Silicon microfabricated beam expander
Othman, A.; Ibrahim, M. N.; Hamzah, I. H.; Sulaiman, A. A.; Ain, M. F.
2015-03-01
The feasibility design and development methods of silicon microfabricated beam expander are described. Silicon bulk micromachining fabrication technology is used in producing features of the structure. A high-precision complex 3-D shape of the expander can be formed by exploiting the predictable anisotropic wet etching characteristics of single-crystal silicon in aqueous Potassium-Hydroxide (KOH) solution. The beam-expander consist of two elements, a micromachined silicon reflector chamber and micro-Fresnel zone plate. The micro-Fresnel element is patterned using lithographic methods. The reflector chamber element has a depth of 40 µm, a diameter of 15 mm and gold-coated surfaces. The impact on the depth, diameter of the chamber and absorption for improved performance are discussed.
Silicon microfabricated beam expander
Energy Technology Data Exchange (ETDEWEB)
Othman, A., E-mail: aliman@ppinang.uitm.edu.my; Ibrahim, M. N.; Hamzah, I. H.; Sulaiman, A. A. [Faculty of Electrical Engineering, Universiti Teknologi MARA Malaysia, 40450, Shah Alam, Selangor (Malaysia); Ain, M. F. [School of Electrical and Electronic Engineering, Engineering Campus, Universiti Sains Malaysia, Seri Ampangan, 14300,Nibong Tebal, Pulau Pinang (Malaysia)
2015-03-30
The feasibility design and development methods of silicon microfabricated beam expander are described. Silicon bulk micromachining fabrication technology is used in producing features of the structure. A high-precision complex 3-D shape of the expander can be formed by exploiting the predictable anisotropic wet etching characteristics of single-crystal silicon in aqueous Potassium-Hydroxide (KOH) solution. The beam-expander consist of two elements, a micromachined silicon reflector chamber and micro-Fresnel zone plate. The micro-Fresnel element is patterned using lithographic methods. The reflector chamber element has a depth of 40 µm, a diameter of 15 mm and gold-coated surfaces. The impact on the depth, diameter of the chamber and absorption for improved performance are discussed.
Grazing incidence beam expander
Energy Technology Data Exchange (ETDEWEB)
Akkapeddi, P.R.; Glenn, P.; Fuschetto, A.; Appert, Q.; Viswanathan, V.K.
1985-01-01
A Grazing Incidence Beam Expander (GIBE) telescope is being designed and fabricated to be used as an equivalent end mirror in a long laser resonator cavity. The design requirements for this GIBE flow down from a generic Free Electron Laser (FEL) resonator. The nature of the FEL gain volume (a thin, pencil-like, on-axis region) dictates that the output beam be very small. Such a thin beam with the high power levels characteristic of FELs would have to travel perhaps hundreds of meters or more before expanding enough to allow reflection from cooled mirrors. A GIBE, on the other hand, would allow placing these optics closer to the gain region and thus reduces the cavity lengths substantially. Results are presented relating to optical and mechanical design, alignment sensitivity analysis, radius of curvature analysis, laser cavity stability analysis of a linear stable concentric laser cavity with a GIBE. Fabrication details of the GIBE are also given.
Principles of the fifth order tuning of beam expanders
Energy Technology Data Exchange (ETDEWEB)
Meot, F.; Aniel, T.
1995-12-31
An analytical treatment of the third and fifth order optics of beam expanders is described, which allows precise tuning of the optical elements of the beam line, and efficient optimization of the beam uniformizing at the extended target. An application to a two-dimensional expander is given as an illustration. (authors). 4 refs.
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Institute of Scientific and Technical Information of China (English)
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Boundary controllability for a nonlinear beam equation
Directory of Open Access Journals (Sweden)
Xiao-Min Cao
2015-09-01
Full Text Available This article concerns a nonlinear system modeling the bending vibrations of a nonlinear beam of length $L>0$. First, we derive the existence of long time solutions near an equilibrium. Then we prove that the nonlinear beam is locally exact controllable around the equilibrium in $H^4(0,L$ and with control functions in $H^2(0,T$. The approach we used are open mapping theorem, local controllability established by linearization, and the induction.
Nonlinear feedback control of Timoshenko beam
Institute of Scientific and Technical Information of China (English)
冯德兴; 张维弢
1995-01-01
This note is concerned with nonlinear boundary feedback control of a Timoshenko beam. Under some nonlinear boundary feedback control, first the nonlinear semigroup theory is used to show the existence and uniqueness of solution for the corresponding closed loop system. Then by using the Lyapunov method, it is proved that the vibration of the beam under the proposed control action decays in a negative power of time t as t→.
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
Institute of Scientific and Technical Information of China (English)
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
A beam expander facility for studying x-ray optics
DEFF Research Database (Denmark)
Christensen, Finn Erland; Hornstrup, Allan; Frederiksen, P.
1992-01-01
The detailed study of the performance of full scale x-ray optics often requires the illumination of large areas. This paper describes a beam expander facility at the Daresbury Synchrotron Radiation Facility. It combines monochromatization and beam expansion in one dimension. The beam expansion...... is obtained from an extremely asymmetric reflection in a large single crystal of Si. An expansion of a factor of 50 was obtained in one dimension. The expanded beam of ~85 mm is limited only by the crystal size. The facility is installed in a 12-m-long hutch. A specific application, in which a high throughput...
Bigelow Expandable Activity Module (BEAM) - ISS Inflatable Module Technology Demonstration
Dasgupta, Rajib; Munday, Steve; Valle, Gerard D.
2014-01-01
INNOVATION: BEAM is a pathway project demonstrating the design, fabrication, test, certification, integration, operation, on-orbit performance, and disposal of the first ever man-rated space inflatable structure. The groundwork laid through the BEAM project will support developing and launching a larger inflatable space structure with even greater mass per volume (M/V) advantages need for longer space missions. OVERVIEW: Inflatable structures have been shown to have much lower mass per volume ratios (M/V) when compared with conventional space structures. BEAM is an expandable structure, launched in a packed state, and then expanded once on orbit. It is a temporary experimental module to be used for gathering structural, thermal, and radiation data while on orbit. BEAM will be launched on Space X-8, be extracted from the dragon trunk, and will attach to ISS at Node 3- Aft. BEAM performance will be monitored over a two-year period and then BEAM will be jettison using the SSRMS.
Nonlinear optimization of beam lines
Tomás Garcia, Rogelio
2006-01-01
The current final focus systems of linear colliders have been designed based on the local compensation scheme proposed by P. Raimondi and A. Seryi [1]. However, there exist remaining aberrations that deteriorate the performance of the system. This paper develops a general algorithm for the optimization of beam lines based on the computation of the high orders of the transfer map using MAD-X [2] and PTC [3]. The algorithm is applied to the CLIC [4] Beam Delivery System (BDS).
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Periodic solutions of nonlinear vibrating beams
Directory of Open Access Journals (Sweden)
J. Berkovits
2003-01-01
Full Text Available The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time-independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free parameter. Since the period of the external forcing is generally unknown a priori, we consider the following natural problem. For a given time-independent nonlinearity, find periods T for which the equation is solvable for any T-periodic forcing. We will also deal with the existence of multiple solutions when the nonlinearity interacts with the spectrum of the linear part. We show that under certain conditions multiple solutions do exist for any small forcing term with suitable period T. The results are obtained via generalized Leray-Schauder degree and reductions to invariant subspaces.
Vibration Analysis of Timoshenko Beams on a Nonlinear Elastic Foundation
Institute of Scientific and Technical Information of China (English)
MO Yihua; OU Li; ZHONG Hongzhi
2009-01-01
The vibrations of beams on a nonlinear elastic foundation were analyzed considering the effects of transverse shear deformation and the rotational inertia of beams. A weak form quadrature element method (QEM) is used for the vibration analysis. The fundamental frequencies of beams are presented for various slenderness ratios and nonlinear foundation parameters for both slender and short beams. The results for slender beams compare well with finite element results. The analysis shows that the transverse shear de-formation and the nonlinear foundation parameter significantly affect the fundamental frequency of the beams.
Freeform optical design of an XY-zoom beam expander
Duerr, Fabian; Thienpont, Hugo
2016-04-01
Laser sources have become indispensable for industrial materials processing applications. These applications are accompanied with a variety of different demands and requirements on the delivered laser irradiance distributions. With a high spatial uniformity, top-hat beams provide benefits for applications like surface heat treatment or welding, in which it is desirable to uniformly illuminate a target surface. Some applications might not only favor a specific beam irradiance distribution but can benefit additionally from time-varying distributions. In this work, we present the analytic design of an XY-zoom beam expander based on movable freeform optics that allows to simultaneously vary the magnification in x- and y-direction, respectively. This optical functionality is not new; what is new is the idea that axially moving freeform lenses are used to achieve such an optical functionality by optimally exploiting the additional degrees of freedom that freeform surfaces offer. The developed analytic solution is fully described by very few initial parameters and does allow an increasingly accurate calculation of four freeform lenses described by high order XY Taylor polynomial surfaces. Moreover, this solution approach can be adapted to cope with additional optical surfaces and/or lens groups to further enhance the overall optical performance. In comparison with (existing) combinations of rotated cylindrically symmetric zoom beam expanders, such a freeform system consists of less optical elements and provides a much more compact solution, yet achieving excellent overall optical performance throughout the full range of zoom positions.
Beam stability & nonlinear dynamics. Formal report
Energy Technology Data Exchange (ETDEWEB)
Parsa, Z. [ed.
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.
Electromagnetic beam propagation in nonlinear media
Institute of Scientific and Technical Information of China (English)
V.V.Semak; M.N.Shneider
2015-01-01
We deduce a complete wave propagation equation that includes inhomogeneity of the dielectric constant and present this propagation equation in compact vector form. Although similar equations are known in narrow fields such as radio wave propagation in the ionosphere and electromagnetic and acoustic wave propagation in stratified media, we develop here a novel approach of using such equations in the modeling of laser beam propagation in nonlinear media. Our approach satisfies the correspondence principle since in the limit of zero-length wavelength it reduces from physical to geometrical optics.
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a
Direct design of laser-beam shapers, zoom-beam expanders, and combinations thereof
Duerr, Fabian; Thienpont, Hugo
2016-10-01
Laser sources have become indispensable for industrial materials processing applications like surface treatment, cutting or welding to name a few examples. Many of these applications pose different requirements on the delivered laser irradiance distribution. Some applications might not only favor a specific irradiance distribution (e.g. a at-top) but can additionally benefit from time-varying distributions. We present an overview of a recently developed design approach that allows direct calculation of virtually any refractive or reflective laser beam shaping system. The derived analytic solution is fully described by few initial parameters and does allow an increasingly accurate calculation of all optical surfaces. Unlike other existing direct design methods for laser beam shaping, there is almost no limitation in the number of surfaces that can be calculated with this approach. This is of particular importance for optical designs of dynamic systems such as variable optical beam expanders that require four (or more) optical surfaces. Besides conventional static beam shapers, we present direct designs of zoom beam expanders, and as a novelty, a class of dynamic systems that shape and expand the input beam simultaneously. Such dynamic zoom beam shapers consist of a minimal number of optical elements and provide a much more compact solution, yet achieving excellent overall optical performance throughout the full range of zoom positions.
Self-effect in expanding electron beam plasma
Energy Technology Data Exchange (ETDEWEB)
Garcia, M
1999-05-07
An analytical model of plasma flow from a metal plate hit by an intense, pulsed, electron beam aims to bridge the gap between radiation-hydrodynamics simulations and experiments, and to quantify the self-effect of the electron beam penetrating the flow. Does the flow disrupt the tight focus of the initial electron bunch, or later pulses in a train? This work aims to model the spatial distribution of plasma speed, density, degree of ionization, and magnetization to inquire. The initial solid density, several eV plasma expands to 1 cm and 10{sup {minus}4} relative density by 2 {micro}s, beyond which numerical simulations are imprecise. Yet, a Faraday cup detector at the ETA-II facility is at 25 cm from the target and observes the flow after 50 {micro}s. The model helps bridge this gap. The expansion of the target plasma into vacuum is so rapid that the ionized portion of the flow departs from local thermodynamic equilibrium. When the temperature (in eV) in a parcel of fluid drops below V{sub i} x [(2{gamma} - 2)/(5{gamma} + 17)], where V{sub i} is the ionization potential of the target metal (7.8 eV for tantalum), and {gamma} is the ratio of specific heats (5/3 for atoms), then the fractional ionization and electron temperature in that parcel remain fixed during subsequent expansion. The freezing temperature as defined here is V{sub i}/19. The balance between the self-pinching force and the space charge repulsion of an electron beam changes on penetrating a flow: (i) the target plasma cancels the space-charge field, (ii) internal eddy currents arise to counter the magnetization of relativistic electrons, and (iii) electron beam heating alters the flow magnetization by changing the plasma density gradient and the magnitude of the conductivity.
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions
Institute of Scientific and Technical Information of China (English)
郭强; 刘曦; 钟宏志
2004-01-01
This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC.
Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam
Directory of Open Access Journals (Sweden)
W. Gafsi
2014-01-01
Full Text Available In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.
Nonlinear Strain Measures, Shape Functions and Beam Elements for Dynamics of Flexible Beams
Energy Technology Data Exchange (ETDEWEB)
Sharf, I. [University of Victoria, Department of Mechanical Engineering (Canada)
1999-05-15
In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape functions for discretization. The issue of rigid-body check for a nonlinear beam element is also considered. An approximate check is introduced for an element based on an (approximate) intermediate strain measure. Several numerical examples are presented to support the analysis. The paper concludes with a discussion on the use of explicit nonlinear beam elements for multibody dynamics simulation.
Solution and Positive Solution to Nonlinear Cantilever Beam Equations
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the "height" of nonlinear term is appropriate on a bounded set.
Institute of Scientific and Technical Information of China (English)
GAO Jie
2009-01-01
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
Optical Beams in Nonlocal Nonlinear Media
DEFF Research Database (Denmark)
Królikowski, W.; Bang, Ole; Wyller, J.
2003-01-01
We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons.......We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....
Use of proton beams with breast prostheses and tissue expanders
Energy Technology Data Exchange (ETDEWEB)
Moyers, Michael F., E-mail: MFMoyers@roadrunner.com [ProCure Proton Therapy Center, Somerset, NJ (United States); Mah, Dennis; Boyer, Sean P.; Chang, Chang [ProCure Proton Therapy Center, Somerset, NJ (United States); Pankuch, Mark [ProCure Proton Therapy Center, Warrenville, IL (United States)
2014-04-01
Since the early 2000s, a small but rapidly increasing number of patients with breast cancer have been treated with proton beams. Some of these patients have had breast prostheses or tissue expanders in place during their courses of treatment. Procedures must be implemented to plan the treatments of these patients. The density, kilovoltage x-ray computed tomography numbers (kVXCTNs), and proton relative linear stopping powers (pRLSPs) were calculated and measured for several test sample devices. The calculated and measured kVXCTNs of saline were 1% and 2.4% higher than the values for distilled water while the calculated RLSP for saline was within 0.2% of the value for distilled water. The measured kVXCTN and pRLSP of the silicone filling material for the test samples were approximately 1120 and 0.935, respectively. The conversion of kVXCTNs to pRLSPs by the treatment planning system standard tissue conversion function is adequate for saline-filled devices but for silicone-filled devices manual reassignment of the pRLSPs is required.
Use of proton beams with breast prostheses and tissue expanders.
Moyers, Michael F; Mah, Dennis; Boyer, Sean P; Chang, Chang; Pankuch, Mark
2014-01-01
Since the early 2000s, a small but rapidly increasing number of patients with breast cancer have been treated with proton beams. Some of these patients have had breast prostheses or tissue expanders in place during their courses of treatment. Procedures must be implemented to plan the treatments of these patients. The density, kilovoltage x-ray computed tomography numbers (kVXCTNs), and proton relative linear stopping powers (pRLSPs) were calculated and measured for several test sample devices. The calculated and measured kVXCTNs of saline were 1% and 2.4% higher than the values for distilled water while the calculated RLSP for saline was within 0.2% of the value for distilled water. The measured kVXCTN and pRLSP of the silicone filling material for the test samples were approximately 1120 and 0.935, respectively. The conversion of kVXCTNs to pRLSPs by the treatment planning system standard tissue conversion function is adequate for saline-filled devices but for silicone-filled devices manual reassignment of the pRLSPs is required. © 2013 Published by American Association of Medical Dosimetrists on behalf of American Association of Medical Dosimetrists.
Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
Directory of Open Access Journals (Sweden)
J. Machalová
2015-01-01
Full Text Available Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.
A New Expanded Method for Solving Nonlinear Differential-difference Equation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-qing
2008-01-01
A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Methodology for nonlinear quantification of a flexible beam with a local, strong nonlinearity
Herrera, Christopher A.; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-02-01
This study presents a methodology for nonlinear quantification, i.e., the identification of the linear and nonlinear regimes and estimation of the degree of nonlinearity, for a cantilever beam with a local, strongly nonlinear stiffness element. The interesting feature of this system is that it behaves linearly in the limits of extreme values of the nonlinear stiffness. An Euler-Bernoulli cantilever beam with two nonlinear configurations is used to develop and demonstrate the methodology. One configuration considers a cubic spring attached at a distance from the beam root to achieve a smooth nonlinear effect. The other configuration considers a vibro-impact element that generates non-smooth effects. Both systems have the property that, in the limit of small and large values of a configuration parameter, the system is almost linear and can be modeled as such with negligible error. For the beam with a cubic spring attachment, the forcing amplitude is the varied parameter, while for the vibro-impact beam, this parameter is the clearance between the very stiff stops and the beam at static equilibrium. Proper orthogonal decomposition is employed to obtain an optimal orthogonal basis used to describe the nonlinear system dynamics for varying parameter values. The frequencies of the modes that compose the basis are then estimated using the Rayleigh quotient. The variations of these frequencies are studied to identify parameter values for which the system behaves approximately linearly and those for which the dynamical response is highly nonlinear. Moreover, a criterion based on the Betti-Maxwell reciprocity theorem is used to verify the existence of nonlinear behavior for the set of parameter values suggested by the described methodology. The developed methodology is general and applicable to discrete or continuous systems with smooth or nonsmooth nonlinearities.
Nonlinear images of scatterers in chirped pulsed laser beams
Institute of Scientific and Technical Information of China (English)
Hu Yong-Hua; Wang You-Wen; Wen Shuang-Chun; Fan Dian-Yuan
2010-01-01
The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer.It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image,while the negative one can enhance it,and that both effects are inversely proportional to the incident pulse duration.Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that,for negatively pre-chirped pulsed beam,the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions.Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.
Temporal nonlinear beam dynamics in infiltrated photonic crystal fibers
DEFF Research Database (Denmark)
Bennet, Francis; Rosberg, Christian Romer; Neshev, Dragomir N.
of nonlinear beam reshaping occurring on a short time scale before the establishment of a steady state regime. In experiment, a 532nm laser beam can be injected into a single hole of an infiltrated PCF cladding structure, and the temporal dynamics of the nonlinear response is measured by monitoring......Liquid-infiltrated photonic crystal fibers (PCFs) offer a new way of studying light propagation in periodic and discrete systems. A wide range of available fiber structures combined with the ease of infiltration opens up a range of novel experimental opportunities for optical detection and bio......-sensing as well as active devices for all-optical switching at low (mW) laser powers. Commercially available PCFs infiltrated with liquids also provide a versatile and compact tool for exploration of the fundamentals of nonlinear beam propagation in periodic photonic structures. To explore the full scientific...
Flexural Behaviour Of Reinforced Concrete Beams Containing Expanded Glass As Lightweight Aggregates
Khatib, Jamal; Jefimiuk, Adrian; Khatib, Sammy
2015-12-01
The flexural properties of reinforced concrete beams containing expanded glass as a partial fine aggregate (sand) replacement are investigated. Four concrete mixes were employed to conduct this study. The fine aggregate was replaced with 0%, 25%, 50% and 100% (by volume) expanded glass. The results suggest that the incorporation of 50% expanded glass increased the workability of the concrete. The compressive strength was decreasing linearly with the increasing amount of expanded glass. The ductility of the concrete beam significantly improved with the incorporation of the expanded glass. However, the load-carrying capacity of the beam and load at which the first crack occurs was reduced. It was concluded that the inclusion of expanded glass in structural concrete applications is feasible.
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.
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for no...... for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions....
Suppressing Transverse Beam Halo with Nonlinear Magnetic Fields
Webb, Stephen D; Abell, Dan T; Danilov, Viatcheslav; Nagaitsev, Sergei; Valishev, Alexander; Danilov, Kirill; Cary, John R
2012-01-01
High intensity proton storage rings are central for the development of advanced neutron sources, drivers for the production of pions in neutrino factories or muon colliders, and transmutation of radioactive waste. Fractional proton loss from the beam must be very small to prevent radioac- tivation of nearby structures, but many sources of beam loss are driven by collective effects that increase with intensity. Recent theoretical work on the use of nonlinear magnetic fields to design storage rings with integrable transverse dynamics is extended here to include collective effects, with numerical results showing validity in the presence of very high beam current. Among these effects is the formation of beam halo, where particles are driven to large amplitude oscillations by coherent space charge forces. The strong variation of particle oscillation frequency with amplitude results in nonlinear decoherence that is observed to suppress transverse halo development in the case studied. We also present a necessary gen...
Reflection of a Gaussian beam from a nonlinear interface.
Marcuse, D
1980-09-15
A numerical analysis of the reflection of a two dimensional Gaussian beam from the interface between a linear and a nonlinear medium is presented. The refractive index of the nonlinear medium is a function of the intensity of the radiation field, having a smaller value than the linear refractive index for zero field intensity. The Gaussian beam is incident from the linear medium and suffers total reflection at low intensity. At sufficiently high intensity nonlinear effects are observed. Above a threshold value the incident beam breaks up into a reflected wave and a surface wave. Once the beam is sufficiently strong for a surface wave to form, its interaction with the boundary becomes surprisingly independent of field intensity; but for very strong fields the reflectivity is increased at the expense of the surface wave. A very different behavior is observed when the refractive index is constrained to remain below a certain maximum value. Now the field detaches itself from the surface and penetrates into the nonlinear medium forming one or more distinct beams. The plane wave theory predicts the existence of hysteresis so that two different solutions should exist for the same physical parameters. A second solution was indeed found in one case with constrained refractive index, but its validity is somewhat uncertain at this time.
Intense DC beam nonlinear transport-analysis & simulation
Institute of Scientific and Technical Information of China (English)
L(U) Jian-Qin; ZHAO Xiao-Song
2009-01-01
The intense dc beam nonlinear transport was analyzed with the Lie algebraic method,and the particle trajectories of the second order approximation were obtained.Based on the theoretical analysis a computer code was designed.To get self-consistent solutions,iteration procedures were used in the code.As an example,we calculated a beam line(drift-electrostatic quadrupole doublet-drift).The results agree to the results calculated by using the PIC method.
Finite rotation and nonlinear beam kinematics
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.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS
Institute of Scientific and Technical Information of China (English)
Yang Xiaodong; Chen Li-Qun
2006-01-01
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
Nonlinearities and effects of transverse beam size in beam position monitors
Kurennoy, Sergey S.
2001-09-01
The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by a pencil beam. The nonlinearities 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.
Nonlinearities and effects of transverse beam size in beam position monitors
Directory of Open Access Journals (Sweden)
Sergey S. Kurennoy
2001-09-01
Full Text Available The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM are calculated and compared to those produced by a pencil beam. The nonlinearities 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.
Laser beam propagation in non-linearly absorbing media
CSIR Research Space (South Africa)
Forbes, A
2006-08-01
Full Text Available Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well...
Non-Linear Vibration of Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Barari, Amin; Kaliji, H. D.; Domairry, G.
2011-01-01
In this paper, variational iteration (VIM) and parametrized perturbation (PPM)methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found...
Bending of a nonlinear beam reposing on an unilateral foundation
Directory of Open Access Journals (Sweden)
Machalová J.
2011-06-01
Full Text Available This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches,Mech. Research Communication, 23 (1 1996. The model is based on the Euler-Bernoulli hypothesis and under assumption of nonzero lateral stress component enables moderately large deflections but with small strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research Communication, 23 (1 1996 has no mention of it. The main alternatives are here the solution of a system of nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian method. This is illustrated by an example in the final part of the article.
Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams
Koissin, Vitaly; Shipsha, Andrey; Skvortsov, Vitaly
2010-01-01
This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou
Nonlinear Evolution of the Ion-Ion Beam Instability
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.
1982-01-01
The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...
Effect of Physical Nonlinearity on Local Buckling in Sandwich Beams
Koysin, V.; Shipsha, Andrey; Skvortsov, Vitaly
2010-01-01
This article deals with experimental, theoretical, and FE characterization of the local buckling in foam-core sandwich beams. In the theoretical approach, this phenomena is considered in a periodic formulation (unbounded wrinkle wave); a nonlinear stress—strain response of the face material is accou
Nonlinear analysis of concrete beams strengthened by date palm fibers
Bouzouaid, Samia; Kriker, Abdelouahed
2017-02-01
The behaviour of concrete beams strengthened with date palm fibers was studied by Nonlinear Finite Element Analysis using ANSYS software. Five beams that were experimentally tested in a previous research were considered. The results obtained from the ANSYS finite element analysis are compared with the experimental data for the five beams with different amounts of fibres, ranging from 0.2% to 0.5% by a step equal to 0.1% and with a fibre length of 0.04 m. The results obtained by FEA showed good agreement with those obtained by the experimental program. This research demonstrates the ability of FEA in predicting the behaviour of beams strengthened with Date Palm fibers. It will help researchers in studying beams with different configurations without the need to go through the lengthy experimental testing programs.
Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads
Directory of Open Access Journals (Sweden)
A. Bellino
2012-01-01
Full Text Available It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.
A Simple Model for Nonlinear Confocal Ultrasonic Beams
Institute of Scientific and Technical Information of China (English)
ZHANG Dong; ZHOU Lin; SI Li-Sheng; GONG Xiu-Fen
2007-01-01
@@ A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented.Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.
Energy Technology Data Exchange (ETDEWEB)
Stancari, Giulio
2014-09-11
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 compensation in LHC luminosity upgrade scenarios with small crossing angles. At Fermilab, we are planning to install an electron lens in the Integrable Optics Test Accelerator (IOTA, a 40-m ring for 150-MeV electrons) as one of the proof-of-principle implementations of nonlinear integrable optics to achieve large tune spreads and more stable beams without loss of dynamic aperture.
Indian Academy of Sciences (India)
Sabapathi Gokulnath; Tavarekere K Chandrashekar
2008-01-01
In this paper, the non-linear optical properties of representative core-modified expanded porphyrins have been investigated with an emphasis on the structure-property relationship between the aromaticity and conformational behaviour. It has been shown that the measured two-photon absorption cross section (2) values depend on the structure of macrocycle, its aromaticity and the number of -electrons in conjugation.
Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances
Directory of Open Access Journals (Sweden)
Ali H. Nayfeh
1998-01-01
Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam
Yue Wu; Jingshi Dong; Xinbo Li; Zhigang Yang; Qingping Liu
2015-01-01
Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used t...
Tracking control of a flexible beam by nonlinear boundary feedback
Directory of Open Access Journals (Sweden)
Bao-Zhu Guo
1995-01-01
Full Text Available This paper is concerned with tracking control of a dynamic model consisting of a flexible beam rotated by a motor in a horizontal plane at the one end and a tip body rigidly attached at the free end. The well-posedness of the closed loop systems considering the dissipative nonlinear boundary feedback is discussed and the asymptotic stability about difference energy of the hybrid system is also investigated.
Quasi-periodic solutions of nonlinear beam equations with quintic quasi-periodic nonlinearities
Directory of Open Access Journals (Sweden)
Qiuju Tuo
2015-01-01
Full Text Available In this article, we consider the one-dimensional nonlinear beam equations with quasi-periodic quintic nonlinearities $$ u_{tt}+u_{xxxx}+(B+ \\varepsilon\\phi(tu^5=0 $$ under periodic boundary conditions, where B is a positive constant, $\\varepsilon$ is a small positive parameter, $\\phi(t$ is a real analytic quasi-periodic function in t with frequency vector $\\omega=(\\omega_1,\\omega_2,\\dots,\\omega_m$. It is proved that the above equation admits many quasi-periodic solutions by KAM theory and partial Birkhoff normal form.
Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam
Directory of Open Access Journals (Sweden)
Yue Wu
2015-08-01
Full Text Available Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used to increase the output displacement at a lower voltage. The system is analytically modeled with Lagrangian functional and Euler–Lagrange equations, numerically simulated with MATLAB, and experimentally realized to demonstrate its enhanced capabilities. The model is validated using an experimental device with several pretensions of the loading spring, therein representing three interesting cases: a linear system, a low natural frequency system with a pre-buckled beam, and a system with a buckled beam. The motivating hypothesis for the current work is that nonlinear phenomena could be exploited to improve the effectiveness of the piezoelectric actuator’s displacement output. The most practical configuration seems to be the pre-buckled case, in which the proposed system has a low natural frequency, a high tip displacement, and a stable balanced position.
Generation of non-classical optical fields by a beam splitter with second-order nonlinearity
Prakash, Hari
2016-01-01
We propose quantum-mechanical model of a beam splitter with second-order nonlinearity and show that non-classical features such as squeezing and sub-Poissonian photon statistics of optical fields can be generated in output fundamental and second harmonic modes when we mix coherent light beams via such a nonlinear beam splitter.
Azimuthal and radial shaping of vortex beams generated in twisted nonlinear photonic crystals.
Shemer, Keren; Voloch-Bloch, Noa; Shapira, Asia; Libster, Ana; Juwiler, Irit; Arie, Ady
2013-12-15
We experimentally demonstrate that the orbital angular momentum (OAM) of a second harmonic (SH) beam, generated within twisted nonlinear photonic crystals, depends both on the OAM of the input pump beam and on the quasi-angular momentum of the crystal. In addition, when the pump's radial index is zero, the radial index of the SH beam is equal to that of the nonlinear crystal. Furthermore, by mixing two noncollinear pump beams in this crystal, we generate, in addition to the SH beams, a new "virtual beam" having multiple values of OAM that are determined by the nonlinear process.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
Quasi-periodic Solutions of the General Nonlinear Beam Equations
Institute of Scientific and Technical Information of China (English)
GAO YI-XIAN
2012-01-01
In this paper,one-dimensional (1D) nonlinear beam equations of the form utt - uxx + uxxxx + mu = f(u)with Dirichlet boundary conditions are considered,where the nonlinearity f is an analytic,odd function and f(u) = O(u3).It is proved that for all m ∈ (0,M*] (∈) R(M* is a fixed large number),but a set of small Lebesgue measure,the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.
Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics
Energy Technology Data Exchange (ETDEWEB)
Alex J. Dragt; Filippo Neri; Govindan Rangarajan; David Douglas; Liam M. Healy; Robert D. Ryne
1988-12-01
The purpose of this paper is to present a summary of new methods, employing Lie algebraic tools, for characterizing beam dynamics in charged-particle optical systems. These methods are applicable to accelerator design, charged-particle beam transport, electron microscopes, and also light optics. The new methods represent the action of each separate element of a compound optical system, including all departures from paraxial optics, by a certain operator. The operators for the various elements can then be concatenated, following well-defined rules, to obtain a resultant operator that characterizes the entire system. This paper deals mostly with accelerator design and charged-particle beam transport. The application of Lie algebraic methods to light optics and electron microscopes is described elsewhere (1, see also 44). To keep its scope within reasonable bounds, they restrict their treatment of accelerator design and charged-particle beam transport primarily to the use of Lie algebraic methods for the description of particle orbits in terms of transfer maps. There are other Lie algebraic or related approaches to accelerator problems that the reader may find of interest (2). For a general discussion of linear and nonlinear problems in accelerator physics see (3).
On two transverse nonlinear models of axially moving beams
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.
On two transverse nonlinear models of axially moving beams
Institute of Scientific and Technical Information of China (English)
DING Hu; CHEN LiQun
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit-ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av-eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif-ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte-gro-partial-differential equation gives better results for large amplitude vibration.
Nonlinear dynamics for charges particle beams with a curved axis in the matrix - recursive model
Energy Technology Data Exchange (ETDEWEB)
Dymnikov, A.D. [University of St Petersburg, (Russian Federation). Institute of Computational Mathematics and Control Process
1993-12-31
In this paper a new matrix and recursive approach has been outlined for treating nonlinear optics of charged particle beams. This approach is a new analytical and computational tool for designers of optimal beam control systems. 9 refs.
Development of a raster electronics system for expanding the APT proton beam
Energy Technology Data Exchange (ETDEWEB)
Chapelle, S.; Hubbard, E.L.; Smith, T.L. [General Atomics, San Diego, CA (United States); Schulze, M.E.; Shafer, R.E. [General Atomics, Los Alamos, NM (United States)
1998-12-31
A 1700 MeV, 100 mA proton linear accelerator is being designed for Accelerator Production of Tritium (APT). A beam expansion system is required to uniformly irradiate a 19 x 190 cm tritium production target. This paper describes a beam expansion system consisting of eight ferrite dipole magnets to raster the beam in the x- and y-planes and also describes the salient features of the design of the electronics that are unique to the expander. Eight Insulated Gate Bipolar Transistor (IGBT)-based modulators drive the raster magnets with triangular current waveforms that are synchronized using phase-locked loops (PLLs) and voltage controlled crystal oscillators (VCXOs). Fault detection circuitry shuts down the beam before the target can be damaged by a failure of the raster system. Test data are presented for the prototype system.
Measuring the criticality of the `magic condition' for a beam-expanding monochromator.
Martinson, Mercedes; Chapman, Dean
2016-11-01
It has been established that for cylindrically bent crystals the optimal beam characteristics occur when the geometric and single-ray foci are matched. In the beam-expanding monochromator developed for the BioMedical Imaging and Therapy beamlines at the Canadian Light Source, it was unclear how critical this `magic condition' was for preserving the transverse coherence of the beam. A study was conducted to determine whether misalignments away from the ideal conditions would severely affect the transverse coherence of the beam, thereby limiting phase-based imaging techniques. The results were that the magic condition has enough flexibility to accommodate deviations of about ±1° or ±5 keV.
