram of Gd2Sn2O7 R S Freitas and J S Gardner Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd2Sn2O7 antiferromagnet P A McClarty, J N Cosman, A G Del Maestro and M J P Gingras Magnetic frustration in the disordered pyrochlore Yb2GaSbO7 J A Hodges, P Dalmas de Réotier, A Yaouanc, P C M Gubbens, P J C King and C Baines Titanium pyrochlore magnets: how much can be learned from magnetization measurements? O A Petrenko, M R Lees and G Balakrishnan Local susceptibility of the Yb2Ti2O7 rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange J D Thompson, P A McClarty and M J P Gingras Slow and static spin correlations in Dy2 + xTi2 - xO7 - ? J S Gardner, G Ehlers, P Fouquet, B Farago and J R Stewart The spin ice Ho2Ti2O7 versus the spin liquid Tb2Ti2O7: field-induced magnetic structures A P Sazonov, A Gukasov and I Mirebeau Magnetic monopole dynamics in spin ice L D C Jaubert and P C W Holdsworth
Prospects for Geometric Complexity Theory Prospects for Geometric Complexity Theory
BĂĽrgisser, Peter
connection between pure math and computer science! #12;Prospects for Geometric Complexity Theory Two majorProspects for Geometric Complexity Theory Prospects for Geometric Complexity Theory Peter BÂ¨urgisser University of Paderborn 27th IEEE Conference on Computational Complexity Porto, June 28, 2012 #12;Prospects
EFFECTS OF TRANSFERSE BEAM SIZE IN BEAM POSITIONS MONITORS
S.S. KURENNOY
2001-06-01
The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by the displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those from a pencil beam. The non-linearities and corrections to BPM signals due to a finite transverse beam size are calculated for an arbitrary chamber cross section. Simple analytical expressions are given for a few particular transverse distributions of the beam current in a circular or rectangular chamber. Of particular interest is a general proof that in an arbitrary homogeneous chamber the beam-size corrections vanish for any axisymmetric beam current distribution.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745
Crystal-Like geometric modeling
Landreneau, Eric Benjamin
2006-08-16
Crystals are natural phenomena that exhibit high degrees of order, symmetry, and recursion. They naturally form interesting and inspiring geometric shapes. This thesis provides geometric modeling techniques for creating shapes with crystallike...
Harrington, J. Patrick
.g., graphics, robotics, computer vision). This paper is an introduction to geometric algebra and geometric of their coordinates in some coordinate system. Efficient algorithms have recently been developed for implementing
Geometrical Wake of a Smooth Flat Collimator
Stupakov, G.V.; /SLAC
2011-09-09
A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.
Geometric Metamorphosis Marc Niethammer12
Welch, Greg
Geometric Metamorphosis Marc Niethammer12 , Gabriel L. Hart3 , Danielle F. Pace3 , Paul M. Vespa5, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a geometric metamorphosis
NASA Astrophysics Data System (ADS)
Sharma, Amalendu; Singh, P.; Abdurrahim; Ghodke, A. D.; Singh, Gurnam
2013-01-01
In charged particle accelerators, higher order optics studies become important from various points of view, such as dynamic aperture, emittance dilution, beam loss, etc. For some new applications, nonlinear study has become important in single pass optics also. For studying the higher order optics, each magnetic element is represented by a higher order transfer function (map, i.e., a function that relates output coordinates of a trajectory with initial coordinates and momentum deviation). Here in this paper we have provided an alternate method to obtain the analytical formulation of the transfer function for a dipole magnet. This formulation is obtained on the basis of basic geometrical analysis and is exact up to all orders under hard edge approximation. Being an analytical expression, the estimation of higher order effects of dipole magnet can be studied quickly. For checking the correctness of this formulation, we separated terms up to third order, which can be used to obtain the standard transfer matrices up to same order. An example of emittance growth and bunch length modification for a C-chicane-type electron beam bunch compressor is provided using the analytical expression.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
B. Zygelman
2012-05-09
We introduce, and propagate wave-packet solutions of, a single qubit system in which geometric gauge forces and phases emerge. We investigate under what conditions non-trivial gauge phenomena arise, and demonstrate how symmetry breaking is an essential ingredient for realization of the former. We illustrate how a "magnetic"-lens, for neutral atoms, can be constructed and find application in the manipulation and interferometry of cold atoms.
Ion-beam Plasma Neutralization Interaction Images
Igor D. Kaganovich; Edward Startsev; S. Klasky; Ronald C. Davidson
2002-04-09
Neutralization of the ion beam charge and current is an important scientific issue for many practical applications. The process of ion beam charge and current neutralization is complex because the excitation of nonlinear plasma waves may occur. Computer simulation images of plasma neutralization of the ion beam pulse are presented.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr. (Principal Investigator)
1996-01-01
The goal of this research project is to develop assumed-stress hybrid elements with rotational degrees of freedom for analyzing composite structures. During the first year of the three-year activity, the effort was directed to further assess the AQ4 shell element and its extensions to buckling and free vibration problems. In addition, the development of a compatible 2-node beam element was to be accomplished. The extensions and new developments were implemented in the Computational Structural Mechanics Testbed COMET. An assessment was performed to verify the implementation and to assess the performance of these elements in terms of accuracy. During the second and third years, extensions to geometrically nonlinear problems were developed and tested. This effort involved working with the nonlinear solution strategy as well as the nonlinear formulation for the elements. This research has resulted in the development and implementation of two additional element processors (ES22 for the beam element and ES24 for the shell elements) in COMET. The software was developed using a SUN workstation and has been ported to the NASA Langley Convex named blackbird. Both element processors are now part of the baseline version of COMET.
