Tadesse, T.; Wiegelmann, T.; Gosain, S.; MacNeice, P.; Pevtsov, A. A.
2014-01-01
Context. The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently, there are several modelling techniques being used to calculate three-dimensional field lines into the solar atmosphere. Aims. For the first time, synoptic maps of a photospheric-vector magnetic field synthesized from the vector spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. Methods. We solve the nonlinear force-free field equations using an optimization principle in spherical geometry. The resulting threedimensional magnetic fields are used to estimate the magnetic free energy content E(sub free) = E(sub nlfff) - E(sub pot), which is the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the atmospheric imaging assembly (AIA) on board the Solar Dynamics Observatory (SDO). Results. For a single Carrington rotation 2121, we find that the global nonlinear force-free field (NLFFF) magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.
NONLINEAR FORCE-FREE MAGNETIC FIELD FITTING TO CORONAL LOOPS WITH AND WITHOUT STEREOSCOPY
International Nuclear Information System (INIS)
Aschwanden, Markus J.
2013-01-01
We developed a new nonlinear force-free magnetic field (NLFFF) forward-fitting algorithm based on an analytical approximation of force-free and divergence-free NLFFF solutions, which requires as input a line-of-sight magnetogram and traced two-dimensional (2D) loop coordinates of coronal loops only, in contrast to stereoscopically triangulated three-dimensional loop coordinates used in previous studies. Test results of simulated magnetic configurations and from four active regions observed with STEREO demonstrate that NLFFF solutions can be fitted with equal accuracy with or without stereoscopy, which relinquishes the necessity of STEREO data for magnetic modeling of active regions (on the solar disk). The 2D loop tracing method achieves a 2D misalignment of μ 2 = 2.°7 ± 1.°3 between the model field lines and observed loops, and an accuracy of ≈1.0% for the magnetic energy or free magnetic energy ratio. The three times higher spatial resolution of TRACE or SDO/AIA (compared with STEREO) also yields a proportionally smaller misalignment angle between model fit and observations. Visual/manual loop tracings are found to produce more accurate magnetic model fits than automated tracing algorithms. The computation time of the new forward-fitting code amounts to a few minutes per active region.
A Non-Linear Force-Free Field Model for the Evolving Magnetic Structure of Solar Filaments
Mackay, Duncan H.; van Ballegooijen, A. A.
2009-12-01
In this paper the effect of a small magnetic element approaching the main body of a solar filament is considered through non-linear force-free field modeling. The filament is represented by a series of magnetic dips. Once the dips are calculated, a simple hydrostatic atmosphere model is applied to determine which structures have sufficient column mass depth to be visible in Hα. Two orientations of the bipole are considered, either parallel or anti-parallel to the overlying arcade. The magnetic polarity that lies closest to the filament is then advected towards the filament. Initially for both the dominant and minority polarity advected elements, right/left bearing barbs are produced for dextral/sinsitral filaments. The production of barbs due to dominant polarity elements is a new feature. In later stages the filament breaks into two dipped sections and takes a highly irregular, non-symmetrical form with multiple pillars. The two sections are connected by field lines with double dips even though the twist of the field is less than one turn. Reconnection is not found to play a key role in the break up of the filament. The non-linear force-free fields produce very different results to extrapolated linear-force free fields. For the cases considered here the linear force-free field does not produce the break up of the filament nor the production of barbs as a result of dominant polarity elements.
Solar Force-free Magnetic Fields
Directory of Open Access Journals (Sweden)
Thomas Wiegelmann
2012-09-01
Full Text Available The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS and space-born (for example Hinode and SDO instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.
Jiang, Chaowei; Wu, S. T.; Feng, Xueshang; Hu, Qiang
2014-05-01
Solar filaments are commonly thought to be supported in magnetic dips, in particular, in those of magnetic flux ropes (FRs). In this Letter, based on the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is a first, in the sense that current NLFFF extrapolations including the presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion lines (PILs) with strong transverse field and magnetic shear, and the existence of an FR is usually predictable. In contrast, the present filament lies along the weak-field region (photospheric field strength barbs very well, which strongly supports the FR-dip model for filaments. The filament is stably sustained because the FR is weakly twisted and strongly confined by the overlying closed arcades.
Energy Technology Data Exchange (ETDEWEB)
Jiang, Chaowei; Wu, S. T.; Hu, Qiang [Center for Space Plasma and Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35899 (United States); Feng, Xueshang, E-mail: cwjiang@spaceweather.ac.cn, E-mail: wus@uah.edu, E-mail: qh0001@uah.edu, E-mail: fengx@spaceweather.ac.cn [SIGMA Weather Group, State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190 (China)
2014-05-10
Solar filaments are commonly thought to be supported in magnetic dips, in particular, in those of magnetic flux ropes (FRs). In this Letter, based on the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is a first, in the sense that current NLFFF extrapolations including the presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion lines (PILs) with strong transverse field and magnetic shear, and the existence of an FR is usually predictable. In contrast, the present filament lies along the weak-field region (photospheric field strength ≲ 100 G), where the PIL is very fragmented due to small parasitic polarities on both sides of the PIL and the transverse field has a low signal-to-noise ratio. Thus, extrapolating a large-scale FR in such a case represents a far more difficult challenge. We demonstrate that our CESE-MHD-NLFFF code is sufficient for the challenge. The numerically reproduced magnetic dips of the extrapolated FR match observations of the filament and its barbs very well, which strongly supports the FR-dip model for filaments. The filament is stably sustained because the FR is weakly twisted and strongly confined by the overlying closed arcades.
Ohmic dissipation and relaxation of force-free magnetic fields
International Nuclear Information System (INIS)
Solov'ev, A.A.
1985-01-01
A study is made of the process of passive ohmic dissipation of a force-free magnetic field in a low-pressure plasma with inhomogeneous conductivity. It is shown that the force-free field (curl →H = α→H) preserves its geometrical shape in the process of the dissipation if the ratio α 2 /σ does not depend on the coordinates. The process of topological resistive relaxation of a force-free field in a twisted magnetic loop to the state with least magnetic energy is investigated. It is found that for fixed external pressure and given moment of the forces at the ends of the magnetic loop a uniformly twisted magnetic filament corresponds to this state. Taylor's relaxation model is analyzed critically. It is shown that a force-free field of variable sign with α = const corresponds to a minimum of only the ratio ε/K, where K is the spirality of the field, and not to a minimum of the total magnetic energy ε /sub m/ of the system
Force-free field model of ball lightning
Tsui, K. H.
2001-03-01
Due to the nature that the force-free magnetic field, whose current carried by the conducting plasma is everywhere parallel to the magnetic field it generates, is the minimum energy configuration under the constraint of magnetic helicity conservation, ball lightning is considered as a self-organized phenomenon with a plasma fireball immersed in a spherical force-free magnetic field. Since this field does not exert force on the plasma, the plasma pressure, by itself, is in equilibrium with the surrounding environment, and the force-free magnetic field can take on any value without affecting the plasma. Due to this second feature, singular solutions of the magnetic field that are otherwise excluded are allowed, which enable a large amount of energy to be stored to sustain the ball lightning. The singularity is truncated only by the physical limit of current density that a plasma can carry. Scaling the customary soccer-size fireball to larger dimensions could account for day and night sightings of luminous objects in the sky.
Energy buildup in sheared force-free magnetic fields
Wolfson, Richard; Low, Boon C.
1992-01-01
Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.
Energy of Force-Free Magnetic Fields in Relation to Coronal Mass Ejections; TOPICAL
International Nuclear Information System (INIS)
G.S. Choe; C.Z. Cheng
2002-01-01
In typical observations of coronal mass ejections (CMEs), a magnetic structure of a helmet-shaped closed configuration bulges out and eventually opens up. However, a spontaneous transition between these field configurations has been regarded to be energetically impossible in force-free fields according to the Aly-Sturrock theorem. The theorem states that the maximum energy state of force-free fields with a given boundary normal field distribution is the open field. The theorem implicitly assumes the existence of the maximum energy state, which may not be taken for granted. In this study, we have constructed force-free fields containing tangential discontinuities in multiple flux systems. These force-free fields can be generated from a potential field by footpoint motions that do not conserve the boundary normal field distribution. Some of these force-free fields are found to have more magnetic energy than the corresponding open fields. The constructed force-free configurations are compared with observational features of CME-bearing active regions. Possible mechanisms of CMEs are also discussed
Linear force-free field of a toroidal symmetry
Czech Academy of Sciences Publication Activity Database
Romashets, E. P.; Vandas, Marek
2009-01-01
Roč. 499, č. 1 (2009), s. 17-20 ISSN 0004-6361 R&D Projects: GA AV ČR(CZ) 1QS300120506; GA MŠk(CZ) ME09032; GA ČR GA205/09/0170 Institutional research plan: CEZ:AV0Z10030501 Keywords : magnetic fields * solar wind * magnetic clouds Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 4.179, year: 2009
Quasi-static evolution of sheared force-free fields and the solar flare problem
Aly, J. J.
1985-01-01
Some new results are given showing the possible evolution of a two-dimensional force-free field in the half-space z greater than 0 toward an open field. This evolution is driven by shearing motions applied to the feet of the field lines on the boundary z = 0. The consequences of these results for a model of the two-ribbon solar flare are discussed.
Magnetohydrodynamic Modeling of Solar Coronal Dynamics with an Initial Non-force-free Magnetic Field
Energy Technology Data Exchange (ETDEWEB)
Prasad, A.; Bhattacharyya, R.; Kumar, Sanjay [Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Bari Road, Udaipur-313001 (India)
2017-05-01
The magnetic fields in the solar corona are generally neither force-free nor axisymmetric and have complex dynamics that are difficult to characterize. Here we simulate the topological evolution of solar coronal magnetic field lines (MFLs) using a magnetohydrodynamic model. The simulation is initialized with a non-axisymmetric non-force-free magnetic field that best correlates with the observed vector magnetograms of solar active regions (ARs). To focus on these ideas, simulations are performed for the flaring AR 11283 noted for its complexity and well-documented dynamics. The simulated dynamics develops as the initial Lorentz force pushes the plasma and facilitates successive magnetic reconnections at the two X-type null lines present in the initial field. Importantly, the simulation allows for the spontaneous development of mass flow, unique among contemporary works, that preferentially reconnects field lines at one of the X-type null lines. Consequently, a flux rope consisting of low-lying twisted MFLs, which approximately traces the major polarity inversion line, undergoes an asymmetric monotonic rise. The rise is attributed to a reduction in the magnetic tension force at the region overlying the rope, resulting from the reconnection. A monotonic rise of the rope is in conformity with the standard scenario of flares. Importantly, the simulated dynamics leads to bifurcations of the flux rope, which, being akin to the observed filament bifurcation in AR 11283, establishes the appropriateness of the initial field in describing ARs.
On the Shape of Force-Free Field Lines in the Solar Corona
Prior, C.
2012-02-02
This paper studies the shape parameters of looped field lines in a linear force-free magnetic field. Loop structures with a sufficient amount of kinking are generally seen to form S or inverse S (Z) shapes in the corona (as viewed in projection). For a single field line, we can ask how much the field line is kinked (as measured by the writhe), and how much neighbouring flux twists about the line (as measured by the twist number). The magnetic helicity of a flux element surrounding the field line can be decomposed into these two quantities. We find that the twist helicity contribution dominates the writhe helicity contribution, for field lines of significant aspect ratio, even when their structure is highly kinked. These calculations shed light on some popular assumptions of the field. First, we show that the writhe of field lines of significant aspect ratio (the apex height divided by the footpoint width) can sometimes be of opposite sign to the helicity. Secondly, we demonstrate the possibility of field line structures which could be interpreted as Z-shaped, but which have a helicity value sign expected of an S-shaped structure. These results suggest that caution should be exercised in using two-dimensional images to draw conclusions on the helicity value of field lines and flux tubes. © 2012 Springer Science+Business Media B.V.
Construction of force-free fields which have toroidal surfaces about a given surface
International Nuclear Information System (INIS)
Bouligand, G.
1983-05-01
A study of two-fields (B vector, rotB vector) of conservative flux which admits a family of toroidal surfaces of parameter phi on a domain limited by a given surface S, suggests their construction by a Cauchy-Arzela method of step by step. Taking into account the Newcomb condition this method is consistent with force-free magnetic fields and with helical equilibria with scalar pressure. The method supposes that B vector is of class C 1 . This construction makes use of the remarkable property of the field B vector to be the surface gradient of a generating multivalued function Q on a closed surface. Consequently, the initial surface will be given with its normal metric coefficient K; that is to say, B vector admits a family F of homotopic surfaces on a infinitesimal domain about S, an element of F. From this, the periodic part of Q is a solution of a Beltrami equation for the flux conservation of which numerical resolution is envisaged. The study of these fields is made in a biorthogonal system of coordinates. The coeffficients of the two fundamental metric forms of magnetic surfaces vary with phi and are interrelated by a sixth order differential system of equations which gives their variation [fr
Current sheet formation in a sheared force-free-magnetic field. [in sun
Wolfson, Richard
1989-01-01
This paper presents the results of a study showing how continuous shearing motion of magnetic footpoints in a tenuous, infinitely conducting plasma can lead to the development of current sheets, despite the absence of such sheets or even of neutral points in the initial state. The calculations discussed here verify the earlier suggestion by Low and Wolfson (1988) that extended current sheets should form due to the shearing of a force-free quadrupolar magnetic field. More generally, this work augments earlier studies suggesting that the appearance of discontinuities - current sheets - may be a necessary consequence of the topological invariance imposed on the magnetic field geometry of an ideal MHD system by virtue of its infinite conductivity. In the context of solar physics, the work shows how the gradual and continuous motion of magnetic footpoints at the solar photosphere may lead to the buildup of magnetic energy that can then be released explosively when finite conductivity effects become important and lead to the rapid dissipation of current sheets. Such energy release may be important in solar flares, coronal mass ejections, and other eruptive events.
Non-linear force-free magnetic dip models of quiescent prominence fine structures
Czech Academy of Sciences Publication Activity Database
Gunár, Stanislav; Mackay, D. H.; Anzer, U.; Heinzel, Petr
2013-01-01
Roč. 551, March (2013), A3/1-A3/9 ISSN 0004-6361 R&D Projects: GA ČR GAP209/12/0906; GA ČR GAP209/10/1680 Institutional support: RVO:67985815 Keywords : Sun filaments * Sun prominences * magnetic fields Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 4.479, year: 2013
Quasi-static evolution of force-free magnetic fields and a model for two-ribbon solar flares
Aly, J. J.
1985-01-01
It is shown that a two-dimensional force-free field in the solar corona can evolve in a quasi-static manner toward an open configuration, assuming the coronal field is invariant with respect to translations parallel to the x-axis. The theoretical result is applied to the quantitative theory of the evolution of two-ribbon solar flares of Kopp and Pneuman (1976), and the results are discussed. It is concluded that the two-dimensional force is the principal mechanism for the opening of the coronal magnetic field prior to reconnection during a solar flare.
Kojima, Yasufumi; Okamoto, Satoki
2018-04-01
A magnetar's magnetosphere gradually evolves by the injection of energy and helicity from the interior. Axisymmetric static solutions for a relativistic force-free magnetosphere with a power-law current model are numerically obtained. They provide information about the configurations in which the stored energy is large. The energy along a sequence of equilibria increases and becomes sufficient to open the magnetic field. A magnetic flux rope, in which a large amount of toroidal field is confined, is formed in the vicinity of the star, for states exceeding the open field energy. These states are energetically metastable, and the excess energy may be ejected as a magnetar outburst.
EFFECT OF POLARIMETRIC NOISE ON THE ESTIMATION OF TWIST AND MAGNETIC ENERGY OF FORCE-FREE FIELDS
International Nuclear Information System (INIS)
Tiwari, Sanjiv Kumar; Venkatakrishnan, P.; Gosain, Sanjay; Joshi, Jayant
2009-01-01
The force-free parameter α, also known as helicity parameter or twist parameter, bears the same sign as the magnetic helicity under some restrictive conditions. The single global value of α for a whole active region gives the degree of twist per unit axial length. We investigate the effect of polarimetric noise on the calculation of global α value and magnetic energy of an analytical bipole. The analytical bipole has been generated using the force-free field approximation with a known value of constant α and magnetic energy. The magnetic parameters obtained from the analytical bipole are used to generate Stokes profiles from the Unno-Rachkovsky solutions for polarized radiative transfer equations. Then we add random noise of the order of 10 -3 of the continuum intensity (I c ) in these profiles to simulate the real profiles obtained by modern spectropolarimeters such as Hinode (SOT/SP), SVM (USO), ASP, DLSP, POLIS, and SOLIS etc. These noisy profiles are then inverted using a Milne-Eddington inversion code to retrieve the magnetic parameters. Hundred realizations of this process of adding random noise and polarimetric inversion is repeated to study the distribution of error in global α and magnetic energy values. The results show that (1) the sign of α is not influenced by polarimetric noise and very accurate values of global twist can be calculated, and (2) accurate estimation of magnetic energy with uncertainty as low as 0.5% is possible under the force-free condition.
Wolfson, Richard
1990-01-01
Thin current sheets arising in tenuous, magnetized solar coronal plasmas may constitute an important mechanism for energy buildups and subsequent energy releases; they could arise from the continuous-and-random motion of magnetic footprints associated with photospheric velocity fields. A model is presented for study of the quasi-static evolution of current sheets due to shearing of the footpoints, in a highly idealized geometry that incorporates an abrupt jump in field-line connectivity. The model highlights that formation of thin current layers and allows large shearing motions prior to violation of the linear approximation. Excess energy comparable to that released by solar flares can be stored in a sheared field.
Chiu, Y. T.; Hilton, H. H.