Evaluation and Correction of the Non-linear Distortion of CEBAF Beam Position Monitors
Energy Technology Data Exchange (ETDEWEB)
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.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Institute of Scientific and Technical Information of China (English)
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Directory of Open Access Journals (Sweden)
E. Mardani
2008-01-01
Full Text Available A prismatic beam made of a behaviorally nonlinear material was analyzed under a concentrated load moving with a known velocity on a nonlinear elastic foundation with a reaction the vibration equation of motion was derived using Hamilton principle and Euler Lagrange equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it was found that there is no critical velocity when the behavior of the beam and foundation material is assumed to be physically nonlinear and there are finite values for the deflection, stress and bending moment of the beam when
Simulating Time-Dependent Energy Transfer Between Crossed Laser Beams in an Expanding Plasma
Energy Technology Data Exchange (ETDEWEB)
Hittinger, J F; Dorr, M R; Berger, R L; Williams, E A
2004-10-11
A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly-damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Finite Element Solution: Nonlinear Flapping Beams for Use with Micro Air Vehicle Design
2007-03-01
used to approximate the nonlinearity in a beam is the SDOF Duffing Oscillator ӱ + C ẏ + ω0 2 y + βy3 = P sin(ωt...Hilbert Transform.......................................................................................................19 Duffing Equation...Amplitude vs Nonlinear Frequency: Fixed-Fixed Steel................................. 36 Figure 26. Duffing Equation Plot: Fixed-Fixed Steel Beam
Nonlinear beam clean-up using resonantly enhanced sum-frequency mixing
DEFF Research Database (Denmark)
Karamehmedovic, Emir; Pedersen, Christian; Jensen, Ole Bjarlin;
2009-01-01
We investigate the possibility of improving the beam quality and obtaining high conversion efficiency in nonlinear sum-frequency generation. A 765 nm beam from an external cavity tapered diode laser is single-passed through a nonlinear crystal situated in the high intracavity field of a 1342 nm Nd...
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Phase-preserving beam expander for biomedical X-ray imaging
Energy Technology Data Exchange (ETDEWEB)
Martinson, Mercedes, E-mail: mercedes.m@usask.ca [University of Saskatchewan, 116 Science Place, Rm 163, Saskatoon, Saskatchewan (Canada); Samadi, Nazanin [University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada); Bassey, Bassey [University of Saskatchewan, 116 Science Place, Rm 163, Saskatoon, Saskatchewan (Canada); Gomez, Ariel [Canadian Light Source, 44 Innovation Boulevard, Saskatoon, Saskatchewan (Canada); Chapman, Dean [University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada); University of Saskatchewan, 116 Science Place, Rm 163, Saskatoon, Saskatchewan (Canada)
2015-04-15
Building on previous work, a phase-preserving bent Laue beam-expanding monochromator was developed with the capability of performing live animal phase contrast dynamic imaging at the Biomedical Imaging and Therapy beamline at the Canadian Light Source. The BioMedical Imaging and Therapy beamlines at the Canadian Light Source are used by many researchers to capture phase-based imaging data. These experiments have so far been limited by the small vertical beam size, requiring vertical scanning of biological samples in order to image their full vertical extent. Previous work has been carried out to develop a bent Laue beam-expanding monochromator for use at these beamlines. However, the first attempts exhibited significant distortion in the diffraction plane, increasing the beam divergence and eliminating the usefulness of the monochromator for phase-related imaging techniques. Recent work has been carried out to more carefully match the polychromatic and geometric focal lengths in a so-called ‘magic condition’ that preserves the divergence of the beam and enables full-field phase-based imaging techniques. The new experimental parameters, namely asymmetry and Bragg angles, were evaluated by analysing knife-edge and in-line phase images to determine the effect on beam divergence in both vertical and horizontal directions, using the flat Bragg double-crystal monochromator at the beamline as a baseline. The results show that by using the magic condition, the difference between the two monochromator types is less than 10% in the diffraction plane. Phase fringes visible in test images of a biological sample demonstrate that this difference is small enough to enable in-line phase imaging, despite operating at a sub-optimal energy for the wafer and asymmetry angle that was used.
Walasik, Wiktor T.; Silahli, Salih Z.; Litchinitser, Natalia M.
2016-09-01
Colloidal metamaterials are a robust and flexible platform for engineering of optical nonlinearities and studies of light filamentation. To date, nonlinear propagation and modulation instability of Gaussian beams and optical vortices carrying orbital angular momentum were studied in such media. Here, we investigate the propagation of necklace beams and the conservation of the orbital angular momentum in colloidal media with saturable nonlinearity. We study various scenarios leading to generation of helical necklace beams or twisted beams, depending on the radius, power, and charge of the input vortex beam. Helical beams are build of two separate solitary beams with circular cross-sections that spiral around their center of mass as a result of the equilibrium between the attraction force of in-phase solitons and the centrifugal force associated with the rotational movement. A twisted beam is a single beam with an elliptical cross-section that rotates around it's own axis. We show that the orbital angular momentum is converted into the rotational motion at different rates for helical and twisted beams. While earlier studies reported that solitary beams are expelled form the initial vortex ring along straight trajectories tangent to the vortex ring, we show that depending on the charge and the power of the initial beam, these trajectories can diverge from the tangential direction and may be curvilinear. These results provide a detailed description of necklace beam dynamics in saturable nonlinear media and may be useful in studies of light filamentation in liquids and light propagation in highly scattering colloids and biological samples.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Suppression of space charge induced beam halo in nonlinear focusing channel
Batygin, Yuri K.; Scheinker, Alexander; Kurennoy, Sergey; Li, Chao
2016-04-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Suppression of Space Charge Induced Beam Halo in Nonlinear Focusing Channel
Batygin, Yuri K; Kurennoy, Sergey; Li, Chao
2016-01-01
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.
Propagation of a Laguerre-Gaussian correlated Schell-model beam in strongly nonlocal nonlinear media
Qiu, Yunli; Chen, Zhaoxi; He, Yingji
2017-04-01
Analytical expressions for the cross-spectral density function and the second-order moments of the Wigner distribution function of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in strongly nonlocal nonlinear media are derived. The propagation properties, such as beam irradiance, beam width, the spectral degree of coherence and the propagation factor of a LGCSM beam inside the media are investigated in detail. The effect of the beam parameters and the input power on the evolution properties of a LGCSM is illustrated numerically. It is found that the beam width varies periodically or keeps invariant for a certain proper input power. And both the beam irradiance and the spectral degree of coherence of the LGCSM beam change periodically with the propagation distance for the arbitrary input power which however has no influence on the propagation factor. The coherent length and the mode order mainly affect the evolution speed of the LGCSM beam in strongly nonlocal nonlinear media.
Nonlinear evolution of Airy-like beams generated by modulated waveguide arrays.
Cao, Zheng; Tan, Qinggui; Li, Xiaojun; Qi, Xinyuan
2016-08-20
We numerically study the formation of modulated waveguide generated Airy-like beams and their subsequent evolution in homogeneous medium. The results show that the Airy-like beams could be generated from narrow Gaussian beams propagating in one-dimensional transverse separation modulated unbent, cosine bent, or logarithm bent waveguide arrays, respectively. The waveguide-generated Airy-like beams maintain their characteristics when propagating without nonlinearity or under the self-defocusing nonlinearity in homogeneous medium, while the beams are distorted under the self-focusing nonlinearity. The deformation depends on the waveguide bending and the outgoing angles of the Airy-like beams. Our results provide a new way to generate and manipulate the Airy-like beam.
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
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.
Alignment tolerant expanded beam connector based on a gapless fiber-lens interface.
Lee, Yong-Geon; Park, Chang-Hyun; Back, Seon-Woo; Kim, Haeng-Jeong; Lee, Sang-Shin
2016-01-10
An expanded beam connector (EBC) has been proposed and realized, where a single-mode fiber is seamlessly integrated with a ball lens exhibiting a near-zero back focal length (BFL) so that the incoming small mode exiting the fiber translates into an enlarged collimated beam via the lens. The structural tolerance for the fiber-optic connector is primarily relaxed by relieving the restrictions imposed on the meticulous control of the gap between the lens and the fiber. The EBC has been designed through rigorous ray-optic simulations and then constructed based on a ball lens in LASF35 (n=∼1.98 at λ=1.3 μm), exhibiting an ultrashort BFL of ∼13 μm. It was practically confirmed that an input mode of a ∼10 μm spot relating to the single-mode fiber could be efficiently converted into a highly collimated beam of a ∼350 μm spot that emanates from the ball lens, leading to a 35-fold beam expansion. The alignment tolerance for the fiber as well as the connector unit was scrutinized with respect to the angular tilt and transverse displacement. The measured insertion loss for the EBC, allowing for no separation between the fiber and ball lens, was slightly over 0.8 dB.
Intermittent Giant Goos-Hanchen shifts from Airy beams at nonlinear interfaces
Chamorro-Posada, Pedro; Aceves, Alejandro B; McDonald, Graham S
2013-01-01
We study the giant Goos-Hanchen shift obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the numerical solution of the nonlinear Helmholtz equation. We report the existence of non-standard intermittent and oscillatory regimes for the nonlinear Goos-Hanchen shifts which can be explained in terms of the competition between the critical coupling to a surface mode of the reflected component of the Airy beam and the soliton emission from the refracted beam component.
Reciprocity breaking during nonlinear propagation of adapted beams through random media.
Palastro, J P; Peñano, J; Nelson, W; DiComo, G; Helle, M; Johnson, L A; Hafizi, B
2016-08-22
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate phase aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown, providing the first analysis of AO applied to high peak power laser beams. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
Widely varying giant Goos-Hänchen shifts from Airy beams at nonlinear interfaces.
Chamorro-Posada, Pedro; Sánchez-Curto, Julio; Aceves, Alejandro B; McDonald, Graham S
2014-03-15
We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence of multiple critical values. These intermittent and oscillatory regimes can be explained in terms of competition between critical coupling to a surface mode and soliton emission from the refracted beam component and how this interplay varies with localization of the initial Airy beam.
Nonlinear Stability of Intense Mismatched Beams in a Uniform Focusing Field
Pakter, Renato; Simeoni, Wilson
2005-01-01
We investigate the nonlinear coupling between axisymmetric and elliptic oscillations in the dynamics of intense beams propagating in a uniform magnetic focusing field. It is shown that finite amplitude mismatched oscillations of an initially round beam may destabilize elliptic oscillations, heavily affecting stability and the shape of the beam. This is a potential mechanics for beam particle loss in such systems. Self consistent simulations are performed to verify the findings.
Tunable nonlinear beam defocusing in infiltrated photonic crystal fibers
DEFF Research Database (Denmark)
Rosberg, Christian Romer; Bennet, Francis H; Neshev, Dragomir N.;
2007-01-01
We demonstrate a novel experimental platform for discrete nonlinear optics based on infiltrated photonic crystal fibers. We observe tunable discrete diffraction and nonlinear self-defocusing, and apply the effects to realize a compact all-optical power limiter....
Stojanović, Vladimir; Petković, Marko D.
2016-12-01
Geometrically nonlinear free and forced vibrations of damaged high order shear deformable beams resting on a nonlinear Pasternak foundation are investigated in this paper. Equations of motion are derived for the beam which is under subjected combined action of arbitrarily distributed or concentrated transverse loading as well as axial loading. To account for shear deformations, the concept of high order shear deformation is used in comparison with the concept of first order shear deformation theory. Analyses are performed to investigate the effects of the specific stiffness of the foundation on the damaged beam frequencies and displacements with the aim of equalising the response of a damaged and an intact beam. According to that, functions of the foundation stiffness are determined depending on the location and size of the damage as a result of the possibility for the damaged beam to behave like one that is intact. An advanced p-version of the finite element method is developed for geometrically nonlinear vibrations of damaged Reddy-Bickford beams. The present study gives a clear view of the nonlinear dynamical behaviour of four types of beams according to high order shear deformation theory - an intact beam, a damaged beam, a damaged beam on an elastic foundation and intact beam on elastic foundation. The paper also presents the derivation of a new set of two nonlinear partial differential equations where only the transverse and axial displacements figure. The forced nonlinear vibrations problem is solved in the time domain using the Newmark integration method. Free vibration analysis carried out by harmonic balance and the use of continuation methods and backbone curves are constructed.
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
Two-dimensional simulations of nonlinear beam-plasma interaction in isotropic and magnetized plasmas
Timofeev, I V
2012-01-01
Nonlinear interaction of a low density electron beam with a uniform plasma is studied using two-dimensional particle-in-cell (PIC) simulations. We focus on formation of coherent phase space structures in the case, when a wide two-dimensional wave spectrum is driven unstable, and we also study how nonlinear evolution of these structures is affected by the external magnetic field. In the case of isotropic plasma, nonlinear buildup of filamentation modes due to the combined effects of two-stream and oblique instabilities is found to exist and growth mechanisms of secondary instabilities destroying the BGK--type nonlinear wave are identified. In the weak magnetic field, the energy of beam-excited plasma waves at the nonlinear stage of beam-plasma interaction goes predominantly to the short-wavelength upper-hybrid waves propagating parallel to the magnetic field, whereas in the strong magnetic field the spectral energy is transferred to the electrostatic whistlers with oblique propagation.
Directory of Open Access Journals (Sweden)
Haitao Che
2011-01-01
Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.
Notes on the nonlinear beam dynamics with strong damping in the CLIC Damping Ring
Levichev, Eugene; Shatilov, Dmitry
2010-01-01
The beam is injected into the CLIC damping ring with the relatively large emittance and energy spread and then is damped to the extremely low phase volume. During the damping process the betatron frequency of each particle changes due to the space charge tune shift and nonlinear dependence of the betatron tune on the amplitude. This nonlinearity is produced by the strong chromatic sextupoles, wiggler nonlinear field components and, again, by the space charge force. During the damping, the particle cross resonances, which can trap some fraction of the beam, cause the loss of intensity, the beam blow up and degrade the beam quality. In this paper we study the evolution of the beam distribution in time during the damping for the original lattice of the CLIC DR (May 2005). Geneva, Switzerland June 2010 CLIC – Note – 850
Chaitanya, N Apurv; Banerji, J; Samanta, G K
2016-01-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Dynamic Nonlinear Focal Shift in Amplitude Modulated Moderately Focused Acoustic Beams
Jiménez, Noé; González-Salido, Nuria
2016-01-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25 kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behaviour, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both, for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by ...
Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.
2016-09-01
Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs.
Development of a bent Laue beam-expanding double-crystal monochromator for biomedical X-ray imaging
Energy Technology Data Exchange (ETDEWEB)
Martinson, Mercedes, E-mail: mercedes.m@usask.ca [University of Saskatchewan, 116 Science Place, Room 163, Saskatoon, Saskatchewan (Canada); Samadi, Nazanin [University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada); Belev, George [Canadian Light Source, 44 Innovation Boulevard, Saskatoon, Saskatchewan (Canada); Bassey, Bassey [University of Saskatchewan, 116 Science Place, Room 163, Saskatoon, Saskatchewan (Canada); Lewis, Rob [University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada); Monash University, Clayton, Victoria 3800 (Australia); Aulakh, Gurpreet [University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada); Chapman, Dean [University of Saskatchewan, 116 Science Place, Room 163, Saskatoon, Saskatchewan (Canada); University of Saskatchewan, 107 Wiggins Road, Saskatoon, Saskatchewan (Canada)
2014-03-13
A bent Laue beam-expanding double-crystal monochromator was developed and tested at the Biomedical Imaging and Therapy beamline at the Canadian Light Source. The expander will reduce scanning time for micro-computed tomography and allow dynamic imaging that has not previously been possible at this beamline. The Biomedical Imaging and Therapy (BMIT) beamline at the Canadian Light Source has produced some excellent biological imaging data. However, the disadvantage of a small vertical beam limits its usability in some applications. Micro-computed tomography (micro-CT) imaging requires multiple scans to produce a full projection, and certain dynamic imaging experiments are not possible. A larger vertical beam is desirable. It was cost-prohibitive to build a longer beamline that would have produced a large vertical beam. Instead, it was proposed to develop a beam expander that would create a beam appearing to originate at a source much farther away. This was accomplished using a bent Laue double-crystal monochromator in a non-dispersive divergent geometry. The design and implementation of this beam expander is presented along with results from the micro-CT and dynamic imaging tests conducted with this beam. Flux (photons per unit area per unit time) has been measured and found to be comparable with the existing flat Bragg double-crystal monochromator in use at BMIT. This increase in overall photon count is due to the enhanced bandwidth of the bent Laue configuration. Whilst the expanded beam quality is suitable for dynamic imaging and micro-CT, further work is required to improve its phase and coherence properties.
Nonlinear dynamic characteristic analysis of jointed beam with clearance
Zhang, Jing; Guo, Hong-Wei; Liu, Rong-Qiang; Wu, Juan; Kou, Zi-Ming; Deng, Zong-Quan
2016-12-01
The impact and elasticity of discontinuous beams with clearance frequently affect the dynamic response of structures used in space missions. This study investigates the dynamic response of jointed beams which are the periodic units of deployable structures. The vibration process of jointed beams includes free-play and impact stages. A method for the dynamic analysis of jointed beams with clearance is proposed based on mode superposition and instantaneous static deformation. Transfer matrix, which expresses the relationship of the responses before and after the impact of jointed beams, is derived to calculate the response of the jointed beams after a critical position. The dynamic responses of jointed beams are then simulated. The effects of various parameters on the displacement and velocity of beams are investigated.
Directory of Open Access Journals (Sweden)
Şeref Doğuşcan Akbaş
2013-01-01
Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.
Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX
Belova, E. V.; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.; Tritz, K.
2017-04-01
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4 -9 , and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.
Bentley, Sean J; Heebner, John E; Boyd, Robert W
2006-04-01
We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.
Management of the orbital angular momentum of vortex beams in a quadratic nonlinear interaction
Bovino, Fabio A; Bertolotti, Mario; Sibilia, Concita
2011-01-01
Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.
Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation
Voss, Thomas; Scherpen, Jacquelien M. A.
2014-01-01
In this paper we develop a mathematical model for the dynamics of a nonlinear Timoshenko beam with piezoelectric actuation. This model can then be used to design controllers with the goal of achieving a desired shape of the beam. The control scheme can be used for several applications, e. g., vibrat
Singh, Navpreet; Gupta, Naveen; Singh, Arvinder
2016-12-01
This paper investigates second harmonic generation (SHG) of an intense Cosh-Gaussian (ChG) laser beam propagating through a preformed underdense collisional plasma with nonlinear absorption. Nonuniform heating of plasma electrons takes place due to the nonuniform irradiance of intensity along the wavefront of laser beam. This nonuniform heating of plasma leads to the self-focusing of the laser beam and thus produces strong density gradients in the transverse direction. The density gradients so generated excite an electron plasma wave (EPW) at pump frequency that interacts with the pump beam to produce its second harmonics. To envision the propagation dynamics of the ChG laser beam, moment theory in Wentzel-Kramers-Brillouin (W.K.B) approximation has been invoked. The effects of nonlinear absorption on self-focusing of the laser beam as well as on the conversion efficiency of its second harmonics have been theoretically investigated.
SOME PROBLEMS CONCERNING FREE NON-LINEAR VIBRATIONS OF BEAM STRUCTURES
Directory of Open Access Journals (Sweden)
S. V. Bosakov
2008-01-01
Full Text Available The paper analyzes an influence of physical non-linearity material account on vibrations of single beams with various support fixing. The authors also analyze power criteria for existing stable periodic vibrations and dependence of vibration period on initial power is determined in the paper. Accurate values of an amplitude and non-linear bending vibration period of beams have been also determined as a conservative system with due account of initial conditions. A number of examples are given that clearly illustrate the obtained solutions and show an influence rate of the mentioned effects on amplitude-frequency characteristics of non-linear systems.
Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect
Institute of Scientific and Technical Information of China (English)
LIU Jin-yang; SHEN Ling-jie; HONG Jia-zhen
2005-01-01
Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with EulerBernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.
A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches
Sedighi, Hamid M.; Shirazi, Kourosh H.; Attarzadeh, Mohammad A.
2013-10-01
This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max-Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency-amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods.
Reciprocity breaking during nonlinear propagation of adapted beams through random media
Palastro, J P; Nelson, W; DiComo, G; Johnson, L A; Helle, M H; Hafizi, B
2016-01-01
Adaptive optics (AO) systems rely on the principle of reciprocity, or symmetry with respect to the interchange of point sources and receivers. These systems use the light received from a low power emitter on or near a target to compensate profile aberrations acquired by a laser beam during linear propagation through random media. If, however, the laser beam propagates nonlinearly, reciprocity is broken, potentially undermining AO correction. Here we examine the consequences of this breakdown. While discussed for general random and nonlinear media, we consider specific examples of Kerr-nonlinear, turbulent atmosphere.
Institute of Scientific and Technical Information of China (English)
ZHANG Zhuo; L(U) Jian-Qin
2008-01-01
In this paper, the nonlinear transport of intense bunched beams in electrostatic quadrupoles is analyzed using the Lie algebraic method, and the results are briefly presented of the linear matrix approximation and the second order correction of particle trajectory in the state space. Beam having K-V distribution and Gaussian distribution approximation are respectively considered. A brief discussion is also given of the total effects of the quadrupole and the space charge forces on the evolution of the beam envelope.
Plasmon beams interaction at interface between metal and dielectric with saturable Kerr nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Ignatyeva, Daria O.; Sukhorukov, Anatoly P. [Lomonosov Moscow State University, Moscow (Russian Federation)
2012-12-15
We present a novel theory of surface plasmon polariton interaction on the surface of dielectric with saturable Kerr nonlinearity. The effect of the total internal reflection of a weak signal plasmon beam from a high-power reference beam is discussed. Both ray and wave theories are used to describe signal propagation. The effect of the signal tunneling through the narrow inhomogeneity induced by the reference beam is considered. (orig.)
Yesayan, G L
2001-01-01
The equations for the width and curvature radius of the wave front for a Gaussian beam of light propagating along the axis of the longitudinally inhomogeneous graded index waveguide with gain and losses in the presence of third-order nonlinearity are obtained. By means of numerical calculations it is shown that in such waveguides the mode of stabilization of the beam width is possible, when the absorption of radiation on the edges of the beam compensates its spreading caused by the longitudinal inhomogeneity and nonlinearity of the waveguide
Effect of transverse shears on complex nonlinear vibrations of elastic beams
Krysko, V. A.; Zhigalov, M. V.; Saltykova, O. A.; Krysko, A. V.
2011-09-01
Models of geometrically nonlinear Euler-Bernoulli, Timoshenko, and Sheremet'ev-Pelekh beams under alternating transverse loading were constructed using the variational principle and the hypothesis method. The obtained differential equation systems were analyzed based on nonlinear dynamics and the qualitative theory of differential equations with using the finite difference method with the approximation O(h2) and the Bubnov-Galerkin finite element method. It is shown that for a relative thickness λ ⩽ 50, accounting for the rotation and bending of the beam normal leads to a significant change in the beam vibration modes.
Determining critical load in the multispan beams with the nonlinear model
DemÑ-r, D. Dönmez; Sinir, B. G.; Usta, L.
2017-01-01
The beams which are one of the most commonly used structural members are quite important for many researchers. Mathematical models determining the response of beams under external loads are concluded from elasticity theory through a series of assumptions concerning the kinematics of deformation and constitutive behavior. In this study, the derivation of the nonlinear model is introduced to determine the critical load in the multispan beams. Since the engineering practice of this kind of problems is very common, determining the critical load is quite important. For this purpose, the nonlinear mathematical model of the multispan Euler-Bernoulli beam is firstly obtained. To be able to obtain the independent of the material and the geometry, the present model are became dimensionless. Then, the critical axial load can be determined via the nonlinear solution of the governing equation.
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and tran
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Institute of Scientific and Technical Information of China (English)
盛冬发; 张燕; 程昌钧
2004-01-01
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
Nonlinear dynamic response of beam and its application in nanomechanical resonator
Institute of Scientific and Technical Information of China (English)
Yin Zhang; Yun Liu; Kevin D. Murphy
2012-01-01
Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application.Two categories of the tension-dominant and curvaturedominant nonlinearities are analyzed.The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach.The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity,its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects.However,for the nanomechanical resonator of the curvature-dominant nonlinearity,its dynamic nonlinearity is only dependent on axial loading.Compared with the tension-dominant nonlinearity,the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects.The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.
Soliton pair generation in the interactions of Airy and nonlinear accelerating beams
Zhang, Yiqi; Wu, Zhenkun; Zheng, Huaibin; Lu, Keqing; Li, Yuanyuan; Zhang, Yanpeng
2013-01-01
We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.
Nonlinear Dynamic Analysis of Functionally Graded Timoshenko Beam fixed to a Rotating Hub
Panigrahi, B.; Pohit, G.
2016-08-01
The present work accounts centrifugal stiffening effect on the nonlinear vibration response of an FGM Timoshenko beam. Analysis is carried out for a cantilever beam fixed with a rotating hub. Material is assumed to have a gradation relation along the depth of the beam. Centrifugal force and axial displacement raised due to the rotating hub is incorporated in the strain energy equations. Subsequent to this, an iterative technique is employed to obtain amplitude dependent vibration response of a rotating Timoshenko beam while material follows a gradation relation along the beam depth. Main objective of the work is to obtain the effects of rotational speeds, hub radius, and different gradation relations on the linear as well as nonlinear frequencies and mode shapes.
Directory of Open Access Journals (Sweden)
Hong Qin
2000-08-01
Full Text Available Collective processes in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The newly developed beam equilibrium, stability, and transport (BEST code is used to simulate the nonlinear stability properties of intense beam propagation, surface eigenmodes in a high-intensity beam, and the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment. Detailed simulations in a parameter regime characteristic of the PSR experiment show that the dipole-mode two-stream instability is stabilized by a modest spread (about 0.1% in axial momentum of the beam particles.
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 Control of Beam Halo-Chaos in Accelerator-Driven Clean Nuclear Power System
Institute of Scientific and Technical Information of China (English)
FANG JinQing; CHEN GuanRong; ZHOU LiuLai; WENG JiaQiang
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry, medicine, and national defense. Some general engineering methods for chaos control have been developed in recent years, but they generally are unsuccessful for beam halo-chaos suppression due to many technical constraints. Beam halo-chaos is essentially a spatiotemporal chaotic motion within a high power proton accelerator. In this paper, some efficient nonlinear control methods, including wavelet function feedback control as a special nonlinear control method, are proposed for controlling beam halo-chaos under five kinds of the initial proton beam distributions (i.e., Kapchinsky-Vladimirsky, full Gauss,3-sigma Gauss, water-bag, and parabola distributions) respectively. Particles-in-cell simulations show that after control of beam halo-chaos, the beam halo strength factor is reduced to zero, and other statistical physical quantities of beam halo-chaos are doubly reduced. The methods we developed is very effective for suppression of proton beam halo-chaos in a periodic focusing channel of accelerator. Some potential application of the beam halo-chaos control in experiments is finally pointed out.
Polarization of a probe laser beam due to nonlinear QED effects
Shakeri, Soroush; Kalantari, Seyed Zafarollah; Xue, She-Sheng
2017-01-01
Nonlinear QED interactions induce different polarization properties on a given probe beam. We consider the polarization effects caused by the photon-photon interaction in laser experiments, when a laser beam propagates through a constant magnetic field or collides with another laser beam. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian for both time-dependent and constant background field to explore the time evolution of the Stokes parameters Q, U, and V describing polarization. Assuming an initially linearly polarized probe laser beam, we also calculate the induced ellipticity and rotation of the polarization plane.
Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams
Hong Qi
2003-01-01
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, ...
Analysis of Nonlinear Thermoelastic Dissipation in Euler-Bernoulli Beam Resonators.
Nourmohammadi, Zahra; Joshi, Surabhi; Vengallatore, Srikar
2016-01-01
The linear theory of thermoelastic damping (TED) has been extensively developed over the past eight decades, but relatively little is known about the different types of nonlinearities that are associated with this fundamental mechanism of material damping. Here, we initiate the study of a dissipative nonlinearity (also called thermomechanical nonlinearity) whose origins reside at the heart of the thermomechanical coupling that gives rise to TED. The finite difference method is used to solve the nonlinear governing equation and estimate nonlinear TED in Euler-Bernoulli beams. The maximum difference between the nonlinear and linear estimates ranges from 0.06% for quartz and 0.3% for silicon to 7% for aluminum and 28% for zinc.
Nonlinear generation of whistler waves by an ion beam
Akimoto, K.; Winske, D.
1989-01-01
An electromagnetic hybrid code is used to simulate a new mechanism for whistler wave generation by an ion beam. First, a field-aligned ion beam becomes unstable to the electromagnetic ion/ion right-hand resonant instability which generates large amplitude MHD-like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the electron/whistler instability are significantly enhanced, and whistlers start to grow above the noise level. At the same time, because of the reduced parallel drift speed of the ion beam, the frequencies of the whistlers are also downshifted. Full simulations were performed to isolate and separately investigate the electron/ion whistler instability. The results are in agreement with the assumption of fluid electrons in the hybrid simulations and with the linear theory of the instability.
Free-Space Nonlinear Beam Combining Towards Filamentation
Rostami, Shermineh; Kepler, Daniel; Baudelet, Matthieu; Litchinitser, Natalia M; Richardson, Martin
2016-01-01
Multi-filamentation opens new degrees of freedom for manipulating electromagnetic waves in air. However, without control, multiple filament interactions, including attraction, repulsion or fusion often result in formation of complex disordered filament distributions. Moreover, high power beams conventionally used in multi-filament formation experiments often cause significant surface damage. The growing number of applications for laser filaments requires fine control of their formation and propagation. We demonstrate, experimentally and theoretically, that the attraction and fusion of ultrashort beams with initial powers below the critical value enable the eventual formation of a filament downstream. Filament formation is delayed to a predetermined distance in space, avoiding optical damage to external beam optics while still enabling robust filaments with controllable properties as if formed from a single high power beam. This paradigm introduces new opportunities for filament engineering eliminating the nee...
Wang, Xin; Zhang, Lei; Fan, Juanjuan; Li, Yufang; Gong, Yao; Dong, Lei; Ma, Weiguang; Yin, Wangbao; Jia, Suotang
2015-11-01
Improvement of measurement precision and repeatability is one of the issues currently faced by the laser-induced breakdown spectroscopy (LIBS) technique, which is expected to be capable of precise and accurate quantitative analysis. It was found that there was great potential to improve the signal quality and repeatability by reducing the laser beam divergence angle using a suitable beam expander (BE). In the present work, the influences of several experimental parameters for the case with BE are studied in order to optimize the analytical performances: the signal to noise ratio (SNR) and the relative standard deviation (RSD). We demonstrate that by selecting the optimal experimental parameters, the BE-included LIBS setup can give higher SNR and lower RSD values of the line intensity normalized by the whole spectrum area. For validation purposes, support vector machine (SVM) regression combined with principal component analysis (PCA) was used to establish a calibration model to realize the quantitative analysis of the ash content. Good agreement has been found between the laboratory measurement results from the LIBS method and those from the traditional method. The measurement accuracy presented here for ash content analysis is estimated to be 0.31%, while the average relative error is 2.36%. supported by the 973 Program of China (No. 2012CB921603), National Natural Science Foundation of China (Nos. 61475093, 61127017, 61178009, 61108030, 61378047, 61275213, 61475093, and 61205216), the National Key Technology R&D Program of China (No. 2013BAC14B01), the Shanxi Natural Science Foundation (Nos. 2013021004-1 and 2012021022-1), the Shanxi Scholarship Council of China (Nos. 2013-011 and 2013-01), and the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, China
Nonlinear interaction of intense hypergeometric Gaussian subfamily laser beams in plasma
Sobhani, H.; Vaziri (Khamedi), M.; Rooholamininejad, H.; Bahrampour, A. R.
2016-07-01
Propagation of Hypergeometric-Gaussian laser beam in a nonlinear plasma medium is investigated by considering the Source Dependent Expansion method. A subfamily of Hypergeometric-Gaussian beams with a non-negative, even and integer radial index, can be expressed as the linear superposition of finite number of Laguerre-Gaussian functions. Propagation of Hypergeometric-Gaussian beams in a nonlinear plasma medium depends on the value of radial index. The bright rings' number of these beams is changed during the propagation in plasma medium. The effect of beam vortex charge number l and initial (input) beam intensity on the self-focusing of Hypergeometric-Gaussian beams is explored. Also, by choosing the suitable initial conditions, Hypergeometric-Gaussian subfamily beams can be converted to one or more mode components that a typical of mode conversion may be occurred. The self-focusing of these winding beams can be used to control the focusing force and improve the electron bunch quality in laser plasma accelerators.
A theoretical and experimental study on geometric nonlinearity of initially curved cantilever beams
Directory of Open Access Journals (Sweden)
Sushanta Ghuku
2016-03-01
Full Text Available This paper presents a theoretical and experimental study on large deflection behavior of initially curved cantilever beams subjected to various types of loadings. The physical system as a straight cantilever beam subjected to a tip concentrated load is considered in this study. Nonlinear differential equations are obtained for large deflection analysis of such a straight cantilever beam, and this problem is known to involve geometrical nonlinearity. The equations are solved numerically with the help of MATLAB® computational platform to get deflection profiles of the concerned problem. These results are imposed subsequently on the center line of an initially curved beam to get theoretical load-deflection behavior of curved beam problems. To verify the theoretical model, experiment is carried out with the master leaf of a leaf spring bundle by modeling it as an initially curved cantilever beam. The effects of initial clamping and geometry variations in the eye-region are observed from experimental investigation which is commonly neglected in the mathematical formulation. Comparisons of the theoretical results with the experimental results are quite good, but the avenues for further improvement are also reported. The proposed approach is further extended to study large deflection behavior of an initially curved cantilever beam subjected to distributed and combined load. These results are successfully validated with existing results for straight beams and some new results are furnished for initially curved cantilever beams.
Efficiency enhancement of a two-beam free-electron laser using a nonlinearly tapered wiggler
Institute of Scientific and Technical Information of China (English)
Maryam Zahedian; B.Maraghechi; M.H.Rouhani
2012-01-01
A nonlinear and non-averaged model of a two-beam free-electron laser (FEL) wiggler that is tapered nonlinearly in the absence of slippage is presented.The two beams are assumed to have different energies,and the fundamental resonance of the higher energy beam is at the third harmonic of the lower energy beam.By using Maxwell's equations and the full Lorentz force equation of motion for the electron beams,coupled differential equations are derived and solved numerically by the fourth-order Runge-Kutta method.The amplitude of the wiggler field is assumed to decrease nonlinearly when the saturation of the third harmonic occurs.By simulation,the optimum starting point of the tapering and the slopes for reducing the wiggler amplitude are found.This technique can be applied to substantially improve the efficiency of the two-beam FEL in the XUV and X-ray regions.The effect of tapering on the dynamical stability of the fast electron beam is also studied.