Overview of the APT high-energy beam transport and beam expanders
Shafer, R.E.; Blind, B.; Gray, E.R.
1997-08-01
The APT high energy beam transport (HEBT) and beam expanders convey the 1700-MeV, 100-mA cw proton beam from the linac to the tritium target/blanket assembly, or a tuning beam stop. The HEBT includes extensive beam diagnostics, collimators, and beam jitter correction, to monitor and control the 170-MW beam prior to expansion. A zero-degree beamline conveys the beam to the beam stop, and an achromatic bend conveys the beam to the tritium production target. Nonlinear beam expanders make use of higher-order multipole magnets and dithering dipoles to expand the beam to a uniform-density, 16-cm wide by 160-cm high rectangular profile on the tritium-production target. The overall optics design will be reviewed, and beam simulations will be presented.
Geometrical Mechanics on algebroids
K. Grabowska; J. Grabowski; P. Urba?ski
2006-05-03
A natural geometric framework is proposed, based on ideas of W. M. Tulczyjew, for constructions of dynamics on general algebroids. One obtains formalisms similar to the Lagrangian and the Hamiltonian ones. In contrast with recently studied concepts of Analytical Mechanics on Lie algebroids, this approach requires much less than the presence of a Lie algebroid structure on a vector bundle, but it still reproduces the main features of the Analytical Mechanics, like the Euler-Lagrange-type equations, the correspondence between the Lagrangian and Hamiltonian functions (Legendre transform) in the hyperregular cases, and a version of the Noether Theorem. Besides, the constructions seem to be more natural and simpler.
Geometrical Detector Considerations in Laser Sensing Applications
NASA Technical Reports Server (NTRS)
Killinger, Dennis
2000-01-01
We have studied the influence of the geometrical interaction of different detectors with the impinging optical/laser received beam for a wide range of laser sensing applications. Although different techniques apply, it is found that similar aspects of geometrical physics plays a role in direct detection of a range-resolved large M(sup 2) OPO atmospheric Lidar, heterodyne multi-detector reception of atmospheric turbulence distorted coherent lidar type laser sensing, and the distribution and summation of laser induced fluorescence signals after being spectrally resolved with a spectrometer and detected by a column summing CCD detector. In each of these systems, the focused received light is spatially and spectrally distributed due to several factors including Field-of-View considerations, laser beam quality/divergence, multi-detector aspects, and hardware and software summation (coherent and non-coherent) of multi-element or spatially integrated signals. This invited talk will present some of our recent results in these areas and show the similarities in the detector spatial and temporal summation techniques of these different laser sensing systems.
Auto calibration of a cone-beam-CT
Gross, Daniel; Heil, Ulrich; Schulze, Ralf; Schoemer, Elmar; Schwanecke, Ulrich
2012-10-15
Purpose: This paper introduces a novel autocalibration method for cone-beam-CTs (CBCT) or flat-panel CTs, assuming a perfect rotation. The method is based on ellipse-fitting. Autocalibration refers to accurate recovery of the geometric alignment of a CBCT device from projection images alone, without any manual measurements. Methods: The authors use test objects containing small arbitrarily positioned radio-opaque markers. No information regarding the relative positions of the markers is used. In practice, the authors use three to eight metal ball bearings (diameter of 1 mm), e.g., positioned roughly in a vertical line such that their projection image curves on the detector preferably form large ellipses over the circular orbit. From this ellipse-to-curve mapping and also from its inversion the authors derive an explicit formula. Nonlinear optimization based on this mapping enables them to determine the six relevant parameters of the system up to the device rotation angle, which is sufficient to define the geometry of a CBCT-machine assuming a perfect rotational movement. These parameters also include out-of-plane rotations. The authors evaluate their method by simulation based on data used in two similar approaches [L. Smekal, M. Kachelriess, S. E, and K. Wa, 'Geometric misalignment and calibration in cone-beam tomography,' Med. Phys. 31(12), 3242-3266 (2004); K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, 'A geometric calibration method for cone beam CT systems,' Med. Phys. 33(6), 1695-1706 (2006)]. This allows a direct comparison of accuracy. Furthermore, the authors present real-world 3D reconstructions of a dry human spine segment and an electronic device. The reconstructions were computed from projections taken with a commercial dental CBCT device having two different focus-to-detector distances that were both calibrated with their method. The authors compare their reconstruction with a reconstruction computed by the manufacturer of the CBCT device to demonstrate the achievable spatial resolution of their calibration procedure. Results: Compared to the results published in the most closely related work [K. Yang, A. L. C. Kwan, D. F. Miller, and J. M. Boone, 'A geometric calibration method for cone beam CT systems,' Med. Phys. 33(6), 1695-1706 (2006)], the simulation proved the greater accuracy of their method, as well as a lower standard deviation of roughly 1 order of magnitude. When compared to another similar approach [L. Smekal, M. Kachelriess, S. E, and K. Wa, 'Geometric misalignment and calibration in cone-beam tomography,' Med. Phys. 31(12), 3242-3266 (2004)], their results were roughly of the same order of accuracy. Their analysis revealed that the method is capable of sufficiently calibrating out-of-plane angles in cases of larger cone angles when neglecting these angles negatively affects the reconstruction. Fine details in the 3D reconstruction of the spine segment and an electronic device indicate a high geometric calibration accuracy and the capability to produce state-of-the-art reconstructions. Conclusions: The method introduced here makes no requirements on the accuracy of the test object. In contrast to many previous autocalibration methods their approach also includes out-of-plane rotations of the detector. Although assuming a perfect rotation, the method seems to be sufficiently accurate for a commercial CBCT scanner. For devices which require higher dimensional geometry models, the method could be used as a initial calibration procedure.