1977-01-01
Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented.
One-Dimensional Vlasov-Maxwell Equilibrium for the Force-Free Harris Sheet
International Nuclear Information System (INIS)
Harrison, Michael G.; Neukirch, Thomas
2009-01-01
In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet
Comparative study of a constant-alpha force-free field and its approximations in an ideal toroid
Czech Academy of Sciences Publication Activity Database
Vandas, Marek; Romashets, E.
2015-01-01
Roč. 580, August (2015), A123/1-A123/7 ISSN 0004-6361 R&D Projects: GA ČR(CZ) GA14-19376S Institutional support: RVO:67985815 Keywords : solar wind * magnetic fields * magnetohydrodynamics Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 4.378, year: 2014
The force-free configuration of flux ropes in geomagnetotail: Cluster observations
Yang, Y. Y.; Shen, C.; Zhang, Y. C.; Rong, Z. J.; Li, X.; Dunlop, M.; Ma, Y. H.; Liu, Z. X.; Carr, C. M.; Rème, H.
2014-08-01
Unambiguous knowledge of magnetic field structure and the electric current distribution is critical for understanding the origin, evolution, and related dynamic properties of magnetic flux ropes (MFRs). In this paper, a survey of 13 MFRs in the Earth's magnetotail are conducted by Cluster multipoint analysis, so that their force-free feature, i.e., the kind of magnetic field structure satisfying J × B = 0, can be probed directly. It is showed that the selected flux ropes with the bipolar signature of the south-north magnetic field component generally lie near the equatorial plane, as expected, and that the magnetic field gradient is rather weak near the axis center, where the curvature radius is large. The current density (up to several tens of nA/m2) reaches their maximum values as the center is approached. It is found that the stronger the current density, the smaller the angles between the magnetic field and current in MFRs. The direct observations show that only quasi force-free structure is observed, and it tends to appear in the low plasma beta regime (in agreement with the theoretic results). The quasi force-free region is generally found to be embedded in the central portion of the MFRs, where the current is approximately field aligned and proportional to the strength of core field. It is shown that ~60% of surveyed MFRs can be globally approximated as force free. The force-free factor α is found to be nonconstantly varied through the quasi force-free MFR, suggesting that the force-free structure is nonlinear.
Field guide to nonlinear optics
Powers, Peter E
2013-01-01
Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics
Ball lightning as a force-free magnetic knot
Ranada; Soler; Trueba
2000-11-01
The stability of fireballs in a recent model of ball lightning is studied. It is shown that the balls shine while relaxing in an almost quiescent expansion, and that three effects contribute to their stability: (i) the formation in each one during a process of Taylor relaxation of a force-free magnetic field, a concept introduced in 1954 in order to explain the existence of large magnetic fields and currents in stable configurations of astrophysical plasmas; (ii) the so called Alfven conditions in magnetohydrodynamics; and (iii) the approximate conservation of the helicity integral. The force-free fields that appear are termed "knots" because their magnetic lines are closed and linked.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non...
Nonlinear smoothing for random fields
Aihara, ShinIchi; Bagchi, Arunabha
1995-01-01
Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the
Nonlinear electromagnetic fields and symmetries
Barjašić, Irena; Gulin, Luka; Smolić, Ivica
2017-06-01
We extend the classical results on the symmetry inheritance of the canonical electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider class of models, which include those of the Born-Infeld, power Maxwell and the Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of electromagnetic scalar potentials and these are proven to be constant on the Killing horizons. Finally, using the relations obtained along the analysis, we generalize and simplify the recent proof for the symmetry inheritance of the 3-dimensional case, as well as give the first constraint for the higher dimensional electromagnetic fields.
Force-free electromagnetic pulses in a laboratory plasma
Stenzel, R. L.; Urrutia, J. M.
1990-01-01
A short, intense current pulse is drawn from an electrode immersed in a magnetized afterglow plasma. The induced magnetic field B(r,t) assumes the shape of a helical double vortex which propagates along B(0) through the uniform plasma as a whistler mode. The observations support a prediction of force-free (J x B + neE = 0) electromagnetic fields and solitary waves. Energy and helicity are approximately conserved.
High field optical nonlinearities in gases
Cheng, Yu-Hsiang
Optical femtosecond self-channeling in gases, also called femtosecond filamentation, has become an important area of research in high field nonlinear optics. Filamentation occurs when laser light self-focuses in a gas owing to self-induced nonlinearity, and then defocuses in the plasma generated by the self-focused beam. The result of this process repeating itself multiple times is an extended region of plasma formation. Filamentation studies have been motivated by the extremely broad range of applications, especially in air, including pulse compression, supercontinuum generation, broadband high power terahertz pulse generation, discharge triggering and guiding, and remote sensing. Despite the worldwide work in filamentation, the fundamental gas nonlinearities governing self-focusing had never been directly measured in the range of laser intensity up to and including the ionization threshold. This dissertation presents the first such measurements. We absolutely measured the temporal refractive index change of O2, N2, Ar, H2, D2 and N2O caused by highfield ultrashort optical pulses with single-shot supercontinuum spectral interferometry, cleanly separating for the first time the instantaneous electronic and delayed rotational nonlinear response in diatomic gases. We conclusively showed that a recent claim by several European groups that the optical bound electron nonlinearity saturates and goes negative is not correct. Such a phenomenon would preclude the need for plasma to provide the defocusing contribution for filamentation. Our results show that the 'standard model of filamentation', where the defocusing is provided by plasma, is correct. Finally, we demonstrated that high repetition rate femtosecond laser pulses filamenting in gases can generate long-lived gas density `holes' which persist on millisecond timescales, long after the plasma has recombined. Gas density decrements up to ~20% have been measured. The density hole refilling is dominated by thermal
Nonlinear relaxation field in charged systems under high electric fields
International Nuclear Information System (INIS)
Morawetz, K.
2000-01-01
The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - On-Sager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared. (author)
The Force-Free Magnetosphere of a Rotating Black Hole
Contopoulos, Ioannis; Kazanas, Demosthenes; Papadopoulos, Demetrios B.
2013-01-01
We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."
Quantization of scalar field with nonlinearity over derivatives
International Nuclear Information System (INIS)
Sveshnikov, K.A.
1978-01-01
The scalar field, whose Lagrangian is nonlinear both over the field and field derivatives, is considered in two-dimensional space-time. It is shown, that some modification of N.N. Bogolyubov transformation allows one to carry out the canonical quantization in spite of the nonlinear connection of canonical momentum with the field derivatives
Nonlinear dynamics in the relativistic field equation
International Nuclear Information System (INIS)
Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An
2007-01-01
We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory
Three-dimensional force-free looplike magnetohydrodynamic equilibria
Finn, John M.; Guzdar, Parvez N.; Usikov, Daniel
1994-01-01
Computations of three-dimensional force-free magnetohydrodynamic (MHD) equilibria, del x B = lambdaB with lambda = lambda(sub 0), a constant are presented. These equilibria are determined by boundary conditions on a surface corresponding to the solar photosphere. The specific boundary conditions used correspond to looplike magnetic fields in the corona. It is found that as lambda(sub 0) is increased, the loops of flux become kinked, and for sufficiently large lambda(sub 0), develop knots. The relationship between the kinking and knotting properties of these equilibria and the presence of a kink instability and related loss of equilibrium is explored. Clearly, magnetic reconnection must be involved for an unknotted loop equilibrium to become knotted, and speculations are made about the creation of a closed hyperbolic field line (X-line) about which this reconnection creating knotted field lines is centered.
Time-Dependent Mean-Field Games with Logarithmic Nonlinearities
Gomes, Diogo A.
2015-10-06
In this paper, we prove the existence of classical solutions for time-dependent mean-field games with a logarithmic nonlinearity and subquadratic Hamiltonians. Because the logarithm is unbounded from below, this nonlinearity poses substantial mathematical challenges that have not been addressed in the literature. Our result is proven by recurring to a delicate argument which combines Lipschitz regularity for the Hamilton-Jacobi equation with estimates for the nonlinearity in suitable Lebesgue spaces. Lipschitz estimates follow from an application of the nonlinear adjoint method. These are then combined with a priori bounds for solutions of the Fokker-Planck equation and a concavity argument for the nonlinearity.
Nonlinear dynamics of semiconductors in strong THz electric fields
DEFF Research Database (Denmark)
Tarekegne, Abebe Tilahun
weak THz and near infrared pulses as probes. Firstly, an intense THz pulse is used to study THz-induced impact ionization (IMI) dynamics in silicon. Local field enhancement by metallic dipole antenna arrays has been used to generate strong electric fields of several MV/cm in the hot spots near...... uniquely. Finally it is demonstrated for the first time that SiC can be tailored to have extremely fast THz-induced nonlinear behavior in moderate THz electric fields by addition of appropriate dopants. A 4H-SiC sample with high concentrations of nitrogen and boron dopants shows a nonlinear THz......In this thesis, we investigate nonlinear interactions of an intense terahertz (THz) field with semiconductors, in particular the technologically relevant materials silicon and silicon carbide. We reveal the time-resolved dynamics of the nonlinear processes by pump-probe experiments that involve...
Nonlinear reversed field pinch dynamics with nonideal boundaries
International Nuclear Information System (INIS)
Ho, Y.L.; Prager, S.C.
1991-03-01
The nonlinear behavior of the reversed field pinch bounded by a resistive shell or a distant conducting wall is investigated with a three-dimensional magnetohydrodynamic code. Nonlinear interaction between modes enhances fluctuation levels as the conducting wall is removed. The enhanced fluctuation induced v x b electric field, which produces the dynamo effect, suppresses toroidal current and enhances surface helicity dissipation. Thus, loop voltage must increase to sustain the current and maintain helicity balance. 46 refs., 21 figs., 2 tabs
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
A novel look at the pulsar force-free magnetosphere
Petrova, S. A.; Flanchik, A. B.
2018-03-01
The stationary axisymmetric force-free magnetosphere of a pulsar is considered. We present an exact dipolar solution of the pulsar equation, construct the magnetospheric model on its basis and examine its observational support. The new model has toroidal rather than common cylindrical geometry, in line with that of the plasma outflow observed directly as the pulsar wind nebula at much larger spatial scale. In its new configuration, the axisymmetric magnetosphere consumes the neutron star rotational energy much more efficiently, implying re-estimation of the stellar magnetic field, B_{new}0=3.3×10^{-4}B/P, where P is the pulsar period. Then the 7-order scatter of the magnetic field derived from the rotational characteristics of the pulsars observed appears consistent with the \\cotχ-law, where χ is a random quantity uniformly distributed in the interval [0,π/2]. Our result is suggestive of a unique actual magnetic field strength of the neutron stars along with a random angle between the magnetic and rotational axes and gives insight into the neutron star unification on the geometrical basis.
Nonlinear piezoelectricity in epitaxial ferroelectrics at high electric fields.
Grigoriev, Alexei; Sichel, Rebecca; Lee, Ho Nyung; Landahl, Eric C; Adams, Bernhard; Dufresne, Eric M; Evans, Paul G
2008-01-18
Nonlinear effects in the coupling of polarization with elastic strain have been predicted to occur in ferroelectric materials subjected to high electric fields. Such predictions are tested here for a PbZr0.2Ti0.8O3 ferroelectric thin film at electric fields in the range of several hundred MV/m and strains reaching up to 2.7%. The piezoelectric strain exceeds predictions based on constant piezoelectric coefficients at electric fields from approximately 200 to 400 MV/m, which is consistent with a nonlinear effect predicted to occur at corresponding piezoelectric distortions.
Force-Free Time-Harmonic Plasmoids
1992-10-01
The author believes that a number of observed phenomena, including ball lightning , "Afireballs" and "charge clusters" that occur in strong plasma...nvestigatora( 3 ). Under diflerent conditions they may have names like "anomalous discharges", "charge dusters", and " ball lightning ." The phenomenona that...not new. Kapitza conjectured that ball lightning was explained by such a model(4). A model having a vortical field identical to a component of the
Second quantization of classical nonlinear relativistic field theory. Pt. 2
International Nuclear Information System (INIS)
Balaban, T.
1976-01-01
The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de
Wormhole Solutions in the Presence of Nonlinear Maxwell Field
Directory of Open Access Journals (Sweden)
S. H. Hendi
2014-01-01
Full Text Available In generalizing the Maxwell field to nonlinear electrodynamics, we look for the magnetic solutions. We consider a suitable real metric with a lower bound on the radial coordinate and investigate the properties of the solutions. We find that in order to have a finite electromagnetic field near the lower bound, we should replace the Born-Infeld theory with another nonlinear electrodynamics theory. Also, we use the cut-and-paste method to construct wormhole structure. We generalize the static solutions to rotating spacetime and obtain conserved quantities.
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
A unified field theory of mesons and their particle sources is proposed and considered in its classical aspects. The theory has static solutions of a singular nature, but finite energy, characterized by spin directions; the number of such entities is a rigorously conserved constant of motion; they interact with an external meson field through a derivative-type coupling with the spins, akin to the formalism of strong-coupling meson theory. There is a conserved current identifiable with isobaric spin, and another that may be related to hypercharge. The postulates include one constant of the dimensions of length, and another that is conjecture necessarily to have the value (h/2π)c, or perhaps 1/2(h/2π)c, in the quantized theory. (author). 5 refs
Critical electric field for maximum tunability in nonlinear dielectrics
Akdogan, E. K.; Safari, A.
2006-09-01
The authors develop a self-consistent thermodynamic theory to compute the critical electric field at which maximum tunability is attained in a nonlinear dielectric. They then demonstrate that the stored electrostatic free energy functional has to be expanded at least up to the sixth order in electric field so as to define the critical field, and show that it depends solely on the fourth and sixth order permittivities. They discuss the deficiency of the engineering tunability metric in describing nonlinear dielectric phenomena, introduce a critical field renormalized tunability parameter, and substantiate the proposed formalism by computing the critical electric field for prototypical 0.9Pb(Mg1/3,Nb2/3)-0.1PbTiO3 and Ba(Ti0.85,Sn0.15)O3 paraelectrics.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Nie, Zongxiu
2016-02-01
The nonlinear harmonics within the ion motion are the fingerprint of the nonlinear fields. They are exclusively introduced by these nonlinear fields and are responsible to some specific nonlinear effects such as nonlinear resonance effect. In this article, the ion motion in the quadrupole field with a weak superimposed octopole component, described by the nonlinear Mathieu equation (NME), was studied by using the analytical harmonic balance (HB) method. Good accuracy of the HB method, which was comparable with that of the numerical fourth-order Runge-Kutta (4th RK), was achieved in the entire first stability region, except for the points at the stability boundary (i.e., β = 1) and at the nonlinear resonance condition (i.e., β = 0.5). Using the HB method, the nonlinear 3β harmonic series introduced by the octopole component and the resultant nonlinear resonance effect were characterized. At nonlinear resonance, obvious resonant peaks were observed in the nonlinear 3β series of ion motion, but were not found in the natural harmonics. In addition, both resonant excitation and absorption peaks could be observed, simultaneously. These are two unique features of the nonlinear resonance, distinguishing it from the normal resonance. Finally, an approximation equation was given to describe the corresponding working parameter, q nr , at nonlinear resonance. This equation can help avoid the sensitivity degradation due to the operation of ion traps at the nonlinear resonance condition.
Ultrafast nonlinear response of silicon carbide to intense THz fields
DEFF Research Database (Denmark)
Tarekegne, Abebe Tilahun; Iwaszczuk, Krzysztof; Kaltenecker, Korbinian J.
2017-01-01
We demonstrate ultrafast nonlinear absorption induced by strong, single-cycle THz fields in bulk, lightly doped 4H silicon carbide. A combination of Zener tunneling and intraband transitions makes the effect as at least as fast as the excitation pulse. The sub-picosecond recovery time makes...
Magnetic-field asymmetry of nonlinear thermoelectric and heat transport
International Nuclear Information System (INIS)
Hwang, Sun-Yong; Sánchez, David; López, Rosa; Lee, Minchul
2013-01-01
Nonlinear transport coefficients do not obey, in general, reciprocity relations. We here discuss the magnetic-field asymmetries that arise in thermoelectric and heat transport of mesoscopic systems. Based on a scattering theory of weakly nonlinear transport, we analyze the leading-order symmetry parameters in terms of the screening potential response to either voltage or temperature shifts. We apply our general results to a quantum Hall antidot system. Interestingly, we find that certain symmetry parameters show a dependence on the measurement configuration. (paper)
Force-free field inside a toroidal magnetic cloud
Czech Academy of Sciences Publication Activity Database
Romashets, E. P.; Vandas, Marek
2003-01-01
Roč. 30, č. 20 (2003), s. 2065, /SSC 8-1 - SSC 8-4/ ISSN 0094-8276 R&D Projects: GA AV ČR IBS1003006; GA ČR GA205/03/0953 Institutional research plan: CEZ:AV0Z1003909 Keywords : magnetic clouds * toroid al flux rope * analytical solution Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 2.422, year: 2003
Force-free state in a superconducting single crystal and angle-dependent vortex helical instability
del Valle, J.; Gomez, A.; Gonzalez, E. M.; Manas-Valero, S.; Coronado, E.; Vicent, J. L.
2017-06-01
Superconducting 2 H -NbS e2 single crystals show intrinsic low pinning values. Therefore, they are ideal materials with which to explore fundamental properties of vortices. (V , I ) characteristics are the experimental data we have used to investigate the dissipation mechanisms in a rectangular-shaped 2 H -NbS e2 single crystal. Particularly, we have studied dissipation behavior with magnetic fields applied in the plane of the crystal and parallel to the injected currents, i.e., in the force-free state where the vortex helical instability governs the vortex dynamics. In this regime, the data follow the elliptic critical state model and the voltage dissipation shows an exponential dependence, V ∝eα (I -IC ∥ ) , IC ∥ being the critical current in the force-free configuration and α a linear temperature-dependent parameter. Moreover, this exponential dependence can be observed for in-plane applied magnetic fields up to 40° off the current direction, which implies that the vortex helical instability plays a role in dissipation even out of the force-free configuration.