An efficient and accurate method for calculating nonlinear diffraction beam fields
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.
Active suppression of nonlinear composite beam vibrations by selected control algorithms
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.
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
Nonlinear features identified by Volterra series for damage detection in a buckled beam
Directory of Open Access Journals (Sweden)
Shiki S. B.
2014-01-01
Full Text Available The present paper proposes a new index for damage detection based on nonlinear features extracted from prediction errors computed by multiple convolutions using the discrete-time Volterra series. A reference Volterra model is identified with data in the healthy condition and used for monitoring the system operating with linear or nonlinear behavior. When the system has some structural change, possibly associated with damage, the index metrics computed could give an alert to separate the linear and nonlinear contributions, besides provide a diagnostic about the structural state. To show the applicability of the method, an experimental test is performed using nonlinear vibration signals measured in a clamped buckled beam subject to different levels of force applied and with simulated damages through discontinuities inserted in the beam surface.
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.
Energy Technology Data Exchange (ETDEWEB)
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel
Sonu Sen; Meenu Asthana Varshney; Dinesh Varshney
2014-01-01
In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have num...
A new solution procedure for a nonlinear infinite beam equation of motion
Jang, T. S.
2016-10-01
Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.
The Nonlinear Interaction of Two-Crossed Focussed Ultrasonic Beams in the Presence of Turbulence
1988-06-10
in water or any fluid medium can be obtained by the vibration of a solid body in the fluid, such as the vibration of a vocal chord or guitar string . In... physical phenomenon due to the nonlinearity of sound arises from the interaction of two sound beams. Nonlinear acoustic theory predictions by Westervelt in...known experimental data for the turbulent velocity field. Goals of this research include mapping out the turbulence and studying the physical
Measurement of nonlinear observables in the Large Hadron Collider using kicked beams
Maclean, E. H.; Tomás, R.; Schmidt, F.; Persson, T. H. B.
2014-08-01
The nonlinear dynamics of a circular accelerator such as the Large Hadron Collider (LHC) may significantly impact its performance. As the LHC progresses to more challenging regimes of operation it is to be expected that the nonlinear single particle dynamics in the transverse planes will play an increasing role in limiting the reach of the accelerator. As such it is vital that the nonlinear sources are well understood. The nonlinear fields of a circular accelerator may be probed through measurement of the amplitude detuning: the variation of tune with single particle emittance. This quantity may be assessed experimentally by exciting the beam to large amplitudes with kicks, and obtaining the tunes and actions from turn-by-turn data at Beam Position Monitors. The large amplitude excitations inherent to such a measurement also facilitate measurement of the dynamic aperture from an analysis of beam losses following the kicks. In 2012 these measurements were performed on the LHC Beam 2 at injection energy (450 GeV) with the nominal magnetic configuration. Nonlinear coupling was also observed. A second set of measurements were performed following the application of corrections for b4 and b5 errors. Analysis of the experimental results, and a comparison to simulation are presented herein.
Directory of Open Access Journals (Sweden)
Husain M. Husain
2013-05-01
Full Text Available In this work a program is developed to carry out the nonlinear analysis (material nonlinearity of prestressed concrete beams using tendons of carbon fiber reinforced polymer (CFRP instead of steel. The properties of this material include high strength, light weight, and insusceptibility to corrosion and magnetism. This material is still under investigation, therefore it needs continuous work to make it beneficial in concrete design. Four beams which are tested experimentally by Yan et al. are examined by the developed computer program to reach a certain analytical approach of the design and analysis of such beams because there is no available restrictions or recommendations covering this material in the codes. The program uses the finite element analysis by dividing the beams into isoparametric 20-noded brick elements. The results obtained are good in comparison with experimental results.
Numerical simulation of nonlinear processes in a beam-plasma system
Energy Technology Data Exchange (ETDEWEB)
Efimova, A. A., E-mail: anna.an.efimova@gmail.com; Berendeev, E. A.; Vshivkov, V. A. [Institute of Computational Mathematics and Mathematical Geophysics SB RAS 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation); Dudnikova, G. I. [University of Maryland, College Park, MD 20742 (United States); Institute of Computational Technologies SB RAS, 6 Acad. Lavrentyev Ave., Novosibirsk 630090 (Russian Federation)
2015-10-28
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.
Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media
Wu, Zhen-Kun; Li, Peng; Gu, Yu-Zong
2017-10-01
We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.
Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability
Pavan, J.; Ziebell, L. F.; Gaelzer, R.; Yoon, P. H.
2009-01-01
Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.
Active Vibration Control of a Nonlinear Beam with Self- and External Excitations
Directory of Open Access Journals (Sweden)
J. Warminski
2013-01-01
Full Text Available An application of the nonlinear saturation control (NSC algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.
ON THE NONLINEAR TIMOSHENKO-KIRCHHOFF BEAM EQUATION
Institute of Scientific and Technical Information of China (English)
A.AROSIO
1999-01-01
When an elastic string with fixed ends is subjected to transverse vibrations, its length vaxiewith the time: this introduces chvages of the tension in the string. Thls induced Kirchoffto propose a nonlinear correction of the classical D'Alembert equation. Later on, Wolnowsky-
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1996-01-01
We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....
Experimental damage detection of cracked beams by using nonlinear characteristics of forced response
Andreaus, U.; Baragatti, P.
2012-08-01
Experimental evaluation of the flexural forced vibrations of a steel cantilever beam having a transverse surface crack extending uniformly along the width of the beam was performed, where an actual fatigue crack was introduced instead - as usual - of a narrow slot. The nonlinear aspects of the dynamic response of the beam under harmonic excitation were considered and the relevant quantitative parameters were evaluated, in order to relate the nonlinear resonances to the presence and size of the crack. To this end, the existence of sub- and super-harmonic components in the Fourier spectra of the acceleration signals was evidenced, and their amplitudes were quantified. In particular, the acceleration signals were measured in different positions along the beam axis and under different forcing levels at the beam tip. The remarkable relevance of the above mentioned nonlinear characteristics, and their substantial independence on force magnitude and measurement point were worthily noted in comparison with the behavior of the intact beam. Thus, a reliable method of damage detection was proposed which was based on simple tests requiring only harmonically forcing and acceleration measuring in any point non-necessarily near the crack. Then, the time-history of the acceleration recorded at the beam tip was numerically processed in order to obtain the time-histories of velocity and displacement. The nonlinear features of the forced response were described and given a physical interpretation in order to define parameters suitable for damage detection. The efficiency of such parameters was discussed with respect to the their capability of detecting damage and a procedure for damage detection was proposed which was able to detect even small cracks by using simple instruments. A finite element model of the cantilever beam was finally assembled and tuned in order to numerically simulate the results of the experimental tests.
Fardad, Shima; Mills, Matthew S; Zhang, Peng; Man, Weining; Chen, Zhigang; Christodoulides, D N
2013-09-15
We demonstrate optical interactions between stable self-trapped optical beams in soft-matter systems with pre-engineered saturable self-focusing optical nonlinearities. Our experiments, carried out in dilute suspensions of particles with negative polarizabilities, show that optical beam interactions can vary from attractive to repulsive, or can display an energy exchange depending on the initial relative phases. The corresponding observations are in good agreement with theoretical predictions.
Energy Technology Data Exchange (ETDEWEB)
Ella, Lior, E-mail: lior.ella@weizmann.ac.il; Yuvaraj, D.; Suchoi, Oren; Shtempluk, Oleg; Buks, Eyal [Faculty of Electrical Engineering, Technion, Haifa 32000 (Israel)
2015-01-07
We present a study of the controllable nonlinear dynamics of a micromechanical beam coupled to a dc-SQUID (superconducting quantum interference device). The coupling between these systems places the modes of the beam in a highly nonlinear potential, whose shape can be altered by varying the bias current and applied flux of the SQUID. We detect the position of the beam by placing it in an optical cavity, which sets free the SQUID to be used solely for actuation. This enables us to probe the previously unexplored full parameter space of this device. We measure the frequency response of the beam and find that it displays a Duffing oscillator behavior which is periodic in the applied magnetic flux. To account for this, we develop a model based on the standard theory for SQUID dynamics. In addition, with the aim of understanding if the device can reach nonlinearity at the single phonon level, we use this model to show that the responsivity of the current circulating in the SQUID to the position of the beam can become divergent, with its magnitude limited only by noise. This suggests a direction for the generation of macroscopically distinguishable superposition states of the beam.
Energy Technology Data Exchange (ETDEWEB)
Zou, Li [Dalian Univ. of Technology, Dalian City (China). State Key Lab. of Structural Analysis for Industrial Equipment; Liang, Songxin; Li, Yawei [Dalian Univ. of Technology, Dalian City (China). School of Mathematical Sciences; Jeffrey, David J. [Univ. of Western Ontario, London (Canada). Dept. of Applied Mathematics
2017-06-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams
Energy Technology Data Exchange (ETDEWEB)
Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab
2016-09-30
Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.
Optimizing nonlinear beam coupling in low-symmetry crystals.
Shumelyuk, A; Volkov, A; Odoulov, S; Grabar, A; Stoyka, I; Evans, D R
2014-10-01
The purpose of this paper is to find the polarizations and spatial orientations of the two interacting counterpropagating coherent light waves which ensure the largest beam coupling in monoclinic photorefractive crystal. The results of calculations are presented that are verified experimentally with Sn₂P₂S₆.
Nonlinear Vibration of an Elastically Restrained Tapered Beam
DEFF Research Database (Denmark)
Karimpour, S; Ganji, S.S; Barari, Amin;
2012-01-01
This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method (EBM) and the iteration perturbation method (IPM). To assess the accuracy of solutions, we compare the results with the harmonic balance method (HBM). The obtained re...
Non-Linear Beam Transport System for the LENS 7 MeV Proton Beam
Jones, William P; Derenchuk, Vladimir Peter; Rinckel, Thomas; Solberg, Keith
2005-01-01
A beam transport system has been designed to carry a high-intensity low-emittance proton beam from the exit of the RFQ-DTL acceleration system of the Indiana University Low Energy Neutron System (LENS)* to the neutron production target. The goal of the design was to provide a beam of uniform density over a 3cm by 3cm area at the target. Two octupole magnets** are employed in the beam line to provide the necessary beam phase space manipulations to achieve this goal. First order calculations were done using TRANSPORT and second order calculations have been performed using TURTLE. Second order simulations have been done using both a Gaussian beam distribution and a particle set generated by calculations of beam transport through the RFQ-DTL using PARMILA. Comparison of the design characteristics with initial measurements from the LENS commissioning process will be made.
Nonlinear dynamics and chaos in an optomechanical beam
Navarro-Urrios, D; Colombano, M F; Garcia, P D; Sledzinska, M; Alzina, F; Griol, A; Martinez, A; Sotomayor-Torres, C M
2016-01-01
Optical non-linearities, such as thermo-optic effects and free-carrier-dispersion, are often considered as undesired effects in silicon-based resonators and, more specifically, optomechanical (OM) cavities, affecting the relative detuning between an optical resonance and the excitation laser. However, the interplay between such mechanisms could also enable unexpected physical phenomena to be used in new applications. In the present work, we exploit those non-linearities and their intercoupling with the mechanical degrees of freedom of a silicon OM nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser, namely its power and wavelength, we demonstrate accurate control for activating bi-dimensional and tetra-dimensional limit-cycles, a period doubling route and chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between bi-dimensional and tetra-dimensional limit-cycles, be...
On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas
Energy Technology Data Exchange (ETDEWEB)
Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190 Toyama City, Toyama 930-8555 (Japan)
2015-02-15
A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation of Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.
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...
Concatenated beam splitters, optical feed-forward and the nonlinear sign gate
Jacobs, K; Jacobs, Kurt; Dowling, Jonathan P.
2006-01-01
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.
Energy Technology Data Exchange (ETDEWEB)
Spata, Michael [Old Dominion Univ., Norfolk, VA (United States)
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.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Nonlinear free vibrations of beams in space due to internal resonance
Stoykov, S.; Ribeiro, P.
2011-08-01
The geometrically nonlinear free vibrations of beams with rectangular cross section are investigated using a p-version finite element method. The beams may vibrate in space, hence they may experience longitudinal, torsional and non-planar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The geometrical nonlinearity is taken into account by considering Green's nonlinear strain tensor. Isotropic and elastic beams are investigated and generalised Hooke's law is used. The equation of motion is derived by the principle of virtual work. Mostly clamped-clamped beams are investigated, although other boundary conditions are considered for validation purposes. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. One constant term, odd and even harmonics are assumed in the Fourier series and convergence with the number of harmonics is analysed. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of backbone curves. Coupling between modes is investigated, internal resonances are found and the ensuing multimodal oscillations are described. Some of the couplings discovered lead from planar oscillations to oscillations in the three dimensional space.
Tanjia, Fatema; Fedele, Renato; Shukla, P K; Jovanovic, Dusan
2011-01-01
A numerical analysis of the self-interaction induced by a relativistic electron/positron beam in the presence of an intense external longitudinal magnetic field in plasmas is carried out. Within the context of the Plasma Wake Field theory in the overdense regime, the transverse beam-plasma dynamics is described by a quantumlike Zakharov system of equations in the long beam limit provided by the Thermal Wave Model. In the limiting case of beam spot size much larger than the plasma wavelength, the Zakharov system is reduced to a 2D Gross-Pitaevskii-type equation, where the trap potential well is due to the external magnetic field. Vortices, "beam halos" and nonlinear coherent states (2D solitons) are predicted.
Beam-Based Nonlinear Optics Corrections in Colliders
Pilat, Fulvia Caterina; Malitsky, Nikolay; Ptitsyn, Vadim
2005-01-01
A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, which gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 3 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non linear correction techniques.
Directory of Open Access Journals (Sweden)
C. E. M. Oliveira
Full Text Available This work investigates the response of two reinforced concrete (RC plane frames after the loss of a column and their potential resistance for progressive collapse. Nonlinear dynamic analysis is performed using a multilayered Euler/Bernoulli beam element, including elasto-viscoplastic effects. The material nonlinearity is represented using one-dimensional constitutive laws in the material layers, while geometrical nonlinearities are incorporated within a corotational beam formulation. The frames were designed in accordance with the minimum requirements proposed by the reinforced concrete design/building codes of Europe (fib [1-2], Eurocode 2 [3] and Brazil (NBR 6118 [4]. The load combinations considered for PC analysis follow the prescriptions of DoD [5]. The work verifies if the minimum requirements of the considered codes are sufficient for enforcing structural safety and robustness, and also points out the major differences in terms of progressive collapse potential of the corresponding designed structures.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
Dynamic nonlinear focal shift in amplitude modulated moderately focused acoustic beams.
Jiménez, Noé; Camarena, Francisco; González-Salido, Nuria
2017-03-01
The phenomenon of the displacement of the position of the pressure, intensity and acoustic radiation force maxima along the axis of focused acoustic beams under increasing driving amplitudes (nonlinear focal shift) is studied for the case of a moderately focused beam excited with continuous and 25kHz amplitude modulated signals, both in water and tissue. We prove that in amplitude modulated beams the linear and nonlinear propagation effects coexist in a semi-period of modulation, giving place to a complex dynamic behavior, where the singular points of the beam (peak pressure, rarefaction, intensity and acoustic radiation force) locate at different points on axis as a function of time. These entire phenomena are explained in terms of harmonic generation and absorption during the propagation in a lossy nonlinear medium both for a continuous and an amplitude modulated beam. One of the possible applications of the acoustic radiation force displacement is the generation of shear waves at different locations by using a focused mono-element transducer excited by an amplitude modulated signal.
Sorokin, Vladislav S; Thomsen, Jon Juel
2016-02-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli-Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.
Mattei, P.-O.; Ponçot, R.; Pachebat, M.; Côte, R.
2016-07-01
In order to control the sound radiation by a structure, one aims to control vibration of radiating modes of vibration using "Energy Pumping" also named "Targeted Energy Transfer". This principle is here applied to a simplified model of a double leaf panel. This model is made of two beams coupled by a spring. One of the beams is connected to a nonlinear absorber. This nonlinear absorber is made of a 3D-printed support on which is clamped a buckled thin small beam with a small mass fixed at its centre having two equilibrium positions. The experiments showed that, once attached onto a vibrating system to be controlled, under forced excitation of the primary system, the light bistable oscillator allows a reduction of structural vibration up to 10 dB for significant amplitude and frequency range around the first two vibration modes of the system.
Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma
Indian Academy of Sciences (India)
R K Khanna; K Baheti
2001-06-01
In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.
Nonlinear Analysis of External Prestressed Reinforced Concrete Beams with BFRP and CFRP
Directory of Open Access Journals (Sweden)
Haleem K. Hussain
2017-05-01
Full Text Available The traditional strengthening methods for concrete structure (girders, beams, columns…. consuming time and could be an economical, a new modern repair methods using the Carbon Fiber Reinforced Polymers (CFRP and Basalt Fiber Reinforced Polymer (BFRP as a laminate strips or bars,and considered a competitive solution that will increase the life-cycle of repaired structures. This study investigated the strengthen reinforced concrete girder. Nonlinear analysis have been adopted to the models using FEM analysis (ANSYS to simulate the theoretical results compared with experimental results.Using finite element packages, more efficient and better analyses can be made to fully understand the response of individual structural components and their contribution to a structure as a whole.Three type of material are used in this study as an external prestressed wire (steel, CFRP and BFRP. The prestressed beam is modeled as simply supported beam with two concentrated point load. The results showed that all tested strengthening beam increased the load carryingcapacity of the beams depend on prestressing force. Obtained Result was compared for different type of beam.This study also was enlarged to include using CFRP and BFRPbarwhich are light weight and moredurable, lead to ease of handling and maintenance. The research conducted analytical work to evaluate the effectiveness of concrete beams reinforced normally by the use of CFRP and BFRP bars. The results showed a significant gain in the beam’s ultimate capacities using CFRP bars comparing with beam reinforced with BFRP bar and reference beam
Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam
Directory of Open Access Journals (Sweden)
Choura S.
2012-07-01
Full Text Available We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.
Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation
Indian Academy of Sciences (India)
R J Somnay; R A Ibrahim
2006-08-01
This study deals with the nonlinear dynamics associated with large deformation of a beam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic–Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deﬂection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic–Frisch-Fay exact solution is given in terms of elliptic functions. A curve ﬁt of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases.
Nonlinear free vibrations of centrifugally stiffened uniform beams at high angular velocity
Bekhoucha, F.; Rechak, S.; Duigou, L.; Cadou, J. M.
2016-09-01
In this paper, we study the bending nonlinear free vibrations of a centrifugally stiffened beam with uniform cross-section and constant angular velocity. The nonlinear intrinsic equations of motion used here are geometrically exact and specific to beams exhibiting large amplitude displacements and rotations associated with small strains. Based on the Timoshenko beam model, these equations are derived from Hamilton's principle, in which the warping is considered. All coupling terms are considered including Coriolis terms. The studied beams are isotropic with clamped-free boundary conditions. By combining the Galerkin method with the harmonic balance method, the equations of motion are converted into a quadratic function treated with a continuation method: the Asymptotic Numerical Method, where the generalized displacement vector is presented as a series expansion. While analysing the effect of the angular velocity, we determine the amplitude versus frequency variations which are plotted as backbone curves. Considering the first lagging and flapping modes, the changes in beam behaviour from hardening to softening are investigated and identified as a function of the angular velocity and the effect of shear. Particular attention is paid to high angular velocities for both Euler-Bernoulli and Timoshenko beams and the natural frequencies so obtained are compared with the results available in the literature.
Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan
2016-06-27
We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.
Directory of Open Access Journals (Sweden)
H. Vázquez-Leal
2013-01-01
Full Text Available In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to 179.99999999∘ yielding a relative error of 0.01222747.
Takahashi, Kazunori; Suzuki, Tatsuya; Ando, Akira
2014-02-01
Diameter of a permanent-magnets-expanded, radiofrequency (rf) plasma source is enlarged up to ∼13 cm for an application to a space propulsion device and tested with being attached to a diffusion chamber. The source is operated at 13.56 MHz 300 W rf power in low-pressure (40 mPa) argon. Measurement of ion energy distribution functions downstream of the source exit shows generation of a supersonic ion beam of about 20 eV. The detailed radial measurements demonstrate that the diameter and energy of the ion beam corresponds to the source tube diameter and the potential difference between the source and downstream plasmas, and that the radial profile of the beam flux is similar to the plasma density profile in the source cavity.
Energy Technology Data Exchange (ETDEWEB)
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.
Nonlinear physics and energetic particle transport features of the beam-plasma instability
Carlevaro, Nakia; Montani, Giovanni; Zonca, Fulvio
2015-01-01
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 $n$ 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 analyzed.
The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities
Chang, Philip; Lamberts, Astrid
2014-01-01
Very-high energy gamma-rays from extragalactic sources pair-produce off of 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 $8\\times 10^{-4}$ of 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 wavenumber 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 ap...
Nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode
Frolov, Nikita S.; Kurkin, Semen A.; Koronovskii, Alexey A.; Hramov, Alexander E.
2017-07-01
In this paper we report on the results of investigations of nonlinear dynamics and bifurcation mechanisms in intense electron beam with virtual cathode in micrometer-scaled source of sub-THz electromagnetic radiation. The numerical analysis is provided by means of 3D electromagnetic particle-in-cell (PIC) simulation. We have studied evolution of the system dynamics with the change of beam current value by means of Fourier and bifurcation analysis. The bifurcation diagram has identified a number of the alternating regions of beam current with regular or chaotic regimes of system dynamics. The study of spatiotemporal dynamics of formed electron structures in the beam has revealed the physical mechanisms responsible for the regimes switchings in the system.
Torrent-Sucarrat, Miquel; Anglada, Josep M.; Luis, Josep M.
2012-11-01
The conformational flexibility of the expanded porphyrins allows them to achieve different topologies with distinct aromaticities and nonlinear optical properties (NLOP). For instance, it is possible to switch between Möbius and Hückel topologies applying only small changes in the external conditions or in the structure of the ring. In this work, we evaluate the electronic and vibrational contributions to static and dynamic NLOP of the Hückel and Möbius conformers of A,D-di-p-benzi[28]hexaphyrin(1.1.1.1.1.1) synthesized by Latos-Grażyński and co-workers [Angew. Chem., Int. Ed. 46, 7869 (2007), 10.1002/anie.200700555]. Calculations are performed at the HF, M052X, and CAM-B3LYP levels using the 6-31G, 6-311G(d), and 6-31+G(d) basis sets. Our results conclude that M052X/6-31G and CAM-B3LYP/6-31G methods provide a correct qualitative description of the electronic and vibrational contributions for the NLOP of expanded porphyrins. The studied systems show high NLOP with large differences between the Möbius and Hückel conformations (around 1 × 106 a.u. for bar γ). The obtained results indicate that the expanded porphyrins are promising systems to manufacture Hückel-to-Möbius topological switches.
Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel
Directory of Open Access Journals (Sweden)
Sonu Sen
2014-01-01
Full Text Available In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have numerical appreciation of the results the propagation equation for plasma is solved using the fourth order Runge-Kutta method for the initial plane wave front of the beam, using boundary conditions. The spot size of the laser beam decreases as the beam penetrates into the plasma and significantly adds self-focusing in plasma. This causes the laser beam to become more focused by reduction of diffraction effect, which is an important phenomenon in inertial confinement fusion and also for the understanding of self-focusing of laser pulses. Numerical computations are presented and discussed in the form of graphs for typical parameters of laser-plasma interaction.
A nonlinear mathematical model for large deflection of incompressible saturated poroelastic beams
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Nonlinear governing equations are established for large deflection of incompressible fluid saturated poroelastic beams under constraint that diffusion of the pore fluid is only in the axial direction of the deformed beams. Then, the nonlinear bending of a saturated poroelastic cantilever beam with fixed end impermeable and free end permeable, subjected to a suddenly applied constant concentrated transverse load at its free end, is examined with the Galerkin truncation method. The curves of deflections and bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure are shown in figures. The results of the large deflection and the small deflection theories of the cantilever poroelastic beam are compared, and the differences between them are revealed. It is shown that the results of the large deflection theory are less than those of the corresponding small deflection theory, and the times needed to approach its stationary states for the large deflection theory are much less than those of the small deflection theory.
Institute of Scientific and Technical Information of China (English)
Xueqiong; Chen; Xiaoyan; Li; Ziyang; Chen; Jixiong; Pu; Guowen; Zhang; Jianqiang; Zhu
2013-01-01
The intensity distributions of a high-power broadband laser beam passing through a nonlinear optical medium with defects and then propagating in free space are investigated based on the general nonlinear Schr¨odinger equation and the split-step Fourier numerical method. The influences of the bandwidth of the laser beam, the thickness of the medium,and the defects on the light intensity distribution are revealed. We find that the nonlinear optical effect can be suppressed and that the uniformity of the beam can be improved for a high-power broadband laser beam with appropriate wide bandwidth. It is also found that, under the same incident light intensity, a thicker medium will lead to a stronger self-focusing intensity, and that the influence of defects in the optical elements on the intensity is stronger for a narrowband beam than for a broadband beam.
Nonlinear dynamics of a vapor bubble expanding in a superheated region of finite size
Annenkova, E. A.; Kreider, W.; Sapozhnikov, O. A.
2015-10-01
Growth of a vapor bubble in a superheated liquid is studied theoretically. Contrary to the typical situation of boiling, when bubbles grow in a uniformly heated liquid, here the superheated region is considered in the form of a millimeter-sized spherical hot spot. An initial micron-sized bubble is positioned at the hot spot center and a theoretical model is developed that is capable of studying bubble growth caused by vapor pressure inside the bubble and corresponding hydrodynamic and thermal processes in the surrounding liquid. Such a situation is relevant to the dynamics of vapor cavities that are created in soft biological tissue in the focal region of a high-intensity focused ultrasound beam with a shocked pressure waveform. Such beams are used in the recently proposed treatment called boiling histotripsy. Knowing the typical behavior of vapor cavities during boiling histotripsy could help to optimize the therapeutic procedure.
Nonlinear dynamics of a vapor bubble expanding in a superheated region of finite size
Energy Technology Data Exchange (ETDEWEB)
Annenkova, E. A., E-mail: a-a-annenkova@yandex.ru [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Kreider, W. [Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105 (United States); Sapozhnikov, O. A. [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98105 (United States)
2015-10-28
Growth of a vapor bubble in a superheated liquid is studied theoretically. Contrary to the typical situation of boiling, when bubbles grow in a uniformly heated liquid, here the superheated region is considered in the form of a millimeter-sized spherical hot spot. An initial micron-sized bubble is positioned at the hot spot center and a theoretical model is developed that is capable of studying bubble growth caused by vapor pressure inside the bubble and corresponding hydrodynamic and thermal processes in the surrounding liquid. Such a situation is relevant to the dynamics of vapor cavities that are created in soft biological tissue in the focal region of a high-intensity focused ultrasound beam with a shocked pressure waveform. Such beams are used in the recently proposed treatment called boiling histotripsy. Knowing the typical behavior of vapor cavities during boiling histotripsy could help to optimize the therapeutic procedure.
Expanded studies of linear collider final focus systems at the Final Focus Test Beam
Energy Technology Data Exchange (ETDEWEB)
Tenenbaum, P.G.
1995-12-01
In order to meet their luminosity goals, linear colliders operating in the center-of-mass energy range from 3,50 to 1,500 GeV will need to deliver beams which are as small as a few Manometers tall, with x:y aspect ratios as large as 100. The Final Focus Test Beam (FFTB) is a prototype for the final focus demanded by these colliders: its purpose is to provide demagnification equivalent to those in the future linear collider, which corresponds to a focused spot size in the FFTB of 1.7 microns (horizontal) by 60 manometers (vertical). In order to achieve the desired spot sizes, the FFTB beam optics must be tuned to eliminate aberrations and other errors, and to ensure that the optics conform to the desired final conditions and the measured initial conditions of the beam. Using a combination of incoming-beam diagnostics. beam-based local diagnostics, and global tuning algorithms, the FFTB beam size has been reduced to a stable final size of 1.7 microns by 70 manometers. In addition, the chromatic properties of the FFTB have been studied using two techniques and found to be acceptable. Descriptions of the hardware and techniques used in these studies are presented, along with results and suggestions for future research.
Institute of Scientific and Technical Information of China (English)
Hu Ding; Li-Qun Chen
2011-01-01
Steady-state periodical response is investigated for an axially moving viscoelastic beam with hybrid supports via approximate analysis with numerical confirmation.It is assumed that the excitation is spatially uniform and temporally harmonic. The transverse motion of axially moving beams is governed by a nonlinear partial-differential equation and a nonlinear integro-partial-differential equation. The material time derivative is used in the viscoelastic constitutive relation. The method of multiple scales is applied to the governing equations to investigate primary resonances under general boundary conditions. It is demonstrated that the mode uninvolved in the resonance has no effect on the steady-state response. Numerical examples are presented to demonstrate the effects of the boundary constraint stiffness on the amplitude and the stability of the steady-state response. The results derived for two governing equations are qualitatively the same, but quantitatively different. The differential quadrature schemes are developed to verify those results via the method of multiple scales.
Ou, Jun; Jiang, Yuesong; Zhang, Jiahua; He, Yuntao
2013-12-01
Partial reflection of linearly polarized Laguerre-Gaussian beams incident at a dielectric interface are studied beyond the paraxial regime. Based on the angular spectrum method and Taylor series expansion, we derive exact analytical expressions for the reflected electric field. This result holds in both the paraxial and nonparaxial regimes. The result is then extended to beams of arbitrary polarization and used to analytically calculate the transverse and longitudinal shifts of the beams' center of gravity. Finally, several numerical examples are performed to verify the analytical formulas we derived near the Brewster angle.
Spoorthi, K.; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Sekkati, M.; El Fakir, A.; Rao, Ashok; Sanjeev, Ganesh; Poornesh, P.
2017-06-01
In this article, we report the third-order nonlinear optical properties of electron beam irradiated gadolinium-doped zinc oxide (GZO) thin films prepared using the spray pyrolysis deposition technique. GZO thin films were treated with an electron beam from a variable energy microtron accelerator at dose rates ranging from 1-5 kGy. Nonlinear optical measurements were conducted by employing the single beam Z-scan technique. A continuous wave He-Ne laser operating at 633 nm was used as the source of excitation. Closed aperture Z-scan results reveal that the films exhibit self-defocusing nonlinearity. Open aperture Z-scan results exhibit a switching over phenomena of reverse saturable absorption to saturable absorption for thin film irradiated at 3 kGy, indicating the influence of electron beams on optical nonlinearity. The significant change in third-order nonlinear optical susceptibility χ (3) ranging from 2.14 × 10-3 to 3.12 × 10-3 esu is attributed to the effect of electron beam irradiation. The study shows that the nonlinear coefficients of GZO films can be tuned by electron beams for use in nonlinear optical device applications.
BEaTriX, expanded X-ray beam facility for testing modular elements of telescope optics: an update
Pelliciari, Carlo; Bonnini, Elisa; Buffagni, Elisa; Ferrari, Claudio; Pareschi, Giovanni; Tagliaferri, Gianpiero
2016-01-01
We present in this paper an update on the design of BEaTriX (Beam Expander Testing X-ray facility), an X-ray apparatus to be realized at INAF/OAB and that will generate an expanded, uniform and parallel beam of soft X-rays. BEaTriX will be used to perform the functional tests of X-ray focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, using the Silicon Pore Optics (SPO) as a baseline technology, and Slumped Glass Optics (SGO) as a possible alternative. Performing the tests in X-rays provides the advantage of an in-situ, at-wavelength quality control of the optical modules produced in series by the industry, performing a selection of the modules with the best angular resolution, and, in the case of SPOs, there is also the interesting possibility to align the parabolic and the hyperbolic stacks directly under X-rays, to minimize the aberrations. However, a parallel beam with divergence below 2 arcsec is necessary in order to measure mirror elements that are expected to reach ...
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.
Rahman, Md. Saifur; Lee, Yiu-Yin
2017-10-01
In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Energy Technology Data Exchange (ETDEWEB)
Chang, Philip; Lamberts, Astrid [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Broderick, Avery E.; Shalaby, Mohamad [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Puchwein, Ewald, E-mail: chang65@uwm.edu [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom)
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.
Numerical Simulations of Nonlinear Dynamics of Electron Cyclotron Maser with a Straight Beam
Institute of Scientific and Technical Information of China (English)
KONG Ling-Bao; HOU Zhi-Ling
2011-01-01
An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered,and the nonlinear equation of beam-wave interaction is presented.With the numerical methods,the nonlinear dynamics of the ADECM is investigated.It is shown that the saturated interaction efficiency of the ADECM approaches 90％ and the interaction length for the saturated efficiency spans about 5-20cm.The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.In the late 1950s,the theoretical studies on the instability of electron cyclotron maser based on normal Doppler effect (NDECM) were performed almost simultaneously by Gaponov,[1] Twiss,[2] and Schneider.[3] Their discoveries have resulted in the most successful fast-wave devices such as the gyrotron and variants.[4,5] The possible applications of microwaves span a wide range of technologies such as in thermonuclear fusion energy,charged particle accelerations,radar systems,and processing of advanced ceramics.[6-16]%An electron cyclotron maser based on anomalous Doppler effect (ADECM) with an initially axial beam velocity is considered, and the nonlinear equation of beam-wave interaction is presented. With the numerical methods, the nonlinear dynamics of the ADECM is investigated. It is shown that the saturated interaction efficiency of the ADECM approaches 90% and the interaction length for the saturated efficiency spans about 5-20 cm. The results may be of importance for designing a compact device in applications in microwave generations or microwave heating of ceramic laminates.
Advances in nonlinear vibration analysis of structures. Part-I. Beams
Indian Academy of Sciences (India)
Sudhakar R Marur
2001-06-01
The development of nonlinear vibration formulations for beams in the literature can be seen to have gone through distinct phases — earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.
Non-linearity of Beam Halo-Chaos in the ADS
Institute of Scientific and Technical Information of China (English)
2001-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applicationsin industry, medicine, and national defense. This latter reviews some general features of complexities and their expressions in accelerator-driven clean nuclear power system (ADS).Complexity has become an important subject for study, especially in the field of nonlinear
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2000-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
非线性粘弹性梁的混沌运动%Chaotic Motions of Nonlinear Viscoelastic Beams
Institute of Scientific and Technical Information of China (English)
陈立群; 程昌; 张能辉
2001-01-01
The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Energy Technology Data Exchange (ETDEWEB)
Romanov, A.; Edstrom, D.; Emanov, F. A.; Koop, I. A.; Perevedentsev, E. A.; Rogovsky, Yu. A.; Shwartz, D. B.; Valishev, A.