Nonlinear transient analysis via energy minimization
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Knight, N. F., Jr.
1978-01-01
The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.
The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method
Omar Maj
2005-11-04
The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.
Manifestation of the geometric phase in neutron spin-echo experiments
Kraan, W. H.; Rekveldt, M. T.; Grigoriev, S. V.
2010-07-15
We show how the geometric (Berry's) phase becomes manifest on adiabatic rotation of the polarization vector in the magnetic field configuration in the arms in a neutron spin echo (NSE) experiment. When the neutron beam used is monochromatic, a geometric phase collected in one spin-echo arm can be exactly compensated in the other arm either by an opposite geometrical rotation or by adding/subtracting a dynamic (Larmor) phase. This is not possible in a white beam, because, contrary to the dynamic phase, the geometric phase is independent of wavelength. Therefore, the NSE pattern can be disturbed. We demonstrate that adiabatic resonant spin flippers inherently produce a geometric phase which can influence the performance of NSE setups based on such flippers. This effect can be avoided by a proper mutual symmetry of the gradient fields in these flippers.
Soliton mode locking by nonlinear Faraday rotation
NASA Astrophysics Data System (ADS)
Wabnitz, S.; Westin, E.; Frey, R.; Flytzanis, C.
1996-11-01
We propose nonlinear Faraday rotation as a mechanism for achieving stable polarization mode locking of a soliton laser. We analyze by perturbation theory and beam-propagation simulations the interplay between bandwidth-limited gain, gain dichroism, and linear and nonlinear Faraday rotation. .
Nonlinear dynamics experiments
Fischer, W.
2011-01-01
The goal of nonlinear dynamics experiments is to improve the understanding of single particle effects that increase the particle amplitude and lead to loss. Particle motion in storage rings is nearly conservative and for transverse dynamics the Hamiltonian in action angle variables (I{sub x},I{sub y},{phi}{sub x},{phi}{sub y}) near an isolated resonance k{nu}{sub x} + l{nu}{sub y} {approx} p is H = I{sub x}{nu}{sub x0} + I{sub y}{nu}{sub y0} + g(I{sub x}, I{sub y}) + h(I{sub x}, I{sub y})cos(k{phi}{sub x} + l{phi}{sub y} - p{theta}), (1) where k, l, p are integers, {theta} = 2{pi}s/L is the azimuth, and s and L are the path length and circumference respectively. The amplitude dependent tunes are given by {nu}{sub x,y}(I{sub x},I{sub y}) = {nu}{sub x0,y0} + {partial_derivative}g(I{sub x},I{sub y})/{partial_derivative}I{sub x,y} (2) and h(I{sub x},I{sub y}) is the resonance driving term (RDT). If the motion is governed by multiple resonances, h(I{sub x},I{sub y}) has to be replace by a series of terms. The particle motion is completely determined by the terms g and h, which can be calculated from higher order multipoles (Sec. ??), or obtained from simulations. Deviations from pure Hamiltonian motion occur due to synchrotron radiation damping (Sec. ??) in lepton or very high energy hadron rings, parameter variations, and diffusion processes such as residual gas and intrabeam scattering. The time scale of the non-Hamiltonian process determines the applicability of the Hamiltonian analysis. Transverse nonlinearities are introduced through sextupoles or higher order multipoles and magnetic field errors in dipoles and quadrupoles. Sextupoles can already drive all resonances. The beam-beam interaction and space charge also introduce nonlinear fields. Intentionally introduced nonlinearities are used to extract beam on a resonance or through capture in stable islands. Localization and minimization of nonlinearities in a ring is a general strategy to decrease emittance growth and increase the beam lifetime. The minimization of nonlinear effects can be done locally or globally. Except for resonant extraction, amplitude increase and particle loss is the result of chaotic particle motion. Large chaotic regions allow particles to increase their amplitudes, and ensures their ultimate loss. However, chaotic particles can, on average, still survive the time period of interest, i.e. the storage time. Nonlinear dynamics experiments aim to determine either the detuning and driving terms g and h directly, or their effect on other quantities. Nonlinear phenomena observed in experiments include phase space deformations and resonant islands in Poincare surfaces of section, nonlinear phase advances, amplitude detuning g, decoherence (Sec. ??), resonance driving terms h, smear, halo formation, echoes (Sec. ??), the tune response matrix, dynamic aperture (Sec. ??), emittance growth, and particle loss. Nonlinear experiments can also be done in the longitudinal plane.
Regular and chaotic oscillations of a Timoshenko beam subjected to mechanical and thermal loadings
NASA Astrophysics Data System (ADS)
Warminska, Anna; Manoach, Emil; Warminski, Jerzy; Samborski, Sylwester
2015-09-01
Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations.