Spinor Field Nonlinearity and Space-Time Geometry
Saha, Bijan
2018-03-01
Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time
Comparison of Simulated and Measured Non-linear Ultrasound Fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are rst compared with the linear...... simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound eld is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both...... fundamental and second harmonic elds. The focused piston transducer with a center frequency of 5 MHz is excited by a waveform generator emitting a 6-cycle sine wave. The hydrophone is mounted in the focal plane 118 mm from the transducer. The point spread functions at the focal depth from Field II...
Yeo, Joonhyun
2009-11-01
We study a zero-dimensional version of the fluctuating nonlinear hydrodynamics (FNH) of supercooled liquids originally investigated by Das and Mazenko (DM) [Shankar P. Das and Gene F. Mazenko Phys. Rev. A 34, 2265 (1986)]. The time-dependent density-like and momentum-like variables are introduced with no spatial degrees of freedom in this toy model. The structure of nonlinearities takes the similar form to the original FNH, which allows one to study in a simpler setting the issues raised recently regarding the field theoretical approaches to glass forming liquids. We study the effects of density nonlinearities on the time evolution of correlation and response functions by developing field theoretic formulations in two different ways: first by following the original prescription of DM and then by constructing a dynamical action which possesses a linear time-reversal symmetry as proposed recently. We show explicitly that, at the one-loop order of the perturbation theory, the DM-type field theory does not support a sharp ergodic-nonergodic transition, while the other admits one. The simple nature of the toy model in the DM formulation allows us to develop numerical solutions to a complete set of coupled dynamical equations for the correlation and response functions at the one-loop order.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Zhang, Lue; Wang, Xiangda; Gong, Xiufen [Key Laboratory of Modern Acoustics, Ministry of Education, Institute of Acoustics, Nanjing University, Nanjing 210093 (China)
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
On the pressure field of nonlinear standing water waves
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
SIMULATION OF SYNCHRONIZATION OF NONLINEAR OSCILLATORS BY THE EXTERNAL FIELD
Directory of Open Access Journals (Sweden)
V. M. Kuklin
2017-05-01
Full Text Available In this paper, the self-consistent model was considered, consisting of a system of oscillators, the coupling between them was assumed to be integral (due to the fields formed as a result of their co-radiation. With the help of this model, the features of synchronization by waves of finite amplitude of a system of oscillators were refined, the initial phase values of which are random. The effect of nonlinearity, in particular, due to the change in the mass of the oscillator due to relativistic effects, was taken into account. It was shown that the nonlinearity does not violate the nature of the energy exchange between the wave and the oscillator system, leading only to a slight decrease in the efficiency of such an exchange.
The nonlinearity of the scalar field in a relativistic mean-field theory of the nucleus
International Nuclear Information System (INIS)
Reinhard, P.G.
1987-10-01
The form of the nonlinear selfcoupling of the scalar meson field in a nuclear relativistic mean-field theory is investigated. The conventional ansatz is shown to produce instabilities in critical applications. A modified selfcoupling is proposed which guarantees stability under all conditions. (orig.)
Nonlinear interactions of focused resonance cone fields with plasmas
International Nuclear Information System (INIS)
Stenzel, R.L.; Gekelman, W.
1977-01-01
A simple yet novel rf exciter structure has been developed for generating remotely intense rf fields in a magnetoplasma. It is a circular line source of radius R in a plane perpendicularB 0 driven with an rf signal at ω 0 E/sub rf/ 2 /nkT/sub e/>0.2, a strong density depression in the focal region (deltan/n>40%) is observed. The density perturbation modifies the cone angle and field distribution. This nonlinear interaction leads to a rapid growth of ion acoustic wave turbulence and a corresponding random rf field distribution in a broadened focal region. The development of the interaction is mapped in space and time
Three dimensional magnetic solutions in massive gravity with (nonlinear field
Directory of Open Access Journals (Sweden)
S.H. Hendi
2017-12-01
Full Text Available The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Gamma-Ray Pulsar Light Curves in Vacuum and Force-Free Geometry
Harding, Alice K.; DeCesar, Megan E.; Miller, M. Coleman; Kalapotharakos, Constantinos; Contopoulos, Ioannis
2011-01-01
Recent studies have shown that gamma-ray pulsar light curves are very sensitive to the geometry of the pulsar magnetic field. Pulsar magnetic field geometries, such as the retarded vacuum dipole and force-free magnetospheres have distorted polar caps that are offset from the magnetic axis in the direction opposite to rotation. Since this effect is due to the sweepback of field lines near the light cylinder, offset polar caps are a generic property of pulsar magnetospheres and their effects should be included in gamma-ray pulsar light curve modeling. In slot gap models (having two-pole caustic geometry), the offset polar caps cause a strong azimuthal asymmetry of the particle acceleration around the magnetic axis. We have studied the effect of the offset polar caps in both retarded vacuum dipole and force-free geometry on the model high-energy pulse profiles. We find that, compared to the profiles derived from symmetric caps, the flux in the pulse peaks, which are caustics formed along the trailing magnetic field lines, increases significantly relative to the off-peak emission, formed along leading field lines. The enhanced contrast produces improved slot gap model fits to Fermi pulsar light curves like Vela, with vacuum dipole fits being more favorable.
Nonlinear mean field theory for nuclear matter and surface properties
International Nuclear Information System (INIS)
Boguta, J.; Moszkowski, S.A.
1983-01-01
Nuclear matter properties are studied in a nonlinear relativistic mean field theory. We determine the parameters of the model from bulk properties of symmetric nuclear matter and a reasonable value of the effective mass. In this work, we stress the nonrelativistic limit of the theory which is essentially equivalent to a Skyrme hamiltonian, and we show that most of the results can be obtained, to a good approximation, analytically. The strength of the required parameters is determined from the binding energy and density of nuclear matter and the effective nucleon mass. For realistic values of the parameters, the nonrelativistic approximation turns out to be quite satisfactory. Using reasonable values of the parameters, we can account for other key properties of nuclei, such as the spin-orbit coupling, surface energy, and diffuseness of the nuclear surface. Also the energy dependence of the nucleon-nucleus optical model is accounted for reasonably well except near the Fermi surface. It is found, in agreement with empirical results, that the Landau parameter F 0 is quite small in normal nuclear matter. Both density dependence and momentum dependence of the NN interaction, but especially the former, are important for nuclear saturation. The required scalar and vector coupling constants agree fairly well with those obtained from analyses of NN scattering phase shifts with one-boson-exchange models. The mean field theory provides a semiquantitative justification for the weak Skyrme interaction in odd states. The strength of the required nonlinear term is roughly consistent with that derived using a new version of the chiral mean field theory in which the vector mass as well as the nucleon mass is generated by the sigma-field. (orig.)
Nonlinear dynamo mode dynamics in reversed field pinches
International Nuclear Information System (INIS)
Fitzpatrick, Richard; Yu, Edmund P.
2000-01-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called ''slinky mode'' locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research. (c) 2000 American Institute of Physics
Nonlinear dynamo mode dynamics in reversed field pinches
Fitzpatrick, Richard; Yu, Edmund P.
2000-09-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called "slinky mode" locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research.
Nonlinear dynamo mode dynamics in reversed field pinches
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, Richard [Institute for Fusion Studies, Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Yu, Edmund P. [Institute for Fusion Studies, Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States)
2000-09-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called ''slinky mode'' locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research. (c) 2000 American Institute of Physics.
Particle reflection along the magnetic field in nonlinear magnetosonic pulses
Ohsawa, Yukiharu
2017-11-01
Reflection of electrons and positrons in oblique, nonlinear magnetosonic pulses is theoretically analyzed. With the use of the parallel pseudo potential F, which is the integral of the parallel electric field along the magnetic field, a simple equation for reflection conditions is derived, which shows that reflection along the magnetic field is caused by two forces: one arising from the parallel pseudo potential multiplied by the particle charge and the other from the magnetic mirror effect. The two forces push electrons in the opposite directions. In compressive solitons, in which the magnetic field is intensified, electrons with large magnetic moments can be reflected by the magnetic mirror effect, whereas in rarefactive solitons, in which the magnetic field is weaker than outside, electrons with small magnetic moments can be reflected by the parallel pseudo potential. Although F is basically positive and large in shock waves, it occasionally becomes negative in some regions behind the shock front in nonstationary wave evolution. These negative spikes of F can reflect electrons. In contrast to the case of electrons, the two forces push positrons in the same direction. For this reason, compressive solitons in an electron-positron-ion plasma reflect a large fraction of positrons compared with electrons, whereas rarefactive solitons will reflect no positrons. A shock wave can reflect a majority of positrons with its large F. However, in a pure electron-positron plasma, in which F becomes zero, positron reflection will rarely occur.
Suppressing Transverse Beam Halo with Nonlinear Magnetic Fields
Energy Technology Data Exchange (ETDEWEB)
Webb, Stephen D. [Tech-X, Boulder; Bruhwiler, David L. [Tech-X, Boulder; Abell, Dan T. [Tech-X, Boulder; Danilov, Viatcheslav [Oak Ridge; Nagaitsev, Sergei [Fermilab; Valishev, Alexander [Fermilab; Danilov, Kirill [Tech-X, Boulder; Cary, John R. [Tech-X, Boulder
2012-05-01
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 generalization of the Kapchinskij-Vladimirskij equilibrium distribution, which was introduced over 50 years ago for modeling linear dynamics in particle accelerators.
Information money fields of cyclic oscillations in nonlinear dynamic economic system
Ledenyov, Dimitri O.; Ledenyov, Viktor O.
2015-01-01
Article introduces the notion of information money fields of the cyclic oscillations of the economic variables in the nonlinear dynamic economic system for the first time, and presents an original research on the Ledenyov theory on the information money fields of the cyclic oscillations of the economic variables in the nonlinear dynamic economic system. The Ledenyov theory on the information money fields of the cyclic oscillations of economic variables in the nonlinear dynamic economic system...
Nonlinear quantum electrodynamic and electroweak processes in strong laser fields
Energy Technology Data Exchange (ETDEWEB)
Meuren, Sebastian
2015-06-24
Various nonlinear electrodynamic and electroweak processes in strong plane-wave laser fields are considered with an emphasis on short-pulse effects. In particular, the momentum distribution of photoproduced electron-positron pairs is calculated numerically and a semiclassical interpretation of its characteristic features is established. By proving the optical theorem, compact double-integral expressions for the total pair-creation probability are obtained and numerically evaluated. The exponential decay of the photon wave function in a plane wave is included by solving the Schwinger-Dyson equations to leading-order in the quasistatic approximation. In this respect, the polarization operator in a plane wave is investigated and its Ward-Takahashi identity verified. A classical analysis indicates that a photoproduced electron-positron pair recollides for certain initial conditions. The contributions of such recollision processes to the polarization operator are identified and calculated both analytically and numerically. Furthermore, the existence of nontrivial electron-spin dynamics induced by quantum fluctuations is verified for ultra-short laser pulses. Finally, the exchange of weak gauge bosons is considered, which is essential for neutrino-photon interactions. In particular, the axial-vector-vector coupling tensor is calculated and the so-called Adler-Bell-Jackiw (ABJ) anomaly investigated.
Nonlinear response of superconductors to alternating fields and currents
Energy Technology Data Exchange (ETDEWEB)
McDonald, Jason [Iowa State Univ., Ames, IA (United States)
1997-10-08
This report discusses the following topics on superconductivity: nonlinearities in hard superconductors such as surface impedance of a type II superconductimg half space and harmonic generation and intermodulation due to alternating transport currents; and nonlinearities in superconducting weak links such as harmonic generation by a long Josephson Junction in a superconducting slab.
Nonlinear Field Oriented Control of Induction Motors using the Backstepping Design
DEFF Research Database (Denmark)
Rasmussen, Henrik; Vadstrup, P.; Børsting, H.
1999-01-01
Using backstepping, which is a recursive nonlinear design method, a novel approach to control of induction motors is developed. The resulting scheme leads to a nonlinear controller for the torque and the amplitude of the field. A combination of nonlinear damping and observer backstepping...... with a simple flux observer is used in the design. Assuming known motor parameters the design achieves stabilioty with garanteed region of attraction. It is also shown how a conventional field oriented controller may be obtained by omitting parts of the nonlinear controller....
Modulation of Radio Frequency Signals by Nonlinearly Generated Acoustic Fields
2014-01-01
accounting for transmitted power, non time-dependent effects, and amplitude solution of the Mathieu equation for path loss, radar cross section, and...for generously sharing his numerical approaches and published code for solving the nonlinear KZK parabolic wave equation . Lastly, I would like to thank...Computation of the Equations of Nonlinear Acoustics . . . . . . . . . . . . . . . 32 2.3.1 Direct Numerical Evaluation of the KZK Equation
Density nonlinearities and a field theory for the dynamics of simple fluids
Mazenko, Gene F.; Yeo, Joonhyun
1994-01-01
We study the role of the Jacobian arising from a constraint enforcing the nonlinear relation: ${\\bf g}=\\rho{\\bf V}$, where $\\rho,\\: {\\bf g}$ and ${\\bf V}$ are the mass density, the momentum density and the local velocity field, respectively, in the field theoretic formulation of the nonlinear fluctuating hydrodynamics of simple fluids. By investigating the Jacobian directly and by developing a field theoretic formulation without the constraint, we find that no changes in dynamics result as co...
Analysis of solutions of a nonlinear scalar field differential equation
Muhamadiev, E. M.; Naimov, A. N.
2017-10-01
We consider a nonlinear differential equation arising in mathematical models of elementary particle theory. For this equation, we examine questions of the extendability of solutions, the boundedness of solutions at infinity, and the search for new conditions for the existence of a positive particle-like solution.
Symmetry properties of some nonlinear field theory models
International Nuclear Information System (INIS)
Shvachka, A.B.
1984-01-01
Various approaches towards the study of symmetry properties of some nonlinear evolution equations as well as possible ways of their computer implementation using the computer algebra systems langage are discussed. Special attention is paid to the method of pseudopotential investigation of formal integrability and isovector method for the equations of balance
Angular spectrum approach for fast simulation of pulsed non-linear ultrasound fields
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt
2011-01-01
The paper presents an Angular Spectrum Approach (ASA) for simulating pulsed non-linear ultrasound fields. The source of the ASA is generated by Field II, which can simulate array transducers of any arbitrary geometry and focusing. The non-linear ultrasound simulation program - Abersim, is used...... as the reference. A linear array transducer with 64 active elements is simulated by both Field II and Abersim. The excitation is a 2-cycle sine wave with a frequency of 5 MHz. The second harmonic field in the time domain is simulated using ASA. Pulse inversion is used in the Abersim simulation to remove...... the fundamental and keep the second harmonic field, since Abersim simulates non-linear fields with all harmonic components. ASA and Abersim are compared for the pulsed fundamental and second harmonic fields in the time domain at depths of 30 mm, 40 mm (focal depth) and 60 mm. Full widths at -6 dB (FWHM) are f0...
Sheykhi, A.; Abdollahzadeh, Z.
2018-03-01
We investigate the effects of an external magnetic field as well as exponential nonlinear electrodynamics on the properties of s-wave holographic superconductors. Our strategy for this study is the matching method, which is based on the match of the solutions near the horizon and on the boundary at some intermediate point. When the magnetic field is turned off, we obtain the critical temperature as well as the condensation operator and show that the critical exponent is still 1/2, which is the universal value in the mean field theory. Then, we turn on the magnetic field and obtain the critical magnetic field, B c , in order to study its behavior in terms of the temperature. Interestingly enough, we find that in the presence of exponential nonlinear electrodynamics, the critical temperature decreases, while the critical magnetic field increases compared to the Maxwell case. We also observe that the critical magnetic field increases with increasing the nonlinear parameter b.
Some nonlinear estimates for lateral propagation of self-generated B fields
International Nuclear Information System (INIS)
Goldman, S.R.
1982-01-01
We present nonlinear estimates which provide plausible guidelines and scalings for the lateral transport of magnetic fields due to laser-plasma interaction in both slab and cylindrical geometries. Limitations of the modelling are also indicated
Relativistic nonlinear electrodynamics the QED vacuum and matter in super-strong radiation fields
Avetissian, Hamlet K
2016-01-01
This revised edition of the author’s classic 2006 text offers a comprehensively updated review of the field of relativistic nonlinear electrodynamics. It explores the interaction of strong and super-strong electromagnetic/laser radiation with the electromagnetic quantum vacuum and diverse types of matter – including free charged particles and antiparticles, acceleration beams, plasma and plasmous media. The appearance of laser sources of relativistic and ultra-relativistic intensities over the last decade has stimulated investigation of a large class of processes under such super-strong radiation fields. Revisions for this second edition reflect these developments and the book includes new chapters on Bremsstrahlung and nonlinear absorption of superintense radiation in plasmas, the nonlinear interaction of relativistic atoms with intense laser radiation, nonlinear interaction of strong laser radiation with Graphene, and relativistic nonlinear phenomena in solid-plasma targets under supershort laser pul...