2017-03-28
Precise beam based measurement and correction of magnetic optics is essential for the successful operation of accelerators. The LOCO algorithm is a proven and reliable tool, which in some situations can be improved by using a broader class of experimental data. The standard data sets for LOCO include the closed orbit responses to dipole corrector variation, dispersion, and betatron tunes. This paper discusses the benefits from augmenting the data with four additional classes of experimental data: the beam shape measured with beam profile monitors; responses of closed orbit bumps to focusing field variations; betatron tune responses to focusing field variations; BPM-to-BPM betatron phase advances and beta functions in BPMs from turn-by-turn coordinates of kicked beam. All of the described features were implemented in the Sixdsimulation software that was used to correct the optics of the VEPP-2000 collider, the VEPP-5 injector booster ring, and the FAST linac.
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.
Nonlinear self-focus of pulsed-wave beams in Kerr media
Energy Technology Data Exchange (ETDEWEB)
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; 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.
Extreme events induced by self-action of laser beams in dynamic nonlinear liquid crystal cells
Bugaychuk, S.; Iljin, A.; Chunikhina, K.
2017-06-01
Optical extreme events represent a feature of nonlinear systems where there may emerge individual pulses possessing very high (or very low) intensity hardly probable statistically. Such property is being connected with the generation of solitons in the nonlinear systems. We carry out the first experiments for detection of extreme events during two-wave mixing with nonlinear dynamical liquid crystal (LC) cells. We investigate the statistics of the extreme events in dependence on relation between the duration of a laser pulse and the time characteristic of dynamic grating relaxation in LC cell. Our research shows that the self-diffraction of laser beams with a dynamical grating support the generation of envelope solitons in this system.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks.
Mangussi, Franco; Zanette, Damián H
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined.
Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks
Mangussi, Franco
2016-01-01
In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829
Expanding the region of convergence for SITAN through improved modelling of terrain nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Hostetler, L.D.; Beckmann, R.C.
1979-01-01
The SITAN (Sandia Inertial Terrain-Aided Navigation) system was originally developed to provide continuous updating of an inertial navigation system by using radar altimeter measurements of the terrain in conjunction with prestored topographic data in an extended Kalman filter. The basic algorithm performs satisfactorily for limited initial position uncertainties, but can diverge when the position uncertainty is so great that terrain linearity assumptions are significantly violated. An improvement to the basic system is described which considerably increases the region of convergence. The improvement is accomplished by modelling the terrain nonlinearities as Gauss-Markov measurement noise whose statistics and frequency content are adaptively varied as the uncertainty region evolves with time. Theoretical development of this modification is given and results of flight test experiments are presented which verify the ability of this modification to significantly increase SITAN's region of convergence.
Analysis of Retrofitting Non-Linear Finite Element Of RCC Beam And Column Using Ansys
Directory of Open Access Journals (Sweden)
T. Subramani
2014-12-01
Full Text Available Many of the existing reinforced concrete structures throughout the world are in urgent need of strengthening, repair or reconstruction because of deterioration due to various factors like corrosion, lack of detailing, failure of bonding between beam-column joints, increase in service loads, etc., leading to cracking, spalling, loss of strength, deflection, etc., Direct observation of these damaged structures has shown that damage occurs usually at the beam-column joints, with failure in bending or shear, depending on geometry and reinforcement distribution type.A nonlinear finite element analysis that is a simulation technique is used in this work to evaluate the effectiveness of retrofitting technique called “wrapping technique” for using carbon fibres (FRP for strengthening of RC beam-column connections damaged due to various reasons. After carrying out a nonlinear finite element analysis of a reinforced concrete frame (Controlled Specimen and reinforced concrete frame where carbon fibres are attached to the beam column joint portion in different patterns ,the measured response histories of the original and strengthened specimens are then subsequently compared. It is seen that the strengthened specimens exhibit significant increase in strength, stiffness, and stability as compared to controlled specimens. It appears that the proposed simulation technique will have a significant impact in engineering practice in the near future.
Nonlinear dynamics of beam-plasma instability in a finite magnetic field
Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.
2017-06-01
The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.
LEADS-DC: A computer code for intense dc beam nonlinear transport simulation
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ~13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously,the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.
3D Nonlinear Numerical Simulation of Intact and Debonded Reinforced Concrete Beams
Institute of Scientific and Technical Information of China (English)
Chen Quan(陈权); Marcus L.
2004-01-01
To study the behaviour of reinforced concrete (RC) structures with sections of concrete removed and the reinforcement exposed, 3D nonlinear numerical analysis was performed upon both intact and debonded RC beams by using finite element techniques. The deformational characteristics and the ultimate loads were obtained through numerical models, as well as crack and stress distributions. The failure modes can also be deduced from computational results. Compared with intact beams, the normal assumptions of plane section behaviour is not hold true and the patterns of stress and strain are different in debonded RC beams. The numerical results show good consistency with experimental data. This kind of numerical simulation is a supplement to existing codes.
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
2012-01-01
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 vivo Caenorhabditis 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
Antony, Albin; Pramodini, S.; Kityk, I. V.; Abd-Lefdil, M.; Douayar, A.; Cherkaoui El Moursli, F.; Sanjeev, Ganesh; Manjunatha, K. B.; Poornesh, P.
2017-10-01
Electron beam induced effects on Fluorine doped ZnO thin films (FZO) grown by chemical spray pyrolysis deposition technique were studied. The samples were exposed to 8 MeV electron beam at different dose rate ranging from 1 kGy to 4 kGy. All films exhibit a polycrystalline nature which shows an increase in crystallanity with irradiation dosages. The electron beam irradiation effectively controls the films surface morphology and its linear optical characteristics. Z-Scan technique was employed to evaluate the sign and magnitude of nonlinear refractive index and nonlinear absorption coefficient using a continuous wave laser at 632.8 nm as light source. Enhancement in the third order nonlinear optical properties was were noted due to electron beam irradiation. Tailoring the physical and NLO properties by electron beam, the FZO thin films becomes a promising candidate for various optoelectronic applications such as phase change memory devices, optical pulse compression, optical switching and laser pulse narrowing.
Design and advancement status of the Beam Expander Testing X-ray facility (BEaTriX)
Spiga, D; Salmaso, B; Arcangeli, L; Bianucci, G; Ferrari, C; Ghigo, M; Pareschi, G; Rossi, M; Tagliaferri, G; Valsecchi, G; Vecchi, G; Zappettini, A
2016-01-01
The BEaTriX (Beam Expander Testing X-ray facility) project is an X-ray apparatus under construction at INAF/OAB to generate a broad (200 x 60 mm2), uniform and low-divergent X-ray beam within a small lab (6 x 15 m2). BEaTriX will consist of an X-ray source in the focus a grazing incidence paraboloidal mirror to obtain a parallel beam, followed by a crystal monochromation system and by an asymmetrically-cut diffracting crystal to perform the beam expansion to the desired size. Once completed, BEaTriX will be used to directly perform the quality control of focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, based on either Silicon Pore Optics (baseline) or Slumped Glass Optics (alternative), and will thereby enable a direct quality control of angular resolution and effective area on a number of mirror modules in a short time, in full X-ray illumination and without being affected by the finite distance of the X-ray source. However, since the individual mirror modules for ATHENA...
Energy Technology Data Exchange (ETDEWEB)
Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V [CEA/LETI-MINATEC, Grenoble (France)
2009-07-08
In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.
Kacem, N; Hentz, S; Pinto, D; Reig, B; Nguyen, V
2009-07-08
In order to compensate for the loss of performance when scaling resonant sensors down to NEMS, it proves extremely useful to study the behavior of resonators up to very high displacements and hence high nonlinearities. This work describes a comprehensive nonlinear multiphysics model based on the Euler-Bernoulli equation which includes both mechanical and electrostatic nonlinearities valid up to displacements comparable to the gap in the case of an electrostatically actuated doubly clamped beam. Moreover, the model takes into account the fringing field effects, significant for thin resonators. The model has been compared to both numerical integrations and electrical measurements of devices fabricated on 200 mm SOI wafers; it shows very good agreement with both. An important contribution of this work is the provision for closed-form expressions of the critical amplitude and the pull-in domain initiation amplitude including all nonlinearities. This model allows designers to cancel out nonlinearities by tuning some design parameters and thus gives the possibility to drive the resonator beyond its critical amplitude. Consequently, the sensor performance can be enhanced to the maximum below the pull-in instability, while keeping a linear behavior.
DEFF Research Database (Denmark)
Sorokin, Vladislav S.; Thomsen, Jon Juel
2016-01-01
The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli– Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature...
Design and advancement status of the Beam Expander Testing X-ray facility (BEaTriX)
Spiga, D.; Pelliciari, C.; Salmaso, B.; Arcangeli, L.; Bianucci, G.; Ferrari, C.; Ghigo, M.; Pareschi, G.; Rossi, M.; Tagliaferri, G.; Valsecchi, G.; Vecchi, G.; Zappettini, A.
2016-09-01
The BEaTriX (Beam Expander Testing X-ray facility) project is an X-ray apparatus under construction at INAF/OAB to generate a broad (200´60 mm2), uniform and low-divergent X-ray beam within a small lab (6´15 m2). BEaTriX will consist of an X-ray source in the focus a grazing incidence paraboloidal mirror to obtain a parallel beam, followed by a crystal monochromation system and by an asymmetrically-cut diffracting crystal to perform the beam expansion to the desired size. Once completed, BEaTriX will be used to directly perform the quality control of focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, based on either Silicon Pore Optics (baseline) or Slumped Glass Optics (alternative), and will thereby enable a direct quality control of angular resolution and effective area on a number of mirror modules in a short time, in full X-ray illumination and without being affected by the finite distance of the X-ray source. However, since the individual mirror modules for ATHENA will have an optical quality of 3-4 arcsec HEW or better, BEaTriX is required to produce a broad beam with divergence below 1-2 arcsec, and sufficient flux to quickly characterize the PSF of the module without being significantly affected by statistical uncertainties. Therefore, the optical components of BEaTriX have to be selected and/or manufactured with excellent optical properties in order to guarantee the final performance of the system. In this paper we report the final design of the facility and a detailed performance simulation.
BEaTriX, expanded x-ray beam facility for testing modular elements of telescope optics: an update
Pelliciari, C.; Spiga, D.; Bonnini, E.; Buffagni, E.; Ferrari, C.; Pareschi, G.; Tagliaferri, G.
2015-09-01
We present in this paper an update on the design of BEaTriX (Beam Expander Testing X-ray facility), an X-ray apparatus to be realized at INAF/OAB and that will generate an expanded, uniform and parallel beam of soft X-rays. BEaTriX will be used to perform the functional tests of X-ray focusing modules of large X-ray optics such as those for the ATHENA X-ray observatory, using the Silicon Pore Optics (SPO) as a baseline technology, and Slumped Glass Optics (SGO) as a possible alternative. Performing the tests in X-rays provides the advantage of an in-situ, at-wavelength quality control of the optical modules produced in series by the industry, performing a selection of the modules with the best angular resolution, and, in the case of SPOs, there is also the interesting possibility to align the parabolic and the hyperbolic stacks directly under X-rays, to minimize the aberrations. However, a parallel beam with divergence below 2 arcsec is necessary in order to measure mirror elements that are expected to reach an angular resolution of about 4 arcsec, since the ATHENA requirement for the entire telescope is 5 arcsec. Such a low divergence over the typical aperture of modular optics would require an X-ray source to be located in a several kilometers long vacuum tube. In contrast, BEaTriX will be compact enough (5 m x 14 m) to be housed in a small laboratory, will produce an expanded X-ray beam 60 mm x 200 mm broad, characterized by a very low divergence (1.5 arcsec HEW), strong polarization, high uniformity, and X-ray energy selectable between 1.5 keV and 4.5 keV. In this work we describe the BEaTriX layout and show a performance simulation for the X-ray energy of 4.5 keV.
Nonlinear flexural waves and chaos behavior in finite-deflection Timoshenko beam
Institute of Scientific and Technical Information of China (English)
Shan-yuan ZHANG; Zhi-fang LIU
2010-01-01
Based on the Timoshenko beam theory,the finite-deflection and the axial inertia are taken into account,and the nonlinear partial differential equations for flexural waves in a beam are derived. Using the traveling wave method and integration skills,the nonlinear partial differential equations can be converted into an ordinary differential equation. The qualitative analysis indicates that the corresponding dynamic system has a heteroclinic orbit under a certain condition. An exact periodic solution of the nonlinear wave equation is obtained using the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function tends to one in the degenerate case,a shock wave solution is given. The small perturbations are further introduced,arising from the damping and the external load to an original Hamilton system,and the threshold condition of the existence of the transverse heteroclinic point is obtained using Melnikov's method. It is shown that the perturbed system has a chaotic property under the Smale horseshoe transform.
Nonlinear and long-term beam dynamics in low energy storage rings
Papash, A. I.; Smirnov, A. V.; Welsch, C. P.
2013-06-01
Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF+ ions at 93keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3-30 keV ions with a gas jet target are summarized.
Nonlinear and long-term beam dynamics in low energy storage rings
Directory of Open Access Journals (Sweden)
A. I. Papash
2013-06-01
Full Text Available Electrostatic storage rings operate at very low energies in the keV range and have proven to be invaluable tools for atomic and molecular physics. Because of the mass independence of electric rigidity, these machines are able to store a wide range of different particles, from light ions to heavy singly charged biomolecules, opening up unique research opportunities. However, earlier measurements have shown strong limitations in maximum beam intensity, fast decay of the stored ion current, and reduced beam lifetime. The nature of these effects has not been fully understood and an improved understanding of the physical processes influencing beam motion and stability in such rings is needed. In this paper, a comprehensive study into nonlinear and long-term beam dynamics studies is presented on the examples of a number of existing and planned electrostatic storage rings using the BETACOOL, OPERA-3D, and MAD-X simulation software. A detailed investigation into ion kinetics, under consideration of effects from electron cooling and multiple scattering of the beam on a supersonic gas jet target, is carried out and yields a consistent explanation of the physical effects in a whole class of storage rings. The lifetime, equilibrium momentum spread, and equilibrium lateral spread during collisions with the target are estimated. In addition, the results from experiments at the Test Storage Ring, where a low-intensity beam of CF^{+} ions at 93 keV/u has been shrunk to extremely small dimensions, are reproduced. Based on these simulations, the conditions for stable ring operation with an extremely low-emittance beam are presented. Finally, results from studies into the interaction of 3–30 keV ions with a gas jet target are summarized.
Energy Technology Data Exchange (ETDEWEB)
Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com [Department of Physics, National Institute of Technology Jalandhar (India); Singh, Navpreet, E-mail: navpreet.nit@gmail.com [Guru Nanak Dev University College, Kapurthala, Punjab (India)
2015-11-15
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.
Non-Linear Beam Dynamics Studies of the Diamond Storage Ring
Bartolini, Riccardo; Belgroune, Mahdia; Henry Rowland, James; Jones, James; Martin, Ian; Singh, Beni
2005-01-01
The non-linear beam dynamics have been investigated for the non-zero dispersion lattice of the Diamond storage ring. Effects in realistic lattice configurations such as the introduction of coupling errors, beta beating, closed orbit correction, quadrupole fringe field and in-vacuum and helical insertion devices have been studied in the presence of realistic physical aperture limitations. Frequency map analysis together with 6D tracking allows identification of the limiting resonances as well as the loss locations and calculation of the influence of non-linear longitudinal motion on the Touschek lifetime. The sensitivity of the lattice to some of these effects leads to the identification of a better working point for the machine.
(3+1)-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material
Institute of Scientific and Technical Information of China (English)
Hu Yong-Hua; Fu Xi-Quan; Wen Shuang-Chun; Su Wen-Hua; Fan Dian-Yuan
2006-01-01
In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized (3+1)-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material (RHM) and left-handed material (LHM) is derived. By the commonly used Drude dispersive model for LHM, a (3+1)-dimensional nonlinear Schr(o)dinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Lund, Erik; Thomsen, Ole Thybo;
2010-01-01
In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which ...... is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed....
Lie algebraic analysis for the nonlinear transport of intense pulsed beams in electrostatics lenses
Institute of Scientific and Technical Information of China (English)
Lu Jian-Qin; Li Jin-Hai
2004-01-01
The Lie algebraic method is applied to the analysis of the nonlinear transport of an intense pulsed beam in cylindrically symmetrical electrostatic lenses, and particle orbits in a six-dimensional phase space (x, px, y, py, τ, pτ)are obtained in the second order approximation. They can also be acquired in the third or higher order approximation if needed. In the analysis, we divide the electrostatic lenses into several segments. Each segment is considered as a uniform accelerating field, and each dividing point is treated as a thin lens. The particle distribution in a three-dimensional ellipsoid is of Gaussian type.
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution
Martins, Weliton Soares; de Silans, Thierry Passerat; Oriá, Marcos; Chevrollier, Martine; 10.1364/AO.51.005080
2012-01-01
Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.
Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies
Energy Technology Data Exchange (ETDEWEB)
Chang, Jing [College of Information Technology, Jilin Agricultural University, Changchun 130118 (China); Gao, Yixian, E-mail: gaoyx643@nenu.edu.cn; Li, Yong [School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024 (China)
2015-05-15
Consider the one dimensional nonlinear beam equation u{sub tt} + u{sub xxxx} + mu + u{sup 3} = 0 under Dirichlet boundary conditions. We show that for any m > 0 but a set of small Lebesgue measure, the above equation admits a family of small-amplitude quasi-periodic solutions with n-dimensional Diophantine frequencies. These Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proofs are based on an infinite dimensional Kolmogorov-Arnold-Moser iteration procedure and a partial Birkhoff normal form. .
Visualizing expanding warm dense matter heated by laser-generated ion beams
Energy Technology Data Exchange (ETDEWEB)
Bang, Woosuk [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-08-24
This PowerPoint presentation concluded with the following. We calculated the expected heating per atom and temperatures of various target materials using a Monte Carlo simulation code and SESAME EOS tables. We used aluminum ion beams to heat gold and diamond uniformly and isochorically. A streak camera imaged the expansion of warm dense gold (5.5 eV) and diamond (1.7 eV). GXI-X recorded all 16 x-ray images of the unheated gold bar targets proving that it could image the motion of the gold/diamond interface of the proposed target.
Calibration of a Non-Linear Beam Position Monitor Electronics by Switching Electrode Signals
Gasior, M
2013-01-01
Button electrode signals from beam position monitors embedded into new LHC collimators will be individually processed with front-end electronics based on compensated diode detectors and digitized with 24-bit audio-range ADCs. This scheme allows sub-micrometre beam orbit resolution to be achieved with simple hardware and no external timing. As the diode detectors only operate in a linear regime with large amplitude signals, offset errors of the electronics cannot be calibrated in the classical way with no input. This paper describes the algorithms developed to calibrate the offset and gain asymmetry of these nonlinear electronic channels. Presented algorithm application examples are based on measurements performed with prototype diode orbit systems installed on the CERN SPS and LHC machines.
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
Porfido, N.
2015-10-12
By photoionizing hyperfine (HF) levels of the Cs state 62P3/2 in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around 180μs) 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.
Nonlinear Breit-Wheeler pair production in a tightly focused laser beam
Di Piazza, A
2016-01-01
The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.
Nonlinear Breit-Wheeler Pair Production in a Tightly Focused Laser Beam
Di Piazza, A.
2016-11-01
The only available analytical framework for investigating QED processes in a strong laser field systematically relies on approximating the latter as a plane wave. However, realistic high-intensity laser beams feature much more complex space-time structures than plane waves. Here, we show the feasibility of an analytical framework for investigating strong-field QED processes in laser beams of arbitrary space-time structure by determining the energy spectrum of positrons produced via nonlinear Breit-Wheeler pair production as a function of the background field in the realistic assumption that the energy of the incoming photon is the largest dynamical energy in the problem. A numerical evaluation of the angular resolved positron spectrum shows significant quantitative differences with respect to the analogous result in a plane wave, such that the present results will be also important for the design of upcoming strong laser facilities aiming at measuring this process.
Twork, Sabine; Wiesmeth, Susanne; Spindler, Milena; Wirtz, Markus; Schipper, Sabine; Pöhlau, Dieter; Klewer, Jörg; Kugler, Joachim
2010-06-07
Progression in disability as measured by increase in the Expanded Disability Status Scale (EDSS) is commonly used as outcome variable in clinical trials concerning multiple sclerosis (MS). In this study, we addressed the question, whether there is a linear relationship between disability status and health related quality of life (HRQOL) in MS. 7305 MS patients were sent a questionnaire containing a German version of the "Multiple Sclerosis Quality of Life (MSQOL)-54" and an assessment of self-reported disability status analogous to the EDSS. 3157 patients participated in the study. Patients were allocated to three groups according to disability status. Regarding the physical health composite and the mental health composite as well as most MSQOL-54 subscales, the differences between EDSS 4.5-6.5 and EDSS > or = 7 were clearly smaller than the differences between EDSS EDSS 4.5-6.5. These results indicate a non-linear relationship between disability status and HRQOL in MS. The EDSS does not seem to be interval scaled as is commonly assumed. Consequently, absolute increase in EDSS does not seem to be a suitable outcome variable in MS studies.
Directory of Open Access Journals (Sweden)
Ruilan Tian
2016-06-01
Full Text Available The coupled system of smooth and discontinuous absorber and beam bridge under moving loads is constructed in order to detect the effectiveness of smooth and discontinuous absorber. It is worth pointing out that the coupled system contains an irrational restoring force which is a barrier for conventional nonlinear techniques. Hence, the harmonic balance method and Fourier expansion are used to obtain the approximate solutions of the system. The first and the second kind of generalized complete elliptic integrals are introduced. Furthermore, using power flow approach, the performance of smooth and discontinuous absorber in vibration reduction is estimated through the input energy, the dissipated energy, and the damping efficiency. It is interesting that only depending on the value of the smoothness parameter, the efficiency parameter of vibration reduction is optimized. Therefore, smooth and discontinuous absorber can adapt itself to effectively reducing the amplitude of the vibration of the beam bridge, which provides an insight to the understanding of the applications of smooth and discontinuous oscillator in engineering and power flow characteristics in nonlinear system.
Misra, Nilanjal; Rapolu, Mounika; Venugopal Rao, S.; Varshney, Lalit; Kumar, Virendra
2016-05-01
The optical nonlinearity of metal nanoparticles in dielectrics is of special interest because of their high polarizability and ultrafast response that can be utilized in potential device applications. In this study nanocomposite thin films containing in situ generated Ag nanoparticles dispersed in an aliphatic urethane acrylate (AUA) matrix were synthesized using electron beam curing technique, in presence of an optimized concentration of diluent Trimethylolpropanetriacrylate (TMPTA). The metal nanocomposite films were characterized using UV-visible spectrophotometry, transmission electron microscope (TEM) and field emission scanning electron microscope (FE-SEM) techniques. Ag nanoparticle impregnated films demonstrated an absorption peak at ∼420 nm whose intensity increased with increase in the Ag concentration. The optical limiting property of the coatings was tested using a nanosecond Nd-YAG laser operated at third harmonic wavelength of 355 nm. For a 25 ns pulse and 10 Hz cycle, Ag-polymer coatings showed good optical limiting property and the threshold fluence for optical limiting was found to be ∼3.8×10-2 J/cm2 while the transmission decreased to 82%. The nonlinear optical coefficients were also determined using the standard Z-scan technique with picosecond (∼2 ps, 1 kHz) and femtosecond (∼150 fs, 100 MHz) pulses. Open aperture Z-scan data clearly suggested two-photon absorption as the dominant nonlinear absorption mechanism. Our detailed studies suggest these composites are potential candidates for optical limiting applications.
An expanded x-ray beam facility (BEaTriX) to test the modular elements of the ATHENA optics
Spiga, D.; Pelliciari, C.; Bonnini, E.; Buffagni, E.; Ferrari, C.; Pareschi, G.; Tagliaferri, G.
2014-07-01
Future large X-ray observatories like ATHENA will be equipped with very large optics, obtained by assembling modular optical elements, named X-ray Optical Units (XOU) based on the technology of either Silicon Pore Optics or Slumped Glass Optics. In both cases, the final quality of the modular optic (a 5 arcsec HEW requirement for ATHENA) is determined by the accuracy alignment of the XOUs within the assembly, but also by the angular resolution of the individual XOU. This is affected by the mirror shape accuracy, its surface roughness, and the mutual alignment of the mirrors within the XOU itself. Because of the large number of XOUs to be produced, quality tests need to be routinely done to select the most performing stacked blocks, to be integrated into the final optic. In addition to the usual metrology based on profile and roughness measurements, a direct measurement with a broad, parallel, collimated and uniform Xray beam would be the most reliable test, without the need of a focal spot reconstruction as usually done in synchrotron light. To this end, we designed the BEaTriX (Beam Expander Testing X-ray facility) to be realized at INAF-OAB, devoted to the functional tests of the XOUs. A grazing incidence parabolic mirror and an asymmetrically cut crystal will produce a parallel X-ray beam broad enough to illuminate the entire aperture of the focusing elements. An X-ray camera at the focal distance from the mirrors will directly record the image. The selection of different crystals will enable to test the XOUs in the 1 - 5 keV range, included in the X-ray energy band of ATHENA (0.2-12 keV). In this paper we discuss a possible BEaTriX facility implementation. We also show a preliminary performance simulation of the optical system.
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing
2017-02-01
In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirmed this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, a focused nonlinear ultrasonic beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.
Nonlinear Free Vibration Analysis of Thin-walled Curved Beam with Non-symmetric Open Cross Section
Institute of Scientific and Technical Information of China (English)
DUAN Hai-juan; SONG Zhen-sen
2008-01-01
A finite element formulation was presented for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies were derived by the virtual principle. The energy function includes the effect of flexural-torsional coupling, the torsion warping and the shear centre location. For finite element analysis, cubic polynomials were utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem was solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.
Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams
Phadte, D. S.; Patidar, C. B.
2013-07-01
Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.
Megapixel imaging camera for expanded H{sup {minus}} beam measurements
Energy Technology Data Exchange (ETDEWEB)
Simmons, J.E.; Lillberg, J.W.; McKee, R.J.; Slice, R.W.; Torrez, J.H. [Los Alamos National Lab., NM (United States); McCurnin, T.W.; Sanchez, P.G. [EG and G Energy Measurements, Inc., Los Alamos, NM (United States). Los Alamos Operations
1994-02-01
A charge coupled device (CCD) imaging camera system has been developed as part of the Ground Test Accelerator project at the Los Alamos National Laboratory to measure the properties of a large diameter, neutral particle beam. The camera is designed to operate in the accelerator vacuum system for extended periods of time. It would normally be cooled to reduce dark current. The CCD contains 1024 {times} 1024 pixels with pixel size of 19 {times} 19 {mu}m{sup 2} and with four phase parallel clocking and two phase serial clocking. The serial clock rate is 2.5{times}10{sup 5} pixels per second. Clock sequence and timing are controlled by an external logic-word generator. The DC bias voltages are likewise located externally. The camera contains circuitry to generate the analog clocks for the CCD and also contains the output video signal amplifier. Reset switching noise is removed by an external signal processor that employs delay elements to provide noise suppression by the method of double-correlated sampling. The video signal is digitized to 12 bits in an analog to digital converter (ADC) module controlled by a central processor module. Both modules are located in a VME-type computer crate that communicates via ethernet with a separate workstation where overall control is exercised and image processing occurs. Under cooled conditions the camera shows good linearity with dynamic range of 2000 and with dark noise fluctuations of about {plus_minus}1/2 ADC count. Full well capacity is about 5{times}10{sup 5} electron charges.
Dávila Pintle, José A; Lara, Edmundo Reynoso; Iturbe Castillo, Marcelo D
2013-07-01
It is presented a criteria for selecting the optimum aperture radius for the one beam Z-scan technique (OBZT), based on the analysis of the transmittance of the aperture. It is also presented a modification to the OBZT by directly measuring the beam radius in the far field with a rotating disk, which allows to determine simultaneously the non-linear absorptive coefficient and non-linear refractive index, much less sensitive to wave front distortions caused by inhomogeneities of the sample with a negligible loss of signal to noise ratio. It is demonstrated its equivalence to the OBZT.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The physical mechanism of the halo-chaos formation for a high intensity proton beam in a periodic-fo cusing channel is analyzed using the transfer mahix theory and a qualiative analysis method.Particles-in-cell simula tims are further used to explore the mechanism of the beam halo-chaos fomation, which concerns not only with thc non linear effect of the beam space charge but also with the lransverse energy exchange belween the particles and the particle core. as well as the chaos generated by the nonlinear resonance ovcrlap. A nonlinear control method is proposed for con trolling tie haho-chaos. Simulation results show lhal the melhod is efhclivc. Somc potemlial applications of the halo chaos conlrol in experimenls are discussed.
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
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.
Energy Technology Data Exchange (ETDEWEB)
Pusterla, M.; Servizi, G.; Turchetti, G.
1985-10-01
Theoretical models, suitable for description of the long behaviour of bunched and unbunched beams of particles in accelerators and storage rings, are becoming more and more appreciated by physicists that want a high luminosity joined with the stability of the beams. Such a point is going to be particulary important for the next generation machines as L.E.P., S.S.C. and L.H.C. In this note we are giving a simplified analysis of the beam-beam non-linear effects for proton colliders on the basis of the latest designs (we think of S.S.C. and L.H.C.). Before doing that, however, we like to consider the general features of the dynamical approaches that describe the beam-beam forces both for the proton proton rings (fixed angle collision) and for proton-antiproton or electronpositron rings (head-on collisions): they follow directly from the recent developments of non-linear classical mechanics, namely the K.A.M. theorem and the transition to a chaotic motion in deterministic mechanical systems.
Cichalewski, w
2010-01-01
The high power amplifiers transfer characteristics nonlinearities can have a negative influence on the overall system performance. This is also true for the TESLA superconducting cavities accelerating field parameters control systems. This Low Level Radio Frequency control systems uses microwave high power amplifiers (like 10 MW klystrons) as actuators in the mentioned feedback loops. The amplitude compression and phase deviations phenomena introduced to the control signals can reduce the feedback performance and cause electron beam energy instabilities. The transfer characteristics deviations in the Free Electron Laser in Hamburg experiment have been investigated. The outcome of this study together with the description of the developed linearization method based on the digital predistortion approach have been described in this paper. Additionally, the results from the linearization tool performance tests in the FLASH's RF systems have been placed.
Lohar, Hareram; Mitra, Anirban; Sahoo, Sarmila
2016-09-01
In the present study non-linear free vibration analysis is performed on a tapered Axially Functionally Graded (AFG) beam resting on an elastic foundation with different boundary conditions. Firstly the static problem is carried out through an iterative scheme using a relaxation parameter and later on the subsequent dynamic problem is solved as a standard eigen value problem. Minimum potential energy principle is used for the formulation of the static problem whereas for the dynamic problem Hamilton's principle is utilized. The free vibrational frequencies are tabulated for different taper profile, taper parameter and foundation stiffness. The dynamic behaviour of the system is presented in the form of backbone curves in dimensionless frequency-amplitude plane.
Measurement of the Beam Longitudinal Profile in a Storage Ring by Non-Linear Laser Mixing
Beche, J.-F.; Byrd, J.; De Santis, S.; Denes, P.; Placidi, M.; Turner, W.; Zolotorev, M.
2004-11-01
We report on the development of a new technique for the measurement of the longitudinal beam profile in storage rings. This technique, which has been successfully demonstrated at the Advanced Light Source, mixes the synchrotron radiation with the light from a mode-locked solid-state laser oscillator in a non-linear crystal. The up-converted radiation is then detected with a photomultiplier and processed to extract, store, and display the required information. The available choices of laser repetition frequency, pulse width, and phase modulation give a wide range of options for matching the bunch configuration of a particular storage ring. Besides the dynamic measurement of the longitudinal profile of each bunch, the instrument can monitor the evolution of the bunch tails, the presence of un trapped particles, and their diffusion into nominally empty RF buckets ("ghost bunches").
Tran Hy, J
1998-01-01
This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...
A Beam-Fourier Technique for the Numerical Investigation of 2D Nonlinear Convective Flows
Papanicolaou, N. C.
2011-11-01
In the current work, we develop a numerical method suitable for treating the problem of nonlinear two-dimensional flows in rectangular domains. For the spatial approximation we employ the Fourier-Galerkin approach. More specifically, our basis functions are products of trigonometric and Beam functions. This choice means that the solutions automatically satisfy the boundary and periodic conditions in the x and y directions respectively. The accuracy of the method is assessed by applying it to model problems which admit exact analytical solutions. The numerical and analytic solutions are found to be in good agreement. The convergence rate of the spectral coefficients is found to be fifth-order algebraic in the x-direction and y-direction, confirming the efficiency and speed of our technique.
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.
Hu, Y. J.; Yang, J.; Kitipornchai, S.
2013-07-01
This paper presents a geometrically nonlinear micro-beam model for the electro-dynamic analysis of an initially curved micro-beam under an applied voltage, with an emphasis on its snap-through and pull-in behaviors. The governing equations of motion and the associated boundary conditions are derived in an arc coordinate system without involving any assumptions on the nonlinear deformation. Differential quadrature method (DQM) and Petzold-Gear Backward Differentiation Formulas (BDF) are employed to solve the governing equations in the space and time domains respectively to obtain the nonlinear fundamental frequency, snap-through voltage, pull-in voltage and the corresponding mode shapes of a micro-beam clamped at both ends. The present analysis is validated through a direct comparison with the published experimental and numerical results. A parametric study is conducted to investigate the influences of the initial gap, base length, arc rise, and initial curved configuration on the snap-through and pull-in behaviors of the micro-beam.