Controlling Second Harmonic Efficiency of Laser Beam Interactions
NASA Technical Reports Server (NTRS)
Barnes, Norman P. (Inventor); Walsh, Brian M. (Inventor); Reichle, Donald J. (Inventor)
2011-01-01
A method is provided for controlling second harmonic efficiency of laser beam interactions. A laser system generates two laser beams (e.g., a laser beam with two polarizations) for incidence on a nonlinear crystal having a preferred direction of propagation. Prior to incidence on the crystal, the beams are optically processed based on the crystal's beam separation characteristics to thereby control a position in the crystal along the preferred direction of propagation at which the beams interact.
Coherence delay augmented laser beam homogenizer
Rasmussen, P.; Bernhardt, A.
1993-06-29
The geometrical restrictions on a laser beam homogenizer are relaxed by ug a coherence delay line to separate a coherent input beam into several components each having a path length difference equal to a multiple of the coherence length with respect to the other components. The components recombine incoherently at the output of the homogenizer, and the resultant beam has a more uniform spatial intensity suitable for microlithography and laser pantogography. Also disclosed is a variable aperture homogenizer, and a liquid filled homogenizer.
Technology Transfer Automated Retrieval System (TEKTRAN)
This work examines the application of a geometric-optical canopy reflectance model to provide measures of woody shrub abundance in desert grasslands at the landscape scale. The approach is through inversion of the non-linear simple geometric model (SGM) against 631 nm multi-angle reflectance data fr...
Coiling of elastic rods from a geometric perspective
NASA Astrophysics Data System (ADS)
Jawed, Mohammad; Brun, Pierre-Thomas; Reis, Pedro
2015-03-01
We present results from a systematic numerical investigation of the pattern formation of coiling obtained when a slender elastic rod is deployed onto a moving substrate; a system known as the elastic sewing machine (ESM). The Discrete Elastic Rods method is employed to explore the parameter space, construct phase diagrams, identify their phase boundaries and characterize the morphology of the patterns. The nontrivial geometric nonlinearities are described in terms of the gravito-bending length and the deployment height. Our results are interpreted using a reduced geometric model for the evolution of the position of the contact point with the belt and the curvature of the rod in its neighborhood. This geometric model reproduces all of the coiling patterns of the ESM, which allows us to establish a universal link between our elastic problem and the analogous patterns obtained when depositing a viscous thread onto a moving surface; a well-known system referred to as the fluid mechanical sewing machine.
Simulation of wavefront reconstruction in beam reshaping system for rectangular laser beam
NASA Astrophysics Data System (ADS)
Zhou, Qiong; Liu, Wenguang; Jiang, Zongfu
2014-05-01
A new method to calculating the wavefront of slap laser is studied in this paper. The method is based on the ray trace theory of geometrical optics. By using the Zemax simulation software and Matlab calculation software, the wavefront of rectangular beam in beam reshaping system is reconstructed. Firstly, with the x- and y-slope measurement of reshaping beam the direction cosine of wavefront can be calculated. Then, the inverse beam path of beam reshaping system is built by using Zemax simulation software and the direction cosine of rectangular beam can be given, too. Finally, Southwell zonal model is used to reconstruct the wavefront of rectangular beam in computer simulation. Once the wavefront is received, the aberration of laser can be eliminated by using the proper configuration of beam reshaping system. It is shown that this method to reconstruct the wavefront of rectangular beam can evidently reduce the negative influence of additional aberration induced by beam reshaping system.
Eliminating material constraints for nonlinearity with plasmonic metamaterials
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-01-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications. PMID:26195182
Eliminating material constraints for nonlinearity with plasmonic metamaterials
NASA Astrophysics Data System (ADS)
Neira, Andres D.; Olivier, Nicolas; Nasir, Mazhar E.; Dickson, Wayne; Wurtz, Gregory A.; Zayats, Anatoly V.
2015-07-01
Nonlinear optical materials comprise the foundation of modern photonics, offering functionalities ranging from ultrafast lasers to optical switching, harmonic and soliton generation. Optical nonlinearities are typically strong near the electronic resonances of a material and thus provide limited tuneability for practical use. Here we show that in plasmonic nanorod metamaterials, the Kerr-type nonlinearity is not limited by the nonlinear properties of the constituents. Compared with gold's nonlinearity, the measured nonlinear absorption and refraction demonstrate more than two orders of magnitude enhancement over a broad spectral range that can be engineered via geometrical parameters. Depending on the metamaterial's effective plasma frequency, either a focusing or defocusing nonlinearity is observed. The ability to obtain strong and fast optical nonlinearities in a given spectral range makes these metamaterials a flexible platform for the development of low-intensity nonlinear applications.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
Geometrical aspects of entanglement
Leinaas, Jon Magne; Myrheim, Jan; Ovrum, Eirik
2006-07-15
We study geometrical aspects of entanglement, with the Hilbert-Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a 'relativistic' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
NASA Astrophysics Data System (ADS)
Bosser, J.; Carli, C.; Chanel, M.; Madsen, N.; Maury, S.; Möhl, D.; Tranquille, G.
2000-02-01
Because of their high density together with extremely small spreads in betatron frequency and momentum, cooled beams are very vulnerable to incoherent and coherent space-charge effects and instabilities. Moreover, the cooling system itself, i.e. the electron beam in the case of e-cooling, presents large linear and non-linear "impedances" to the circulating ion beam, in addition to the usual beam-environment coupling impedances of the storage ring. Beam blow-up and losses, attributed to such effects, have been observed in virtually all the existing electron cooling rings. The adverse effects seem to be more pronounced in those rings, like CELSIUS, that are equipped with a cooler capable of reaching the presently highest energy (100-300 keV electrons corresponding to 180-560 MeV protons). The stability conditions will be revisited with emphasis on the experience gained at LEAR. It will be argued that for all present coolers, three conditions are necessary (although probably not sufficient) for the stability of intense cold beams: (i) operation below transition energy, (ii) active damping to counteract coherent instability, and (iii) careful control of the e-beam neutralisation. An extrapolation to the future "medium energy coolers", planned to work for (anti)protons of several GeV, will also be attempted.