A two-fluid study of oblique tearing modes in a force-free current sheet
Akçay, Cihan; Daughton, William; Lukin, Vyacheslav S.; Liu, Yi-Hsin
2016-01-01
Kinetic simulations have demonstrated that three-dimensional reconnection in collisionless regimes proceeds through the formation and interaction of magnetic flux ropes, which are generated due to the growth of tearing instabilities at multiple resonance surfaces. Since kinetic simulations are intrinsically expensive, it is desirable to explore the feasibility of reduced two-fluid models to capture this complex evolution, particularly, in the strong guide field regime, where two-fluid models are better justified. With this goal in mind, this paper compares the evolution of the collisionless tearing instability in a force-free current sheet with a two-fluid model and fully kinetic simulations. Our results indicate that the most unstable modes are oblique for guide fields larger than the reconnecting field, in agreement with the kinetic results. The standard two-fluid tearing theory is extended to address the tearing instability at oblique angles. The resulting theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
Backstepping design of a Nonlinear Observer for the Rotor Field of an Induction Motor
DEFF Research Database (Denmark)
Rasmussen, Henrik
2000-01-01
Using backstepping, which is a recursive nonlinear design method, a new approach for the design of flux observers is developed. The resulting scheme leads to a nonlinear full order observer for the amplitude and angle of the field. Assuming motor parameters known the design achieves stability...... with guaranteed region of attraction. Rubustness due to variation of motor parameters is analysed by simulation. The result is compared to the flux estimate used in a conventional field oriented controller Using backstepping, which is a recursive nonlinear design method, a new approach for the design of flux...... observers is developed. The resulting scheme leads to a nonlinear full order observer for the amplitude and angle of the field. Assuming motor parameters known the design achieves stability with guaranteed region of attraction. Rubustness due to variation of motor parameters is analysed by simulation...
Ulku, Huseyin Arda
2015-02-01
An explicit marching on-in-time (MOT) based time domain electric field volume integral equation (TDVIE) solver for characterizing electromagnetic wave interactions on scatterers with nonlinear material properties is proposed. Discretization of the unknown electric field intensity and flux density is carried out by half and full Schaubert-Wilton-Glisson basis functions, respectively. Coupled system of spatially discretized TDVIE and the nonlinear constitutive relation between the field intensity and the flux density is integrated in time to compute the samples of the unknowns. An explicit PE(CE)m scheme is used for this purpose. Explicitness allows for \\'easy\\' incorporation of the nonlinearity as a function only to be evaluated on the right hand side of the coupled system of equations. A numerical example that demonstrates the applicability of the proposed MOT scheme to analyzing electromagnetic interactions on Kerr-nonlinear scatterers is presented. © 2015 IEEE.
Giant-spin nonlinear response theory of magnetic nanoparticle hyperthermia: A field dependence study
Carrião, M. S.; Aquino, V. R. R.; Landi, G. T.; Verde, E. L.; Sousa, M. H.; Bakuzis, A. F.
2017-05-01
Understanding high-field amplitude electromagnetic heat loss phenomena is of great importance, in particular, in the biomedical field, because the heat-delivery treatment plans might rely on analytical models that are only valid at low field amplitudes. Here, we develop a nonlinear response model valid for single-domain nanoparticles of larger particle sizes and higher field amplitudes in comparison to the linear response theory. A nonlinear magnetization expression and a generalized heat loss power equation are obtained and compared with the exact solution of the stochastic Landau-Lifshitz-Gilbert equation assuming the giant-spin hypothesis. The model is valid within the hyperthermia therapeutic window and predicts a shift of optimum particle size and distinct heat loss field amplitude exponents, which is often obtained experimentally using a phenomenological allometric function. Experimental hyperthermia data with distinct ferrite-based nanoparticles and third harmonic magnetization data support the nonlinear model, which also has implications for magnetic particle imaging and magnetic thermometry.
Nonlinear electromagnetic fields in 0.5 MHz inductively coupled plasmas
DEFF Research Database (Denmark)
Ostrikov, K.N.; Tsakadze, E.L.; Xu, S.
2003-01-01
Radial profiles of magnetic fields in the electrostatic (E) and electromagnetic (H) modes of low-frequency (similar to500 kHz) inductively coupled plasmas have been measured using miniature magnetic probes. In the low-power (similar to170 W) E-mode, the magnetic field pattern is purely linear......, with the fundamental frequency harmonics only. After transition to higher-power (similar to1130 W) H-mode, the second-harmonic nonlinear azimuthal magnetic field B-phi(2omega) that is in 4-6 times larger than the fundamental frequency component B-phi(omega), has been observed. A simplified plasma fluid model...... explaining the generation of the second harmonics of the azimuthal magnetic field in the plasma source is proposed. The nonlinear second harmonic poloidal (r-z) rf current generating the azimuthal magnetic field B-phi(2omega) is attributed to nonlinear interactions between the fundamental frequency radial...
Tackling non-linearities with the effective field theory of dark energy and modified gravity
Frusciante, Noemi; Papadomanolakis, Georgios
2017-12-01
We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.
Inflation and acceleration of the universe by nonlinear magnetic monopole fields
Energy Technology Data Exchange (ETDEWEB)
Oevguen, A. [Eastern Mediterranean Univ., Famagusta (Country Unknown). Dept. of Physics
2017-02-15
Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields. (orig.)
Inflation and acceleration of the universe by nonlinear magnetic monopole fields
Övgün, A.
2017-02-01
Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.
Feasibility of non-linear simulation for Field II using an angular spectrum approach
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Jørgen Arendt
2008-01-01
Simulation of non-linear fields is most often restricted to single element, circularly symmetric sources, which is not used in clinical scanning. To obtain a general and valuable simulation, array transducers of any geometry with any excitation, focusing, and apodization should be modeled. Field II...... to the transducer surface. This calculation is performed using Field II and, thus, includes modeling array transducers of any geometry with any excitation, focusing, and apodization. The propagation in the linear or non-linear medium is then performed using the angular spectrum approach. The first step in deriving...
Construction of local and non-local conservation laws for non-linear field equations
International Nuclear Information System (INIS)
Vladimirov, V.S.; Volovich, I.V.
1984-08-01
A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)
Energy Technology Data Exchange (ETDEWEB)
Guo, Y. [School of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University, Nanjing 210023 (China); Pariat, E.; Moraitis, K. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Université, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, F-92190 Meudon (France); Valori, G. [University College London, Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, RH5 6NT (United Kingdom); Anfinogentov, S. [Institute of Solar-Terrestrial Physics SB RAS 664033, Irkutsk, P.O. box 291, Lermontov Street, 126a (Russian Federation); Chen, F. [Max-Plank-Institut für Sonnensystemforschung, D-37077 Göttingen (Germany); Georgoulis, M. K. [Research Center for Astronomy and Applied Mathematics of the Academy of Athens, 4 Soranou Efesiou Street, 11527 Athens (Greece); Liu, Y. [W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305 (United States); Thalmann, J. K. [Institute of Physics, Univeristy of Graz, Universitätsplatz 5/II, A-8010 Graz (Austria); Yang, S., E-mail: guoyang@nju.edu.cn [Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China)
2017-05-01
We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov–Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger–Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.
Nonlinear Decoupling of Torque and Field Amplitude in an Induction Motor
DEFF Research Database (Denmark)
Rasmussen, Henrik; Vadstrup, P.; Børsting, H.
1997-01-01
A novel approach to control of induction motors, based on nonlinear state feedback, is presented. The resulting scheme gives a linearized input-output decoupling of the torque and the amplitude of the field. The proposed approach is used to design controllers for the field amplitude and the motor...... torque. The method is tested both by simulation and by experiments on a motor drive....
MgB_{2} nonlinear properties investigated under localized high rf magnetic field excitation
Directory of Open Access Journals (Sweden)
Tamin Tai
2012-12-01
Full Text Available The high transition temperature and low surface resistance of MgB_{2} attracts interest in its potential application in superconducting radio frequency accelerating cavities. However, compared to traditional Nb cavities, the viability of MgB_{2} at high rf fields is still open to question. Our approach is to study the nonlinear electrodynamics of the material under localized rf magnetic fields. Because of the presence of the small superconducting gap in the π band, the nonlinear response of MgB_{2} at low temperature is potentially complicated compared to a single-gap s-wave superconductor such as Nb. Understanding the mechanisms of nonlinearity coming from the two-band structure of MgB_{2}, as well as extrinsic sources of nonlinearity, is an urgent requirement. A localized and strong rf magnetic field, created by a magnetic write head, is integrated into our nonlinear-Meissner-effect scanning microwave microscope [T. Tai et al., IEEE Trans. Appl. Supercond. 21, 2615 (2011ITASE91051-822310.1109/TASC.2010.2096531]. MgB_{2} films with thickness 50 nm, fabricated by a hybrid physical-chemical vapor deposition technique on dielectric substrates, are measured at a fixed location and show a strongly temperature-dependent third harmonic response. We propose that several possible mechanisms are responsible for this nonlinear response.
Bahramiyan, H.
2018-01-01
In this work, we have investigated the effect of electric field and impurity position on nonlinear optical rectification of a double cone like quantum dot in the effective mass approximation and by using compact density-matrix formalism. We have calculated the energy levels and wave functions using finite element method (FEM) in the presence of impurity and influence of electric field. The results show that: (i) the binding energy changes with the impurity position and it is changed by the applied electric field, (ii) nonlinear optical rectification peak position of this system present the blue or red shift due to the applied electric field and changing the impurity position. (iii) for low electric field, impurity position plays an important role in electronic and optical properties, but for larger electric field, impurity position role becomes non-significant. (iv) the optical rectification changes due to the impurity position and the electric field are considerable.
Nonlinear boundary value problems in quantum field theory
International Nuclear Information System (INIS)
Schrader, R.
1989-01-01
We discuss the general structure of a quantum field theory which is free in the interior of a bounded set B of R n . It is shown how to recover the field theory in the interior of B from a certain quantum field theory on the boundary. With an application to string theory in mind, we discuss the example where B equals an interval and the boundary value problem is given in terms of a euclidean functional integral with a P(var phi) interaction restricted to the boundary. copyright 1989 Academic Press, Inc
Parametrization-dependence of nonlinear quantum field theories
International Nuclear Information System (INIS)
Tyutin, I.
1982-01-01
It is shown that in an arbitrary quantum field theory a change of variables (transition to a different parametrization) leads only to a change of the field variables in the renormalized action and in the generating functional for the vertex functions. As a consequence of this it is shown that the beta-functions in two-dimensional chiral theories do not depend on the choice of parametrization. A remark on the uniqueness of the renormalized action concludes the paper
Fast simulation of non-linear pulsed ultrasound fields using an angular spectrum approach
DEFF Research Database (Denmark)
Du, Yigang; Jensen, Jørgen Arendt
2013-01-01
A fast non-linear pulsed ultrasound field simulation is presented. It is implemented based on an angular spectrum approach (ASA), which analytically solves the non-linear wave equation. The ASA solution to the Westervelt equation is derived in detail. The calculation speed is significantly...... increased compared to a numerical solution using an operator splitting method (OSM). The ASA has been modified and extended to pulsed non-linear ultrasound fields in combination with Field II, where any array transducer with arbitrary geometry, excitation, focusing and apodization can be simulated...... with a center frequency of 5 MHz. The speed is increased approximately by a factor of 140 and the calculation time is 12 min with a standard PC, when simulating the second harmonic pulse at the focal point. For the second harmonic point spread function the full width error is 1.5% at 6 dB and 6.4% at 12 d...
Carrasco, F. L.; Reula, O. A.
2017-09-01
Force-free electrodynamics (FFE) describes a particular regime of magnetically dominated relativistic plasmas, which arises on several astrophysical scenarios of interest such as pulsars or active galactic nuclei. In this article, we present a full 3D numerical implementation of the FFE evolution around a Kerr black hole. The novelty of our approach is three-folded: (i) We use the "multiblock" technique [1 L. Lehner, O. Reula, and M.Tiglio, Multi-block simulations in general relativity: High-order discretizations, numerical stability and applications, Classical Quantum Gravity 22, 5283 (2005)., 10.1088/0264-9381/22/24/006] to represent a domain with S2×R+ topology within a stable finite-differences scheme. (ii) We employ as evolution equations those arising from a covariant hyperbolization of the FFE system [2 F. Carrasco and O. Reula, Covariant hyperbolization of force-free electrodynamics, Phys. Rev. D 93, 085013 (2016)., 10.1103/PhysRevD.93.085013]. (iii) We implement stable and constraint-preserving boundary conditions to represent an outer region given by a uniform magnetic field aligned or misaligned respect to the symmetry axis. The construction of appropriate and consistent boundary conditions, both preserving the constraints and physically immersing the system in a uniform magnetic field, has allowed us to obtain long-term stationary solutions representing jets of astrophysical relevance. These numerical solutions are shown to be consistent with previous studies.
International Nuclear Information System (INIS)
Kapuria, S; Yaqoob Yasin, M
2013-01-01
In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)
Entanglement of a nonlinear two two-level atoms interacting with deformed fields in Kerr medium
Abdel-Khalek, S.; El-Saman, Y. S.; Abdel-Aty, M.
2018-01-01
In this paper we investigate the entanglement dynamics between two two-level atoms interacting with two coherent fields in two spatially separated cavities which are filled with a Kerr-like medium. We examine the effect of nonlinear medium on the dynamical properties of entanglement and atomic occupation probabilities in the case of even and odd deformed coherent states. The results show that the deformed fields play important roles in the evolution of entanglement. Also, the results demonstrate that entanglement sudden death, sudden birth and long-distance can be controlled by the deformation and nonlinear parameters.
Solitons of scalar field with induced nonlinearity and their stability
International Nuclear Information System (INIS)
Saha, B.
1999-09-01
Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered FRW and Goedel universes as external gravitational field with spherical and cylindrical symmetry respectively. Beside the usual solitons some special regular solutions known as droplets, anti-droplets and hats (confined in finite interval and having trivial value beyond it) have been obtained. It has been shown that in FRW space-time equations with different interaction terms may have stable solutions while within the scope of Goedel model only the droplet-like and the hat-like configurations may be stable, providing that they are located in the region where g 00 > 0. (author)
Variational methods in nonlinear field equations solitary waves, hylomorphic solitons and vortices
Benci, Vieri
2014-01-01
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
Nonlinear analysis of generalized cross-field current instability
International Nuclear Information System (INIS)
Yoon, P.H.; Lui, A.T.Y.
1993-01-01
Analysis of the generalized cross-field current instability is carried out in which cross-field drift of both the ions and electrons and their temperatures are permitted to vary in time. The unstable mode under consideration is the electromagnetic generalization of the classical modified-two-stream instability. The generalized instability is made of the modified-two-stream and ion-Weibel modes. The relative importance of the features associated with the ion-Weibel mode and those of the modified-two-stream mode is assessed. Specific applications are made to the Earth's neutral sheet prior to substorm onset and to the Earth's bow shock. The numerical solution indicates that the ion-Weibel mode dominates in the Earth's neutral sheet environment. In contrast, the situation for the bow shock is dominated by the modified-two-stream mode. Notable differences are found between the present calculation and previous results on ion-Weibel mode which restrict the analysis to only parallel propagating waves. However, in the case of Earth's bow shock for which the ion-Weibel mode plays no important role, the inclusion of the electromagnetic ion response is found to differ little from the previous results which treats ions responding only to the electrostatic component of the excited waves
Mean field games with nonlinear mobilities in pedestrian dynamics
Burger, Martin
2014-04-01
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
Equations of motion for anisotropic nonlinear elastic continuum in gravitational field
International Nuclear Information System (INIS)
Sokolov, S.N.
1994-01-01
Equations of motion for anisotropic nonlinear elastic continuum in the gravitational field are written in the form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors frozen in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given. 47 refs
Nonlinear optics using the multipolar Hamiltonian : The Bloch-Maxwell equations and local fields
Knoester, Jasper; Mukamel, Shaul
1989-01-01
A systematic method for calculating nonlinear-optical susceptibilities in condensed phases, which incorporates intermolecular forces and spontaneous emission in a consistent way, is developed, using the multipolar (µ•D) Hamiltonian. Reduced equations of motion that couple the electromagnetic field
Nonlinear microscopy of localized field enhancements in fractal shaped periodic metal nanostructures
DEFF Research Database (Denmark)
Beermann, I.; Evlyukhin, A.; Boltasseva, Alexandra
2008-01-01
Fractal shaped periodic nanostructures formed with a 100 nm period square lattice of gold nanoparticles placed on a gold film are characterized using far-field nonlinear scanning optical microscopy, in which two-photon photoluminescence (TPL) excited with a strongly focused femtosecond laser beam...
Nonlinear instability of wormholes supported by exotic dust and a magnetic field
Sarbach, Olivier; Zannias, Thomas
2010-01-01
Recently, spherically symmetric, static wormholes supported by exotic dust and a radial magnetic field have been derived and argued to be stable with respect to linear radial fluctuations. In this report we point out that these wormholes are unstable due to the formation of shell-crossing singularities when the nonlinearities of the theory are taken into account.
Nakata, Takayoshi; Takahashi, N.; Fujiwara, K.; Okamoto, N.; Muramatsu, Kazuhiro
1992-01-01
In order to overcome the divergence of the Newton-Raphson iteration in the nonlinear magnetic field analysis, a relaxation factor is introduced and its optimum value is examined. It is shown that the modified Newton-Raphson method proposed exhibits quick and successful convergence even in the case when the conventional Newton-Raphson method fails in convergence
Infinite sets of conservation laws for linear and nonlinear field equations
International Nuclear Information System (INIS)
Mickelsson, J.
1984-01-01
The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of the space-time symmetry group is established. It is shown that each symmetric element of the enveloping algebra of the space-time symmetry group of a linear field equation generates a one-parameter group of symmetries of the field equation. The cases of the Maxwell and Dirac equations are studied in detail. Then it is shown that (at least in the sense of a power series in the 'coupling constant') the conservation laws of the linear case can be deformed to conservation laws of a nonlinear field equation which is obtained from the linear one by adding a nonlinear term invariant under the group of space-time symmetries. As an example, our method is applied to the Korteweg-de Vries equation and to the massless Thirring model. (orig.)