Nonlinear Forced Vibration of a Viscoelastic Buckled Beam with 2 : 1 Internal Resonance
Directory of Open Access Journals (Sweden)
Liu-Yang Xiong
2014-01-01
Full Text Available Nonlinear dynamics of a viscoelastic buckled beam subjected to primary resonance in the presence of internal resonance is investigated for the first time. For appropriate choice of system parameters, the natural frequency of the second mode is approximately twice that of the first providing the condition for 2 : 1 internal resonance. The ordinary differential equations of the two mode shapes are established using the Galerkin method. The problem is replaced by two coupled second-order differential equations with quadratic and cubic nonlinearities. The multiple scales method is applied to derive the modulation-phase equations. Steady-state solutions of the system as well as their stability are examined. The frequency-amplitude curves exhibit the steady-state response in the directly excited and indirectly excited modes due to modal interaction. The double-jump, the saturation phenomenon, and the nonperiodic region phenomena are observed illustrating the influence of internal resonance. The validity range of the analytical approximations is assessed by comparing the analytical approximate results with a numerical solution by the Runge-Kutta method. The unstable regions in the internal resonance are explored via numerical simulations.
Sedighi, H. M.; Shirazi, K. H.
2014-11-01
This article attains a new formulation of beam vibrations on an elastic foundation with quintic nonlinearity, including exact expressions for the beam curvature. To achieve a proper design of the beam structures, it is essential to realize how the beam vibrates in its transverse mode, which, in turn, yields the natural frequency of the system. In this direction, a powerful analytical method called the parameter expansion method is employed to obtain the exact solution of the frequency-amplitude relationship. It is clearly shown that the first term in series expansions is sufficient to produce a highly accurate approximation of the above-mentioned system. Finally, the accuracy of the present analytic procedure is evaluated through comparisons with numerical calculations.
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
Energy Technology Data Exchange (ETDEWEB)
Romanchenko, I. V., E-mail: riv@lfe.hcei.tsc.ru; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu. [Institute of high current electronics SB RAS, Akademichesky 2/3, 634055, Tomsk (Russian Federation)
2015-06-07
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.
Experimental nonlinear beam dynamics studies with turn- by-turn phase space monitors
Terebilo, Andrei Gennadyevich
1999-10-01
This thesis presents an experimental study of single particle and collective beam dynamics undertaken by the author in SPEAR electron storage ring. The technique used for measurement consists of exciting transverse oscillations of a bunch circulating in the ring with a fast kicker and observing the center of mass oscillations every turn for several thousand turns. The goal of this study was to develop new applications of the turn-by-turn technique to accelerator diagnostics. One innovation introduced is the use of a collective mode of the beam motion as a phase space probe. When in this mode the bunch behaves similar to a macroparticle and oscillates coherently. It is possible to control the growth/damping rate of this oscillation by adjusting the accelerator parameters. Another new tool proposed is the analysis of phase space trajectories in the time-frequency domain. This technique makes it possible to conduct nonlinear dynamics experiments such as observation of high order resonances in the frequency map and single-kick measurement of the tune dependence on the amplitude of oscillations.
A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation
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.
Directory of Open Access Journals (Sweden)
Muhammet Karaton
2014-01-01
Full Text Available 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-α 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.
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-α 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.
Lenci, Stefano; Rega, Giuseppe
2016-06-01
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed. Furthermore, the softening versus hardening nature of the backbone curves is investigated in depth. The results are summarized by means of behaviour charts that illustrate the different possible classes of motion in the parameter space. New, and partially unexpected, phenomena, such as the changing of the nonlinear behaviour from softening to hardening by adding/removing the axial vibrations, are highlighted.
2012-06-09
these formulations employ some form of either the Euler-Bernoulli or Timoshenko beam theories and are mostly restricted to small strain analysis. The...and Kadioglu [1], wherein a Timoshenko beam element is de- veloped using mixed variational principles. In their work, the finite element model...method in their analysis of cylindrical helical rods (based on the Timoshenko beam hypotheses). Additional numerical formulations for viscoelastic beams
leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul
2004-10-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Non-linear beam dynamics tests in the LHC: LHC dynamic aperture MD on Beam 2 (24th of June 2012)
Maclean, E H; Persson, T H B; Redaelli, S; Schmidt, F; Tomas, R; Uythoven, J
2013-01-01
This MD note summarizes measurements performed on LHC Beam 2 during the non-linear machine development (MD) of 24 June 2012. The aim of the measurement was to observe the dynamic aperture of LHC Beam 2, and obtain turn-by-turn (TbT) betatron oscillation data, enabling the study of amplitude detuning and resonance driving terms (RDTs). The regular injections required by the MD also represented an opportunity to test a new coupling feedback routine based on the analysis of injection oscillation data. Initial measurements were performed on the nominal state of the LHC at injection. On completion of this study the Landau octupoles were turned off and corrections for higher-order chromaticities were implemented to reduce the non-linearity of the machine as far as possible. A second set of measurements were then performed. All studies were performed using the LHC aperture kicker (MKA).
Directory of Open Access Journals (Sweden)
Iman Eshraghi
2016-09-01
Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.
Directory of Open Access Journals (Sweden)
S.C. Chin
2012-05-01
Full Text Available This study presents the experimental study and numerical analysis of Reinforced Concrete (RC beams with large square openings placed in the shear region, at a distance 0.5d and d away from the support, strengthened by Carbon Fiber Reinforced Polymer (CFRP laminates. This research aims to investigate the strength losses in RC beam due to the presence of large square openings placed at two different locations in shear region. Also, in order to re-gain the beam structural capacity loss due to the openings, strengthening by CFRP laminates around the openings were studied. A total of six RC beams were tested to failure under four point loading including control beams, un-strengthened and strengthened RC beams with large square openings in shear region at a distance 0.5d and d away from the support. The CFRP strengthening configuration considered in this study was a full wrapping system around the square openings. A nonlinear finite element program, ATENA was used to validate the results of the tested beams. Comparisons between the finite element predictions and experimental results in terms of crack patterns and load deflection relationships are presented. The crack pattern results of the finite element model show good agreement with the experimental data. The load midspan deflection curves of the finite element models exhibited a stiffer result compared to the experimental beams. The possible reason may be due to the perfect bond assumption between the concrete and steel reinforcement.
Energy Technology Data Exchange (ETDEWEB)
Nariyuki, Y. [Faculty of Human Development, University of Toyama, 3190, Toyama City, Toyama 930-8555 (Japan); Hada, T. [Department of Earth System Science and Technology, Kyushu University, 6-1, Kasuga City, Fukuoka 816-8580 (Japan); Tsubouchi, K., E-mail: nariyuki@edu.u-toyama.ac.jp [Graduate School of Science, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550 (Japan)
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.
Ding, Hu; Chen, Li-Qun; Yang, Shao-Pu
2012-05-01
The present paper investigates the convergence of the Galerkin method for the dynamic response of an elastic beam resting on a nonlinear foundation with viscous damping subjected to a moving concentrated load. It also studies the effect of different boundary conditions and span length on the convergence and dynamic response. A train-track or vehicle-pavement system is modeled as a force moving along a finite length Euler-Bernoulli beam on a nonlinear foundation. Nonlinear foundation is assumed to be cubic. The Galerkin method is utilized in order to discretize the nonlinear partial differential governing equation of the forced vibration. The dynamic response of the beam is obtained via the fourth-order Runge-Kutta method. Three types of the conventional boundary conditions are investigated. The railway tracks on stiff soil foundation running the train and the asphalt pavement on soft soil foundation moving the vehicle are treated as examples. The dependence of the convergence of the Galerkin method on boundary conditions, span length and other system parameters are studied.
Wahlstrand, J K; McCole, E T; Cheng, Y -H; Palastro, J P; Levis, R J; Milchberg, H M
2013-01-01
Nonlinear optics experiments measuring phase shifts induced in a weak probe pulse by a strong pump pulse must account for coherent effects that only occur when the pump and probe pulses are temporally overlapped. It is well known that a weak probe beam experiences a greater phase shift from a strong pump beam than the pump beam induces on itself. The physical mechanism behind the enhanced phase shift is diffraction of pump light into the probe direction by a nonlinear refractive index grating produced by interference between the two beams. For an instantaneous third-order response, the effect of the grating is to simply double the probe phase shift, but when delayed nonlinearities are considered, the effect is more complex. A comprehensive treatment is given for both degenerate and nondegenerate pump-probe experiments in noble and diatomic gases. Results of numerical calculations are compared to a recent transient birefringence measurement [Loriot et al., Opt. Express 17, 13429 (2009)] and a recent spectral i...
Institute of Scientific and Technical Information of China (English)
Jianqin Lü; Xiaosong Zhao
2008-01-01
Nonlinear transport of intense continuous beam in the axial-symmetric electrostatic fields is analyzed with the Lie algebraic method.The K-V particle distribution is adopted in the analysis. The results obtained can be used in the calculations of the intense continuous beam dynamics in the beam optical systems consisting of drift spaces, electrostatic lenses, and DC electrostatic accelerating tubes. A com-puter code has been designed for practical simulations. To meet the needs of accurate calculation, all the elements are divided into many small segments, the electric fields in each segment are regarded as uniform fields, and the dividing points are treated as thin lenses. Iter-ation procedures are adopted in the code to obtain self-consistent solutions. The code can be used to design low energy dc beam transport systems, electrostatic accelerators, and ion implantation machines.
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.
Energy Technology Data Exchange (ETDEWEB)
Regis Junior, Oswaldo; Cavalcanti, Sebastiao J. Gusmao; Wavrik, Jose Felipe A.G. [Companhia Hidroeletrica do Sao Francisco (CHESF), Recife, PE (Brazil); Maia, Marcelo J. Albuquerque [ELETROBRAS, Rio de Janeiro, RJ (Brazil); Podporkin, Georgij Viktorovich [Centro de Pesquisas de Energia Eletrica, Rio de Janeiro, RJ (Brazil)
1995-12-31
Using the concept of high natural power transmission line, this technical report presents a new alternative for the re capacitance of existent transmission lines through the expansion of conductor beams. It is related the experience of CHESF (Sao Francisco Hydroelectric Power Public Utility) in the study, project and pursuance of an experimental stretch energized in december 1994. It is also presented technical and economical evaluations in order to approve expanded beams in the 230 kV power transmission line, changeable to 500 kV 4 refs., 9 figs., 6 tabs.
Nonlinear fracture mechanics investigation on the ductility of reinforced concrete beams
Directory of Open Access Journals (Sweden)
A. Carpinteri
Full Text Available In the present paper, a numerical algorithm based on the finite element method is proposed for the prediction of the mechanical response of reinforced concrete (RC beams under bending loading. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing. According to this model, the concrete dam- age in compression is represented by means of a fictitious interpenetration. The larger is the interpenetration, the lower are the transferred forces across the damaged zone. The well-known Cohesive Crack Model in tension and an elastic-perfectly plastic stress versus crack opening displacement relationship describing the steel reinforcement behavior are also integrated into the numerical algorithm. The application of the proposed Cohesive-Overlapping Crack Model to the assessment of the minimum reinforcement amount neces- sary to prevent unstable tensile crack propagation and to the evaluation of the rotational capacity of plastic hinges, permits to predict the size-scale effects evidenced by several experimental programs available in the literature. According to the obtained numerical results, new practical design formulae and diagrams are proposed for the improvement of the current code provisions which usually disregard the size effects.
Pavelko, V.; Lapsa, K.; Pavlovskis, P.
2016-07-01
The aim of this study is estimation of the effect of large deflections of a double-cantilever beam (DCB) on the accuracy of determination of the mode I interlaminar fracture toughness GIc of layered composites by using the nonlinear theory of bending of beams. The differential equation of the deflection curve of arm of the DCB specimen in the natural form was used to analyze the strain energy of the specimen and its strain energy release rate GI upon propagation of delamination under the action of cleavage forces at the ends of cantilevers. An algorithm for calculating the strain energy and its release rate in the DCB specimens is realized in the form of a MATLAB code. An experimental study was carried out on DCB specimens of a highly flexible carbon/epoxy laminate. The validity of the nonlinear model developed is demonstrated. The standard methods used to determine GIc are refined for the case of highly flexible specimens.
Energy Technology Data Exchange (ETDEWEB)
Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo (Brazil); Balthazar, José M., E-mail: jmbaltha@gmail.com [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Universidade Estadual Paulista, Faculdade de Engenharia Mec and #x00E (Brazil); Francisco, Cayo Prado Fernandes [Universidade Federal do ABC (UFABC), Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CECS) / Aerospace Engineering Santo André, São Paulo, Brazil and Instituto de Aeronáutica e Espaço, Departamento de (Brazil)
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.
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 (Vϕ) 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.
Institute of Scientific and Technical Information of China (English)
刘灿昌; 李红艳
2011-01-01
提出非线性的分阶最优控制策略,并将其应用于悬臂梁非线性振动的压电减振控制.建立悬臂梁非线性压电减振系统动力学模型,导出减振系统的非线性动力学运动微分方程.将梁振动挠度和压电驱动器的控制电压同时展开为小参数形式,利用摄动法实现非线性压电控制微分方程的线性化.通过空间解耦,得到状态空间方程.设计非线性分阶控制器,对该减振系统进行分阶最优控制.%A non-linear grade optimal control scheme is proposed and used in the piezoelectric vibration reduction control of non-linear cantilever beam. The dynamic model of non-linear vibration reduction beam with piezoelectric damper is built. The non-linear dynamic differential equations of the vibration reduction system are derived. The vibrational deflection and the piezoelectricity driver control voltage of beam are expanded as the small parametric form. The differential equation is linearized into a set of linear equations by means of perturbation. The state space equations are obtained by decoupling in the space coordinates. The vibration reduction system is controlled by the non-linear grade controllers.
Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam
Ruzziconi, Laura
2016-12-05
This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity
Al-Rousan, R. Z.
2015-09-01
The main objective of this study was to assess the effect of the number and schemes of carbon-fiber-reinforced polymer (CFRP) sheets on the capacity of bending moment, the ultimate displacement, the ultimate tensile strain of CFRP, the yielding moment, concrete compression strain, and the energy absorption of RC beams and to provide useful relationships that can be effectively utilized to determine the required number of CFRP sheets for a necessary increase in the flexural strength of the beams without a major loss in their ductility. To accomplish this, various RC beams, identical in their geometric and reinforcement details and having different number and configurations of CFRP sheets, are modeled and analyzed using the ANSYS software and a nonlinear finite-element analysis.
Energy Technology Data Exchange (ETDEWEB)
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.
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.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Mezher, M H; Nady, A; Penny, R; Chong, W Y; Zakaria, R
2015-11-20
This paper details the fabrication process for placing single-layer gold (Au) nanoparticles on a planar substrate, and investigation of the resulting optical properties that can be exploited for nonlinear optics applications. Preparation of Au nanoparticles on the substrate involved electron beam deposition and subsequent thermal dewetting. The obtained thin films of Au had a variation in thicknesses related to the controllable deposition time during the electron beam deposition process. These samples were then subjected to thermal annealing at 600°C to produce a randomly distributed layer of Au nanoparticles. Observation from field-effect scanning electron microscope (FESEM) images indicated the size of Au nanoparticles ranges from ∼13 to ∼48 nm. Details of the optical properties related to peak absorption of localized surface plasmon resonance (LSPR) of the nanoparticle were revealed by use of UV-Vis spectroscopy. The Z-scan technique was used to measure the nonlinear effects on the fabricated Au nanoparticle layers where it strongly relates LSPR and nonlinear optical properties.
Calibration of Cone Beam Rotational X-Ray Image Sequence
Institute of Scientific and Technical Information of China (English)
YUHengyong; MOUXuanqin; CAIYuanlong
2004-01-01
The real X-ray projection does not abide by Lambert-Beer Law, since the X-ray is polychromatic and the imaging chains are nonlinear. Based on the generating process of X-ray images, an equivalent nonlinear transform model is firstly proposed which considers all the nonlinear factors as one nonlinear transform. Then the 3D (three-dimensional) X-ray projection of cone beam is defined. The constraints of Radon transform, named H-L (Helgasson-ludwig) consistency conditions, are expanded to fan-beam. After that an algorithm is developed to calibrate Rotational X-ray image sequence (RXIS). The algorithm uses a set of exponential functions to approximate the nonlinear inverse transform. According to expanded H-L consistency conditions, finally a kind of nonlinear measure for RXIS is defined. Experimental results show that the proposed algorithm can decrease the nonlinear measure to below 0.01.
Directory of Open Access Journals (Sweden)
Ahmad Mamandi
2011-01-01
Full Text Available In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.
Energy Technology Data Exchange (ETDEWEB)
C. L. Bohn (deceased), 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.
Extension of non-linear beam models with deformable cross sections
Sokolov, I.; Krylov, S.; Harari, I.
2015-12-01
Geometrically exact beam theory is extended to allow distortion of the cross section. We present an appropriate set of cross-section basis functions and provide physical insight to the cross-sectional distortion from linear elastostatics. The beam formulation in terms of material (back-rotated) beam internal force resultants and work-conjugate kinematic quantities emerges naturally from the material description of virtual work of constrained finite elasticity. The inclusion of cross-sectional deformation allows straightforward application of three-dimensional constitutive laws in the beam formulation. Beam counterparts of applied loads are expressed in terms of the original three-dimensional data. Special attention is paid to the treatment of the applied stress, keeping in mind applications such as hydrogel actuators under environmental stimuli or devices made of electroactive polymers. Numerical comparisons show the ability of the beam model to reproduce finite elasticity results with good efficiency.
Linear and nonlinear theory of the proton beam transit-time oscillator (TTO)
Walsh, John E.; Mostrom, Michael A.; Clark, Randy M.; Arman, M. Joseph; Campbell, Mark M.
1989-07-01
A theoretical characterization is presented for both the small- and large-amplitude behaviors of the intense beam-driven transit-time oscillator device which encompasses the effects of the beam self-fields and space-charge effects. The theory has been employed in the development of expressions for comparison with particle simulation results. Attention is given to the effect of beam-plasma frequency on gain, saturation growth in the monotron, the effects of space-charge depression on the transit angle, and the dependence of monotron performance on beam energy.
Energy Technology Data Exchange (ETDEWEB)
Gao, Q. D., E-mail: qgao@swip.ac.cn [Southwestern Institute of Physics, Chengdu 610041 (China); Budny, R. V. [Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
2015-03-15
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 (T{sub i,e}) and toroidal velocity (V{sub ϕ}) 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.
Reliability-based design optimization of a nonlinear elastic plastic thin-walled T-section beam
Ba-Abbad, Mazen A.
A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with T-section. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to
Energy Technology Data Exchange (ETDEWEB)
Wang, Qian [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); University of the Chinese Academy of Sciences, Beijing 100039 (China); Li, Bincheng, E-mail: bcli@uestc.ac.cn [Institute of Optics and Electronics, Chinese Academy of Sciences, P. O. Box 350, Shuangliu, Chengdu 610209 (China); School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2015-12-07
In this paper, photocarrier radiometry (PCR) technique with multiple pump beam sizes is employed to determine simultaneously the electronic transport parameters (the carrier lifetime, the carrier diffusion coefficient, and the front surface recombination velocity) of silicon wafers. By employing the multiple pump beam sizes, the influence of instrumental frequency response on the multi-parameter estimation is totally eliminated. A nonlinear PCR model is developed to interpret the PCR signal. Theoretical simulations are performed to investigate the uncertainties of the estimated parameter values by investigating the dependence of a mean square variance on the corresponding transport parameters and compared to that obtained by the conventional frequency-scan method, in which only the frequency dependences of the PCR amplitude and phase are recorded at single pump beam size. Simulation results show that the proposed multiple-pump-beam-size method can improve significantly the accuracy of the determination of the electronic transport parameters. Comparative experiments with a p-type silicon wafer with resistivity 0.1–0.2 Ω·cm are performed, and the electronic transport properties are determined simultaneously. The estimated uncertainties of the carrier lifetime, diffusion coefficient, and front surface recombination velocity are approximately ±10.7%, ±8.6%, and ±35.4% by the proposed multiple-pump-beam-size method, which is much improved than ±15.9%, ±29.1%, and >±50% by the conventional frequency-scan method. The transport parameters determined by the proposed multiple-pump-beam-size PCR method are in good agreement with that obtained by a steady-state PCR imaging technique.
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...
Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams
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
Tilley, Steven; Siewerdsen, Jeffrey H.; Zbijewski, Wojciech; Stayman, J. Webster
2016-03-01
Flat-panel cone-beam CT (FP-CBCT) is a promising imaging modality, partly due to its potential for high spatial resolution reconstructions in relatively compact scanners. Despite this potential, FP-CBCT can face difficulty resolving important fine scale structures (e.g, trabecular details in dedicated extremities scanners and microcalcifications in dedicated CBCT mammography). Model-based methods offer one opportunity to improve high-resolution performance without any hardware changes. Previous work, based on a linearized forward model, demonstrated improved performance when both system blur and spatial correlations characteristics of FP-CBCT systems are modeled. Unfortunately, the linearized model relies on a staged processing approach that complicates tuning parameter selection and can limit the finest achievable spatial resolution. In this work, we present an alternative scheme that leverages a full nonlinear forward model with both system blur and spatially correlated noise. A likelihood-based objective function is derived from this forward model and we derive an iterative optimization algorithm for its solution. The proposed approach is evaluated in simulation studies using a digital extremities phantom and resolution-noise trade-offs are quantitatively evaluated. The correlated nonlinear model outperformed both the uncorrelated nonlinear model and the staged linearized technique with up to a 86% reduction in variance at matched spatial resolution. Additionally, the nonlinear models could achieve finer spatial resolution (correlated: 0.10 mm, uncorrelated: 0.11 mm) than the linear correlated model (0.15 mm), and traditional FDK (0.40 mm). This suggests the proposed nonlinear approach may be an important tool in improving performance for high-resolution clinical applications.
Focal-Plane Imaging of Crossed Beams in Nonlinear Optics Experiments
Bivolaru, Daniel; Herring, G. C.
2007-01-01
An application of focal-plane imaging that can be used as a real time diagnostic of beam crossing in various optical techniques is reported. We discuss two specific versions and demonstrate the capability of maximizing system performance with an example in a combined dual-pump coherent anti-Stokes Raman scattering interferometric Rayleigh scattering experiment (CARS-IRS). We find that this imaging diagnostic significantly reduces beam alignment time and loss of CARS-IRS signals due to inadvertent misalignments.
1992-12-01
Dugundji (12) have developed a theory to predict large deflections of laminated beams. Minguet and Dugundji assume transverse shear strains are constant...nine elements as shown in figure 3.3. 3.2 Cantilevered Composite Beam The next problem considered is one considered by Minguet and Dugundji (12) in...in figure 3.4. Minguet and Dugundji (M&D) formulated an updated Lagrangian displacement scheme based on Euler angles which track the rigid body motion
Sinclair, Werner
2013-02-01
Atypical vascular lesion of the skin is an uncommon usually benign condition, thus far reported almost exclusively from mammary skin after radiotherapy for carcinoma of the breast. Some clinical and histological overlap exists with early angiosarcoma, which can also occur on irradiated skin. The lesions are divided into vascular and lymphatic types, the first representing a higher risk for development of angiosarcoma and the latter being more common. This article reports a rare case of widespread, progressive, vascular-type atypical vascular lesion after repeated whole-body electron beam irradiation administered as treatment for mycosis fungoides.
Antony, Albin; Pramodini, S.; Poornesh, P.; Kityk, I. V.; Fedorchuk, A. O.; Sanjeev, Ganesh
2016-12-01
We present the studies on third-order nonlinear optical properties of Al doped ZnO thin films irradiated with electron beam at different dose rate. Al doped ZnO thin films were deposited on a glass substrate by spray pyrolysis deposition technique. The thin films were irradiated using the 8 MeV electron beam from microtron ranging from 1 kG y to 5 kG y. Nonlinear optical studies were carried out by employing the single beam Z-scan technique to determine the sign and magnitude of absorptive and refractive nonlinearities of the irradiated thin films. Continuous wave He-Ne laser operating at 633 nm was used as source of excitation. The open aperture Z-scan measurements indicated the sample displays reverse saturable absorption (RSA) process. The negative sign of the nonlinear refractive index n2 was noted from the closed aperture Z-scan measurements indicates, the films exhibit self-defocusing property due to thermal nonlinearity. The third-order nonlinear optical susceptibility χ(3) varies from 8.17 × 10-5 esu to 1.39 × 10-3 esu with increase in electron beam irradiation. The present study reveals that the irradiation of electron beam leads to significant changes in the third-order optical nonlinearity. Al doped ZnO displays good optical power handling capability with optical clamping of about ∼5 mW. The irradiation study endorses that the Al doped ZnO under investigation is a promising candidate photonic device applications such as all-optical power limiting.
Energy Technology Data Exchange (ETDEWEB)
Lee, S; Li, Z [University of Florida Proton Therapy Institute, Jacksonville, FL (United States); Jalaj, S; McGaw, C; B K, John; J S, Scolapio; J C, Munoz [Division of Gastoenterology, Department of Medicine, University of Florida, Jacksonville, FL (United States)
2014-06-01
Purpose: This work investigates dose perturbations due to Self-expandable metal and polyester esophageal stents undergoing proton radiotherapy for esophageal cancer. Methods: Five commercially available esophageal stents made of nitinol (Evolution, Wallflex and Ultraflex), stainless steel (Z-Stent) and polyester (Polyflex) were tested. Radiochromic film (GafChromic EBT3 film, Ashland, Covington, KY) wrapped around a stent and a 12cc syringe was irradiated with 2CGE (Cobalt Gray Equivalent) of proton beam in a custom fabricated acrylic phantom. An air-hollow syringe simulates the esophagus. Results: The Z-stent created the largest dose perturbations ranges from -14.5% to 6.1% due to the steel composition. The WallFlex, Evolution and Ultraflex stents produced the dose perturbation ranges of (−9.2%∼8.6%), (−6.8%∼5.7%) and (−6.2%∼6.2%), respectively. The PolyFlex stent contains the radiopaque tungsten markers located top, middle and bottom portions. When the focal cold spots induced by the markers were excluded in the analysis, the dose perturbation range was changed from (−11.6%∼6.4%) to (−0.6%∼5.0%). Conclusion: The magnitude of dose perturbation is related to material of a metallic stent. The non-metallic stent such as PolyFlex shows relatively lower dose perturbation than metallic stents except a radiopaque marker region. Overall Evolution and Ultraflex stent appear to be less dose perturbations. The largest dose perturbations (cold spots) were located at both edges of stents in distal area for the single proton beam irradiation study. The analysis of more than two proton beam which is more typical clinical beam arrangement would be necessary to minimize the doe perturbation effect in proton ratiotherapy.
Katsouleas, Thomas; Sahai, Aakash
2015-11-01
The excitation of a non-linear ion-wake by a train of non-linear electron wake of an electron and a positron beam is modeled and its use for positron acceleration is explored. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton similar to the solution of the cKdV equation. The phases of the oscillating radial electric fields of the slowly-propagating electron wake are asymmetric in time and excite time-averaged inertial ion motion radially. The radial field of the electron compression region sucks-in the ions and the field of space-charge region of the wake expels them, driving a cylindrical ion-soliton structure with on-axis and bubble-edge density-spikes. Once formed, the channel-edge density-spike is driven radially outwards by the thermal pressure of the thermalized wake energy. Its channel-like structure due to the flat-residue left behind by the propagating ion-soliton, is independent of the energy-source driving the non-linear electron wake. We explore the use of the partially-filled channel formed by the cylindrical ion-soliton for a novel regime of positron acceleration. PIC simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration (arXiv:1504.03735). Work supported by the US Department of Energy under DE-SC0010012 and the National Science Foundation under NSF-PHY-0936278.
Institute of Scientific and Technical Information of China (English)
Miha Brojan; Matjaz Cebron; Franc Kosel
2012-01-01
This work studies large deflections of slender,non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed continuous load and a concentrated load at the free end of the beam.The material of the cantilever is assumed to be nonlinearly elastic.Different nonlinear relations between stress and strain in tensile and compressive domain are considered.The accuracy of numerical solutions is evaluated by comparing them with results from previous studies and with a laboratory experiment.
Belova, Elena; Gorelenkov, N. N.; Crocker, N. A.; Lestz, J. B.; Fredrickson, E. D.; Tang, S.
2016-10-01
Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n =4-9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfven wave (KAW) that occurs on the high-field side at the Alfven resonance location. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. This mechanism provides an alternative explanation to the observed reduced heating of the plasma core in the NSTX. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power. This research was supported by the U.S. DOE contract # DE-AC02-09CH11466.
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
Chaotic dynamics of the size-dependent non-linear micro-beam model
Krysko, A. V.; Awrejcewicz, J.; Pavlov, S. P.; Zhigalov, M. V.; Krysko, V. A.
2017-09-01
In this work, a size-dependent model of a Sheremetev-Pelekh-Reddy-Levinson micro-beam is proposed and validated using the couple stress theory, taking into account large deformations. The applied Hamilton's principle yields the governing PDEs and boundary conditions. A comparison of statics and dynamics of beams with and without size-dependent components is carried out. It is shown that the proposed model results in significant, both qualitative and quantitative, changes in the nature of beam deformations, in comparison to the so far employed standard models. A novel scenario of transition from regular to chaotic vibrations of the size-dependent Sheremetev-Pelekh model, following the Pomeau-Manneville route to chaos, is also detected and illustrated, among others.
DEFF Research Database (Denmark)
Christensen, Finn Erland; Hornstrup, Allan; Frederiksen, P. K.;
1995-01-01
The on- and off-axis imaging properties of the first of two SODART flight telescopes have been studied using the expanded beam x-ray facility at the Daresbury synchrotron. From on- axis measurements the encircled power distribution and the point spread function at three energies 6.627 keV, 8.837 ke......V, and 11.046 keV have been measured using a one dimensional position sensitive detector. The data have been used to calculate the half power diameter (HPD) for three different SODART focal plane detectors, the high energy proportional counter (HEPC), the low energy proportional counter (LEPC) and the 19...... element solid state array detector (SIXA). We found that the HPD decreases with increasing energy due to poorer figure error of the outermost mirrors. The HPD falls in the range from 2.3 to 3 arcmin for all detectors. Residual misalignment of the individual quadrants of the telescope was found...
DEFF Research Database (Denmark)
Christensen, Finn Erland; Hornstrup, Allan; Frederiksen, P.;
1994-01-01
The imaging properties of a test model of the SODART telescopes have been studied using an expanded beam X-ray facility at the Daresbury synchrotron. The encircled power and the point spread function at three energies 6.627 keV, 8.837 keV and 11.046 keV have been measured using 1D and 2D position......V the HPD is 2.5 - 3.0 arcmin for all detectors whereas it is somewhat larger at 11.046 keV for HEPC and LEPC but essentially unchanged for SIXA. Finally, the data are used to point to improvements that can be introduced during the manufacture of the flight telescopes....
Energy Technology Data Exchange (ETDEWEB)
Ali Shan, S. [Theoretical Plasma Physics Division, PINSTECH, Nilore, 44000 Islamabad (Pakistan); National Centre For Physics (NCP), Shahdra Valley Road, 44000 Islamabad (Pakistan); Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad (Pakistan); El-Tantawy, S. A.; Moslem, W. M. [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt)
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.
Nonlinear analysis of flexible beams undergoing large rotations Via symbolic computations
Directory of Open Access Journals (Sweden)
Yuan Xiaofeng
2001-01-01
Full Text Available In this paper, a two-stage approach is presented for analyzing flexible beams undergoing large rotations. In the first stage, the symbolic forms of equations of motion and the Jacobian matrix are generated by means of MATLAB and written into a MATLAB script file automatically, where the flexible beams are described by the unified formulation presented in our previous paper. In the second stage, the derived equations of motion are solved by means of implicit numerical methods. Several comparison computations are performed. The two-stage approach proves to be much more efficient than pure numerical one.
Progress on optimization of the nonlinear beam dynamics in the MEIC collider rings
Energy Technology Data Exchange (ETDEWEB)
Nosochkov, Y. M. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Cai, Y. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Sullivan, M. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wang, M-H [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wienands, U. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Morozov, V. S. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Derbenev, Ya. S. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Lin, F. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Pilat, F. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Zhang, Y. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2015-07-13
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 10^{34} cm^{-2}s^{-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.
Progress on Optimization of the Nonlinear Beam Dynamics in the MEIC Collider Rings
Energy Technology Data Exchange (ETDEWEB)
Morozov, Vasiliy S. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Derbenev, Yaroslav S. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Lin, Fanglei [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Pilat, Fulvia [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Zhang, Yuhong [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Cai, Y. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Nosochkov, Y. M. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Sullivan, Michael [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wang, M.-H. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wienands, Uli [SLAC National Accelerator Lab., Menlo Park, CA (United States)
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 10^{34} cm^{-2}s^{-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.
Nonlinear Steady-State Vibration Analysis of a Beam with Breathing Cracks
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.
ALICE EMCal Reconstructable Energy Non-Linearity From Test Beam Monte Carlo
Carter, Thomas Michael
2017-01-01
Calorimeters play many important roles in modern high energy physics detectors, such as event selection, triggering, and precision energy measurements. EMCal, in the case of the ALICE experiment provides triggering on high energy jets, improves jet quenching study measurement bias and jet energy resolution, and improves electron and photon measurements [3]. With the EMCal detector in the ALICE experiment taking on so many important roles, it is important to fully understand, characterize and model its interactions with particles. In 2010 SPS and PS electron test beam measurements were performed on an EMCal mini-module [2]. Alongside this, the test beam setup and geometry was recreated in Geant4 by Nico [1]. Figure 1 shows the reconstructable energy linearity for the SPS test beam data and that obtained from the test beam monte carlo, indicating the amount of energy deposit as hits in the EMCal module. It can be seen that for energies above ∼ 100 GeV there is a signiﬁcant drop in the reconstructableenergym...
Computation of displacements for nonlinear elastic beam models using monotone iterations
Directory of Open Access Journals (Sweden)
Philip Korman
1988-01-01
Full Text Available We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present computations, which suggest efficiency of monotone methods for fourth order boundary value problems.