Clique topology reveals intrinsic geometric structure in neural correlations
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-01-01
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown. PMID:26487684
Clique topology reveals intrinsic geometric structure in neural correlations.
Giusti, Chad; Pastalkova, Eva; Curto, Carina; Itskov, Vladimir
2015-11-01
Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown. PMID:26487684
Nonlinear aspects of acoustic radiation force in biomedical applications
NASA Astrophysics Data System (ADS)
Ostrovsky, Lev; Tsyuryupa, Sergey; Sarvazyan, Armen
2015-10-01
In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual "finger" for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.
ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY
Caruntu, Dumitru I. - Mechanical Engineering Department, University of Texas
ON NONLINEAR RESPONSE NEAR-HALF NATURAL FREQUENCY OF ELECTROSTATICALLY ACTUATED MICRORESONATORS for a parametrically excited comb drive system.3 Electrostatic actuation creates a variety of nonlinear parametric This paper deals with the nonlinear response of electrostatically actuated cantilever beam microresonators
Ring for test of nonlinear integrable optics
Valishev, A.; Nagaitsev, S.; Kashikhin, V.; Danilov, V.; /SNS Project, Oak Ridge
2011-03-01
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and make the beam immune to instabilities. Recent theoretical work has identified a possible way to implement stable nonlinear optics by incorporating nonlinear focusing elements into a specially designed machine lattice. In this report we propose the design of a test accelerator for a proof-of-principle experiment. We discuss possible studies at the machine, requirements on the optics stability and sensitivity to imperfections.
Beam-Beam Effect with an External Noise in LHC
Ohmi, K; Höfle, Wolfgang; Tomás, R; Zimmermann, F
2007-01-01
In absence of synchrotron radiation, proton beams do not have any damping mechanism for incoherent betatron motion. A noise, which kicks beam particles in the transverse plane, gives a coherent betatron amplitude. If the system is linear, the coherent motion is maintained in amplitude. Nonlinear force, beam-beam and beam-electron cloud interactions, cause a decoherence of the betatron motion keeping the amplitude of each beam particle, with the result that an emittance growth arises. We focus only on fast noise with a correlation time of 1-100 turns. Slower noise is less serious, because it is regarded as an adiabatic change like a closed orbit change. As sources of the noise, we consider the bunch by bunch feedback system and phase jitter of cavities which turns to transverse noise via a crab cavity.
A Primer on Geometric Mechanics
Christian Lessig
2012-06-14
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance of the subject for an understanding of "mechanics".
Progress with Tevatron Electron Lens Head-On Beam-Beam Compensation
Valishev, A.; Kuznetsov, G.; Shiltsev, V.; Stancari, G.; Zhang, X.
2010-05-19
Tevatron electron lenses have been successfully used to mitigate bunch-to-bunch differences caused by longrange beam-beam interactions. For this purpose, the electron beam with uniform transverse density distribution was used. Another planned application of the electron lens is the suppression of tune spread due to head-on beam-beam collisions. For this purpose, the transverse distribution of the E{sup -} beam must be matched to that of the antiproton beam. In 2009, the Gaussian profile electron gun was installed in one of the Tevatron electron lenses. We report on the first experiments with non-linear beam-beam compensation. Discussed topics include measurement and control of the betatron tune spread, importance of the beam alignment and stability, and effect of electron lens on the antiproton beam lifetime.
Geometric nonlinearity and mechanical anisotropy in strained helical nanoribbons
NASA Astrophysics Data System (ADS)
Chen, Z.
2014-07-01
Fabrication and synthesis of helical nanoribbons have received increasing attention because of the broad applications of helical nanostructures in nano-elecromechanical/micro-electromechanical systems (NEMS/MEMS), sensors, active materials, drug delivery, etc. In this paper, I study the mechanical principles used in designing strained helical nanoribbons, and propose the use of a full three-dimensional finite element method to simulate the coexistence of both left- and right-handed segments in the same strained nanoribbon. This work can both help understand the large deformation behaviours of such nanostructures and assist in the design of helical nanostructures for engineering applications.
Geometric nonlinearity and mechanical anisotropy in strained helical nanoribbons.
Chen, Z
2014-08-21
Fabrication and synthesis of helical nanoribbons have received increasing attention because of the broad applications of helical nanostructures in nano-elecromechanical/micro-electromechanical systems (NEMS/MEMS), sensors, active materials, drug delivery, etc. In this paper, I study the mechanical principles used in designing strained helical nanoribbons, and propose the use of a full three-dimensional finite element method to simulate the coexistence of both left- and right-handed segments in the same strained nanoribbon. This work can both help understand the large deformation behaviours of such nanostructures and assist in the design of helical nanostructures for engineering applications. PMID:24837718
Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange
M. Sebawe Abdalla; Faisal A. A. El-Orany; J. Perina
2011-07-29
In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed in dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state $|1>$ enters the first waveguide and the vacuum state $|0>$ enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.
Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange
Abdalla, M Sebawe; Perina, J
2011-01-01
In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed in dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state $|1>$ enters the first waveguide and the vacuum state $|0>$ enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler play...
Stochastic pump effect and geometric phases in dissipative and stochastic systems
Sinitsyn, Nikolai
2008-01-01
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).
Nonlinear Dynamics 21: 3153, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands.
Zegeling, Paul
nonlinear beam equations as suspension-bridge models.) This led to the beam equation with restoring force wave behaviour in the Golden Gate Bridge in San Francisco motivated McKenna and Walter [21] to study idealized nonlinearity f is chosen to model the effect that the cable holds the beam up but the constant
A General Slice Moment Decomposition of RMS Beam Emittance
Mitchell, Chad
2015-01-01
The square of the horizontal projected (rms) beam emittance is expressed as the sum of four nonnegative contributions, each described using the slice moments of the beam and possessing a natural interpretation in terms of the geometrical properties of the beam in the six-dimensional phase space. The mathematical formalism describing the relationships between projected beam quantities and slice beam quantities is reviewed. The results may be used to reconstruct the moments and emittances of the beam from the moments of its subpopulations, as well as to isolate and better understand a variety of slice and interslice dynamical contributions to the projected beam emittance growth.
Geometric algebra, qubits, geometric evolution, and all that
Soiguine, Alexander M
2015-01-01
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.
Geometric algebra, qubits, geometric evolution, and all that
Alexander M. Soiguine
2015-02-07
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.
Manipulating the spin-dependent splitting by geometric Doppler effect.
Liu, Yachao; Ke, Yougang; Zhou, Junxiao; Luo, Hailu; Wen, Shuangchun
2015-06-29
We report the manipulation of spin-dependent splitting by geometric Doppler effect based on dielectric metasurfaces. The extrapolation of rotational Doppler effect from temporal to spatial coordinate gives the phase change when the local optical axes of dielectric metasurfaces are rotating in space. Therefore, the continuous variation of local optical axes in a certain direction will introduce a phase gradient in the same direction at the beam cross section. This is additive to the phase gradient appeared when breaking the rotational symmetry of linearly polarized cylindrical vector beams, which leads to the deflections of different spin components of light, i.e., photonic spin Hall effect. Hence, it is possible to manipulate the spin-dependent splitting by introducing the geometric Doppler effect. Theoretically and experimentally, we show that the magnitude and orientation of the spin-dependent splitting are both tunable when changing the spatial rotation rate of local optical axes and incident polarization. PMID:26191680
Lifetime and Tail Simulations for Beam-Beam Effects in PEP-II B Factory
Shatilov, D.N.; Zholents, A.A.
1994-12-01
A fast tracking technique for doing beam tail simulations has been applied to a study of beam-beam effects in the SLAC/LBL/LLNL PEP-II B Factory. In particular, the dependence of beam lifetime and particle density distribution due to vacuum pressure, damping times, machine nonlinearity and parasitic crossings has been analyzed. Effects of accidental orbit separation and dispersion function at the interaction point (IP) have also been considered.
Beam hysteresis via reorientational self-focusing.
Alberucci, Alessandro; Piccardi, Armando; Kravets, Nina; Assanto, Gaetano
2014-10-15
We theoretically investigate light self-trapping in nonlinear dielectrics with a reorientational response subject to threshold, specifically nematic liquid crystals. Beyond a finite excitation, two solitary waves exist for any given power, with an hysteretic dynamics due to feedback between beam size, self-focusing and the nonlinear threshold. Soliton stability is discussed on the basis of the system free energy. PMID:25361096
NASA Astrophysics Data System (ADS)
Aharon, Oren
2014-02-01
In various modern scientific and industrial laser applications, beam-shaping optics manipulates the laser spot size and its intensity distribution. However the designed laser spot frequently deviates from the design goal due to real life imperfections and effects, such as: input laser distortions, optical distortion, heating, overall instabilities, and non-linear effects. Lasers provide the ability to accurately deliver large amounts of energy to a target area with very high accuracy. Thus monitoring beam size power and beam location is of high importance for high quality results and repeatability. Depending on the combination of wavelength, beam size and pulse duration , laser energy is absorbed by the material surface, yielding into processes such as cutting, welding, surface treatment, brazing and many other applications. This article will cover the aspect of laser beam measurements, especially at the focal point where it matters the most. A brief introduction to the material processing interactions will be covered, followed by fundamentals of laser beam propagation, novel measurement techniques, actual measurement and brief conclusions.
Towards modeling of nonlinear laser-plasma interactions with hydrocodes: the thick-ray approach.
Colaďtis, A; Duchateau, G; Nicolaď, P; Tikhonchuk, V
2014-03-01
This paper deals with the computation of laser beam intensity in large-scale radiative hydrocodes applied to the modeling of nonlinear laser-plasma interactions (LPIs) in inertial confinement fusion (ICF). The paraxial complex geometrical optics (PCGO) is adapted for light waves in an inhomogeneous medium and modified to include the inverse bremsstrahlung absorption and the ponderomotive force. This thick-ray model is compared to the standard ray-tracing (RT) approach, both in the chic code. The PCGO model leads to different power deposition patterns and better diffraction modeling compared to standard RT codes. The intensity-reconstruction technique used in RT codes to model nonlinear LPI leads to artificial filamentation and fails to reproduce realistic ponderomotive self-focusing distances, intensity amplifications, and density channel depletions, whereas PCGO succeeds. Bundles of Gaussian thick rays can be used to model realistic non-Gaussian ICF beams. The PCGO approach is expected to improve the accuracy of ICF simulations and serve as a basis to implement diverse LPI effects in large-scale hydrocodes. PMID:24730950
Jacobi equations and particle accelerator beam dynamics
Ricardo Gallego Torrome
2012-03-27
A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi equation of an affine averaged Lorentz connection. We introduce a specific notion reference trajectory as integral curves of the main velocity vector field. A perturbation caused by the statistical nature of the bunch of particles is considered.