Nonlinear decoupling of torque and field amplitude in an induction motor
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, H. [Aalborg University, Aalborg (Denmark); Vadstrup, P.; Boersting, H. [Grundfos A/S, Bjerringbro (Denmark)
1997-12-31
A novel approach to control of induction motors, based on nonlinear state feedback, is presented. The resulting scheme gives a linearized input-output decoupling of the torque and the amplitude of the field. The proposed approach is used to design controllers for the field amplitude and the motor torque. The method is tested both by simulation and by experiments on a motor drive. (orig.) 12 refs.
International Nuclear Information System (INIS)
Khalil, Sh.M.; El-Sherif, N.; El-Siragy, N.M.; Tanta Univ.; El-Naggar, I.A.; Alexandria Univ.
1985-01-01
Investigation is made for nonlinear interaction between incident radiation and a surface wave in a magnetized plasma layer. Both interacting waves are of P polarization. The generated currents and fields at combination frequencies are obtained analytically. Unlike the S-polarized interacting waves, the magnetic field affects the fundamental waves and leads to an amplification of generated waves when their frequencies approach the cyclotron frequency. (author)
Nonlinear Optimization of CLIC DRS New Design with Variable Bends and High Field Wigglers
Ghasem, H.; Alabau-Gonzalvo, J.; Papadopoulou, S.; Papaphilippou, Y.
2016-01-01
The new design of CLIC damping rings is based on longitudinal variable bends and high field superconducting wiggler magnets. It provides an ultra-low horizontal normalised emittance of 412 nm-rad at 2.86 GeV. In this paper, nonlinear beam dynamics of the new design of the damping ring (DR) with trapezium field profile bending magnets have been investigated in detail. Effects of the misalignment errors have been studied in the closed orbit and dynamic aperture.
Nonlinear instability of thin current sheets in antiparallel and guided magnetic fields
Silin, I.; Büchner, J.
2003-09-01
The influence of a current-aligned guide magnetic field on the nonlinear resonant instability of thin current sheets is investigated by means of three-dimensional Vlasov-code simulations. Similarly to the zero-guide field case, the pressure gradient excites lower-hybrid-drift (LHD) waves at the current sheet edges. However, since the LHD waves are excited perpendicular to the local magnetic field they propagate obliquely to the current direction. As a result, the number of resonant particles, i.e., the drift-resonance efficiency, decreases with increasing guide field strength. Hence, the driving of global current sheet kink/sausage instabilities becomes less efficient.
Nonlinear instability of thin current sheets in antiparallel and guided magnetic fields
International Nuclear Information System (INIS)
Silin, I.; Buechner, J.
2003-01-01
The influence of a current-aligned guide magnetic field on the nonlinear resonant instability of thin current sheets is investigated by means of three-dimensional Vlasov-code simulations. Similarly to the zero-guide field case, the pressure gradient excites lower-hybrid-drift (LHD) waves at the current sheet edges. However, since the LHD waves are excited perpendicular to the local magnetic field they propagate obliquely to the current direction. As a result, the number of resonant particles, i.e., the drift-resonance efficiency, decreases with increasing guide field strength. Hence, the driving of global current sheet kink/sausage instabilities becomes less efficient
A Model for Periodic Nonlinear Electric Field Structures in Space Plasmas
International Nuclear Information System (INIS)
Qureshi, M.N.S.; Shi Jiankui; Liu Zhenxing
2009-01-01
In this study, we present a physical model to explain the generation mechanism of nonlinear periodic waves with a large amplitude electric field structures propagating obliquely and exactly parallel to the magnetic field. The 'Sagdeev potential' from the MHD equations is derived and the nonlinear electric field waveforms are obtained when the Mach number, direction of propagation, and the initial electric field satisfy certain plasma conditions. For the parallel propagation, the amplitude of the electric field waves with ion-acoustic mode increases with the increase of initial electric field and Mach number but its frequency decreases with the increase of Mach number. The amplitude and frequency of the electric field waves with ion-cyclotron mode decrease with the increase of Mach number and become less spiky, and its amplitude increases with the increase of initial electric field. For the oblique propagation, only periodic electric field wave with an ion-cyclotron mode obtained, its amplitude and frequency increase with the increase of Mach number and become spiky. From our model the electric field structures show periodic, spiky, and saw-tooth behaviours corresponding to different plasma conditions.
Web Platform for Sharing Modeling Software in the Field of Nonlinear Optics
Directory of Open Access Journals (Sweden)
Dubenskaya Julia
2018-01-01
Full Text Available We describe the prototype of a Web platform intended for sharing software programs for computer modeling in the rapidly developing field of the nonlinear optics phenomena. The suggested platform is built on the top of the HUBZero open-source middleware. In addition to the basic HUBZero installation we added to our platform the capability to run Docker containers via an external application server and to send calculation programs to those containers for execution. The presented web platform provides a wide range of features and might be of benefit to nonlinear optics researchers.
Marino, A A; Wolcott, R M; Chervenak, R; Jourd'heuil, F; Nilsen, E; Frilot, C; Pruett, S B
2001-01-01
The characteristic biological effects of low-frequency electromagnetic fields (EMFs) appear to be functional changes in the central nervous, endocrine and immune systems. For unapparent reasons, however, the results of similar studies have often differed markedly from one another. We recognized that it had generally been assumed, in the studies, that EMF effects would exhibit a dose-effect relationship, which is a basic property of linear systems. Prompted by recent developments in the theory on nonlinear systems, we hypothesized that there was a nonlinear relationship between EMFs and the effects they produced in the endocrine and immune systems. We developed a novel analytical method that could be used to distinguish between linear and nonlinear effects, and we employed it to examine the effect of EMFs on the endocrine and immune systems. Mice exposed to 5 G, 60 Hz for 1-175 days in 7 independent experiments reliably exhibited changes in serum corticosterone and lymphoid phenotype when the data were analyzed while allowing that the field exposure and the resulting effects could be nonlinearly related. When the analysis was restricted to linear relationships, no effects due to the field were found. The results indicated that transduction of EMFs resulted in changes in both the endocrine and immune systems, and that the laws governing the changes in each system were not the type that govern conventional dose-effect relationships. Evidence based on mathematical modeling was found suggesting that the coincident changes could have been causally related. Copyright 2001 S. Karger AG, Basel
Nonlinear optics response of semiconductor quantum wells under high magnetic fields
International Nuclear Information System (INIS)
Chemla, D.S.
1993-07-01
Recent investigations on the nonlinear optical response of semiconductor quantum wells in a strong perpendicular magnetic field, H, are reviewed. After some introductory material the evolution of the linear optical properties of GaAs QW's as a function of H is discussed; an examination is made of how the magneto-excitons (MX) extrapolate continuously between quasi-2D QW excitons (X) when H = 0, and pairs of Landau levels (LL) when H → ∞. Next, femtosecond time resolved investigations of their nonlinear optical response are presented; the evolution of MX-MX interactions with increasing H is stressed. Finally, how, as the dimensionality is reduced by application of H, the number of scattering channels is limited and relaxation of electron-hole pairs is affected. How nonlinear optical spectroscopy can be exploited to access the relaxation of angular momentum within magneto-excitons is also discussed
Local-field enhancement effect on the nonlinear optical response of gold-silver nanoplanets.
Cesca, T; Calvelli, P; Battaglin, G; Mazzoldi, P; Mattei, G
2012-02-13
We report on the nonlinear optical properties of Au-Ag nanoplanets produced by ion implantation and irradiation in silica, experimentally investigated by means of the single beam z-scan technique. The measurements provided experimental evidence of the intense local-field enhancement effect theoretically demonstrated for these plasmonic nanosystems. In particular, this has a dramatic impact on their nonlinear absorption behavior and results in a tunable changeover from reverse saturable absorption to saturable absorption by slightly varying the pump intensity and in the possibility to activate and observe nonlinear phenomena of the electron dynamics otherwise unaccessible in the intensity range that can be employed to study these materials. Finally, for the nanoplanet configuration we found a dramatic decrease of the intensity-dependent absorption coefficient, which could be very promising for obtaining optical gain materials.
Kravets, Nina; Brasselet, Etienne
2018-01-01
We propose to couple the optical orientational nonlinearities of liquid crystals with their ability to self-organize to tailor them to control space-variant-polarized optical fields in a nonlinear manner. Experimental demonstration is made using a liquid crystal light valve that behaves like a light-driven geometric phase optical element. We also unveil two original nonlinear optical processes, namely self-induced separability and nonseparability. These results contribute to the advancement of nonlinear singular optics that is still in its infancy despite 25 years of effort, which may foster the development of nonlinear protocols to manipulate high-dimensional optical information both in the classical and quantum regimes.
Nonlinear intersubband optical absorption of Si {delta}-doped GaAs under an electric field
Energy Technology Data Exchange (ETDEWEB)
Yildirim, Hasan; Tomak, Mehmet [Middle East Technical University, Department of Physics, Ankara 06531 (Turkey)
2006-10-15
We study the nonlinear intersubband optical absorption of a single Si {delta}-doped GaAs sheet placed in the middle of a GaAs quantum well and subjected to an electric field. The Schroedinger and Poisson equations are solved self-consistently for various electric field strengths. The self-consistent solutions provide us with the correct confining potential, the wave functions, the corresponding subband energies and the subband occupations. The nonlinear optical intersubband absorption spectra are discussed within the framework of the density matrix formulation for various electric field strengths, well widths, and sheet thicknesses in which Si atoms are distributed uniformly. We include both the depolarization and exciton shifts in calculations. The depolarization effect not only shifts the peak value but also makes the nonlinear absorption spectrum strongly asymmetric with the increasing intensity of the optical field. The blue-shift associated with the depolarization shift is decreased when the intensity is increased. The absorption line shape becomes more asymmetric at smaller well widths and thicker doping layers. The electric field restores the symmetry of the absorption line shape at larger well widths and thinner doping layers, but it decreases the peak value of the line shape. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Micro-/nanoscale multi-field coupling in nonlinear photonic devices
Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu
2017-08-01
The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.
International Nuclear Information System (INIS)
Chau, L.L.
1984-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Riemann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Backlund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N ≥ 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed
Light bending by nonlinear electrodynamics under strong electric and magnetic field
Energy Technology Data Exchange (ETDEWEB)
Kim, Jin Young; Lee, Taekoon, E-mail: jykim@kunsan.ac.kr, E-mail: tlee@kunsan.ac.kr [Department of Physics, Kunsan National University, Daihakro 558, Kunsan 573-701 (Korea, Republic of)
2011-11-01
We calculate the bending angles of light under the strong electric and magnetic fields by a charged black hole and a magnetized neutron star according to the nonlinear electrodynamics of Euler-Heisenberg interaction. The bending angle of light by the electric field of charged black hole is computed from geometric optics and a general formula is derived for light bending valid for any orientation of the magnetic dipole. The astronomical significance of the light bending by magnetic field of a neutron star is discussed.
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.
Nonlinear propagation of strong-field THz pulses in doped semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2012-01-01
We report on nonlinear propagation of single-cycle THz pulses with peak electric fields reaching 300 kV/cm in n-type semiconductors at room temperature. Dramatic THz saturable absorption effects are observed in GaAs, GaP, and Ge, which are caused by the nonlinear electron transport in THz fields......-effective-mass states in the energy-momentum space of the conduction band. Further, we observe the typical accompanying effects of saturable absorption on the THz pulses, such as an increase of the group delay, as the peak electric field of the pulse increases. In this paper we present the results of nonlinear THz time....... The semiconductor conductivity, and hence the THz absorption, is modulated due to the acceleration of carriers in strong THz fields, leading to an increase of the effective mass of the electron population, as the electrons are redistributed from the low-momentum, low-effective-mass states to the high-momentum, high...
International Nuclear Information System (INIS)
Mirzade, F. Kh.
2006-01-01
A system of equations is formulated to describe the self-consistent behavior of elastic displacement fields and the concentration field of point defects in irradiated crystals with a symmetry center (germanium, silicon). In accordance with the values of the defect relaxation times, the model evolution equations are derived, describing the steady-state nonlinear longitudinal waves, with regard to the flexoelectric effect. The effect is due to the dielectric polarization induced by nonuniform elastic deformations of the lattice. For a particular relationship between the coefficients of these equations, i.e., between the parameters of the subsystem of defects and those of the nonlinear elastic medium, the exact solutions are obtained, which describe the generation of solitons and low-intensity shock waves. The contributions of the strain-defect interaction and the flexoelectric effect to the linear velocity of sound and the dispersion properties of the medium are estimated
Nonlinear cloudy bag model in the meson mean-field approximation
International Nuclear Information System (INIS)
Bunatyan, G.G.
1989-01-01
We investigate the cloudy bag model for the nucleon, including the essentially nonlinear interaction of the quarks with the meson field. From the boundary conditions, which guarantee the stability of the bag, we obtain equations for the size R of the bag, for the momentum p of the quarks, and for the mean pion field var-phi. We obtain an expression for the total energy E of the bag nucleon. By taking the appropriate averages of all the relations the calculations reduce to the case of a spherically symmetric bag. We show that in the general nonlinear cloudy bag model in question the equations for R, p, and var-phi have a simultaneous solution which corresponds to the absolute minimum of the bag energy E and, consequently, that there exists a stable equilibrium state of the bag nucleon
Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field
International Nuclear Information System (INIS)
Haegele, G.
1979-01-01
The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)
Characterization of the nonlinear propagation of diffracting, finite amplitude ultrasonic fields
Wallace, Kirk Dennis
The scope of this thesis is to investigate the nonlinear physics fundamental to the progressive distortion of a bounded finite amplitude ultrasonic beam. Emphasis is placed on the experimental characterization of the spatial dependence in harmonic frequency content for a finite amplitude ultrasonic field generated by a narrowband bounded source. Asymptotic forms of the Burgers equation are considered to facilitate analysis of finite amplitude measurements (Fubini solution) and simulation of strongly shocked waveforms (Fay solution). The impact of the Kramers-Kronig dispersion relationship on shock wave evolution in media with frequency dependent power law attenuation is demonstrated. A numerical simulation tool incorporating the complete form of the nonlinear Burgers equation into a linear angular spectrum description of the three dimensional ultrasonic field is developed and presented. Experimental validation of the numerical simulation tool is achieved through comparison with a series of detailed hydrophone measurements of the finite amplitude ultrasonic field generated by a clinical echocardiographic imaging system. Once validated, the simulation tool is used to assist the design and motivation of experimental measurements of intrinsic acoustic parameters in liquid mixtures. A novel experimental technique is utilized to determine both nonlinear and linear acoustic parameters in mixtures of isopropyl alcohol and water.
Dynamic updating atlas for heart segmentation with a nonlinear field-based model.
Cai, Ken; Yang, Rongqian; Yue, Hongwei; Li, Lihua; Ou, Shanxing; Liu, Feng
2017-09-01
Segmentation of cardiac computed tomography (CT) images is an effective method for assessing the dynamic function of the heart and lungs. In the atlas-based heart segmentation approach, the quality of segmentation usually relies upon atlas images, and the selection of those reference images is a key step. The optimal goal in this selection process is to have the reference images as close to the target image as possible. This study proposes an atlas dynamic update algorithm using a scheme of nonlinear deformation field. The proposed method is based on the features among double-source CT (DSCT) slices. The extraction of these features will form a base to construct an average model and the created reference atlas image is updated during the registration process. A nonlinear field-based model was used to effectively implement a 4D cardiac segmentation. The proposed segmentation framework was validated with 14 4D cardiac CT sequences. The algorithm achieved an acceptable accuracy (1.0-2.8 mm). Our proposed method that combines a nonlinear field-based model and dynamic updating atlas strategies can provide an effective and accurate way for whole heart segmentation. The success of the proposed method largely relies on the effective use of the prior knowledge of the atlas and the similarity explored among the to-be-segmented DSCT sequences. Copyright © 2016 John Wiley & Sons, Ltd.
Linear Stability Analysis of a Collisionless Distribution Function for the Force-Free Harris Sheet
Wilson, Fiona; Neukirch, Thomas
2013-04-01
A discussion is presented of the first linear stability analysis of the collisionless distribution function recently found by Harrison and Neukirch for the force-free Harris sheet (Physical Review Letters 102, 135003, 2009). Macroscopic instabilities are considered, and the perturbations are assumed to be two-dimensional only. The stability analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. In addition to the full problem, the long wavelength limit is considered, and the results of the two cases are compared. The dependence of the stability on various equilibrium parameters is investigated.
International Nuclear Information System (INIS)
Denisov, V.I.; Krivchenkov, I.V.; Denisov, I.P.
2002-01-01
The study on the electromagnetic waves propagation in the neutron star magnetic dipole and gravitation fields, taking place according to the vacuum nonlinear electrodynamics laws, is carried out. It is shown that depending on the polarization the electromagnetic signals in this field propagate by different beams and with various velocities. The law on these signals motion by beams is established. The calculation of differences in the times of the electromagnetic signals propagation, having the same source up to the detector, is presented. It is shown that this difference in some cases may reach enough measurable value of 1 μs [ru
Nonlinearity in MCF7 Cell Survival Following Exposure to Modulated 6 MV Radiation Fields
Lacoste-Collin, Laetitia; Castiella, Marion; Franceries, Xavier; Cassol, Emmanuelle; Vieillevigne, Laure; Pereda, Veronica; Bardies, Manuel; Courtade-Sa?di, Monique
2015-01-01
The study of cell survival following exposure to nonuniform radiation fields is taking on particular interest because of the increasing evidence of a nonlinear relationship at low doses. We conducted in vitro experiments using the MCF7 breast cancer cell line. A 2.4 × 2.4 cm2 square area of a T25 flask was irradiated by a Varian Novalis accelerator delivering 6 MV photons. Cell survival inside the irradiation field, in the dose gradient zone and in the peripheral zone, was determined using a ...