Energy Technology Data Exchange (ETDEWEB)
Welsch, Dominic Markus
2010-03-10
The High-Energy Storage Ring (HESR) is part of the upcoming Facility for Antiproton and Ion Research (FAIR) which is planned as a major extension to the present facility of the Helmholtzzentrum fuer Schwerionenforschung (GSI) in Darmstadt. The HESR will provide antiprotons in the momentum range from 1.5 to 15 GeV/c for the internal target experiment PANDA. The demanding requirements of PANDA in terms of beam quality and luminosity together with a limited production rate of antiprotons call for a long beam life time and a minimum of beam loss. Therefore, an effective closed orbit correction and a sufficiently large dynamic aperture of the HESR are crucial. With this thesis I present my work on both of these topics. The expected misalignments of beam guiding magnets have been estimated and used to simulate the closed orbit in the HESR. A closed orbit correction scheme has been developed for different ion optical settings of the HESR and numerical simulations have been performed to validate the scheme. The proposed closed orbit correction method which uses the orbit response matrix has been benchmarked at the Cooler Synchrotron COSY of the Forschungszentrum Juelich. A chromaticity correction scheme for the HESR consisting of sextupole magnets has been developed to reduce tune spread and thus to minimize the emittance growth caused by betatron resonances. The chromaticity correction scheme has been optimized through dynamic aperture calculations. The estimated field errors of the HESR dipole and quadrupole magnets have been included in the non-linear beam dynamics studies. Investigations concerning their optimization have been carried out. The ion optical settings of the HESR have been improved using dynamic aperture calculations and the technique of frequency map analysis. The related diffusion coefficient was also used to predict long-term stability based on short-term particle tracking. With a reasonable reduction of the quadrupole magnets field errors and a
Nonlinear analysis and analog simulation of a piezoelectric buckled beam with fractional derivative
Mokem Fokou, I. S.; Buckjohn, C. Nono Dueyou; Siewe Siewe, M.; Tchawoua, C.
2017-08-01
In this article, an analog circuit for implementing fractional-order derivative and a harmonic balance method for a vibration energy harvesting system under pure sinusoidal vibration source is proposed in order to predict the system response. The objective of this paper is to discuss the performance of the system with fractional derivative and nonlinear damping (μb). Bifurcation diagram, phase portrait and power spectral density (PSD) are provided to deeply characterize the dynamics of the system. These results are corroborated by the 0-1 test. The appearance of the chaotic vibrations reduces the instantaneous voltage. The pre-experimental investigation is carried out through appropriate software electronic circuit (Multisim). The corresponding electronic circuit is designed, exhibiting periodic and chaotic behavior, in accord with numerical simulations. The impact of fractional derivative and nonlinear damping is presented with detail on the output voltage and power of the system. The agreement between numerical and analytical results justifies the efficiency of the analytical technique used. In addition, by combining the harmonic excitation with the random force, the stochastic resonance phenomenon occurs and improves the harvested energy. It emerges from these results that the order of fractional derivative μ and nonlinear damping μb play an important role in the response of the system.
An expanded X-ray beam facility (BEaTriX) to test the modular elements of the ATHENA optics
Spiga, D; Bonnini, E; Buffagni, E; Ferrari, C; Pareschi, G; Tagliaferri, G
2015-01-01
Future large X-ray observatories like ATHENA will be equipped with very large optics, obtained by assembling modular optical elements, named X-ray Optical Units (XOU) based on the technology of either Silicon Pore Optics or Slumped Glass Optics. In both cases, the final quality of the modular optic (a 5 arcsec HEW requirement for ATHENA) is determined by the accuracy alignment of the XOUs within the assembly, but also by the angular resolution of the individual XOU. This is affected by the mirror shape accuracy, its surface roughness, and the mutual alignment of the mirrors within the XOU itself. Because of the large number of XOUs to be produced, quality tests need to be routinely done to select the most performing stacked blocks, to be integrated into the final optic. In addition to the usual metrology based on profile and roughness measurements, a direct measurement with a broad, parallel, collimated and uniform X- ray beam would be the most reliable test, without the need of a focal spot reconstruction as...
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
Franchetti, G.
2015-01-01
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 phas...
Nonlinear optical properties of bulk cuprous oxide using single beam Z-scan at 790 nm
Energy Technology Data Exchange (ETDEWEB)
Serna, J.; Rueda, E. [Grupo de Óptica y Fotónica, Instituto de Física, Universidad de Antioquia U de A, Calle 70 No. 52-21, Medellín (Colombia); García, H., E-mail: hgarcia@siue.edu [Department of Physics, Southern Illinois University, Edwardsville, Illinois 60026 (United States)
2014-11-10
The two-photon absorption (TPA) coefficient β 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 β 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 β 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.
A non-linear procedure for the numerical analysis of crack development in beams failing in shear
Directory of Open Access Journals (Sweden)
P. Bernardi
2016-01-01
Full Text Available In this work, a consistent formulation for the representation of concrete behavior before and after cracking has been implemented into a non-linear model for the analysis of reinforced concrete structures, named 2D-PARC. Several researches have indeed pointed out that the adoption of an effective modeling for concrete, combined with an accurate failure criterion, is crucial for the correct prediction of the structural behavior, not only in terms of failure load, but also with reference to a realistic representation of crack initiation and development. This last aspect is particularly relevant at serviceability conditions in order to verify the fulfillment of structural requirements provided by Design Codes, which limit the maximum crack width due to appearance and durability issues. In more details, a constitutive model originally proposed by Ottosen and based on non-linear elasticity has been here incorporated into 2D-PARC in order to improve the numerical efficiency of the adopted algorithm, providing at the same time an accurate prediction of the structural response. The effectiveness of this procedure has been verified against significant experimental results available in the technical literature and relative to reinforced concrete beams without stirrups failing in shear, which represent a problem of great theoretical and practical importance in the field of structural engineering. Numerical results have been compared to experimental evidences not only in terms of global structural response (i.e. applied load vs. midspan deflection, but also in terms of crack pattern evolution and maximum crack widths.
Directory of Open Access Journals (Sweden)
V.V. Lalin
2015-02-01
Full Text Available The problem of verification of different program suites for structural analysis has recently become an important component of the construction science. One of the most extensively used benchmark problem is a classical geometrically nonlinear problem of deflection of the cantilever beam of linear elastic material, under the action of external vertical concentrated load at the free end. In fact, the solution for Kirchhoff’s rod is used as an analytical result. This rod is inextensible and Kirchhoff’s rod theory disregards flexibility of the rod in tension and shear. But in modern program suites Cosserat-Timoshenko rod is often used because Cosserat-Timoshenko rod theory is a geometrically exact theory. It considers not only bending strain but also shear and tensile strain. This means that it is necessary to get a model solution for Cosserat – Timoshenko rod, which can be used for verification of different software suites. This paper presents solutions of the geometrically nonlinear problem obtained by Cosserat – Timoshenko and Kirchhoff’s rod theory with comparison of those results. The findings can be used as a benchmark problem for verification of software suites.
Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system
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.
SOVIET AND POLISH RESEARCH ON THE SELF-TRAPPING OF OPTICAL BEAMS IN NONLINEAR MEDIA.
Physical Review Letters in October 1964, was preceded in the Soviet literature by the works of G. A. Askar’yan of the Lebedev Institute and V. I. Talanov of the Scientific-Research Radiophysics Institute at Gor’kiy State University, which were published in June 1962 and 1964, respectively. Since that time Soviet researchers have contributed some 15 papers on various aspects of the self-focusing of optical beams. Significant research on the self-trapping of optical
Natural Frequencies and Mode Shapes of a Nonlinear, Uniform Cantilevered Beam
2006-09-01
spectrum” [13]. The speaker is shown in Figure 11. 16 Figure 11: Excitation Force 3.1.6 Laser Vibrometer The Polytec Scanning...system. This investigation used the 3-D method. The 3-D laser vibrometer used Polytec software version 8.3 to analyze the data. Once the beam was...measured by the lasers were sent to the Polytec software which applied a Fast Fourier Transform (FFT) to find the frequencies. From the FFT the natural
Directory of Open Access Journals (Sweden)
Ronald C. Davidson
2015-09-01
Full Text Available 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⟨ϕ⟩=-e_{b}g_{0}∂λ_{b}/∂z-e_{b}g_{2}r_{w}^{2}∂^{3}λ_{b}/∂z^{3}, where g_{0} and g_{2} are constant geometric factors, λ_{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 ⟨E_{z}⟩.
Institute of Scientific and Technical Information of China (English)
WANG Jun-Min
2011-01-01
With the aid of Mathematica, three auxiliary equations, i.e.the Riccati equation, the Lenard equation and the Hyperbolic equation, are employed to investigate traveling wave solutions of a cosh-Gaussian laser beam in both Kerr and cubic quintic nonlinear media. As a result, many traveling wave solutions are obtained, including soliton-like solutions, hyperbolic function solutions and trigonometric function solutions.
Second-Order Nonlinear Analysis of Steel Tapered Beams Subjected to Span Loading
Directory of Open Access Journals (Sweden)
Ali Hadidi
2014-03-01
Full Text Available A second-order elastic analysis of tapered steel members with I-shaped sections subjected to span distributed and concentrated loadings is developed. Fixed end forces and moments as well as exact stiffness matrix of tapered Timoshenko-Euler beam are obtained with exact geometrical properties of sections. The simultaneous action of bending moment, shear, and axial force including P−δ effects is also considered in the analysis. A computer code has been developed in MATLAB software using a power series method to solve governing second-order differential equation of equilibrium with variable coefficients for beams with distributed span loading. A generalized matrix condensation technique is then utilized for analysis of beams with concentrated span loadings. The accuracy and efficiency of the results of the proposed method are verified through comparing them to those obtained from other approaches such as finite element methods, which indicates the robustness and time saving of this method even for large scale frames with tapered members.
Indian Academy of Sciences (India)
R K Khanna; R C Chouhan
2003-10-01
A somewhat more general analysis for solving spatial propagation characteristics of intense Gaussian beam is presented and applied to the laser beam propagation in step-index proﬁle as well as parabolic proﬁle dielectric ﬁbers with Kerr non-linearity. Considering self-action due to saturating and non-saturating non-linearity in the refractive index, a general theory has been developed without any kind of power series expansion for the dielectric constant as is usually done in other theories that make use of paraxial approximation. Result of the steady state self-focusing analysis indicates that the Kerr non-linearity acts as a perturbation on the radial inhomogeneity due to ﬁber geometry. Analysis indicates that the paraxial rays and peripheral rays focus at different points, indicating aberration effect. Calculated critical power matches with the experimentally reported result.
Nonlinear ion-acoustic solitary waves in ion-beam plasma
Energy Technology Data Exchange (ETDEWEB)
Das, G.C.; Karmakar, B. (Manipur Univ., Imphal (India). Dept. of Mathematics); Singh, K.I. (Modern Coll., Imphal, Manipur (India))
1989-01-01
The dynamics of solitary waves in an ion-beam plasma having multiple electron temperatures are investigated. The investigation is based on the derivation of the Korteweg-de Vries (Kd V) equation by applying the reductive perturbation technique to the basic equations governing the plasma dynamics. Fascinating results are derived first for a plasma with a small percentage of non-isothermality, then the soliton's behaviour is obtained for an isothermal as well as for a non-isothermal plasma, and finally a general comparison is made and conclusions given. (author).
Hybrid interferometer with nonlinear four-wave mixing process and linear beam splitter.
Liu, Shengshuai; Jing, Jietai
2017-07-10
Optical interferometer has played an important role in optics. Up to now, many kinds of interferometers have been realized and found their applications. In this letter, we experimentally construct an interferometer by using parametric amplifier as a wave splitter and beam splitter as a wave combiner. We make measurements of interference fringes and explore the relationships between the interference visibility of the interferometer and various system parameters, such as the gain of the parametric amplifier, the one-photon detuning and the temperature of the Rb-85 vapor cell.
Quasi-periodic solutions for d-dimensional beam equation with derivative nonlinear perturbation
Energy Technology Data Exchange (ETDEWEB)
Mi, Lufang, E-mail: milufang@126.com [Department of Mathematics, Binzhou University, Shandong 256600 (China); Cong, Hongzi, E-mail: conghongzi@dlut.edu.cn [School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024 (China)
2015-07-15
In this paper, we consider the d-dimensional beam equation with convolution potential under periodic boundary conditions. We will apply the Kolmogorov-Arnold-Moser theorem in Eliasson and Kuksin [Ann. Math. 172, 371-435 (2010)] into this system and obtain that for sufficiently small ε, there is a large subset S′ of S such that for all s ∈ S′, the solution u of the unperturbed system persists as a time-quasi-periodic solution which has all Lyapunov exponents equal to zero and whose linearized equation is reducible to constant coefficients.
Transverse beam dynamics in non-linear Fixed Field Alternating Gradient accelerators
Energy Technology Data Exchange (ETDEWEB)
Haj, Tahar M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2016-03-02
In this paper, we present some aspects of the transverse beam dynamics in Fixed Field Ring Accelerators (FFRA): we start from the basic principles in order to derive the linearized transverse particle equations of motion for FFRA, essentially FFAGs and cyclotrons are considered here. This is a simple extension of a previous work valid for linear lattices that we generalized by including the bending terms to ensure its correctness for FFAG lattice. The space charge term (contribution of the internal coulombian forces of the beam) is contained as well, although it is not discussed here. The emphasis is on the scaling FFAG type: a collaboration work is undertaken in view of better understanding the properties of the 150 MeV scaling FFAG at KURRI in Japan, and progress towards high intensity operation. Some results of the benchmarking work between different codes are presented. Analysis of certain type of field imperfections revealed some interesting features about this machine that explain some of the experimental results and generalize the concept of a scaling FFAG to a non-scaling one for which the tune variations obey a well-defined law.
Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation
Hazim, Hamad
2009-01-01
Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the...
Kaczmarek, Malgosia; D'Alessandro, Giampaolo; Proctor, Matthew B.
2016-09-01
The manipulation and processing of light beams can be efficiently accomplished through devices based on soft matter placed in a hybrid "symbiosis" with other organic or inorganic, photoresponsive materials. The performance of such smart modulating systems often relies on a subtle balance between individual properties of each component, together with the varying interaction between organic and inorganic elements. Some promising demonstrations in the visible as well as in the THz regimes include liquid crystals integrated with plasmonic or ferroelectric nanoparticles, photoconductive or photosensitive polymers as well as metamaterials. They offer adaptive, flexible and tailor-made solutions for applications in displays and optoelectronics, switching, steering and modulating electromagnetic waves. Hybrid configurations that include multiple photoresponsive layers, sandwiched with liquid crystals, led to stronger modulation and steering of light beams in the visible. Such effects can also be observed in the other regions of spectrum, as inorganic nanoparticles dispersed in liquid crystals modify the magnitude of the material refractive indices measured in THz. The development of such hybrid materials has to be accompanied by comprehensive characterisation of their uniformity, stability and optical quality across the whole surface of the device, capable of determining their optical, electrical and physical parameters.
Energy Technology Data Exchange (ETDEWEB)
Tsysar, S. A., E-mail: sergey@acs366.phys.msu.ru; Nikolaeva, A. V.; Khokhlova, V. A.; Yuldashev, P. V. [Physics Faculty, Moscow State University, Leninskie Gory, Moscow 119991 (Russian Federation); Svet, V. D. [Andreyev Acoustics Institute, 4, Shvernik Street, Moscow 117036 (Russian Federation); Sapozhnikov, O. A. [Physics Faculty, Moscow State University, Leninskie Gory, Moscow 119991 (Russian Federation); Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, WA 98105 (United States)
2015-10-28
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.
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.
Davidson, Ronald C
2015-01-01
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 $r_{w}$. The average axial electric field is expressed as $\\langle E_{z}\\rangle=-(\\partial/\\partial z)\\langle\\phi\\rangle=-e_{b}g_{0}\\partial\\lambda_{b}/\\partial z-e_{b}g_{2}r_{w}^{2}\\partial^{3}\\lambda_{b}/\\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $\\lambda_{b}(z,t)=\\int dp_{z}F_{b}(z,p_{z},t)$ 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 (solitons) 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: (a) the nonlinear waterbag distribution, w...
Chang, You Min; Lee, Junsu; Lee, Ju Han
2010-09-13
Proposed herein is an alternative photonic scheme for the generation of a doublet UWB pulse, which is based on the nonlinear polarization rotation of an elliptically polarized probe beam. The proposed scheme is a modified optical-fiber Kerr shutter that uses an elliptically polarized probe beam together with a linearly polarized control beam. Through theoretical analysis, it was shown that the optical-fiber-based Kerr shutter is capable of producing an ideal transfer function for the successful conversion of input Gaussian pulses into doublet pulses under special elliptical polarization states of the probe beam. An experimental verification was subsequently carried out to verify the working principle. Finally, the system performance of the generated UWB doublet pulses was assessed by propagating them over a 25-km-long standard single-mode fiber link, followed by wireless transmission. Error-free transmission was successfully achieved.
Joglekar, D. M.; Mitra, Mira
2017-02-01
The nonlinear interaction of a dual frequency flexural wave with a breathing crack generates a peculiar frequency mixing phenomena, which is manifested in form of the side bands or peaks at combinations frequencies in frequency spectrum of the response. Although these peaks have been proven useful in ascertaining the presence of crack, they barely carry any information about the crack location. In this regards, the present article analyzes the time domain representation of the response obtained by employing a wavelet spectral finite element method. The study reveals that the combination tones generated at the crack location travel with dissimilar speeds along the waveguide, owing to its dispersive nature. The separation between the lobes corresponding to these combination tones therefore, depends on the distance that they have travelled. This observation is then used to formulate a method to predict the crack location with respect to the sensor. A brief parametric study shows marginal errors in predicting the crack location, which ascertains the validity of the method. This article also studies the frequency spectrum of the response. The peaks at combination tones are quantified in terms of a modulate parameter which depends on the severity of the crack. The inferences drawn from the time and the frequency domain study can be instrumental in designing a robust strategy for detecting location and severity of the crack.
Saletes, Izella; Gilles, Bruno; Bera, Jean-Christophe
2011-01-01
Enhancing cavitation activity with minimal acoustic intensities could be interesting in a variety of therapeutic applications where mechanical effects of cavitation are needed with minimal heating of surrounding tissues. The present work focuses on the relative efficiency of a signal combining two neighbouring frequencies and a one-frequency signal for initiating ultrasound inertial cavitation. Experiments were carried out in a water tank, using a 550kHz piezoelectric composite spherical transducer focused on targets with 46μm roughness. The acoustic signal scattered, either by the target or by the cavitation bubbles, is filtered using a spectral and cepstral-like method to obtain an inertial cavitation activity measurement. The ultrasound excitations consist of 1.8ms single bursts of single frequency f(0)=550kHz excitation, in the monofrequency case, and of dual frequency f(1)=535kHz and f(2)=565kHz excitation, in the bifrequency case. It is shown that depending on the value of the monofrequency cavitation threshold intensity the bifrequency excitation can increase or reduce the cavitation threshold. The analysis of the thresholds indicates that the mechanisms involved are nonlinear. The progress of the cavitation activity beyond the cavitation threshold is also studied. The slope of the cavitation activity considered as a function of the acoustic intensity is always steeper in the case of the bifrequency excitation. This means that the delimitation of the region where cavitation occurs should be cleaner than with a classical monofrequency excitation.
Silva, Clodoaldo J.; Daqaq, Mohammed F.
2017-02-01
Despite the shear amount of research studies on nonlinear flexural dynamics of cantilever beams, very few efforts address the practical geometry involving a constant thickness and linearly-varying width. This stems from the nature of the associated linear eigenvalue problem which cannot be easily solved in closed form. In this paper, we present a closed-form solution to this particular linear eigenvalue problem in the form of a general Meijer-G differential equation for which a solution is readily available in the shape of the Meijer-G functions. Using this approach, the exact linear modal frequencies and shapes are obtained and used in the discretization of the nonlinear partial-differential equation describing the dynamics of the system. The discretized system of ordinary-differential equations is then solved using the method of multiple scales to obtain an approximate analytical solution describing the primary resonance behavior of a given vibration mode. An analytical expression for the modal effective nonlinearity is obtained and used to analyze the influence of the beam's tapering on the nonlinear primary resonance behavior of the response (softening/hardening). Results are then compared to a finite element (FE) solution of the linear eigenvalue problem in which the modal shapes obtained using the FE method are fit into a set of orthogonal polynomial functions and used to discretize the nonlinear problem. It is shown that, while the modal frequencies obtained using the FE method approximate those obtained analytically with negligible error (less than 1%), there is a substantial error in the resulting estimates of the modal effective nonlinearity. This indicates that, even negligible errors in the approximate solution of the linear problem, can propagate to become significant when analyzing the nonlinear problem further reinforcing the importance of the exact solution.
Energy Technology Data Exchange (ETDEWEB)
Kaminski, Adam
2017-08-22
A method and apparatus to generate harmonically related laser wavelengths includes a pair of lenses at opposing faces of a non-linear optical material. The lenses are configured to promote incoming and outgoing beams to be normal to each outer lens surface over a range of acceptance angles of the incoming laser beam. This reduces reflection loss for higher efficiency operation. Additionally, the lenses allow a wider range of wavelengths for lasers for more universal application. Examples of the lenses include plano-cylindrical and plano-spherical form factors.
Zheng, Ziyi; Sun, Mingshan; Pavkovich, John; Star-Lack, Josh
2011-03-01
A challenge in using on-board cone beam computed tomography (CBCT) to image lung tumor motion prior to radiation therapy treatment is acquiring and reconstructing high quality 4D images in a sufficiently short time for practical use. For the 1 minute rotation times typical of Linacs, severe view aliasing artifacts, including streaks, are created if a conventional phase-correlated FDK reconstruction is performed. The McKinnon-Bates (MKB) algorithm provides an efficient means of reducing streaks from static tissue but can suffer from low SNR and other artifacts due to data truncation and noise. We have added truncation correction and bilateral nonlinear filtering to the MKB algorithm to reduce streaking and improve image quality. The modified MKB algorithm was implemented on a graphical processing unit (GPU) to maximize efficiency. Results show that a nearly 4x improvement in SNR is obtained compared to the conventional FDK phase-correlated reconstruction and that high quality 4D images with 0.4 second temporal resolution and 1 mm3 isotropic spatial resolution can be reconstructed in less than 20 seconds after data acquisition completes.
Fiber Optic Expanded Beam Connector.
1982-11-01
Impervious to Repetitive Mating * Sand Proof . Low Insertion Loss (ɚ dB) SDust Proof . Reasonably Priced dust which may damage the optical surface of...exchange methods are used. The first uses a molten salt bath. Here the salt, KNO3 , is maintained at approximately 500C which is near the softening (R)j
Rasouli, Saifollah; Ghasemi, H; Tavassoly, M T; Khalesifard, H R
2011-06-01
In this paper, the application of "parallel" moiré deflectometry in measuring the nonlinear refractive index of materials is reported. In "parallel" moiré deflectometry the grating vectors are parallel, and the resulting moiré fringes are also parallel to the grating lines. Compared to "rotational" moiré deflectometry and the Z-scan technique, which cannot easily determine the moiré fringe's angle of rotation and is sensitive to power fluctuations, respectively, "parallel" moiré deflectometry is more reliable, which allows one to measure the radius of curvature of the light beam by measuring the moiré fringe spacing. The nonlinear refractive index of the sample, including the sense of the change, is obtained from the moiré fringe spacing curve. The method is applied for measuring the nonlinear refractive index of ferrofluids.
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.
Institute of Scientific and Technical Information of China (English)
盛冬发; 张燕; 程昌钧
2004-01-01
Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.
Indian Academy of Sciences (India)
Ibrahim Eren
2008-02-01
In this study, large deﬂection of cantilever beams of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. In calculations, both material and geometrical non-linearity have been considered. Horizontal and vertical deﬂections magnitudes were calculated throughout Euler–Bernoulli curvature-moment relationship assuming different arc lengths. Vertical deﬂections were calculated by using Runge–Kutta method. More simple and easily understandable results have been obtained compared to the previous studies about the issue and compatible values have been obtained for most of the compared values.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Ma, Nana; Liu, Chunguang; Qiu, Yongqing; Sun, Shiling; Su, Zhongmin
2012-01-15
The second-order nonlinear optical (NLO) properties of the Cp*Co(C(2)H(5))(2)C(2)B(4)H(3)-expanded (metallo)porphyrins (Cp* = C(5)Me(5)) have been investigated by using ab inito RHF and density functional theory (DFT) methods. The investigation shows that the compound with expand porphyrin possesses remarkable large molecular hyperpolarizability β(tot) value, ~414.1 × 10(-30) esu (at LC-ωPBE level), and might be an excellent second-order NLO material. From the character of charge transfer (CT) transition, it indicates that the -Cp*Co(C(2)H(5))(2)C(2)B(4)H(3) acts as an electron donor in this kind of systems. As a result of the redox behavior on expanded (metallo)porphyrin, the redox switching character of the NLO responses for the systems 2a-4a has also been studied. The results show that the β(tot) values of reduced forms are larger than that of neutral ones. Furthermore, the time-dependent DFT calculation illustrates that reduced forms have a significant difference on the CT patterns versus neutral ones. The present investigation provides insight into the comparison with DFT results on estimating first hyperpolarizability and the NLO properties of the series of push-pull compounds. Copyright © 2011 Wiley Periodicals, Inc.
Jonker, J.B.; Meijaard, J.P.
2013-01-01
A beam finite element formulation for large deflection problems in the analysis of flexible multibody systems has been proposed. In this formulation, a set of independent discrete deformation modes are defined for each element which are related to conventional small deflection beam theory in a co-ro
Hramov, A E; Koronovskii, A A; Filatova, A E; 10.1063/1.4765062
2013-01-01
The report is devoted to the results of the numerical study of the virtual cathode formation conditions in the relativistic electron beam 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.
Nonlinear Deformation Analysis of Saturated Poroelastic Timoshenko Beam%饱和多孔弹性Timoshenko梁的非线性变形分析
Institute of Scientific and Technical Information of China (English)
宋少沪; 卢欣; 杨骁
2012-01-01
基于微观不可压饱和多孔介质理论和固相骨架有限变形假定,在孔隙流体仅沿梁轴向扩散的限定下,建立了饱和多孔弹性Timoshenko梁非线性弯曲变形的数学模型.在此基础上,利用Galerkin截断法,研究了两端可渗透简支饱和多孔Timoshenko梁在突加横向载荷作用下的拟静态弯曲,给出了饱和多孔弹性Timoshenko梁弯曲时固相挠度、弯矩和孔隙流体压力等效力偶等随时间的响应.比较了饱和多孔 Timoshenko梁和Euler-Bernoulli梁的非线性弯曲,揭示了他们间的差异,指出Timoshenko梁的挠度始终大于Euler-Bernoulli梁的挠度.但不同于Euler-Bernoulli梁,由于剪切变形产生的附加挠度,当载荷突加于梁时,Timoshenko梁挠度由零突增为非零,且随着时间的增加,其挠度逐渐增大至稳态值.同时,由于孔隙流体压力等效力偶逐渐减小至零,梁骨架逐步承担全部的外载荷.%Based on the theory of microscopic incompressible saturated porous media and the hypothesis of finite deformation solid skeleton, a mathematical model for nonlinear bending of saturated poroelastic Timoshenko beams was presented under constraint of diffusion of the pore fluid only existing in the axial direction of beams. Then, quasi-static bending of a simply-supported saturated poroelastic Timoshenko beam with two ends permeable, subjected to a step constant transverse load, was investigated with the Galerkin truncation method. The responses of deflections, bending moments of the beam skeleton and the equivalent couples of the pore fluid pressure with respect to the time were shown in figures. The results of the nonlinear bending of the saturated poroelastic Timoshenko beam were compared with those of the saturated poroelastic Euler-Bernoulli beam, and the differences between them were revealed. It was shown that the deflection of the saturated poroelastic Timoshenko beam is larger than that of the saturated poroelastic Euler
Energy Technology Data Exchange (ETDEWEB)
Carey, S.W.
1976-01-01
Arguments in favor of an expanding earth are presented. The author believes that the theory of plate tectonics is a classic error in the history of geology. The case for the expanding earth is organized in the following way: introductory review - face of the earth, development of expanding earth concept, necessity for expansion, the subduction myth, and definitions; some principles - scale of tectonic phenomena, non-uniformitarianism, tectonic profile, paleomagnetism, asymmetry of the earth, rotation of the earth, and modes of crustal extension; regional studies - western North America, Central America, South-East Asia, and the rift oceans; tests and cause of expansion. 824 references, 197 figures, 11 tables. (RWR)
Do, K. D.
2017-02-01
Equations of motion of extensible and shearable slender beams with large translational and rotational motions under external loads in three-dimensional space are first derived in a vector form. Boundary feedback controllers are then designed to ensure that the beams are practically K∞-exponentially stable at the equilibrium. The control design, well-posedness, and stability analysis are based on two Lyapunov-type theorems developed for a class of evolution systems in Hilbert space. Numerical simulations on a slender beam immersed in sea water are included to illustrate the effectiveness of the proposed control design.
Laser molecular-beam epitaxy and second-order optical nonlinearity of BaTiO3/SrTiO3 superlattices
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A series of c-axis oriented BaTiO3/SrTiO3 superlattices with the atomic-scale precision were epitaxially grown on single-crystal SrTiO3 (100) substrates using laser molecular-beam epitaxy (LMBE). A periodic modulation of the intensity of reflection high-energy electron diffraction (RHEED) in BaTiO3 and SrTiO3 layers was observed and attributed to the lattice-misfit-induced periodic variation of the terrace density in film surface. The relationship between the second-order nonlinear optical susceptibilities and the superlattice structure was systematically studied. The experimental and theoretical fitting results indicate that the second-order nonlinear optical susceptibilities of BaTiO3/SrTiO3 superlattices were greatly enhanced with the maximum value being more than one order of magnitude larger than that of bulk BaTiO3 crystal. The mechanism of the enhancement of the second-order optical nonlinearity was discussed by taking into account the stress-induced lattice distortion and polarization enhancement.
非线性诱导的功率控制高斯光束变换效应%Power-Controlled Transformation of Gaussian Beams Induced by Nonlinearity
Institute of Scientific and Technical Information of China (English)
陆大全
2013-01-01
研究了强非局域非线性介质中功率控制的高斯光束变换效应.通过自由传输与强非局域非线性传输的关系,得到了强非局域非线性介质出射端的场分布,并进一步得到了出射后高斯光束的解析表达式.随着功率的增加,出射后的光束束腰在出射面左右交替变化,束腰宽度也振荡变化.选取适当的功率区间,可通过功率调节对高斯光束进行连续可调的变换.%The power-controlled transformation of Gaussian beams in strongly nonlocal nonlinear media is investigated.Based on the relation between the solution for the free propagation and that for the strongly nonlocal nonlinear propagation,the field at the output plane is obtained,and then the analytical solution for the output Gaussian beam is obtained.With the increase of the input power,the waist is located alternatively at the left-and right-hand side of the output plane; and the waist width varies oscillatorily.Therefore,one can make a continuously steerable transformation on the Gaussian beam if appropriate input power range is chosen.
Comment on "Nonlinear refraction measurements of materials using the moiré deflectometry"
Rashidian Vaziri, M. R.
2015-12-01
In an influential paper Jamshidi-Ghaleh and Mansour [1] (Opt. Commun. 234 (2004) 419), have reported on a new method for measuring the nonlinear refractive index of materials using the rotational moiré deflectometry technique. In the cited work, the authors apply the ray matrix theory for finding the beam deflection angle on the plane of the first grating in the used geometry. To this end, using the parabolic approximation, the exponential term in the beam irradiance is expanded and retaining the first two resultant terms, the nonlinear sample is treated as a thin lens with a position dependent focal length. In this comment, the effective focal length of the nonlinear sample has been rederived in detail using the Gaussian beam theory and it is shown that it must contain a correction factor. The relative error introduced by ignoring this factor can be as large as 73.5-84.4% in determining the nonlinear refractive index of thin samples.
Energy Technology Data Exchange (ETDEWEB)
Saberian, E. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of); Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur (Iran, Islamic Republic of); Esfandyari-Kalejahi, A.; Rastkar-Ebrahimzadeh, A.; Afsari-Ghazi, M. [Department of Physics, Faculty of Sciences, Azarbaijan Shahid Madani University, 53714-161 Tabriz (Iran, Islamic Republic of)
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.
NONLINEAR FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE BEAMS IN FIRE%火灾下钢筋混凝土梁非线性有限元分析
Institute of Scientific and Technical Information of China (English)
廖艳芬; 漆雅庆; 马晓茜
2011-01-01
Through numerical simulation of the whole process of heat transfer and deformation on three different conditions groups of reinfored concrete beams,it is analysed the non-linear changing process of the temperature distribution and structural deformation of reinfored concrete beams in fire.Based on thermal characteristics and the temperature-strain-stress constitutive characteristics of reinforced concrete beams it is analysied the influences of the evolutionary processes of the reinfored concrete beams temperature distribution in fire,as well as reinforcement ratio,initial load and heating time on the fire resistance capacity of reinfored concrete beams.Results show that the overall instability of the beams is caused by the reduction of material strength,weight and the initial load,as well as the internal stress because of the uneven heating in fire.The influences of initial load on the residual bearing capacity is little,but increase the number of rebars can effectively improve the fire resistance capacity of reinforced concrete beams.%为分析钢筋混凝土梁在火灾过程中的温度分布、结构变形非线性变化过程,在三组不同条件下对火灾后钢筋混凝土梁构件内部传热及变形过程进行全过程仿真。基于钢筋混凝土热工特性、温度-应变-应力本构特性,分析钢筋混凝土梁在受火时的温度分布演化过程,以及配筋率、初始载荷和受火时间等参数对钢筋混凝土梁防火承载力的影响。结果表明：火灾中材料强度的降低,自重和初始载荷以及不均匀升温引起的内部应力共同作用引起了构件的整体失稳。初始载荷对梁剩余承载力的影响不大,提高混凝土中钢筋数量能有效地提高钢筋混凝土梁的防火承载力。
Linearizing Intra-Train Beam-Beam Deflection Feedback
Energy Technology Data Exchange (ETDEWEB)
Smith, S.R.; /SLAC
2006-02-22
Beam-beam deflection feedback acting within the crossing time of a single bunch train may be needed to keep linear collider beams colliding at high luminosity. In a short-pulse machine such as the Next Linear Collider (NLC) this feedback must converge quickly to be useful. The non-linear nature of beam-beam deflection vs. beam-beam offset in these machines precludes obtaining both rapid convergence and a stable steady-state lock to beam offsets with a linear feedback algorithm. We show that a simply realizable programmable non-linear amplifier in the feedback loop can linearize the feedback loop, approximately compensating the beam-beam deflection non-linearity. Performance of a prototype non-linear amplifier is shown. Improvement of convergence and stability of the beam-beam feedback loop is simulated.
2010-10-01
millimeter wave interferometer for remote vibration sensing, M. Smith, J. Scales, M. Weiss, B. Zadler, in press, Journal of Applied Physics List of...PIERS). Enhancing the nonlinear conversion in ultrasonic parametric arrays, to be submitted to Journal of Applied Physics . (d) Manuscripts Number of
DEFF Research Database (Denmark)
Lundgaard Andersen, Linda; Soldz, Stephen
2012-01-01
A major theme in recent psychoanalytic thinking concerns the use of therapist subjectivity, especially “countertransference,” in understanding patients. This thinking converges with and expands developments in qualitative research regarding the use of researcher subjectivity as a tool to understa...