Scale-invariant nonlinear optics in gases
Heyl, C M; Miranda, M; Louisy, M; Kovacs, K; Tosa, V; Balogh, E; Varjú, K; L'Huillier, A; Couairon, A; Arnold, C L
2015-01-01
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for example, parasitic nonlinear effects, damage problems and geometrical considerations. Here, we show that many nonlinear optics phenomena in gaseous media are scale-invariant if spatial coordinates, gas density and laser pulse energy are scaled appropriately. We develop a general scaling model for (3+1)-dimensional wave equations, demonstrating the invariant scaling of nonlinear pulse propagation in gases. Our model is numerically applied to high-order harmonic generation and filamentation as well as experimentally verified using the example of pulse post-compression via filamentation. Our results provide a simple recipe for up-or downscaling of nonlinear processes in gases with numerous applications in many areas of science.
Nonlinear optical protection against frequency agile lasers
McDowell, V.P.
1988-08-04
An eye-protection or equipment-filter device for protection from laser energy is disclosed. The device may be in the form of a telescope, binoculars, goggles, constructed as part of equipment such as image intensifiers or range designators. Optical elements focus the waist of the beam within a nonlinear frequency-doubling crystal or nonlinear optical element or fiber. The nonlinear elements produce a harmonic outside the visible spectrum in the case of crystals, or absorb the laser energy in the case of nonlinear fibers. Embodiments include protectors for the human eye as well as filters for sensitive machinery such as TV cameras, FLIR systems or other imaging equipment.
Transient response of structures with uncertain properties to nonlinear shock loading
NASA Astrophysics Data System (ADS)
Caresta, Mauro; Langley, Robin S.; Woodhouse, Jim
2013-10-01
A method is presented to predict the transient response of a structure at the driving point following an impact or a shock loading. The displacement and the contact force are calculated solving the discrete convolution between the impulse response and the contact force itself, expressed in terms of a nonlinear Hertzian contact stiffness. Application of random point process theory allows the calculation of the impulse response function from knowledge of the modal density and the geometric characteristics of the structure only. The theory is applied to a wide range of structures and results are experimentally verified for the case of a rigid object hitting a beam, a plate, a thin and a thick cylinder and for the impact between two cylinders. The modal density of the flexural modes for a thick slender cylinder is derived analytically. Good agreement is found between experimental, simulated and published results, showing the reliability of the method for a wide range of situations including impacts and pyroshock applications.
Natural Oscillations of Welded Steel Beams in the Span Structures of Conveyor Galleries
NASA Astrophysics Data System (ADS)
Volkova, V.; Smolii, I.
2015-11-01
This article presents the results of numerical simulation of dynamic behaviour of welded metal beams in conveyor galleries. Investigations were carried out for the beams having symmetrical cross-sections and evenly-spaced transversal ribs with various spacing between the ribs in different beams. The regularities of changes in the vibration mode shapes depending on the beam geometric characteristics have been investigated.
Functional facets for nonlinear crystals Asia Shapira a,n
Arie, Ady
Beam shaping Focused ion beam Computer generated hologram a b s t r a c t We report on a new optical to save space and cost, it is desired to combine the nonlinear process and the above mentioned functions patterning the gold according to a design of a computer generated hologram (CGH) [8]. Both the pump beam
Antenna with Dielectric Having Geometric Patterns
NASA Technical Reports Server (NTRS)
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Optimization of beam configuration in laser fusion based on the laser beam pattern
Xu, Teng; Xu, Lixin; Wang, Anting; Gu, Chun; Wang, Shengbo; Liu, Jing; Wei, Ankun
2013-12-15
A simple method based on the laser beam pattern is proposed and numerically demonstrated to optimize a beam configuration for direct drive laser fusion. In this method, both the geometrical factor G{sub l} and the single beam factor B{sub l} are considered. By diminishing the product of B{sub l}·G{sub l}, the irradiation nonuniformity can be decreased to the order of 10{sup ?5}. This optimization method can be applied on the design of irradiation systems for an arbitrary number of beams and any axially symmetric beam patterns.
NASA Technical Reports Server (NTRS)
Mog, Robert A.; Price, D. Marvin
1990-01-01
A unique methodology providing global optimization of spacecraft protective structures is presented. The Geometric Programming optimization technique, which has a long history of application to structural design problems, is employed to minimize spacecraft weight of protective structural systems exposed to meteoroid and space debris hypervelocity impacts. The space debris and meteoroid environment are defined followed by the formulation of the general weight objective function. The Wilkinson, Burch, and Nysmith hypervelocity impact predictor models are then used in example cases to display Geometric Programming capabilities. Results show that global nonlinear design optimization can be performed for hypervelocity impact models that follow the Geometric Programming form.
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2004-01-01
The results of a parametric study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thinwalled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The imperfections considered include initial geometric shell-wall midsurface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these imperfections on the nonlinear responses and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable response characteristics.