Nonlinear Spinor Field in Non-Diagonal Bianchi Type Space-Time
Directory of Open Access Journals (Sweden)
Saha Bijan
2018-01-01
Full Text Available Within the scope of the non-diagonal Bianchi cosmological models we have studied the role of the spinor field in the evolution of the Universe. In the non-diagonal Bianchi models the spinor field distribution along the main axis is anisotropic and does not vanish in the absence of the spinor field nonlinearity. Hence within these models perfect fluid, dark energy etc. cannot be simulated by the spinor field nonlinearity. The equation for volume scale V in the case of non-diagonal Bianchi models contains a term with first derivative of V explicitly and does not allow exact solution by quadratures. Like the diagonal models the non-diagonal Bianchi space-time becomes locally rotationally symmetric even in the presence of a spinor field. It was found that depending on the sign of the coupling constant the model allows either an open Universe that rapidly grows up or a close Universe that ends in a Big Crunch singularity.
Effect of sample shape on nonlinear magnetization dynamics under an external magnetic field
International Nuclear Information System (INIS)
Vagin, Dmitry V.; Polyakov, Oleg P.
2008-01-01
Effect of sample shape on the nonlinear collective dynamics of magnetic moments in the presence of oscillating and constant external magnetic fields is studied using the Landau-Lifshitz-Gilbert (LLG) approach. The uniformly magnetized sample is considered to be an ellipsoidal axially symmetric particle described by demagnetization factors and uniaxial crystallographic anisotropy formed some angle with an applied field direction. It is investigated as to how the change in particle shape affects its nonlinear magnetization dynamics. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. In this paper, we show that the sample's (particle's) shape and its orientation with respect to the external field (system configuration) determine the character of magnetization dynamics: deterministic behavior and appearance of chaotic states. A simple change in the system's configuration or in the shapes of its parts can transfer it from chaotic to periodic or even static regime and back. Moreover, the effect of magnetization precession stall and magnetic moments alignment parallel or antiparallel to the external oscillating field is revealed and the way of control of such 'polarized' states is found. Our results suggest that varying the particle's shape and fields' geometry may provide a useful way of magnetization dynamics control in complex magnetic systems
Non-Linear Dynamics of a Porous Medium Saturated With Electrolyte in the Magnetic Field
Perepechko, Y.
2006-12-01
The correct description of dynamics of saturated porous media in the magnetic field is one of the topical problems for mechanics of electromagnetic multi-phase media. This report studies the non-linear model of the conducting liquid flow through non-conducting deformable porous medium in the external magnetic field. We consider the most interesting case with the magnetic field, transverse to the fluid flow, what allows us to examine interaction between the magnetic field and transverse oscillations. The determining equations of the model, including non-linear two-velocity equations for dynamics of saturated porous deformable medium and Maxwell equation in magnetic-hydrodynamic approximation, are invariant relative to Galileo transformation and coordinated from the point of thermal dynamics. This model includes two longitudinal types of acoustic waves and two transverse types of magnetic-acoustic waves, which are transformed into transverse sound-waves and Alfven waves without magnetic-acoustic interaction. The effect of external magnetic field on the pattern of non- linear filtration of electrolyte through an inelastically-deformable porous medium is studied numerically together with the analysis of coordinated magnetic fields, generated during electrolyte filtration and porous matrix deformation. An increase in the magnetic field by a liquid conducting phase is examined in two cases: for the trapped magnetic field and for diffusion of the magnetic field due to electric conductivity of electrolyte. This model allows investigation of magnetic-seismic and seismic-magnetic effects and their use in applied geophysics, particularly, for earthquake forecast and development of new methods for geophysical research. This research was supported by the Russian Foundation for Basic Research grant 06.05.65110, by the President's grants NSh.1573.2003.5, and by the Russian Ministry Science and Education grant RNP.2.1.1.702.
Dynamics modeling for a rigid-flexible coupling system with nonlinear deformation field
International Nuclear Information System (INIS)
Deng Fengyan; He Xingsuo; Li Liang; Zhang Juan
2007-01-01
In this paper, a moving flexible beam, which incorporates the effect of the geometrically nonlinear kinematics of deformation, is investigated. Considering the second-order coupling terms of deformation in the longitudinal and transverse deflections, the exact nonlinear strain-displacement relations for a beam element are described. The shear strains formulated by the present modeling method in this paper are zero, so it is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motions. Then, considering the coupling terms of deformation in two dimensions, finite element shape functions of a beam element and Lagrange's equations are employed for deriving the coupling dynamical formulations. The complete expression of the stiffness matrix and all coupling terms are included in the formulations. A model consisting of a rotating planar flexible beam is presented. Then the frequency and dynamical response are studied, and the differences among the zero-order model, first-order coupling model and the new present model are discussed. Numerical examples demonstrate that a 'stiffening beam' can be obtained, when more coupling terms of deformation are added to the longitudinal and transverse deformation field. It is shown that the traditional zero-order and first-order coupling models may not provide an exact dynamic model in some cases
A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Chen, Suming; Nie, Zongxiu
2015-08-01
In comparison with numerical methods, theoretical characterizations of ion motion in the nonlinear Paul traps always suffer from low accuracy and little applicability. To overcome the difficulties, the theoretical harmonic balance (HB) method was developed, and was validated by the numerical fourth-order Runge-Kutta (4th RK) method. Using the HB method, analytical ion trajectory and ion motion frequency in the superimposed octopole field, ɛ, were obtained by solving the nonlinear Mathieu equation (NME). The obtained accuracy of the HB method was comparable with that of the 4th RK method at the Mathieu parameter, q = 0.6, and the applicable q values could be extended to the entire first stability region with satisfactory accuracy. Two sorts of nonlinear effects of ion motion were studied, including ion frequency shift, Δ β, and ion amplitude variation, Δ( C 2 n / C 0) ( n ≠ 0). New phenomena regarding Δ β were observed, although extensive studies have been performed based on the pseudo-potential well (PW) model. For instance, the |Δ β| at ɛ = 0.1 and ɛ = -0.1 were found to be different, but they were the same in the PW model. This is the first time the nonlinear effects regarding Δ( C 2 n / C 0) ( n ≠ 0) are studied, and the associated study has been a challenge for both theoretical and numerical methods. The nonlinear effects of Δ( C 2 n / C 0) ( n ≠ 0) and Δ β were found to share some similarities at q < 0.6: both of them were proportional to ɛ, and the square of the initial ion displacement, z(0)2.
Subcycle Extreme Nonlinearities in GaP Induced by an Ultrastrong Terahertz Field
Vicario, Carlo; Shalaby, Mostafa; Hauri, Christoph P.
2017-02-01
We report on the experimental observation of extreme laser spectral broadening and a change in optical transmission in gallium phosphite induced by 25 MV /cm terahertz (THz) single-cycle internal field. Such intense THz radiation leads to twofold transient modifications of the optical properties in the electro-optical crystal. First, the electric field provokes extensive cross-phase modulation via the χ(2 ) and χ(3 ) nonlinearities on a copropagating 50 fs near infrared laser pulse which turns into 500% spectral broadening. Second, we observe an instantaneous change of the optical transmission occurring at the THz field which is alleged to interband Zener tunneling and charge carrier density modification by impact ionization turning the semiconductor in a metal-like transient state. The presented scheme displays a pathway to coherently control the optical properties of semiconductors on an ultrafast time scale by a strong THz field.
Modeling of nonlinear microscopy of localized field enhancements in random metal nanostructures
DEFF Research Database (Denmark)
Beermann, Jonas; Bozhevolnyi, Sergey I.; Coello, Victor
2006-01-01
Nonlinear microscopy of localized field enhancements in random metal nanostructures with a tightly focused laser beam scanning over a sample surface is modeled by making use of analytic representations of the Green dyadic in the near- and far-field regions, with the latter being approximated...... by the part describing the scattering via excitation of surface plasmon polaritons. The developed approach is applied to scanning second-harmonic (SH) microscopy of small gold spheres placed randomly on a gold surface. We calculate self-consistent fundamental harmonic (FH) and SH field distributions...... at the illuminated sample surface and, thereby, FH and SH images for different polarization configurations of the illuminating and detected fields. The simulated images bear close resemblance to the images obtained experimentally, exhibiting similar sensitivity to the wavelength and polarization, as well...
A nonlinear scenario for development of vortex layer instability in gravity field
International Nuclear Information System (INIS)
Goncharov, V. P.
2007-01-01
A Hamiltonian version of contour dynamics is formulated for models of constant-vorticity plane flows with interfaces. The proposed approach is used as a framework for a nonlinear scenario for instability development. Localized vortex blobs are analyzed as structural elements of a strongly perturbed wall layer of a vorticity-carrying fluid with free boundary in gravity field. Gravity and vorticity effects on the geometry and velocity of vortex structures are examined. It is shown that compactly supported nonlinear solutions (compactons) are candidates for the role of particle-like vortex structures in models of flow breakdown. An analysis of the instability mechanism demonstrates the possibility of a self-similar collapse. It is found that the vortex shape stabilizes at the final stage of the collapse, while the vortex sheet strength on its boundary increases as (t 0 - t) -1 , where t 0 is the collapse time
Magnetic resonance imaging with nonlinear gradient fields signal encoding and image reconstruction
Schultz, Gerrit
2013-01-01
Within the past few decades magnetic resonance imaging has become one of the most important imaging modalities in medicine. For a reliable diagnosis of pathologies further technological improvements are of primary importance. This text deals with a radically new approach of image encoding: The fundamental principle of gradient linearity is challenged by investigating the possibilities of acquiring anatomical images with the help of nonlinear gradient fields. Besides a thorough theoretical analysis with a focus on signal encoding and image reconstruction, initial hardware implementations are tested using phantom as well as in-vivo measurements. Several applications are presented that give an impression about the implications that this technological advancement may have for future medical diagnostics. Contents n Image Reconstruction in MRI n Nonlinear Gradient Encoding: PatLoc Imaging n Presentation of Initial Hardware Designs n Basics of Signal Encoding and Image Reconstruction in PatLoc Imaging n ...
REALISTIC NON-LINEAR MODEL AND FIELD QUALITY ANALYSIS IN RHIC INTERACTION REGIONS.
Energy Technology Data Exchange (ETDEWEB)
BEEBE-WANG,J.; JAIN, A.
2007-06-25
The existence of multipole components in the dipole and quadrupole magnets is one of the factors limiting the beam stability in the RHIC operations. So, a realistic non-linear model is crucial for understanding the beam behavior and to achieve the ultimate performance in RHIC. A procedure is developed to build a non-linear model using the available multipole component data obtained from measurements of RHIC magnets. We first discuss the measurements performed at different stages of manufacturing of the magnets in relation to their current state in RHIC. We then describe the procedure to implement these measurement data into tracking models, including the implementation of the multipole feed down effect due to the beam orbit offset from the magnet center. Finally, the field quality analysis in the RHIC interaction regions (IR) is presented.
Li, Jipeng; Li, Haitao; Zheng, Jun; Zheng, Botian; Huang, Huan; Deng, Zigang
2017-06-01
The nonlinear vibration of high temperature superconducting (HTS) bulks in an applied permanent magnetic array (Halbach array) field, as a precondition for commercial application to HTS maglev train and HTS bearing, is systematically investigated. This article reports the actual vibration rules of HTS bulks from three aspects. First, we propose a new numerical model to simplify the calculation of levitation force. This model could provide precise simulations, especially the estimation of eigenfrequency. Second, an approximate analytic solution of the vibration of the HTS bulks is obtained by using the method of harmonic balance. Finally, to verify the results mentioned above, we measure the vertical vibration acceleration signals of an HTS maglev model, consisting of eight YBaCuO bulks, oscillating freely above a Halbach array with large displacement excitation. Higher order harmonic components, which indicate the nonlinear vibration phenomenon, are detected in the responses. All the three results are compared and agreed well with each other. This study combines the experimental and theoretical analyses and provides a deep understanding of the physical phenomenon of the nonlinear vibration and is meaningful for the vibration control of the relevant applications.
Energy Technology Data Exchange (ETDEWEB)
Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation)
2015-10-28
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
Nonlinear bound on unstable field energy in relativistic electron beams and plasmas
International Nuclear Information System (INIS)
Davidson, R.C.; Yoon, P.H.
1989-01-01
This paper makes use of Fowler's method [J. Math Phys. 4, 559 (1963)] to determine the nonlinear thermodynamic bound on field energy in unstable plasmas or electron beams in which the electrons are relativistic. Treating the electrons as the only active plasma component, the nonlinear Vlasov--Maxwell equations and the associated global conservation constraints are used to calculate the lowest upper bound on the field energy [ΔE-script/sub F/]/sub max/ that can evolve for the general initial electron distribution function f/sub b//sub / 0 equivalentf/sub b/(x,p,0). The results are applied to three choices of the initial distribution function f/sub b//sub / 0 . Two of the distribution functions have an inverted population in momentum p/sub perpendicular/ perpendicular to the magnetic field B 0 e/sub z/, and the third distribution function reduces to a bi-Maxwellian in the nonrelativistic limit. The lowest upper bound on the efficiency of radiation generation, eta/sub max/ = [ΔE-script/sub F/]/sub max//[V -1 ∫ d 3 x∫ d 3 p(γ-1)mc 2 f/sub b//sub / 0 ], is calculated numerically over a wide range of system parameters for varying degrees of initial anisotropy
Field-induced non-linear optical features of p-aminoazobenzene crystals
Krishnakumar, V.; Eazhilarasi, G.; Nagalakshmi, R.; Piasecki, M.; Kityk, I. V.; Bragiel, P.
2008-06-01
Using ethanol as a solvent p-aminoazobenzene (p-AAZB), an organic nonlinear optical crystal having good optical quality was grown by slow evaporation solution technique. Structural and optical properties were studied by applying XRD and UV-Vis spectroscopy. The measurement of the second harmonic generation was performed using the fundamental Nd:YAG 10 ns laser beam with wavelength 1.064 μm. Dependence of the second order susceptibilities for the two principal second order susceptibility tensor components d14 and d25 with the simultaneously applied dc- and UV-laser fields were investigated and discussed.
Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields
Gulin, Luka; Smolić, Ivica
2018-01-01
We present a direct, geometric derivation of the generalized Smarr formula for the stationary axially symmetric black holes with nonlinear electromagnetic fields. The additional term is proven to be proportional to the integral of the trace of the electromagnetic energy-momentum tensor and can be written as a product of two conjugate variables. From the novel relation we can deduce all previously proposed forms of the generalized Smarr formula, which were derived only for the spherically symmetric black holes, and provide the lowest order quantum correction to the classical relation from the Euler–Heisenberg Lagrangian.
Three dimensional magnetic solutions in massive gravity with (non)linear field
Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Momennia, M.
2017-12-01
The Noble Prize in physics 2016 motivates one to study different aspects of topological properties and topological defects as their related objects. Considering the significant role of the topological defects (especially magnetic strings) in cosmology, here, we will investigate three dimensional horizonless magnetic solutions in the presence of two generalizations: massive gravity and nonlinear electromagnetic field. The effects of these two generalizations on properties of the solutions and their geometrical structure are investigated. The differences between de Sitter and anti de Sitter solutions are highlighted and conditions regarding the existence of phase transition in geometrical structure of the solutions are studied.
Light-Matter Interaction Atoms and Molecules in External Fields and Nonlinear Optics
Hill, Wendell T
2006-01-01
This book draws together the principal ideas that form the basis of atomic, molecular, and optical science and engineering. It covers the basics of atoms, diatomic molecules, atoms and molecules in static and electromagnetic fields and nonlinear optics. Exercises and bibliographies supplement each chapter, while several appendices present such important background information as physics and math definitions, atomic and molecular data, and tensor algebra. Accessible to advanced undergraduates, graduate students, or researchers who have been trained in one of the conventional curricula of physic
Smith, David D.
2002-01-01
This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.
φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
Sornette, D.; Simonetti, P.; Andersen, J. V.
2000-08-01
Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
International Nuclear Information System (INIS)
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-01-01
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented
Yamaguchi, Maiku; Nobusada, Katsuyuki; Yatsui, Takashi
2015-10-01
Electron dynamics excited by an optical near field (ONF) in a two-dimensional quantum dot model was investigated by solving a time-dependent Schrödinger equation. It was found that the ONF excitation of the electron caused two characteristic phenomena: a two-photon absorption and an induction of a magnetic dipole moment with a strong third-harmonic component. By analyzing the interaction dynamics of the ONF and the electron, we explained that the physical mechanism underlying these phenomena was the second-harmonic electric-field component concomitant with the near-field excitation originating from the nonuniformity of the ONF. Despite a y -polarized ONF source, the second-harmonic component of an x -polarized electric field was inherently generated. The effect of the second-harmonic electric-field component is not due to usual second-order nonlinear response but appears only when we explicitly consider the electron dynamics interacting with the ONF beyond the conventional optical response assuming the dipole approximation.
Force-free swimming of a model helical flagellum in viscoelastic fluids.