Self-expanding/shrinking structures by 4D printing
Bodaghi, M.; Damanpack, A. R.; Liao, W. H.
2016-10-01
The aim of this paper is to create adaptive structures capable of self-expanding and self-shrinking by means of four-dimensional printing technology. An actuator unit is designed and fabricated directly by printing fibers of shape memory polymers (SMPs) in flexible beams with different arrangements. Experiments are conducted to determine thermo-mechanical material properties of the fabricated part revealing that the printing process introduced a strong anisotropy into the printed parts. The feasibility of the actuator unit with self-expanding and self-shrinking features is demonstrated experimentally. A phenomenological constitutive model together with analytical closed-form solutions are developed to replicate thermo-mechanical behaviors of SMPs. Governing equations of equilibrium are developed for printed structures based on the non-linear Green-Lagrange strain tensor and solved implementing a finite element method along with an iterative incremental Newton-Raphson scheme. The material-structural model is then applied to digitally design and print SMP adaptive lattices in planar and tubular shapes comprising a periodic arrangement of SMP actuator units that expand and then recover their original shape automatically. Numerical and experimental results reveal that the proposed planar lattice as meta-materials can be employed for plane actuators with self-expanding/shrinking features or as structural switches providing two different dynamic characteristics. It is also shown that the proposed tubular lattice with a self-expanding/shrinking mechanism can serve as tubular stents and grippers for bio-medical or piping applications.
Institute of Scientific and Technical Information of China (English)
姚明辉; 李印波; 张伟
2015-01-01
为了解决双稳态压电悬臂梁输出电压小等问题,引入了上吸引下排斥纵向辅助磁力,通过实验研究了辅助磁力对于双稳态压电悬臂梁复杂非线性动力学行为的影响. 实验所用的材料为上下对称的层合梁,压电层的材料为极化后的PVDF,基层的材料为黄铜. 对压电悬臂梁进行简谐激励,通过电压和位移的正向扫频和逆向扫频研究系统的跳跃现象,研究辅助磁力对于系统动力学行为的影响,分析纵向辅助磁力对系统由倍周期分叉进入混沌运动的影响. 实验结果表明:当辅助磁铁与主磁铁之间的距离较大时,该双稳态系统表现出明显的硬弹簧特性;当辅助磁铁与主磁铁之间的距离较小时,该双稳态系统表现出明显的软弹簧特性;当辅助磁铁与主磁铁之间的距离由小变大时,系统表现出复杂化的非线性行为.%This paper introduced the auxiliary magnetic force based on the bistable piezoelectric cantilever beam in order to improve the voltage output of the bistable piezoelectric cantilever beam. The influence of the auxiliary magnetic force on the complex nonlinear dynamic responses of the bistable piezoelectric cantilever beam was studied. The experiment structure was a symmetric laminated beam. The material of the piezoelectric layer was PVDF, and the material of the basic layer was brass. The excitation of the piezoelectric cantilever beam was the harmonic excitation. The jump phenomenon was studied by the forward sweep frequency and the reverse sweep frequency of the voltage and displacement. The effect of longitudinal auxiliary magnetic force on the chaotic motion of the system was researched. Experimental results showed that when the distance between the auxiliary magnet and the primary magnet is large, the bistable system exhibits obvious hard spring characteristic. When the distance between the auxiliary magnet and the primary magnet is small, the bistable system exhibits
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Energy Technology Data Exchange (ETDEWEB)
Afeyan, Bedros [Polymath Research Inc., Pleasanton, CA (United States); Hueller, Stefan [Centre de Physique Theorique de l' Ecole Polytechnique (France); Montgomery, David S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Hammer, James H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Meezan, Nathan B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Heebner, John E. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-10-24
The various implementations of the STUD pulse program (spike trains of uneven duration and delay) for LPI (laser-plasma instability) control were studied in depth, and novel regimes were found. How to generate STUD pulses with large time-bandwidth products, how to measure their optical scattering signatures, and how to experimentally demonstrate their usefulness were explored. Theoretical and numerical studies were conducted on Stimulated Brillouin Scattering (SBS) and Crossed Beam Energy Transfer (CBET) including statistical models. We established how LPI can be tamed and gain democratized in space and time. Implementing STUD pulses on NIF was also studied. Future high rep rate lasers and fast diagnostics will aid in the adoption of the whole STUD pulse program for LPI control in High Energy Density Plasmas (HEDP).
Second-order nonlinear optical properties of Ge-Ga-Ag-S glass irradiated by electron beam
Institute of Scientific and Technical Information of China (English)
TAO Hai-zheng; DONG Guo-ping; XIAO Hai-yan; LIN Chang-gui; ZHAO Xiu-jian
2006-01-01
Ge-Ga-Ag-S chalcogenide glasses with the composition Ge30Ga3Ag4S63 were obtained by the conventional melt-quenching method. According to the visible-infrared and infrared spectra,Ge30Ga3Ag4S63 chalcogenide glass possesses wide transmittance window from 510 nm in the visible region up to 11.5 ìm in the infrared region. And the present glass has better glass-forming ability (the difference between glass transition temperature and the peak temperature of crystallization is larger than 100 ℃). Utilizing maker-fringe technique,a prominent second-harmonic generation was observed in Ge30Ga3Ag4S63 chalcogenide glass after irradiated by an electron beam (Accelerating voltage: 25 kV:Irradiating current: 15 nA:Irradiating time: 10 min). And the mechanism of second-harmonic generation in the Ge-Ga-Ag-S system glasses was discussed.
Chortis, Dimitris I
2013-01-01
This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...
Existence Theorems of Positive Solution to a Nonlinear Cantilever Beam Equation%非线性悬臂梁方程的正解存在定理
Institute of Scientific and Technical Information of China (English)
姚庆六
2012-01-01
The positive solution is studied for the nonlinear cantilever beam equation u(4)t)=f(t,u(t),u'{t)), 0≤t<1, u(0) = u'(0) = u"(l) = u"'(1) = 0, where the nonlinear term f(t,u,v) may be singular at t = 0, t = 1. By making use of Krasnosel'skii fixed point theorem in degree theory and Lebesgue dominated convergence theorem and Fatou lemma in real variable, two new existence theorems of positive solution are proved when there are growth limit functions lim f(t,u,v)/(u + v), lim f(t,u,v)/(u + v). U+v→ + 0 U+V→ + ∞%研究了非线性悬臂梁方程u(4)(t)=f(t,u(t),u′(t)), 0＜t＜1, u(0)=u′(0)=u″(1)=u′′′(1)=0的正解,其中非线性项f(t,u,v)可以在t=0,t=1处奇异.在增长极限函数lim u+v→+o f(t,u,v)/(u+v), lim u+v-→∞f(t,u,v)/(u+v) 存在的情况下利用度数理论中的Krasnosel'skii不动点定理、实变函数中的Lebesgue控制收敛定理和Fatou引理证明了两个新的正解存在定理.
NON-LINEAR FREE VIBRATION OF FINITE-LENGTH BEAMS ON THE WINKLER FOUNDATION%Winkler地基上有限长梁非线性自由振动
Institute of Scientific and Technical Information of China (English)
马建军; 刘齐建; 王连华; 赵跃宇
2012-01-01
基于经典Winkler地基模型及Euler—Bernoulli梁理论，考虑梁的几何非线性效应，运用Newton第二定律建立了弹性地基上有限长梁的非线性运动方程。采用Galerkin方法对运动方程进行一阶模态截断，进而利用多尺度法求得了该系统自由振动的一阶近似解。揭示了两端简支梁的非线性自由振动特性，分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响。并通过该系统的位移时程曲线，分析了阻尼对弹性地基上梁运动特性的影响。%The non-linear free vibration of a finite-length beam on the elastic foundation is investigated. Based on the Winkler foundation model and Euler-Bernoulli beam theory, the nonlinear motion equation of the finite-length beam on an elastic foundation with geometric nonlinearity is deduced based on the Newton＇s Second Law. The first-order mode truncation of the vibration function is obtained using the Galerkin method. The approximate solution of the free vibration of the finite-length beam is derived utilizing the multi-scale method to illustrate the behaviour of the non-linear free vibration. The effects of the slenderness ratio of beam, the modulus of elastic system and the stiffness of foundation on the natural frequency of the hinged-hinged beam on the Winkler foundation are analyzed. The influence of damping of the soil-beam system on the motion of the beam is also discussed.
Empirical model for controlling beam-beam effects in ISABELLE
Energy Technology Data Exchange (ETDEWEB)
Parzen, G
1980-01-01
The beam-beam interaction may limit the beam intensity in ISABELLE. Although considerable progress has been made in understanding the beam-beam interaction, there appears to be no reliable method at present for computing the effects of the beam-beam interaction. The steps taken at ISABELLE to limit beam-beam effects are based largely on the experience accumulated at the ISR. At the ISR, the beam-beam effects do not appear to be large, and the beam intensity at the ISR does not appear to be limited by beam-beam effects. The beam-beam effects may be much stronger in ISABELLE because of factors like higher intensity and stronger non-linearities.
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.
1999-01-01
We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...
RESEARCH AND DEVELOPMENT OF THREE NONLINEAR BEAM-COLUMN ELEMENTS%三种非线性梁柱单元的研究及单元开发
Institute of Scientific and Technical Information of China (English)
陈学伟; 韩小雷; 孙思为
2011-01-01
Since the elastoplastic damages occur in concrete structures and components in plastic stage under a severe earthquake, precise prediction of nonlinear behavior of structures in the earthquake is important to assess the seismic safety of the structures. A structural elastoplastic analysis program MEASP which bases on macro elements is compiled with object oriented language and three kinds of nonlinear beam-column elements are implemented in MESAP: stiffness-based fiber element, flexibility-based fiber element and flexibility-based plastic hinge element. Differences between the elements are compared by case study. Four kinds of integration methods for obtaining the flexibility matrix of the plastic hinge element are studied. The results show that a flexibility-based plastic binge element is an accurate macro element with low computation cost. Only two integration points are required by the Gauss-Radau integration method handling a nonlinear analysis. It is accuracy and its computational efficiency is applicable in the entire structure nonlinear analysis and practical in engineering.%罕遇地震作用下混凝土梁柱构件易进入塑性阶段而发生弹塑性损伤,正确地模拟结构进入非线性状态后的力学行为对评价结构的抗震安全性具有重要的意义.通过面向对象语言编制了基于宏观单元的结构弹塑性分析软件平台MESAP,增加了三种非线性梁柱单元:基于刚度法纤维单元、基于柔度法纤维单元及基于柔度法的塑性铰单元.通过算例分析三种非线性梁柱单元之间的差异.基于柔度法塑性铰单元的柔度矩阵积分方法可分为四种,通过算例讨论四种积分方法的差异.算例分析结果表明基于柔度法的塑性铰单元是一种精度高具计算成本低的宏观单元.Gauss-Radau积分法要求进行塑性计算的积分点只有两个,该积分法计算效率较高且精度良好,适用于整体结构的非线性分析之中,具有实际工程应用意义.
Nonlinear Metamaterials for Holography
Almeida, Euclides; Prior, Yehiam
2015-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multi-layer metamaterial holograms where by the nonlinear process of Third Harmonic Generation, a background free image is formed at a new frequency which is the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analyzed and prospects for future device applications are discussed.
Two Expanding Integrable Models of the Geng-Cao Hierarchy
Directory of Open Access Journals (Sweden)
Xiurong Guo
2014-01-01
interesting results. In the paper, we will deduce two kinds of expanding integrable models of the Geng-Cao (GC hierarchy by constructing different 6-dimensional Lie algebras. One expanding integrable model (actually, it is a nonlinear integrable coupling reduces to a generalized Burgers equation and further reduces to the heat equation whose expanding nonlinear integrable model is generated. Another one is an expanding integrable model which is different from the first one. Finally, the Hamiltonian structures of the two expanding integrable models are obtained by employing the variational identity and the trace identity, respectively.
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.
BOUNDARY STABILIZATION OF TIMOSHENKO BEAM
Institute of Scientific and Technical Information of China (English)
YAN Qingxu
2000-01-01
In this paper, the stabilization problem of Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory and energy-perturbed method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t → ∞.
Non-Linear Vibrations, Stability, and Dynamics of Structures and Mechanisms
1989-08-01
particle of matter can occupy only one position in space. On the basis of this law, it is not difficult to show that a rigid body can assume only one...Em+n) is desired, with m > 0, then all terms of O(em +n) must be retained in the expanded equations. With this in mind , we address some other...concerning the 3 nonlinear non-planar response of inextensional beams and of beam-like structures. These include modal interactins both in the
NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE
Xu, Tiantian
2015-06-01
Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems development....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304....... In this article, we report the first highly controlled measurements of the nonlinear response of nanomechanical cantilevers using an ultralinear detection system. This is performed for an extensive range of devices to probe the validity of Euler-Bernoulli theory in the nonlinear regime. We find that its...
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora; Prior, Yehiam
2016-08-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency--the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed.
Nonlinear metamaterials for holography
Almeida, Euclides; Bitton, Ora
2016-01-01
A hologram is an optical element storing phase and possibly amplitude information enabling the reconstruction of a three-dimensional image of an object by illumination and scattering of a coherent beam of light, and the image is generated at the same wavelength as the input laser beam. In recent years, it was shown that information can be stored in nanometric antennas giving rise to ultrathin components. Here we demonstrate nonlinear multilayer metamaterial holograms. A background free image is formed at a new frequency—the third harmonic of the illuminating beam. Using e-beam lithography of multilayer plasmonic nanoantennas, we fabricate polarization-sensitive nonlinear elements such as blazed gratings, lenses and other computer-generated holograms. These holograms are analysed and prospects for future device applications are discussed. PMID:27545581
Energy Technology Data Exchange (ETDEWEB)
Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka [Department of Physics, Laser-Plasma Computational Laboratory, DAV PG College, Dehradun, Uttarakhand (India); Chauhan, Prashant [Department of Physics and Material Science and Engineering, Jaypee Institute of Information Technology, Uttar Pradesh (India); Mahmoud, Saleh T. [Department of Physics, College of Science, UAE University, PO Box 17551 Al-Ain (United Arab Emirates)
2015-05-15
This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled laser beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Photonics linear and nonlinear interactions of laser light and matter
Menzel, R
2007-01-01
This book covers the fundamental properties and the description of single photons and light beams, experimentally and theoretically. It explains the essentials of linear interactions and most nonlinear interactions between light and matter in both the transparent and absorbing cases. It also provides a basic understanding of modern quantum optics and lasers, as well as the principles of nonlinear optical spectroscopy. It is self-consistent and enriched by a large number of calculated illustrations, examples, and descriptive tables. Graduate students in physics and electrical engineering, as well as other sciences, will find this book a thorough introduction to the field, while for lecturers and scientists it is a rich source of useful information and a ready-to-hand reference. The new edition has been thoroughly expanded and revised in all sections
Institute of Scientific and Technical Information of China (English)
王希军
2011-01-01
Aiming at realizing the laser energy transaction in a long distance, the optical design optimizations were analyzed and the experiment was set up to study the changes of the afocus influencing of the telescope system on the laser spot emitted form the laser antenna. In the experiment, utilizing the third-order aberration theory of optics, the effect on the manipulating accuracy of afocus of the telescope optical system was decreased because of the aberration of the laser radiation antenna, and the measurement of far field laser spot in a series of ranges was set up. By the Gauss curve fitting annihilating the laser irradiation saturation of the CCD device, the experimental precision was obtained to measure the laser beam waist in far field. In the condition of the constraint of the smaller diameters of the object lens and the lower multiply of the telescope expander, the 60 micro-Radian divergence design and measurement of the laser radiation antenna were attained. Both theoretical and experimental results expressed there is a phenomenon of the laser spot minimum deviated of the afocus zero position, and the deviation in the same negative direction of the afocus.%为了实现远距离激光能量传输,根据光学相差理论和优化的组合透镜设计,着重研究了影响激光发射天线发射的激光光束随望远光学系统离焦量的变化规律和初步的实验测试.实验中利用三级像差理论消除激光天线系统像差对离焦量控制精度的影响,在不同的距离,实现了远场激光光斑的测量.采用高斯曲线拟合法,消除CCD探测器的饱和影响,提高了远场激光束腰的测量精度.在小口径和低倍率光学扩束系统约束条件下,实现了60微弧度激光发射天线的设计和测量.实验初步说明组合透镜消除了像差对离焦量的影响,进而提高了光斑测量精度.同时理论和实验两方面初步说明存在激光光束最小值偏离零离焦量现象,而且偏离的方向均是离焦量负向.
Institute of Scientific and Technical Information of China (English)
方锦清; 罗晓曙; 陈关荣; 翁甲强
2001-01-01
Beam halo-chaos is essentially a complex spatiotemporal chaotic motion in a periodic-focusing channel of a highpower linear proton accelerator. The controllability condition for beam halo-chaos is analysed qualitatively. A special nonlinear control method, i.e. the wavelet-based function feedback, is proposed for controlling beam halochaos. Particle-in-cell simulations are used to explore the nature of halo-chaos formation, which has shown that the beam hMo-chaos is suppressed effectively after using nonlinear control for the proton beam with an initial full Gaussian distribution. The halo intensity factor Hav is reduced from 14%o to zero, and the other statistical physical quantities of beam halo-chaos are more than doubly reduced. The potential applications of such nonlinear control in experiments are briefly pointed out.
An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes
Xu, Tiantian
2014-08-17
Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.
What Expands in an Expanding Universe?
Pacheco, José A De Freitas
2015-01-01
In the present investigation, the possible effects of the expansion of the Universe on systems bonded either by gravitational or electromagnetic forces, are reconsidered. It will be shown that the acceleration (positive or negative) of the expanding background, is the determinant factor affecting planetary orbits and atomic sizes. In the presently accepted cosmology (ΛCDM) all bonded systems are expanding at a decreasing rate that tends to be zero as the universe enters in a de Sitter phase. It is worth mentioning that the estimated expansion rates are rather small and they can be neglected for all practical purposes.
What Expands in an Expanding Universe?
Directory of Open Access Journals (Sweden)
JOSÉ A. DE FREITAS PACHECO
2015-12-01
Full Text Available ABSTRACT In the present investigation, the possible effects of the expansion of the Universe on systems bonded either by gravitational or electromagnetic forces, are reconsidered. It will be shown that the acceleration (positive or negative of the expanding background, is the determinant factor affecting planetary orbits and atomic sizes. In the presently accepted cosmology (ΛCDM all bonded systems are expanding at a decreasing rate that tends to be zero as the universe enters in a de Sitter phase. It is worth mentioning that the estimated expansion rates are rather small and they can be neglected for all practical purposes.
Polarization shaping for control of nonlinear propagation
Bouchard, Frédéric; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W
2016-01-01
We study the nonlinear optical propagation of two different classes of space-varying polarized light beams -- radially symmetric vector beams and Poincar\\'e beams with lemon and star topologies -- in a rubidium vapour cell. Unlike Laguerre-Gauss and other types of beams that experience modulational instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Polarization Shaping for Control of Nonlinear Propagation.
Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W
2016-12-02
We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Nonlinear Stokes Mueller Polarimetry
Samim, Masood; Barzda, Virginijus
2015-01-01
The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarim...
Energy Technology Data Exchange (ETDEWEB)
Trombetta, Debora M.; Silva, Ademir X. da, E-mail: dtrombetta@con.ufrj.b [Universidade Federal do Rio de Janeiro (PEN/COPPE/UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-Graduacao de Engenharia. Programa de Energia Nuclear; Cardoso, Simone C. [Universidade Federal do Rio de Janeiro (IF/UFRJ), RJ (Brazil). Inst. de Fisica; Facure, Alessandro [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil); Rosa, Luiz A.R. da [Instituto de Radioprotecao e Dosimetria (IRD/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2010-06-15
In this work, the effects produced in attenuation of 6 MV radiotherapic beam as consequence of metallic heterogeneities present in some types of tissue expanders, used in the process of mammary reconstruction, were studied. The study was developed through the quantification relative transmission making use of computer simulations with Monte Carlo method, using the code MCNPX. The results showed that the presence of this metallic heterogeneity alters the transmission of the beam, causing a reduction up to 20% in the geometric shadowed region. According to dosimetry protocols, the reduction in the dose should be lower of 5%. Therefore the difference found in the study could be relevant to consider the presence of heterogeneity in the irradiation field for the treatment planning. (author)
Institute of Scientific and Technical Information of China (English)
岳东旭; 于虹; 袁卫民
2011-01-01
理论分析了亚微米尺寸的悬臂梁结构的非线性力学模型,研究了非线性产生的物理机制.采用外部静电激励机制,使悬臂梁谐振器产生谐振,借助Polytec激光多普勒测振系统检测了悬臂梁的频率响应曲线.测试结果表明,悬臂梁具有显著的非线性效应(即"弹簧变软"效应).实验证实了这种非线性效应几乎和交流电压无关,却随着直流电压的增大而显著增大,最大峰值偏移达到0.5 MHz.提取出3组-阶机械弹性系数分别为79.62,31.75和14.92 N/m,实验结果符合理论规律.对实验中的偏差做了进-步的分析和讨论,利用软件ANSYS对过腐蚀对结构刚度和频率响应的影响做了相应的模拟,结果和实验测量数据相吻合.%A nonlinear mechanical model for sub-micron cantilevers was analyzed in detail and its physical mechanism was researched to provide a theoretical basis for experiments. The electrostatical force was used to achieve the resonance state cantilever beams and a Polytec laser Doppler vibration measurement system was taken to observe the frequency response curve. Experimental results show that the beams have significant nonlinear effects (the spring softening effect) and the nonlinearity is relatively independent on the AC voltage, but it is markedly enhanced with increasing the DC voltage.The obtained maximum peak shift is 0. 5 MHz and extracted first-order mechanical elasticity coefficients are 79.62, 31.75, and 14.92 N/m, respectively. Furthermore,the deviation of the experiment was also disccussed and analyzed. The effects of overetching by wet chemical etching on the stiffness and frequency response were stimulated by ANSYS software. In conclusion, the corresponding simulation results are well coincident with the experimental data.
Energy Technology Data Exchange (ETDEWEB)
Serkez, Svitozar; Kocharyan, Vitali; Saldin, Evgeni; Zagorodnov, Igor [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany)
2013-09-15
We demonstrate that the output radiation characteristics of the European XFEL sources at nominal operation point can be easily made significantly better than what is currently reported in the TDRs of scientific instruments and X-ray optics. In fact, the output SASE characteristics of the baseline European XFEL have been previously optimized assuming uniform undulators at a nominal operating point of 5 kA peak current, without considering the potential of undulator tapering in the SASE regime. In order to illustrate this point, we analyze the case of an electron bunch with nominal parameters. Based on start-to-end simulations, we demonstrate that nonlinear undulator tapering allows one to achieve up to a tenfold increase in peak power and photon spectral density in the conventional SASE regime, without modification to the baseline design. The FEL code Genesis has been extensively used for these studies. In order to increase our confidence in simulation results, we cross-checked outcomes by reproducing simulations in the deep nonlinear SASE regime with tapered undulator using the code ALICE.
Infiltrated microstructured fibers as tunable and nonlinear optical devices
DEFF Research Database (Denmark)
Rosberg, Christian Romer; Bennet, Francis; Neshev, Dragomir N.;
We study the light guiding properties of microstructured optical fibers infiltrated with nonlinear liquids and demonstrate their applicability for spatial beam control in novel type tunable and nonlinear optical devices....
Lyle, Karen H.; Vassilakos, Gregory J.
2015-01-01
This report summarizes initial modeling of the local response of the Bigelow Expandable Activity Module (BEAM) to micrometeorite and orbital debris (MMOD) impacts using a structural, non-linear, transient dynamic finite element code. Complementary test results for a local BEAM structure are presented for both hammer and projectile impacts. Review of these data provided guidance for the transient dynamic model development. The local model is intended to support predictions using the global BEAM model, described in a companion report. Two types of local models were developed. One mimics the simplified Soft-Goods (fabric envelop) part of the BEAM NASTRAN model delivered by the project. The second investigates through-the-thickness modeling challenges for MMOD-type impacts. Both the testing and the analysis summaries contain lessons learned and areas for future efforts.
Kisner, W H
1991-02-01
The use of the forehead flap for nasal reconstruction has long been used by reconstructive surgeons. A case is presented in which comprised forehead skin is utilized following expansion by a tissue expander.
Statics and rotational dynamics of composite beams
Ghorashi, Mehrdaad
2016-01-01
This book presents a comprehensive study of the nonlinear statics and dynamics of composite beams and consists of solutions with and without active elements embedded in the beams. The static solution provides the initial conditions for the dynamic analysis. The dynamic problems considered include the analyses of clamped (hingeless) and articulated (hinged) accelerating rotating beams. Two independent numerical solutions for the steady state and the transient responses are presented. The author illustrates that the transient solution of the nonlinear formulation of accelerating rotating beam converges to the steady state solution obtained by the shooting method. Other key areas considered include calculation of the effect of perturbing the steady state solution, coupled nonlinear flap-lag dynamics of a rotating articulated beam with hinge offset and aerodynamic damping, and static and dynamic responses of nonlinear composite beams with embedded anisotropic piezo-composite actuators. The book is intended as a t...
Nonlinear Dynamic Force Spectroscopy
Björnham, Oscar
2016-01-01
Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information of the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear regime. For example, bacterial adhesion pili and polymers with worm-like chain properties are examples of structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory we modeled a bio-complex expressed on a stiff, an elastic and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found th...
Nonlinear dynamics of structures
Oller, Sergio
2014-01-01
This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics. This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects. Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution are studied, and the theoretical concepts and its programming algorithms are presented.
Tailoring the nonlinear response of MEMS resonators using shape optimization
DEFF Research Database (Denmark)
Li, Lily L.; Polunin, Pavel M.; Dou, Suguang
2017-01-01
We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge-type mic......We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with non-uniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge...
Nonlinear Photonics and Novel Optical Phenomena
Morandotti, Roberto
2012-01-01
Nonlinear Photonics and Novel Optical Phenomena contains contributed chapters from leading experts in nonlinear optics and photonics, and provides a comprehensive survey of fundamental concepts as well as hot topics in current research on nonlinear optical waves and related novel phenomena. The book covers self-accelerating airy beams, integrated photonics based on high index doped-silica glass, linear and nonlinear spatial beam dynamics in photonic lattices and waveguide arrays, polariton solitons and localized structures in semiconductor microcavities, terahertz waves, and other novel phenomena in different nanophotonic and optical systems.
Effects of Transverse Beam Size in Beam Position Monitors
Kurennoy, S S
2001-01-01
The fields produced by a long beam with a given transverse charge distribution in a homogeneous vacuum chamber are studied. Signals induced by a displaced finite-size beam on electrodes of a beam position monitor (BPM) are calculated and compared to those produced by 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.
Effects of transverse beam size in beam position monitors.
Energy Technology Data Exchange (ETDEWEB)
Kurennoy, S. (Sergey)
2001-01-01
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.
EFFECTS OF TRANSFERSE BEAM SIZE IN BEAM POSITIONS MONITORS
Energy Technology Data Exchange (ETDEWEB)
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.
Nonlinear scattering in plasmonic nanostructures
Chu, Shi-Wei
2016-09-01
Nonlinear phenomena provide novel light manipulation capabilities and innovative applications. Recently, we discovered nonlinear saturation on single-particle scattering of gold nanospheres by continuous-wave laser excitation and innovatively applied to improve microscopic resolution down to λ/8. However, the nonlinearity was limited to the green-orange plasmonic band of gold nanosphere, and the underlying mechanism has not yet been fully understood. In this work, we demonstrated that nonlinear scattering exists for various material/geometry combinations, thus expanding the applicable wavelength range. For near-infrared, gold nanorod is used, while for blue-violet, silver nanospheres are adopted. In terms of mechanism, the nonlinearity may originate from interband/intraband absorption, hot electron, or hot lattice, which are spectrally mixed in the case of gold nanosphere. For gold nanorod and silver nanosphere, nonlinear scattering occurs at plasmonic resonances, which are spectrally far from interband/intraband absorptions, so they are excluded. We found that the nonlinear index is much larger than possible contributions from hot electrons in literature. Therefore, we conclude that hot lattice is the major mechanism. In addition, we propose that similar to z-scan, which is the standard method to characterize nonlinearity of a thin sample, laser scanning microscopy should be adopted as the standard method to characterize nonlinearity from a nanostructure. Our work not only provides the physical mechanism of the nonlinear scattering, but also paves the way toward multi-color superresolution imaging based on non-bleaching plasmonic scattering.
几何非线性新梁柱单元及结构程序设计%A geometric nonlinear new beam-column element and structure program design
Institute of Scientific and Technical Information of China (English)
张俊峰; 王利娟; 郝际平; 李天
2011-01-01
基于更新拉格朗日构形的增量虚位移原理,在其势能项中引入了全部6个应力分量,采用可计人单元剪切变形影响的三次多项式插值函数,详细推导了考虑剪切变形及翘曲的空间梁一柱单元几何非线性切线刚度矩阵.根据面向对象的程序设计思想,将整个有限元域划分为8个基本类,在单元基类的基础上派生了新的单元类,采用C++语言编制了面向对象的空间钢结构分析程序.几何非线性算例分析结果表明,本文提出的理论分析方法和计算程序是正确的和高效的.%According to the increment virtual displacement principle based on the updated Lagrange configuration,the potential energy associated with all six stress components was taken into account. The cubic interpolation function which can be used to consider the shear deformation effects has been applied to derive the geometrical nonlinear stiffness matrix of the space beam-column element considering the shear deformation and warping effects. Based on the object-oriented design conception, the finite element analysis domain is divided into eight classes. A new class is derived from the base element class. Using C+ + language,the spatial steel frame advanced analysis program is complied. Numerical examples including both geometric and material nonlinearities are used to demonstrate the accuracy and efficiency of the proposed analytical method and computer program.
Serkez, Svitozar; Saldin, Evgeni; Zagorodnov, Igor; Geloni, Gianluca
2013-01-01
We demonstrate that the output radiation characteristics of the European XFEL sources at nominal operation point can be easily made significantly better than what is currently reported in the TDRs of scientific instruments and X-ray optics. In fact, the output SASE characteristics of the baseline European XFEL have been previously optimized assuming uniform undulators at a nominal operating point of 5 kA peak current, without considering the potential of udulator tapering in the SASE regime. In order to illustrate this point, we analyze the case of an electron bunch with nominal parameters. Based on start-to-end simulations, we demonstrate that nonlinear undulator tapering allows one to achieve up to a tenfold increase in peak power and photon spectral density in the conventional SASE regime, without modification to the baseline design. The FEL code Genesis has been extensively used for these studies. In order to increase our confidence in simulation results, we cross-checked outcomes by reproducing simulatio...
Institute of Scientific and Technical Information of China (English)
苏栋
2012-01-01
The p-y curve method is one of the most commonly used approaches in the analysis and design of piles under horizontal loadings. A p-y model is proposed within the framework of bounding surface elasto-plastic theory. In comparison with the traditional p-y curves, the model can simulate p-y relationships with different degrees of nonlinearity by choosing appropriate values for the model parameters, and can also simulate the soil-pile interaction under cyclic loadings. By adopting the incremental finite element method for beams on nonlinear foundation incorporating the proposed elasto-plastic p-y model, a finite element program is formulated. Soil-pile systems in the field or in the laboratory tests under monotonic or cyclic horizontal loadings are analyzed by use of the finite element program. By comparing the calculated and measured results, the capacity of the method and the proposed elasto-plastic p-y model in modeling the nonlinear response of the piles is demonstrated.%在水平受荷桩基的分析与计算中，P—Y曲线法是应用较为广泛的方法之一。在边界面弹塑性理论的框架内，建立了一个P—Y模型。与传统的P—Y曲线比较，该模型能通过不同的参数取值，模拟不同非线性特性的P—Y关系，并能模拟往复荷载作用下的桩土相互作用。同时采用非线性地基梁的增量有限元法，结合提出的弹塑性P—Y模型，编制了有限元分析程序，对单调和往复水平荷载作用下的桩土系统进行实例分析，结果表明该方法能有效的模拟水平荷载作用下的桩基非线性响应。
Wu, Yingquan
2008-01-01
The paper has a threefold purpose. The first purpose is to present an explicit description of expanded cyclic codes defined in $\\GF(q^m)$. The proposed explicit construction of expanded generator matrix and expanded parity check matrix maintains the symbol-wise algebraic structure and thus keeps many important original characteristics. The second purpose of this paper is to identify a class of constant-weight cyclic codes. Specifically, we show that a well-known class of $q$-ary BCH codes excluding the all-zero codeword are constant-weight cyclic codes. Moreover, we show this class of codes achieve the Plotkin bound. The last purpose of the paper is to characterize expanded cyclic codes utilizing the proposed expanded generator matrix and parity check matrix. We analyze the properties of component codewords of a codeword and particularly establish the precise conditions under which a codeword can be represented by a subbasis. With the new insights, we present an improved lower bound on the minimum distance of...
Nonlinear and active RF metamaterial applications using embedded devices
Katko, Alexander R.; Hawkes, Allen M.; Cummer, Steven A.
Nonlinear metamaterials have received considerable attention in recent years. The inclusion of nonlinear and active effects in metamaterials expands the possibilities for engineering media with designer properties. We detail our recent efforts to create nonlinear and active metamaterials at RF with useful properties through the inclusion of embedded nonlinear or active elements. We demonstrate some of the possible applications of such nonlinear and active metamaterials experimentally, with properties including saturable absorption, phase conjugation, and power harvesting.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Nonlinear theory of beam-wave interaction in gyro-TWT with spiral waveguide%螺旋波纹波导回旋行波管注波互作用非线性理论
Institute of Scientific and Technical Information of China (English)
薛智浩; 刘濮鲲; 杜朝海
2012-01-01
螺旋波纹波导回旋行波管与采用光滑圆波导的回旋管相比,有较大的带宽.介绍了该类回旋行波管的非线性注波互作用理论.计算结果表明该理论计算结果与实际实验报道的结果基本符合,相应的电子效率达到29％,饱和增益达到37 dB,工作磁场0.21 T,电压185 kV,电流19A.%Gyro-TWT (traveling wave tube) with helical waveguide has wider instantaneous frequency bandwidth than that with smooth waveguide. This paper introduces the nonlinear theory of its beam-wave interaction. The calculation shows that, the electron efficiency reaches 29% . and the saturated gain is 37 dB, when the working magnetic field is 0. 21 T. the voltage is 185 kV and the current is 19 A. The calculated results accord with that reported in literature.