Geometric phases in astigmatic optical modes of arbitrary order
Steven J. M. Habraken; Gerard Nienhuis
2013-07-18
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of non-astigmatic optical modes with orbital angular momentum states in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights in the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schr\\"odinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
Tunable refraction and reflection of self-confined light beams
Loss, Daniel
LETTERS Tunable refraction and reflection of self-confined light beams MARCO PECCIANTI1 *, ANDRIY on linear/nonlinear or nonlinear/nonlinear interfaces. Here we report the robust propagation, refraction by refraction and total internal reflection by as much as -18 and +22 degrees, respectively. Moreover
A wire scanning based method for geometric calibration of high resolution CT system
NASA Astrophysics Data System (ADS)
Jiang, Ruijie; Li, Guang; Gu, Ning; Chen, Gong; Luo, Shouhua
2015-03-01
This paper is about geometric calibration of the high resolution CT (Computed Tomography) system. Geometric calibration refers to the estimation of a set of parameters that describe the geometry of the CT system. Such parameters are so important that a little error of them will degrade the reconstruction images seriously, so more accurate geometric parameters are needed in the higher-resolution CT systems. But conventional calibration methods are not accurate enough for the current high resolution CT system whose resolution can reach sub-micrometer or even tens of nanometers. In this paper, we propose a new calibration method which has higher accuracy and it is based on the optimization theory. The superiority of this method is that we build a new cost function which sets up a relationship between the geometrical parameters and the binary reconstruction image of a thin wire. When the geometrical parameters are accurate, the cost function reaches its maximum value. In the experiment, we scanned a thin wire as the calibration data and a thin bamboo stick as the validation data to verify the correctness of the proposed method. Comparing with the image reconstructed with the geometric parameters calculated by using the conventional calibration method, the image reconstructed with the parameters calculated by our method has less geometric artifacts, so it can verify that our method can get more accurate geometric calibration parameters. Although we calculated only one geometric parameter in this paper, the geometric artifacts are still eliminated significantly. And this method can be easily generalized to all the geometrical parameters calibration in fan-beam or cone-beam CT systems.
Analytic Nonlinear Methods for Beam Optics
Irwin, John; /SLAC
2011-08-31
In recent years there have been major advances in the computation and use of high-order maps for the design, optimization and operation of beamlines. We will describe five practical examples for both linear and circular colliders. From least to most complex these examples will be: use of similarity transformations (FFTB design, SLC diagnosis); statistical maps (SSC smear and tune-shift); aberrations (SLC upgrade); resonance basis and nPB tracking (PEP-II design); and kick factorization (possibly LHC).
Kikuchi, Takashi; Horioka, Kazuhiko
2009-05-15
Possible emittance growths of intense, nonuniform beams during a transport in a focusing channel are derived as a function of nonlinear field energy and space charge tune depression factors. The nonlinear field energy of the beam with thermal equilibrium distribution is estimated by considering the particle distribution across the cross section of the beam. The results show that the possible emittance growth can be suppressed by keeping the beam particle in thermal equilibrium distribution during the beam transport.
NASA Astrophysics Data System (ADS)
Liu, Chang; Dodin, Ilya Y.
2015-08-01
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
Chaotic dynamics of flexible Euler-Bernoulli beams
NASA Astrophysics Data System (ADS)
Awrejcewicz, J.; Krysko, A. V.; Kutepov, I. E.; Zagniboroda, N. A.; Dobriyan, V.; Krysko, V. A.
2013-12-01
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c2) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q0 and frequency ?p of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.
Chaotic dynamics of flexible Euler-Bernoulli beams
Awrejcewicz, J.; Kutepov, I. E. Zagniboroda, N. A. Dobriyan, V. Krysko, V. A.
2013-12-15
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ?{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.
Chaotic dynamics of flexible Euler-Bernoulli beams.
Awrejcewicz, J; Krysko, A V; Kutepov, I E; Zagniboroda, N A; Dobriyan, V; Krysko, V A
2013-12-01
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c(2)) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q(0) and frequency ?(p) of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics. PMID:24387569
Observation of shape-preserving accelerating underwater acoustic beams
NASA Astrophysics Data System (ADS)
Bar-Ziv, Uri; Postan, Aharon; Segev, Mordechai
2015-09-01
We present the experimental generation and observation of an underwater acoustic accelerating beam. The beam was generated by phase modulating a single projector using a tailored acoustic phase mask. The beam is propagating for a range in excess of 800 wavelengths, which are about six Rayleigh lengths, while preserving its shape and transversely accelerating. Such beams have promising applications in the fields of sonar, hydrography, and medical ultrasound and can provide new means to study nonlinear interaction of acoustic beams.
Geometrical Interpretations of Gauge Theory
Alsid, Scott T
2013-01-01
We seek common ground with three camps that have developed geometric interpretations of gauge theory over the last century: those who use the compactified dimensions of Kaluza-Klein theory, those who use an embedding to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. This paper seeks to directly relate the geometrical interpretations of the three camps. Each camp attempts to isolate the gauge-invariant core responsible for the resulting physics. By providing a mapping between geometrical interpretations, physicists can borrow and share results between each camp. In addition, we provide visual examples of the geometrical representation of each camp for simple electric and magnetic fields of a U(1) gauge theory.
Geometric algorithms for reconfigurable structures
Benbernou, Nadia M
2011-01-01
In this thesis, we study three problems related to geometric algorithms of reconfigurable structures. In the first problem, strip folding, we present two universal hinge patterns for a strip of material that enable the ...