Liu, Bin; Powers, Thomas R; Breuer, Kenneth S
2011-12-06
We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids. The fluids are highly viscous to replicate the low Reynolds number environment of microorganisms. The helix, a macroscopic scale model for the bacterial flagellar filament, is rigid and rotated at a constant rate while simultaneously translated along its axis. By adjusting the translation speed to make the net hydrodynamic force vanish, we measure the force-free swimming speed as a function of helix rotation rate, helix geometry, and fluid properties. We compare our measurements of the force-free swimming speed of a helix in a high-molecular weight silicone oil with predictions for the swimming speed in a Newtonian fluid, calculated using slender-body theories and a boundary-element method. The excellent agreement between theory and experiment in the Newtonian case verifies the high accuracy of our experiments. For the viscoelastic fluid, we use a polymer solution of polyisobutylene dissolved in polybutene. This solution is a Boger fluid, a viscoselastic fluid with a shear-rate-independent viscosity. The elasticity is dominated by a single relaxation time. When the relaxation time is short compared to the rotation period, the viscoelastic swimming speed is close to the viscous swimming speed. As the relaxation time increases, the viscoelastic swimming speed increases relative to the viscous speed, reaching a peak when the relaxation time is comparable to the rotation period. As the relaxation time is further increased, the viscoelastic swimming speed decreases and eventually falls below the viscous swimming speed.
Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir
2018-05-01
Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.
GiRaFFE: An Open-Source General Relativistic Force-Free Electrodynamics Code
Etienne, Zachariah B.; Wan, Mew-Bing; Babiuc, Maria C.; McWilliams, Sean T.; Choudhary, Ashok
2017-01-01
We present GiRaFFE, the first open-source general relativistic force-free electrodynamics (GRFFE) code for dynamical, numerical-relativity generated spacetimes. GiRaFFE adopts the strategy pioneered by McKinney and modified by Paschalidis and Shapiro to convert a GR magnetohydrodynamic (GRMHD) code into a GRFFE code. In short, GiRaFFE exists as a modification of IllinoisGRMHD, a user-friendly, open-source, dynamical-spacetime GRMHD code. Both GiRaFFE and IllinoisGRMHD leverage the Einstein To...
Energy principle for stability of general force-free MHD equilibria
International Nuclear Information System (INIS)
Chu, M.S.; Jensen, T.H.; Lee, J.K.
1982-01-01
An energy principle has been constructed for the determination of stability of general force-free equilibria against ideal- and dissipative-(tearing)-MHD modes. The concept of accessible neighbouring equilibria, with the inclusion of singular currents on mode rational surfaces, is used. The driving source of these instabilities may be either the parallel current density or the parallel current density gradient. This energy prnciple is well suited for numerical implementation. Reduction of this energy principle to some known cases is also presented. (author)
Nonlinear dynamics of magnetic island interacting with external helical magnetic field
International Nuclear Information System (INIS)
Nishimura, S.; Yagi, M.; Itoh, S.-I.; Itoh, K.
2009-01-01
Full text: The control of magnetic islands is one of important issues for magnetically confined fusion plasmas. Magnetic islands strongly affect the achievable β''-value by modifying transports, equilibrium fields (i.e. radial profiles of electric current, pressure and electric field) and the stability of plasmas. The induction of resonant helical magnetic fields, which interact with magnetic islands, is an effective method to control the dynamics of magnetic islands. In the Large Helical Device (LHD), magnetic islands are excited by the external magnetic, and the generation of equilibrium poloidal E x B flows by magnetic islands is observed. On the other hand, the external helical magnetic fields have been used to control the poloidal rotation and the stability of magnetic islands in tokamak plasmas. The error field, which is caused by the misalignment of toroidal magnetic coil, plays a similar role to the external helical magnetic field. The locking of the rotation of magnetic islands by error field triggers the disruption in tokamak plasmas. Thus, it is important to understand the basic mechanism of the interaction between magnetic islands and external helical magnetic fields. In this study, nonlinear simulation of drift tearing mode is performed using a set of reduced two-fluid equations, and the detailed study of the interaction between magnetic islands with external helical magnetic fields is reported. The external helical field associated with magnetic islands is imposed by means of finite amplitude of perturbed magnetic flux (vector potential) at edge boundary. In our simulation, the locking (stop) of the rotation of magnetic islands is observed. The rotation of magnetic island is basically driven by the diamagnetic drift flow and E x B flow. It is found that contributions of these flows approximately cancel each other inside the separatrix of magnetic island in the locking phase. The detailed mechanism of the locking of magnetic island rotation is
Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations
Qi, Y.; Xiao, W.; Yue, D. K. P.
2014-12-01
We propose to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields using direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987). We implement a robust phenomenological-based energy dissipation model in HOS to capture the effect of wave-breaking dissipation on the overall wave-field evolution (Xiao et al 2013). The efficacy of this model is confirmed by direct comparisons against measurements for the energy loss in 2D and 3D breaking events. By comparing simulated wave-fields with and without the dissipation model in HOS, we obtain the dissipation field δ(x,y,t), which provides the times, locations and intensity of wave breaking events (δ>δc). This is validated by comparison of HOS simulations with Airborne Terrain Mapper (ATM) measurements in the recent ONR Hi-Res field experiment. Figure (a) shows one frame of simulated wave-field (with dissipation model). Figure (b) is the corresponding measurement from ATM, where a large wave breaking event was captured. Figure (c) is the 3D view of the simulated wave-field with the colored region representing dissipation with δ>δc. The HOS predicted high-dissipation area is found to agree well with the measured breaking area. Based on HOS predicted high-dissipation area (δ>δc), we calculate Λ(c) (Phillips 1985), the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity c. Figure (d) shows the distribution Λ(c) calculated from HOS. For breaking speeds c greater than 5m/s, the simulated Λ(c) is in qualitative agreement with Phillips theoretical power-law of Λ(c)~c-6. From δ(x,y,t), we further quantify wave breaking by calculating the whitecap coverage rate Wr(t) and energy dissipation rate ΔE'(t), and study the evolution of Wr and ΔE' to understand the role of wave breaking in nonlinear wave-field evolution. We obtain HOS simulations
Near-field soil-structure interaction analysis using nonlinear hybrid modeling
International Nuclear Information System (INIS)
Katayama, I.; Chen, C.; Lee, Y.J.; Jean, W.Y.; Penzien, J.
1989-01-01
The hybrid modeling method (Gupta and Penzien 1980) and associated analysis procedure for solving a three-dimensional soil-structure interaction problem was developed by Gupta and Penzien (1981) and Gupta et al.(1982). Subsequently, successive modifications have been made to the original modeling method and analysis procedure allowing more general treatment of the SSI problem (Penzien, 1988). Through many correlation studies of field test data obtained under forced-vibration and earthquake-excitation conditions, it has been shown that the HASSI programs can effectively predict the dynamic response of a soil-structure system, if realistic soil parameters are adopted. In the above, the entire structure-foundation system is considered to respond in a linear fashion. Since the reflected three-dimensional waves at the soil-structure interface decays very rapidly with distance away from the structure (Katayama, 1987 (a)), the response of the soil close to the base of the structure may greatly affect its response; therefore, proper modeling of the non-linear soil behavior characteristic is essential. The nonlinear behavior of near-field soil has been taken into consideration in HASSI-7 by the standard equivalent linearization procedures used in programs SHAKE and FLUSH
Study on the near-field non-linearity (SMILE) of high power diode laser arrays
Zhang, Hongyou; Jia, Yangtao; Li, Changxuan; Zah, Chung-en; Liu, Xingsheng
2018-02-01
High power laser diodes have been found a wide range of industrial, space, medical applications, characterized by high conversion efficiency, small size, light weight and a long lifetime. However, due to thermal induced stress, each emitter in a semiconductor laser bar or array is displaced along p-n junction, resulting of each emitter is not in a line, called Near-field Non-linearity. Near-field Non-linearity along laser bar (also known as "SMILE") determines the outcome of optical coupling and beam shaping [1]. The SMILE of a laser array is the main obstacle to obtain good optical coupling efficiency and beam shaping from a laser array. Larger SMILE value causes a larger divergence angle and a wider line after collimation and focusing, respectively. In this letter, we simulate two different package structures based on MCC (Micro Channel Cooler) with Indium and AuSn solders, including the distribution of normal stress and the SMILE value. According to the theoretical results, we found the distribution of normal stress on laser bar shows the largest in the middle and drops rapidly near both ends. At last, we did another experiment to prove that the SMILE value of a laser bar was mainly affected by the die bonding process, rather than the operating condition.
Nonlinearity in MCF7 Cell Survival Following Exposure to Modulated 6 MV Radiation Fields
Castiella, Marion; Franceries, Xavier; Cassol, Emmanuelle; Vieillevigne, Laure; Pereda, Veronica; Bardies, Manuel; Courtade-Saïdi, Monique
2015-01-01
The study of cell survival following exposure to nonuniform radiation fields is taking on particular interest because of the increasing evidence of a nonlinear relationship at low doses. We conducted in vitro experiments using the MCF7 breast cancer cell line. A 2.4 × 2.4 cm2 square area of a T25 flask was irradiated by a Varian Novalis accelerator delivering 6 MV photons. Cell survival inside the irradiation field, in the dose gradient zone and in the peripheral zone, was determined using a clonogenic assay for different radiation doses at the isocenter. Increased cell survival was observed inside the irradiation area for doses of 2, 10, and 20 Gy when nonirradiated cells were present at the periphery, while the cells at the periphery showed decreased survival compared to controls. Increased survival was also observed at the edge of the dose gradient zone for cells receiving 0.02 to 0.01 Gy when compared with cells at the periphery of the same flask, whatever the isocenter dose. These data are the first to report cell survival in the dose gradient zone. Radiotherapists must be aware of this nonlinearity in dose response. PMID:26740805
Nonlinearity in MCF7 Cell Survival Following Exposure to Modulated 6 MV Radiation Fields
Directory of Open Access Journals (Sweden)
Laetitia Lacoste-Collin MD, PhD
2015-10-01
Full Text Available The study of cell survival following exposure to nonuniform radiation fields is taking on particular interest because of the increasing evidence of a nonlinear relationship at low doses. We conducted in vitro experiments using the MCF7 breast cancer cell line. A 2.4 × 2.4 cm2 square area of a T25 flask was irradiated by a Varian Novalis accelerator delivering 6 MV photons. Cell survival inside the irradiation field, in the dose gradient zone and in the peripheral zone, was determined using a clonogenic assay for different radiation doses at the isocenter. Increased cell survival was observed inside the irradiation area for doses of 2, 10, and 20 Gy when nonirradiated cells were present at the periphery, while the cells at the periphery showed decreased survival compared to controls. Increased survival was also observed at the edge of the dose gradient zone for cells receiving 0.02 to 0.01 Gy when compared with cells at the periphery of the same flask, whatever the isocenter dose. These data are the first to report cell survival in the dose gradient zone. Radiotherapists must be aware of this nonlinearity in dose response.
Nonlinear resonance and dynamical chaos in a diatomic molecule driven by a resonant ir field
International Nuclear Information System (INIS)
Berman, G.P.; Bulgakov, E.N.; Holm, D.D.
1995-01-01
We consider the transition from regular motion to dynamical chaos in a classical model of a diatomic molecule which is driven by a circularly polarized resonant ir field. Under the conditions of a nearly two-dimensional case, the Hamiltonian reduces to that for the nonintegrable motion of a charged particle in an electromagnetic wave [A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, City, 1983)]. In the general case, the transition to chaos is connected with the overlapping of vibrational-rotational nonlinear resonances and appears even at rather low radiation field intensity, S approx-gt 1 GW/cm 2 . We also discuss the possibility of experimentally observing this transition
A universal nonlinear relation among boundary states in closed string field theory
International Nuclear Information System (INIS)
Kishimoto, Isao; Matsuo, Yutaka; Watanabe, Eitoku
2004-01-01
We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis [hep-th/0306189] in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the α parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation. (author)
On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field
Xu, Lanxi; Lan, Wanli
2017-12-01
Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M, where M is the maximum of the absolute value of the velocity field of the laminar flow.
Impurity-related nonlinear optical properties in delta-doped quantum rings: Electric field effects
International Nuclear Information System (INIS)
Restrepo, R.L.; Morales, A.L.; Martínez-Orozco, J.C.; Baghramyan, H.M.; Barseghyan, M.G.; Mora-Ramos, M.E.; Duque, C.A.
2014-01-01
Using a variational procedure within the effective mass approximation, we have calculated the donor impurity binding energy for the ground (1s-like) and the excited (2p z -like) states as well as the impurity-related nonlinear optical absorption and relative changes in the refraction index in a GaAs single quantum ring with axial n-type delta-doping. The delta-like potential along the z-direction is an approximate model analytically described using a Lorentzian function with two parameters. Additionally we consider the application of an electric field along the z-direction. It is found that the changes in the geometry of the quantum ring, the change in the 2D impurity density of the delta-like doping, and different values of the electric field lead to a shifting of the resonant peaks of the optical responses spectrum
Gupta, Satyapriya; Taupin, Vincent; Fressengeas, Claude; Jrad, Mohamad
2018-03-27
The displacement discontinuity arising between crack surfaces is assigned to smooth densities of crystal defects referred to as disconnections, through the incompatibility of the distortion tensor. In a dual way, the disconnections are defined as line defects terminating surfaces where the displacement encounters a discontinuity. A conservation statement for the crack opening displacement provides a framework for disconnection dynamics in the form of transport laws. A similar methodology applied to the discontinuity of the plastic displacement due to dislocations results in the concurrent involvement of dislocation densities in the analysis. Non-linearity of the geometrical setting is assumed for defining the elastic distortion incompatibility in the presence of both dislocations and disconnections, as well as for their transport. Crack nucleation in the presence of thermally-activated fluctuations of the atomic order is shown to derive from this nonlinearity in elastic brittle materials, without any algorithmic rule or ad hoc material parameter. Digital image correlation techniques applied to the analysis of tensile tests on ductile Al-Cu-Li samples further demonstrate the ability of the disconnection density concept to capture crack nucleation and relate strain localization bands to consistent disconnection fields and to the eventual occurrence of complex and combined crack modes in these alloys.
Response to perturbations of the force-free aligned pulsar atmosphere
International Nuclear Information System (INIS)
Jackson, E.A.
1978-01-01
To clarify the likely structure of the pulsar atmosphere, the response of various plasma configurations near a rotating neutron star with aligned rotational and dipole magnetic axes is investigated. These configurations represent both general infinitesimal perturbations along B of the force-free (E.B = O) atmosphere, as well as a heuristic class of finite perturbations (shell atmospheres). It is shown that the general infinitesimal perturbations along B which preserve spatial ordering involve regions of both negative and positive work, whose boundaries are at the surfaces E.B = O(E is not equal to O) and those of zero charge density (cos 2 theta = 1/3). At the latter surfaces, and on one side of the system will produce mixing of charges of opposite sign. The intersecting E.B=O surface, the response of the recombination of these charges, and their removal by gravity, shows that the force-free atmosphere is physically unstable, favouring a lower density at mid-latitude. The response of various plasma shell atmospheres is also examined and confirms the likelihood of the plasma atmosphere previously predicted from a near-vacuum analysis, provided the density is not too large. Larger density shells are found to break up into 'striated' configurations, containing two electron and one or two ion groups, which however may not develop into stable configurations. Criteria on the plasma density related to this and other responses of the plasma shells are discussed. (author)
Measurements of Rayleigh-Taylor-Induced Magnetic Fields in the Linear and Non-linear Regimes
Manuel, Mario
2012-10-01
Magnetic fields are generated in plasmas by the Biermann-battery, or thermoelectric, source driven by non-collinear temperature and density gradients. The ablation front in laser-irradiated targets is susceptible to Rayleigh-Taylor (RT) growth that produces gradients capable of generating magnetic fields. Measurements of these RT-induced magnetic fields in planar foils have been made using a combination of x-ray and monoenergetic-proton radiography techniques. At a perturbation wavelength of 120 μm, proton radiographs indicate an increase of the magnetic-field strength from ˜1 to ˜10 Tesla during the linear growth phase. A characteristic change in field structure was observed later in time for irradiated foils of different initial surface perturbations. Proton radiographs show a regular cellular configuration initiated at the same time during the drive, independent of the initial foil conditions. This non-linear behavior has been experimentally investigated and the source of these characteristic features will be discussed.
Agapitov, O. V.; Krasnoselskikh, V; Mozer, F. S.; Artemyev, A.V.; Volokitin, A.S.
2015-01-01
International audience; Huge numbers of different nonlinear structures (double layers, electron holes, nonlinear whistlers, etc., referred to as Time Domain Structures, TDS) have been observed by the electric field experiment on the Van Allen Probes. Some of them are associated with whistler waves. Such TDS often emerge on the forward edges of the whistler wave packets and form chains. The parametric decay of a whistler wave into a whistler wave propagating in the opposite direction and an el...
Baraskar, Priyanka; Chouhan, Romita; Agrawal, Arpana; Choudhary, R. J.; Sen, Pranay K.; Sen, Pratima
2018-03-01
We report the magnetic field effect on the linear and nonlinear optical properties of pulse laser ablated Ti-incorporated Cr2O3 nanostructured thin film. Optical properties have been experimentally analyzed under Voigt geometry by performing ultraviolet-visible spectroscopy and closed aperture Z-scan technique using a continuous wave He-Ne laser source. Nonlinear optical response reveals a single peak-valley feature in the far field diffraction pattern in absence of magnetic field (B = 0) confirming self-defocussing effect. This feature switches to a valley-peak configuration for B = 5000G, suggesting self-focusing effect. For B ≤ 750G, oscillations were observed revealing the occurrence of higher order nonlinearity. Origin of nonlinearity is attributed to the near resonant d-d transitions observed from the broad peak occurring around 2 eV. These transitions are of magnetic origin and get modified under the application of external magnetic field. Our results suggest that magnetic field can be used as an effective tool to monitor the sign of optical nonlinearity and hence the thermal expansion in Ti-incorporated Cr2O3 nanostructured thin film.