Spatial solitons in nonlinear liquid waveguides
Indian Academy of Sciences (India)
R Barillé; G Rivoire
2001-11-01
Spatial solitons are studied in a planar waveguide ﬁlled with nonlinear liquids. Spectral and spatial measurements for different geometries and input power of the laser beam show the inﬂuence of different nonlinear effects as stimulated scatterings on the soliton propagation and in particular on the beam polarization. The stimulated scattering can be used advantageously to couple the two polarization components. This effect can lead to multiple applications in optical switching.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
Verbeek, P.P.C.C.
2012-01-01
In his article In Between Us, Yoni van den Eede expands existing theories of mediation into the realm of the social and the political, focusing on the notions of opacity and transparency. His approach is rich and promising, but two pitfalls should be avoided. First, his concept of ‘in-between’ runs
Expanding Student Assessment Opportunities.
Bartscher, Beth; Carter, Andrea; Lawlor, Anna; McKelvey, Barbara
This paper describes an approach for expanding assessment opportunities for students to demonstrate their understanding of content. The targeted population consisted of elementary and junior high school students in two schools in a growing middle-class community in north central Illinois. The elementary school enrolled 467 students and the junior…
Wells, Nathan D.; Madaras, Eric I.
2017-01-01
Expandable modules for use in space and on the Moon or Mars offer a great opportunity for volume and mass savings in future space exploration missions. This type of module can be compressed into a relatively small shape on the ground, allowing them to fit into space vehicles with a smaller cargo/fairing size than a traditional solid, metallic structure based module would allow. In April 2016, the Bigelow Expandable Activity Module (BEAM) was berthed to the International Space Station (ISS). BEAM is the first human-rated expandable habitat/module to be deployed and crewed in space. BEAM is a NASA managed ISS payload project in partnership with Bigelow Aerospace. BEAM is intended to stay attached to ISS for an operational period of 2 years to help advance the technology readiness for future expandable modules. BEAM has been instrumented with a suite of space flight certified sensors systems which will help characterize the module's performance for thermal, radiation shielding and impact monitoring against potential Micro Meteoroid/Orbital Debris (MM/OD) providing fundamental information on the BEAM environment for potential health monitoring requirements and capabilities. This paper will provide an overview of how the sensors/instrumentation systems were developed, tested, installed and an overview of the current sensor system operations. It will also discuss how the MM/OD impact detection system referred to as the Distributed Impact Detection System (DIDS) data is being processed and reviewed on the ground by the principle investigators.
Metallic beam development for the Facility for Rare Isotope Beam
Energy Technology Data Exchange (ETDEWEB)
Machicoane, Guillaume, E-mail: machicoa@nscl.msu.edu; Cole, Dallas; Leitner, Daniela; Neben, Derek; Tobos, Larry [Facility for Rare Isotope Beam, Michigan State University, East Lansing, Michigan 48824 (United States)
2014-02-15
The Facility for Rare Isotope Beams (FRIB) at Michigan State University (MSU) will accelerate a primary ion beam to energies beyond 200 MeV/u using a superconducting RF linac and will reach a maximum beam power of 400 kW on the fragmentation target. The beam intensity needed from the ECR ion source is expected to be between 0.4 and 0.5 emA for most medium mass to heavy mass elements. Adding to the challenge of reaching the required intensity, an expanded list of primary beams of interest has been established based on the production rate and the number of isotope beams that could be produced with FRIB. We report here on the development done for some of the beam in the list including mercury (natural), molybdenum ({sup 98}Mo), and selenium ({sup 82}Ser)
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
Effect of Scanning Beam Profile to Fabricate Fused Fiber Tapers by CO_2 Laser Irradiation Method
Institute of Scientific and Technical Information of China (English)
Bayle; Fabien; Luo; Aiping; Marin; Emmanuel; Meunier; Jean-Pierre
2003-01-01
Beam uniformity is a crucial building block of CO2 experiments aimed at fusing and stretching optical fibers in a lossless manner. When the irradiation beam is expanded through a galvanometer mirror, ways to achieve beam uniformity are investigated.
Effect of Scanning Beam Profile to Fabricate Fused Fiber Tapers by CO2 Laser Irradiation Method
Institute of Scientific and Technical Information of China (English)
Bayle Fabien; Luo Aiping; Marin Emmanuel; Meunier Jean-Pierre
2003-01-01
Beam uniformity is a crucial building block of CO2 experiments aimed at fusing and stretching optical fibers in a lossless manner. When the irradiation beam is expanded through a galvanometer mirror, ways to achieve beam uniformity are investigated.
Expanding the HAWC Observatory
Energy Technology Data Exchange (ETDEWEB)
Mori, Johanna [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-08-17
The High Altitude Water Cherenkov Gamma-Ray Observatory is expanding its current array of 300 water tanks to include 350 outrigger tanks to increase sensitivity to gamma rays above 10 TeV. This involves creating and testing hardware with which to build the new tanks, including photomultiplier tubes, high voltage supply units, and flash analog to digital converters. My responsibilities this summer included preparing, testing and calibrating that equipment.
Controlling Second Harmonic Efficiency of Laser Beam Interactions
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.
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Numerical Simulation of Beam-Beam Effects in the Proposed Electron-Ion Colider at Jefferson Lab
Energy Technology Data Exchange (ETDEWEB)
Balsa Terzic, Yuhong Zhang
2010-05-01
One key limiting factor to a collider luminosity is beam-beam interactions which usually can cause serious emittance growth of colliding beams and fast reduction of luminosity. Such nonlinear collective beam effect can be a very serious design challenge when the machine parameters are pushed into a new regime. In this paper, we present simulation studies of the beam-beam effect for a medium energy ring-ring electron-ion collider based on CEBAF.
Institute of Scientific and Technical Information of China (English)
文颖; 李特; 孙明文; 曾庆元
2016-01-01
T he existing methods of geometric nonlinear analysis is generally considered as time‐consu‐ming and computational intensive under the framework of the incremental‐iterative scheme .By assum‐ing an inverse deformationprocess of the U .L .(updated Lagrangian) approach i .e .,natural deforma‐tion to rigid body motion ,a potential energy formulation was presented and applied to the planar beam member as an illustration .An explicit incremental secant stiffness matrix was correspondingly devel‐oped via the Castigliano′s theorem .The derived secant stiffness matrix was rigid body motion test qualified ,membrane locking free and symmetric as well as simple in form as compared with the one obtained by the U .L .approach making it suitable for a general use in the solutions of geometrical nonlinear problems .By applying the incremental secant stiffness matrix to both the ‘predictor’ and‘corrector’ phases of a typical iteration of geometric nonlinear analysis ,a direct iteration procedure making use of the cylindrical arc‐length constraint equation was proposed for tracing complete equilib‐rium path .Meanwhile ,a root selection algorithm which was capable of successfully giving correct so‐lution direction was presented for specifically dealing with the general cases of non‐proportional load‐ing .T he results of numerical validations demonstrate that the proposed method can reliably avoid the‘turning back’ of solution direction and the phenomenon of divergence during iterative process even in the case of tracing prudent equilibrium path .In comparison of the New ton‐Raphson method ,a reduc‐tion in the total number of incremental steps and computation time can be achieved to effectively im‐prove the analysis efficiency .%针对增量‐迭代技术背景下几何非线性分析耗时长、代价大的问题，通过颠倒U．L．（更新的拉格朗日）列式隐含的自然变形‐刚性运动过程，建立了平面梁全新势
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.
Kaltenhauser, Kristin
2015-01-01
Expanding your horizons is a bi-annual “Science Day” for girls aged 11 to 14, held at the University of Geneva on 14 November. The girls had the opportunity to take part in hands-on workshops held by local professional women in the field of science, mathematics, engineering and technology. For the fourth time, CERN was part of this event, offering three workshops as well as a booth at the Discovery Fair, including Higgnite, an interactive visualization of the Higgs Field.
Lew, Kristi
2011-01-01
People have always been fascinated with the stars above and the universe that contains them. Over the years, astronomers have developed numerous theories to explain how the universe began, how it works, and what its ultimate fate will be. But all of the scientists' questions are far from answered. The Expanding Universe goes beyond the creation of the universe to explain how scientists think the universe works, grows, and changes, including what great thinkers Isaac Newton and Albert Einstein had to say about its fate. Readers will also learn about how researchers are slowly shedding light on
Nonlinear phased array imaging
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
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
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Energy Technology Data Exchange (ETDEWEB)
Gao, J
2000-12-01
Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. [1], in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam-beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam-beam tune shift, {zeta}{sub y,max}, around 0.045 for e{sup +}e{sup -} circular colliders, and why one can use round beams to double this value approximately. Comparisons with some machine parameters are given. Finally, we discuss the mechanism of the luminosity reduction due to a definite collision crossing angle. (author)
Nonlinear opto-mechanical pressure
Conti, Claudio
2014-01-01
A transparent material exhibits ultra-fast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, as optical manipulation, biophysics, cavity optomechanics, quantum optics, optical tractors, and is relevant in fundamental problems as the Abraham-Minkoswky dilemma, or the Casimir effect. Here we show that an ultra-fast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order of magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
Airy beam optical parametric oscillator.
Aadhi, A; Chaitanya, N Apurv; Jabir, M V; Vaity, Pravin; Singh, R P; Samanta, G K
2016-05-04
Airy beam, a non-diffracting waveform, has peculiar properties of self-healing and self-acceleration. Due to such unique properties, the Airy beam finds many applications including curved plasma wave-guiding, micro-particle manipulation, optically mediated particle clearing, long distance communication, and nonlinear frequency conversion. However, many of these applications including laser machining of curved structures, generation of curved plasma channels, guiding of electric discharges in a curved path, study of nonlinear propagation dynamics, and nonlinear interaction demand Airy beam with high power, energy, and wavelength tunability. Till date, none of the Airy beam sources have all these features in a single device. Here, we report a new class of coherent sources based on cubic phase modulation of a singly-resonant optical parametric oscillator (OPO), producing high-power, continuous-wave (cw), tunable radiation in 2-D Airy intensity profile existing over a length >2 m. Based on a MgO-doped periodically poled LiNbO3 crystal pumped at 1064 nm, the Airy beam OPO produces output power more than 8 W, and wavelength tunability across 1.51-1.97 μm. This demonstration gives new direction for the development of sources of arbitrary structured beams at any wavelength, power, and energy in all time scales (cw to femtosecond).
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.
Institute of Scientific and Technical Information of China (English)
钟加峰
2012-01-01
利用有限元分析软件建立了混合梁独塔斜拉桥的空间模型，分析了混合梁独塔斜拉桥在有、无辅助墩情况下的非线性静动力特性的异同，讨论了在有、无辅助墩情况下对混合梁独塔斜拉桥非线性静动力特性的影响，得出了有指导意义的结论。%The paper establishes spatial model of single stayed-cable bridge with composite beam by using finite element analysis software, ana- lyzes similarities and differences of non-linear static and dynamic characteristics of single stayed-cable bridge with composite beam under the con- dition of with and without auxiliary pier, and discusses the impacts of within and without auxiliary pier upon non-linear dynamic and static char- acteristics of single stayed-cable bridge with composite beam, and finally draws some guiding conclusions.
Stagnation of electron flow by a nonlinearly generated whistler wave
Taguchi, Toshihiro; Mima, Kunioki
2016-01-01
Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel propagating whistler that stops the beam. In this letter, we will show the phenomena in detail and explain the mechanism of whistler mediated beam stagnation.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Use and application of MADYMO 5.3 foam material model for expanded polypropylene foam
Kant, A.R.; Suffis, B.; Lüsebrink, H.
1998-01-01
The dynamic material characteristics of expanded polypropylene are discussed. The in-depth studies, carried out by JSP International, in cooperation with TNO, are used to validate the MADYMO foam material model. The dynamic compression of expanded polypropylene follows a highly non-linear stress-str
Energy Technology Data Exchange (ETDEWEB)
Bassett, B A [Institute of Cosmology and Gravitation, University of Portsmouth (United Kingdom)
2005-07-29
The cosmos is an awfully big place and there is no better guide to its vast expanse and fascinating nooks and crannies than John Barrow. A professor of mathematical sciences at Cambridge University, Barrow embodies that rare combination of highly polished writer and expert scientist. His deft touch brings together the disparate threads of human knowledge and weaves them into a tapestry as rich and interesting for the expert as it is for the layperson. The Artful Universe Expanded is an updated edition of this popular book first published in 1995. It explores the deeply profound manner in which natural law and the nature of the cosmos have moulded and shaped us, our cultures and the very form of our arts and music-a new type of 'cosmic' anthropology. The main themes Barrow chooses for revealing this new anthropology are the subjects of evolution, the size of things, the heavens and the nature of music. The book is a large, eclectic repository of knowledge often unavailable to the layperson, hidden in esoteric libraries around the world. It rivals The Da Vinci Code for entertainment value and insights, but this time it is Nature's code that is revealed. It is rare indeed to find common threads drawn through topics as diverse as The Beetles, Bach and Beethoven or between Jackson Pollock, the Aztecs, Kant, Picasso, Byzantine mosaics, uranium-235 and the helix nebula. Barrow unerringly binds them together, presenting them in a stimulating, conversational style that belies the amount of time that must have gone into researching this book. Dip into it at random, or read it from cover to cover, but do read it. The Artful Universe Expanded is an entertaining antidote to the oft-lamented pressures to know more and more about less and less and the apparently inexorable march of specialization. On reading this book one can, for a short time at least, hold in one's mind a vision that unifies science, art and culture and glimpse a universal tapestry of great
Liu, Chang
2015-01-01
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.
Feedback Control of Vibrations in a Micromachined Cantilever Beam with Electrostatic Actuators
Wang, P. K. C.
1998-06-01
The problem of feedback control of vibrations in a micromachined cantilever beam with nonlinear electrostatic actuators is considered. Various forms of nonlinear feedback controls depending on localized spatial averages of the beam velocity and displacement near the beam tip are derived by considering the time rate-of-change of the total energy of the beam. The physical implementation of the derived feedback controls is discussed briefly. The dynamic behaviour of the beam with the derived feedback controls is determined by computer simulation.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Cooling of Relativistic Electron-Beams
Bazylev, V. A.; Tulupov, A. V.
1993-01-01
A method of reducing the energy spread of an electron beam in a free-electron laser is suggested. The electron beam compression is based on a nonlinear mechanism of electron interactions with a ponderomotive wave in the presence of a constant and uniform magnetic field perpendicular to the electron
An introduction to beam physics
Berz, Martin; Wan, Weishi
2015-01-01
The field of beam physics touches many areas of physics, engineering, and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas, ranging from electron microscopes, particle spectrometers, medical radiation facilities, powerful light sources, and astrophysics to large synchrotrons and storage rings such as the LHC at CERN. An Introduction to Beam Physics is based on lectures given at Michigan State University’s Department of Physics and Astronomy, the online VUBeam program, the U.S. Particle Accelerator School, the CERN Academic Training Programme, and various other venues. It is accessible to beginning graduate and upper-division undergraduate students in physics, mathematics, and engineering. The book begins with a historical overview of methods for generating and accelerating beams, high...
Beam Instabilities in the Scale Free Regime
Folli, Viola; Conti, Claudio; 10.1103/PhysRevLett.108.033901
2012-01-01
The instabilities arising in a one-dimensional beam sustained by the diffusive photorefractive nonlinearity in out-of-equilibrium ferroelectrics are theoretically and numerically investigated. In the "scale-free model", in striking contrast with the well-known spatial modulational instability, two different beam instabilities dominate: a defocusing and a fragmenting process. Both are independent of the beam power and are not associated to any specific periodic pattern.
Parametric resonance in concrete beam-columns
Sharma,Mamta R.; Singh,Arbind K; Benipal,Gurmail S
2014-01-01
A dynamic instability, called parametric resonance, is exhibited by undampedelastic beam-columns when under the action of pulsating axial force. The scope of the existing theory of parametric resonance is restricted to physically linear beam-columns undergoing finite lateral displacements. In this Paper, the dynamic behaviour of physically nonlinear elastic cracked concrete beam-columns under pulsating axial force and constant lateral force is investigated. The constitutive equations derived ...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
An optical Hamiltonian experiment and the beam dynamics
Energy Technology Data Exchange (ETDEWEB)
Bazzani, A. [Department of Physics and CIG, University of Bologna, INFN sezione di Bologna (Italy)]. E-mail: bazzani@bo.infn.it; Freguglia, P. [Department of Pure and Applied Mathematics, University of L' Aquila (Italy); Fronzoni, L. [Department of Physics and CISC, University of Pisa (Italy); Turchetti, G. [Department of Physics and CIG, University of Bologna, INFN sezione di Bologna (Italy)
2006-06-01
The analogy between geometric optics and Hamiltonian mechanics is used to propose an experiment that simulates the beam propagation in a focusing magnetic lattice of a particle accelerator. A laser beam is reflected several times by a parabolic mirror and the resulting pattern is registered by a photo camera. This experiment allows to illustrate some aspects of nonlinear beam transport in presence of nonlinearities and stochastic perturbations. The experimental results are discussed and compared with computer simulations.
Expanding contraceptive options.
1989-01-01
The goals of Family Health International (FHI) have been to introduce a variety of birth control options to people in developing countries, and to provide information to the user on the advantages and disadvantages of each method. FHI has worked with many developing countries in clinical trials of established as well as new contraceptive methods. These trials played an important part in making 2 sterilization procedures, laparoscopy and minilaparotomy popular for women. Further research improved the methods and have made them the most popular in the world, chosen by 130 million users. FHI is doing clinical trials on a new IUD, that is a copper bearing T-shaped device called the TCu380A. they have collected data on over 10,000 women using IUD's and early analysis indicates TCu380A is more effective than others. FHI is also evaluating devices such as Norplant that will prevent pregnancy up to 5 years by implanting the capsules in the arm. More than 8,000 women are being tested to determine the acceptability of implants in different geographical locations. Other research groups are doing work in 10 additional countries: Bangladesh will expand its program to 24,000 women and Nepal to 8,000 women. Trials are also being conducted on progestogen pills, since they do not lesson the volume of milk in breast feeding. FHI has also worked to introduce creative community-based distribution channels. In one case, specially trained health workers delivered contraceptives door-to-door in over 150,000 households. They found that 2 of 3 women accepted the pills and in a follow up survey 90% were still using them. FHI is now focusing on ways to improve moving new contraceptives from clinical testing on everyday use. They will coordinate training programs, educational material, media campaigns, and efforts with other international organizations, government agencies, and family planning groups.
Barrow, John D.
2005-07-01
Our love of art, writes John Barrow, is the end product of millions of years of evolution. How we react to a beautiful painting or symphony draws upon instincts laid down long before humans existed. Now, in this enhanced edition of the highly popular The Artful Universe , Barrow further explores the close ties between our aesthetic appreciation and the basic nature of the Universe. Barrow argues that the laws of the Universe have imprinted themselves upon our thoughts and actions in subtle and unexpected ways. Why do we like certain types of art or music? What games and puzzles do we find challenging? Why do so many myths and legends have common elements? In this eclectic and entertaining survey, Barrow answers these questions and more as he explains how the landscape of the Universe has influenced the development of philosophy and mythology, and how millions of years of evolutionary history have fashioned our attraction to certain patterns of sound and color. Barrow casts the story of human creativity and thought in a fascinating light, considering such diverse topics as our instinct for language, the origins and uses of color in nature, why we divide time into intervals as we do, the sources of our appreciation of landscape painting, and whether computer-generated fractal art is really art. Drawing on a wide variety of examples, from the theological questions raised by St. Augustine and C.S. Lewis to the relationship between the pure math of Pythagoras and the music of the Beatles, The Artful Universe Expanded covers new ground and enters a wide-ranging debate about the meaning and significance of the links between art and science.
Switching behaviour of a nonlinear Mach–Zehnder interferometer
Indian Academy of Sciences (India)
Arpita Srivastava; Punya Prasanna Paltani; S Medhekar
2010-04-01
In the present paper, a detailed investigation on the switching behaviour of a nonlinear Mach–Zehnder interferometer (NMZI) has been carried out using beam propagation method (BPM). A thorough investigation on input vs. output characteristic has been carried out by varying different parameters like length of the arms, refractive index of the linear/nonlinear arm, wavelength of the input beams and nonlinear coefficient of the material of the nonlinear arm. The input vs. output characteristic has also been investigated by shifting the balance point of the NMZI. The present paper provides a physically intuitive understanding of the effect of change in different parameters of the NMZI on its switching behaviour.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Transformation design and nonlinear Hamiltonians
Brougham, Thomas; Jex, Igor
2009-01-01
We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.
Terahertz beam shaping with metasurface
He, Jingwen; Wang, Sen; Zhang, Yan
2016-11-01
Based on metasurface, two beam shapers are designed to modulate the wavefront of the terahertz beam. One of the beam shapers is THz ring-Airy beam generator and the other is THz four-focus lens. Each beam shaper is composed of a serious of C-shaped slot antennas, which can be used to modulate the phase and amplitude of the cross-polarized scattered wave. A THz holographic imaging system is utilized to measure the field of the generated beams. The ring- Airy beam shaper is designed by replacing both the phase and amplitude of its initial electric field with the corresponding antennas. In the experiment, an abrupt focus following a parabolic trajectory is subsequently observed. This method can be expanded to other wavebands, such as the visible band, in which the ring-Airy beam shaper can replace traditional computer-generated holography to avoid undesirable multiple diffraction orders. The phase distribution of the four-focus lens is obtained by using the Yang-Gu amplitude-phase retrieval algorithm and then encoded to the antennas. Both the focusing and imaging properties are demonstrated. A clear image can be obtained with a bandwidth of 110 GHz. This type of transmissive metasurface beam shaper serves as an attractive alternative to conventional diffractive optical elements based on its small size, ease of fabrication, and low cost.
Yaglom law in the expanding solar wind
Gogoberidze, G; Carbone, V
2013-01-01
We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els\\"asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom's third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
Observation of Nonlinear Compton Scattering
Energy Technology Data Exchange (ETDEWEB)
Kotseroglou, T.
2003-12-19
This experiment tests Quantum Electrodynamics in the strong field regime. Nonlinear Compton scattering has been observed during the interaction of a 46.6 GeV electron beam with a 10{sup 18} W/cm{sup 2} laser beam. The strength of the field achieved was measured by the parameter {eta} = e{var_epsilon}{sub rms}/{omega}mc = 0.6. Data were collected with infrared and green laser photons and circularly polarized laser light. The timing stabilization achieved between the picosecond laser and electron pulses has {sigma}{sub rms} = 2 ps. A strong signal of electrons that absorbed up to 4 infrared photons (or up to 3 green photons) at the same point in space and time, while emitting a single gamma ray, was observed. The energy spectra of the scattered electrons and the nonlinear dependence of the electron yield on the field strength agreed with the simulation over 3 orders of magnitude. The detector could not resolve the nonlinear Compton scattering from the multiple single Compton scattering which produced rates of scattered electrons of the same order of magnitude. Nevertheless, a simulation has studied this difference and concluded that the scattered electron rates observed could not be accounted for only by multiple ordinary Compton scattering; nonlinear Compton scattering processes are dominant for n {ge} 3.
Bigelow Expandable Activity Module Project
National Aeronautics and Space Administration — The BEAM project advances inflatable habitat technology further and conducts flight demonstration of a commercially-designed inflatable system to achieve Technology...
Nonlinear Energy Collimation System for Linear Colliders
Resta-Lopez, Javier
2011-01-01
The post-linac energy collimation system of multi-TeV linear colliders is designed to fulfil an important function of protection of the Beam Delivery System (BDS) against miss-steered beams likely generated by failure modes in the main linac. For the case of the Compact Linear Collider (CLIC), the energy collimators are required to withstand the impact of a full bunch train in case of failure. This is a very challenging task, assuming the nominal CLIC beam parameters at 1.5 TeV beam energy. The increase of the transverse spot size at the collimators using nonlinear magnets is a potential solution to guarantee the survival of the collimators. In this paper we present an alternative nonlinear optics based on a skew sextupole pair for energy collimation. Performance simulation results are also presented.
Development of Self-Expanding Idealflo (tm) Sandcontrol Technology
Energy Technology Data Exchange (ETDEWEB)
Jeff A. Spray
2007-09-30
Development of Self-Expanding Idealflo{trademark} Sandscreen Technology was a successfully executed design-by-analysis through field demonstration project. This final report is presented as a two-part progression of concept development and manufacturing activities. The first part, conceptual development activities, discusses novel specifications creation and non-linear analytical design generation. The second part, manufacturing, contains achievement related information for detailed-design, fabrication, mechanical testing, and field demonstration activities.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Particles formation in an expanding plasma
Energy Technology Data Exchange (ETDEWEB)
Lescoute, E.; Hallo, L.; Chimier, B.; Tikhonchuk, V.T.; Stenz, C. [Bordeaux-1 Univ., CELIA, CNRS-CEA, 33 - Talence (France); Hebert, D.; Chevalier, J.M.; Rullier, J.L.; Palmier, S. [CEA Centre d' Etudes Scientifiques et Techniques d' Aquitaine, 33 - Le Barp (France)
2009-08-15
Interaction of a laser beam with a target generates a high velocity expanding plasma plume, solid debris and liquid nano- and micro-particles. They are produced from plasma recombination and vapor condensation and can be deposited on optical elements located nearby the target. Two distinct kinds of particles were observed depending on the temperature achieved in the plasma plume: large micrometer-size fragments for temperatures lower than the critical temperature, and very small nanometer-size particles for higher temperatures. The paper presents experimental observations of fragments and nano-particles in plasma plumes and a comparison with models. A good agreement has been found for nano-particle sizes and distributions. This simple modeling can also be used for nuclei production in the nanosecond time scale. Our estimates show that particle size can be correlated to laser wavelength and fluences.
Vibrations and stability of complex beam systems
Stojanović, Vladimir
2015-01-01
This book reports on solved problems concerning vibrations and stability of complex beam systems. The complexity of a system is considered from two points of view: the complexity originating from the nature of the structure, in the case of two or more elastically connected beams; and the complexity derived from the dynamic behavior of the system, in the case of a damaged single beam, resulting from the harm done to its simple structure. Furthermore, the book describes the analytical derivation of equations of two or more elastically connected beams, using four different theories (Euler, Rayleigh, Timoshenko and Reddy-Bickford). It also reports on a new, improved p-version of the finite element method for geometrically nonlinear vibrations. The new method provides more accurate approximations of solutions, while also allowing us to analyze geometrically nonlinear vibrations. The book describes the appearance of longitudinal vibrations of damaged clamped-clamped beams as a result of discontinuity (damage). It...
High-power laser delocalization in plasmas leading to long-range beam merging
Energy Technology Data Exchange (ETDEWEB)
Nakatsutsumi, M.; Marques, J.R.; Antici, P.; Bourgeois, N.; Romagnani, L.; Audebert, P.; Fuchs, J. [UPMC, CEA, CNRS, LULI, Ecole Polytech, F-91128 Palaiseau (France); Nakatsutsumi, M.; Kodama, R. [Osaka Univ, Grad Sch Engn, Suita, Osaka 5650871 (Japan); Antici, P. [Univ Roma La Sapienza, Dipartimento SBAI, I-00161 Rome (Italy); Feugeas, J.L.; Nicolai, P. [Univ Bordeaux 1, CNRS, CEA, Ctr Lasers Intenses and Applicat, F-33405 Talence (France); Lin, T. [Fox Chase Canc Ctr, Philadelphia, PA 19111 (United States)
2010-07-01
Attraction and fusion between co-propagating light beams, mutually coherent or not, can take place in nonlinear media as a result of the beam power modifying the refractive index of the medium. In the context of high-power light beams, induced modifications of the beam patterns could potentially impact many topics, including long-range laser propagation, the study of astrophysical colliding blast waves and inertial confinement fusion. Here, through experiments and simulations, we show that in a fully ionized plasma, which is a nonlinear medium, beam merging can take place for high-power and mutually incoherent beams that are initially separated by several beam diameters. This is in contrast to the usual assumption that this type of interaction is limited to beams separated by only one beam diameter. This effect, which is orders of magnitude more significant than Kerr-like nonlinearity in gases, demonstrates the importance of potential cross-talk amongst multiple beams in plasma. (authors)
Lyle, Karen H.; Vassilakos, Gregory J.
2015-01-01
This report summarizes the initial modeling of the global response of the Bigelow Expandable Activity Module (BEAM) to micrometeorite and orbital debris(MMOD) impacts using a structural, nonlinear, transient dynamic, finite element code. These models complement the on-orbit deployment of the Distributed Impact Detection System (DIDS) to support structural health monitoring studies. Two global models were developed. The first focused exclusively on impacts on the soft-goods (fabric-envelop) portion of BEAM. The second incorporates the bulkhead to support understanding of bulkhead impacts. These models were exercised for random impact locations and responses monitored at the on-orbit sensor locations. The report concludes with areas for future study.
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.
Gamp, Alexander
2013-01-01
We begin by giving a description of the radio-frequency generator-cavity-beam coupled system in terms of basic quantities. Taking beam loading and cavity detuning into account, expressions for the cavity impedance as seen by the generator and as seen by the beam are derived. Subsequently methods of beam-loading compensation by cavity detuning, radio-frequency feedback and feedforward are described. Examples of digital radio-frequency phase and amplitude control for the special case of superconducting cavities are also given. Finally, a dedicated phase loop for damping synchrotron oscillations is discussed.
Trofimov, Vyacheslav A.; Lysak, T. M.
2016-05-01
We demonstrate a new possibility of a soliton velocity control at its propagation in a nonlinear layered structure (1D photonic crystal) which is placed in a nonlinear ambient medium. Nonlinear response of the ambient medium, as well as the PhC layers, is cubic. At the initial time moment, a soliton is spread over a few layers of PhC. Then, soliton propagates across the layered structure because of the initial wave-vector direction presence for the laser beam. The soliton reaches the PhC faces and reflects from them or passes through the face. As a nonlinear medium surrounds the PhC, the laser beam obtains additional impulse after interaction with this medium and accelerates (or slows down or stops near the PhC face). Nonlinear response of the ambient medium can be additionally created by another laser beam which shines near the PhC faces.
Design method of coaxial reflex hollow beam generator
Wang, Jiake; Xu, Jia; Fu, Yuegang; He, Wenjun; Zhu, Qifan
2016-10-01
In view of the light energy loss in central obscuration of coaxial reflex optical system, the design method of a kind of hollow beam generator is introduced. First of all, according to the geometrical parameter and obscuration ratio of front-end coaxial reflex optical system, calculate the required physical dimension of hollow beam, and get the beam expanding rate of the hollow beam generator according to the parameters of the light source. Choose the better enlargement ratio of initial expanding system using the relational expression of beam expanding rate and beam expanding rate of initial system; the traditional design method of the reflex optical system is used to design the initial optical system, and then the position of rotation axis of the hollow beam generator can be obtained through the rotation axis translation formula. Intercept the initial system bus bar using the rotation axis after the translation, and rotate the bus bar around the rotation axis for 360°, so that two working faces of the hollow beam generator can be got. The hollow beam generator designed by this method can get the hollow beam that matches the front-end coaxial reflex optical system, improving the energy utilization ratio of beam and effectively reducing the back scattering of transmission system.
Trivalent expanders and hyperbolic surfaces
Ivrissimtzis, Ioannis; Vdovina, Alina
2012-01-01
We introduce a family of trivalent expanders which tessellate compact hyperbolic surfaces with large isometry groups. We compare this family with Platonic graphs and modifications of them and prove topological and spectral properties of these families.
Focused Ion Beam Technology for Optoelectronic Devices
Reithmaier, J. P.; Bach, L.; Forchel, A.
2003-08-01
High-resolution proximity free lithography was developed using InP as anorganic resist for ion beam exposure. InP is very sensitive on ion beam irradiation and show a highly nonlinear dose dependence with a contrast function comparable to organic electron beam resists. In combination with implantation induced quantum well intermixing this new lithographic technique based on focused ion beams is used to realize high performance nano patterned optoelectronic devices like complex coupled distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers.
THREE-BEAM INSTABILITY IN THE LHC*
Burov, A
2013-01-01
In the LHC, a transverse instability is regularly observed at 4TeV right after the beta-squeeze, when the beams are separated by about their ten transverse rms sizes [1-3], and only one of the two beams is seen as oscillating. So far only a single hypothesis is consistent with all the observations and basic concepts, one about a third beam - an electron cloud, generated by the two proton beams in the high-beta areas of the interaction regions. The instability results from a combined action of the cloud nonlinear focusing and impedance.
Energy Technology Data Exchange (ETDEWEB)
Yano, Yasushige; Goto, Akira; Katayama, Takeshi [Institute of Physical and Chemical Research, Wako, Saitama (Japan)
1997-03-01
The RARF proposes `RIKEN RI Beam Factory` as a next facility-expanding project. The factory makes it the primary aim to provide RI (Radioactive Isotope) beams covering over the whole atomic-mass range with the world-highest intensity in a wide energy range up to several hundreds MeV/nucleon. These RI beams are generated by the fragmentation of high-intensity heavy-ion beams. For the efficient production heavy-ion energies will be boosted up to over 100 MeV/nucleon even for very heavy ions by a K2500-MeV superconducting ring cyclotron serving as a post accelerator of the existing K540-MeV ring cyclotron. A new type of experimental installation called `MUSES` (Multi-USe Experimental Storage rings) will be constructed as well. With MUSES, various types of unique colliding experiments will become possible. (author)
Dynamic Response of Axially Loaded Euler-Bernoulli Beams
DEFF Research Database (Denmark)
Bayat, M.; Barari, Amin; Shahidi, M.
2011-01-01
expressions for geometrically nonlinear vibration of beams are provided. The effect of vibration amplitude on the nonlinear frequency is discussed. Comparison between Energy Balance Method results and those available in literature demonstrates the accuracy of this method. In Energy Balance Method contrary...... to the conventional methods, only one iteration leads to high accuracy of the solutions which are valid for a wide range of vibration amplitudes.......The current research deals with application of a new analytical technique called Energy Balance Method (EBM) for a nonlinear problem. Energy Balance Method is used to obtain the analytical solution for nonlinear vibration behavior of Euler-Bernoulli beams subjected to axial loads. Analytical...