Agapitov, Oleksiy; Drake, James; Mozer, Forrest
2016-04-01
Huge numbers of different nonlinear structures (double layers, electron holes, non-linear whistlers, etc. referred to as Time Domain Structures - TDS) have been observed by the electric field experiment on board the Van Allen Probes. A large part of the observed non-linear structures are associated with whistler waves and some of them can be directly driven by whistlers. The parameters favorable for the generation of TDS were studied experimentally as well as making use of 2-D particle-in-cell (PIC) simulations for the system with inhomogeneous magnetic field. It is shown that an outward propagating front of whistlers and hot electrons amplifies oblique whistlers which collapse into regions of intense parallel electric field with properties consistent with recent observations of TDS from the Van Allen Probe satellites. Oblique whistlers seed the parallel electric fields that are driven by the beams. The resulting parallel electric fields trap and heat the precipitating electrons. These electrons drive spikes of intense parallel electric field with characteristics similar to the TDSs seen in the VAP data. The decoupling of the whistler wave and the nonlinear electrostatic component is shown in PIC simulation in the inhomogeneous magnetic field system. These effects are observed by the Van Allen Probes in the radiation belts. The precipitating hot electrons propagate away from the source region in intense bunches rather than as a smooth flux.
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
Instability of wormholes supported by a ghost scalar field: II. Nonlinear evolution
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J A; Guzman, F S; Sarbach, O [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Cd. Universitaria, A P 2-82, 58040 Morelia, Michoacan (Mexico)
2009-01-07
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article, we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here, we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and those collapsing to a black hole, and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.
Nonlinear approach to NN interactions using self-interacting meson fields
International Nuclear Information System (INIS)
Jaede, L.; von Geramb, H.V.
1997-01-01
Motivated by the success of models based on chiral symmetry in NN interactions, we investigate self-interacting scalar, pseudoscalar, and vector meson fields and their impact for NN forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange NN potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson-exchange potentials and thus yields a phenomenological understanding of this part of the NN interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields np phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data. copyright 1997 The American Physical Society
International Nuclear Information System (INIS)
Frank, T D; Mongkolsakulvong, S
2015-01-01
In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)
Timokhin, A. N.; Arons, J.
2013-01-01
We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of rotation-powered pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the force-free magnetosphere. We apply a new 1D hybrid plasma simulation code to the dynamical problem, using Particle-in-Cell methods for the dynamics of the charged particles, including a determination of the collective electrostatic fluctuations in the plasma, combined with a Monte Carlo treatment of the high-energy gamma-rays that mediate the formation of the electron-positron pairs.We assume the electric current flowing through the pair creation zone is fixed by the much higher inductance magnetosphere, and adopt the results of force-free magnetosphere models to provide the currents which must be carried by the accelerator. The models are spatially one dimensional, and designed to explore the physics, although of practical relevance to young, high-voltage pulsars. We observe novel behaviour (a) When the current density j is less than the Goldreich-Julian value (0 current carrying beam is mild, with the full Goldreich-Julian charge density comprising the charge densities of the beam and a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are of the order of mc(sup 2)/e, and pair creation is absent. (b) When the current density exceeds the Goldreich-Julian value (j/j(sub GJ) > 1), the system develops high voltage drops (TV or greater), causing emission of curvature gamma-rays and intense bursts of pair creation. The bursts exhibit limit cycle behaviour, with characteristic time-scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). (c) In return current regions, where j/j(sub GJ) currents and adjust the charge density and average electric field to force-free conditions. We also
Size-dependent nonlinear weak-field magnetic behavior of maghemite nanoparticles.
de Montferrand, Caroline; Lalatonne, Yoann; Bonnin, Dominique; Lièvre, Nicole; Lecouvey, Marc; Monod, Philippe; Russier, Vincent; Motte, Laurence
2012-06-25
The magnetic behavior at room temperature of maghemite nanoparticles of variable sizes (from 7 to 20 nm) is compared using a conventional super quantum interference device (SQUID) and a recently patented technology, called MIAplex. The SQUID usually measures the magnetic response versus an applied magnetic field in a quasi-static mode until high field values (from -4000 to 4000 kA m(-1)) to determine the field-dependence and saturation magnetization of the sample. The MIAplex is a handheld portable device that measures a signal corresponding to the second derivative of the magnetization around zero field (between -15 and 15 kA m(-1)). In this paper, the magnetic response of the size series is correlated, both in diluted and powder form, between the SQUID and MIAplex. The SQUID curves are measured at room temperature in two magnetic field ranges from -4000 to 4000 kA m(-1) (-5T to 5T) and from -15 to 15 kA m(-1). Nonlinear behavior at weak fields is highlighted and the magnetic curves for diluted solutions evolve from quasi-paramagnetic to superparamagnetic behavior when the size of the nanoparticles increases. For the 7-nm sample, the fit of the magnetization with the Langevin model weighted with log-normal distribution corresponds closely to the magnetic size. This confirms the accuracy of the model of non-interacting superparamagnetic particles with a magnetically frustrated surface layer of about 0.5 nm thickness. For the other samples (10-nm to 21-nm), the experimental weak-field magnetization curves are modeled by more than one population of magnetically responding species. This behavior is consistent with a chemically uniform but magnetically distinct structure composed of a core and a magnetically active nanoparticle canted shell. Accordingly the weak-field signature corresponds to the total assembly of the nanoparticles. The impact of size polydispersity is also discussed. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Barati, Mohammad Reza
2018-02-01
Nonlocal and surface effects on nonlinear vibration characteristics of a flexoelectric nanobeams under magnetic field are examined. Eringen’s nonlocal elasticity as well as surface elasticity theories are employed to describe the size-dependency of the flexoelectric nanobeam. Also, flexoelectricity is an important size-dependent phenomena for piezoelectric structures at nanoscale, related to the strain gradient-electric polarization coupling. After the derivation of governing equation via Hamilton’s principle, Galerkin method is employed to satisfy boundary conditions. Also, analytical procedures are implemented to obtain the closed-form nonlinear frequency of flexoelectric nanobeam. It is showed that magnetic field intensity, flexoelectric parameter, nonlocal parameter, elastic foundation and applied voltage on the top surface of the nanobeam have great influences on nonlinear vibration frequency.
International Nuclear Information System (INIS)
Lee, Jounghun; Hahn, Oliver; Porciani, Cristiano
2009-01-01
Galaxies on the largest scales of the universe are observed to be embedded in the filamentary cosmic web, which is shaped by the nonlinear tidal field. As an efficient tool to quantitatively describe the statistics of this cosmic web, we present the anisotropic two-point correlation functions of the nonlinear traceless tidal field in the principal-axis frame, which are measured using numerical data from an N-body simulation. We show that both the nonlinear density and traceless tidal fields are more strongly correlated along the directions perpendicular to the eigenvectors associated with the largest eigenvalues of the local tidal field. The correlation length scale of the traceless tidal field is found to be ∼20 h -1 Mpc, which is much larger than that of the density field ∼5 h -1 Mpc. We also provide analytic fitting formulae for the anisotropic correlation functions of the traceless tidal field, which turn out to be in excellent agreement with the numerical results. We expect that our numerical results and analytical formula are useful to disentangle cosmological information from the filamentary network of the large-scale structures.
Non-linear regression techniques are used widely to fit weed field emergence patterns to soil microclimatic indices using S-type functions. Artificial neural networks present interesting and alternative features for such modeling purposes. In this work, a univariate hydrothermal-time based Weibull m...
Crouch, R.S.; Bennett, T.
2000-01-01
This paper presents results and observations from the use of a rigorous method of treating the dynamic far-field as part of a non-linear FE analysis. The technique de-veloped by Wolf and Song (referred to as the Scaled Boundary Finite-Element Method) is incorporated into a 3-D time-domain analysis
DEFF Research Database (Denmark)
Denisov, S.; Flach, S.; Ovchinnikov, A. A.
2002-01-01
We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is em...... is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.......We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response...
Directory of Open Access Journals (Sweden)
R. Sharma
2013-04-01
Full Text Available In an Electric Submersible Pump (ESP lifted oil field, the ESP of each oil well should be operated inside its operating window. The total power consumed by the ESPs in the oil field should be minimized. The speed of the ESPs and the production choke valve opening should be optimally chosen for maximizing the total oil produced from the oil field. At the same time, the capacity of the separator should not be exceeded. In this paper, nonlinear steady state optimization based on Sequential Quadratic Programming (SQP is developed. Two optimal control structures are proposed in this paper. In the first case, the optimal pump speed is controlled by a PI controller by varying the electrical excitation signal to the motors. The optimal fluid flow rate through each oil well is controlled by another PI controller by varying the production choke valve opening. The paper shows that the production choke valve for each oil well has to be always 100% open to maintain the optimal fluid flow rate. In the second case, the production choke valves are considered to be always 100% open as hard constraints. The optimal fluid flow rate through each oil well is controlled by a PI controller by varying the pump speed. It is shown that when the optimal fluid flow rate is tracked by the controller, the speed of each of the pumps is equal to the optimal pump speed calculated by the optimizer. This basically means that we can achieve the optimization objective with the same optimal results as in the first case by using only a single PI controller. The limitations of these two optimal control structures for very low values and for very high values of the separator capacity are discussed. For the feasible range of separator capacities, the optimal locus of the fluid flow rate and the pump speed are shown in this paper.
Nonlinear magnetohydrodynamics. Progress report, December 15, 1977--December 14, 1978
International Nuclear Information System (INIS)
Vahala, G.
1978-01-01
Incompressible MHD turbulence is considered for both 2D and 3D plasmas in cylindrical geometry. It is found that for virtually all initial conditions (including quiescent ones) the plasma is nonlinearly unstable in that mean square turbulent velocity fields develop. However, there is a unique stable state of extremal magnetic helicity/energy ratio for which no turbulent fields develop [in 2D with B/sub z/ = const., it is the state of extremal mean square vector potential/energy]. It is force free and is just the Taylor state. A conjecture can be put forward (based on a dual cascade argument for resistive MHD) to explain Taylor's hypothesis. In spherical geometry, the stable axisymmetric state is the spheromak
Nonlinear seismic behavior of a CANDU containment building subjected to near-field ground motions
International Nuclear Information System (INIS)
Choi, In Kil; Ahn, Seong Moon; Choun, Young Sun; Seo, Jeong Moon
2004-01-01
The standard response spectrum proposed by US NRC has been used as a design earthquake for the design of Korean nuclear power plant structures. A survey on some of the Quaternary fault segments near Korean nuclear power plants is ongoing. It is likely that these faults will be identified as active ones. If the faults are confirmed as active ones, it will be necessary to reevaluate the seismic safety of the nuclear power plants located near the fault. Near-fault ground motions are the ground motions that occur near an earthquake fault. In general, the near-fault ground motion records exhibit a distinctive long period pulse like time history with very high peak velocities. These features are induced by the slip of the earthquake fault. Near-fault ground motions, which have caused much of the damage in recent major earthquakes, can be characterized by a pulse-like motion that exposes the structure to a high input energy at the beginning of the motion. In this study, nonlinear dynamic time-history analyses were performed to investigate the seismic behavior of a CANDU containment structure subjected to various earthquake ground motions including the near-field ground motions
Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem
Directory of Open Access Journals (Sweden)
Roshan Sharma
2012-01-01
Full Text Available Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the emph'fmincon' solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.
International Nuclear Information System (INIS)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references
Baskaran, Arvind; Hu, Zhengzheng; Lowengrub, John S.; Wang, Cheng; Wise, Steven M.; Zhou, Peng
2013-10-01
In this paper we present two unconditionally energy stable finite difference schemes for the modified phase field crystal (MPFC) equation, a sixth-order nonlinear damped wave equation, of which the purely parabolic phase field crystal (PFC) model can be viewed as a special case. The first is a convex splitting scheme based on an appropriate decomposition of the discrete energy and is first order accurate in time and second order accurate in space. The second is a new, fully second-order scheme that also respects the convex splitting of the energy. Both schemes are nonlinear but may be formulated from the gradients of strictly convex, coercive functionals. Thus, both are uniquely solvable regardless of the time and space step sizes. The schemes are solved by efficient nonlinear multigrid methods. Numerical results are presented demonstrating the accuracy, energy stability, efficiency, and practical utility of the schemes. In particular, we show that our multigrid solvers enjoy optimal, or nearly optimal complexity in the solution of the nonlinear schemes.
Computation of nonlinear ultrasound fields using a linearized contrast source method
Verweij, M.D.; Demi, L.; Van Dongen, K.W.A.
2013-01-01
Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging
Weak field nonlinear optical response of fermions in Frenkel exciton chains
International Nuclear Information System (INIS)
Spano, F.C.
1992-01-01
In this paper, the third order nonlinear optical response of a Frenkel chain composed of N dipole-dipole coupled two-level molecules is reviewed. The fundamantal electronic excitations of such a system are, in fact, fermions, a property which greatly simplifies the eigenspectrum for multiexciton states. The introduction of site disorder does not disrupt the fermion nature and is therefore easily incorporated into a general expression of the third order nonlinear optical susceptibility
Shih, C. C.
1973-01-01
In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.
International Nuclear Information System (INIS)
Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.
2012-01-01
In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.
Serebryannikov, E E; Zheltikov, A M
2014-07-25
Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.
Moraitis, Kostas; Archontis, Vasilis; Tziotziou, Konstantinos; Georgoulis, Manolis K.
We calculate the instantaneous free magnetic energy and relative magnetic helicity of solar active regions using two independent approaches: a) a non-linear force-free (NLFF) method that requires only a single photospheric vector magnetogram, and b) well known semi-analytical formulas that require the full three-dimensional (3D) magnetic field structure. The 3D field is obtained either from MHD simulations, or from observed magnetograms via respective NLFF field extrapolations. We find qualitative agreement between the two methods and, quantitatively, a discrepancy not exceeding a factor of 4. The comparison of the two methods reveals, as a byproduct, two independent tests for the quality of a given force-free field extrapolation. We find that not all extrapolations manage to achieve the force-free condition in a valid, divergence-free, magnetic configuration. This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: Thales. Investing in knowledge society through the European Social Fund.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
Chen, C.; Xia, J.; Liu, J.; Feng, G.
2006-01-01
Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant
International Nuclear Information System (INIS)
Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.; Cothran, C.D.; Brown, M.R.; Schaffer, M.J.
2004-01-01
Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by the counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good agreement with results from the SSX-FRC experiment. Simulations show formation of an FRC in about 30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects
Winjum, B. J.; Tableman, A.; Tsung, F. S.; Mori, W. B.
2017-10-01
Nonlinear wave-particle interactions can significantly affect the evolution of stimulated Raman scattering (SRS) for ICF-relevant parameters. An imposed magnetic field can alter the dynamics of these interactions and thereby the dynamics of SRS, altering the instability threshold and saturation. Particles resonant with an SRS-generated electron plasma wave can be rotated in velocity space, disrupting the nonlinear damping of electron plasma waves and changing the kinetically inflated SRS threshold. Resonant particles can also be rotated in physical space, changing the transverse kinetic dissipation of electron plasma waves and restricting trapped particle motion both within a single laser speckle as well as between neighboring laser speckles. We show PIC simulations of driven multi-dimensional electron plasma waves in the presence of an external field and illustrate how their nonlinear evolution is altered, particularly with regard to the dynamical behavior that can impact SRS. Work was supported by the DOE under Grant Nos. DE-NA0001833 and DE-FC02-04ER54789.
Linear and nonlinear stability in resistive magnetohydrodynamics
International Nuclear Information System (INIS)
Tasso, H.
1994-01-01
A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its open-quotes nearnessclose quotes to necessity is analysed. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with open-quotes unconditionalclose quotes stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed. 23 refs
Non-linear Springing Excitation Due to a Bidirectional Wave Field
DEFF Research Database (Denmark)
Vidic-Perunovic, Jelena; Jensen, Jørgen Juncher
2005-01-01
Significant springing vibrations in ships have recently been measured in a large ocean-going bulk carrier. So far calculations using various linear and non-linear hydrodynamic procedures have not been able to predict the measured responses. In the present paper it is shown that the springing resp...
Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining
2018-05-01
The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
Ranjbaran, M.; Tehranchi, M. M.; Hamidi, S. M.; Khalkhali, S. M. H.
2017-11-01
Optically pumped atomic magnetometers have found widespread application in biomagnetic studies. Most of the studies utilize MX gradiometers as sensitive and simple arrangements. One the sensitivity improvement methods in the MX configurations is detection of magnetic resonance at higher harmonics due to nonlinear precession of spin polarization. To enhance the harmonic components, we have proposed square wave RF magnetic fields with various duty cycles as substitute for sinusoidal fields. Our results revealed that detection of the 5th harmonic of a 10% duty cycle square wave magnetic field, improved the magnetometer sensitivity by a factor of 4.5 respect to the first harmonic which could be a reliable option to generate high sensitivity MX magnetometers in the MCG applications.
Directory of Open Access Journals (Sweden)
J. Gwinner
2013-01-01
Full Text Available The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.
Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)
1999-01-01
Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.
Bao, Guzhi; Wickenbrock, Arne; Rochester, Simon; Zhang, Weiping; Budker, Dmitry
2018-01-01
The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with ˜100 Hz width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.
International Nuclear Information System (INIS)
Mehdian, H.; Mohammadzahery, Z.; Hasanbeigi, A.
2014-01-01
In this work, we study the defect mode and bistability behavior of 1-D photonic band gap structure with magnetized plasma and coupled nonlinear defects. The transfer matrix method has been employed to investigate the magnetic field effect on defect mode frequency and bistability threshold. The obtained results show that the frequency of defect mode and bistability threshold can be altered, without changing the structure of the photonic multilayer. Therefore, the bistability behavior of the subjected structure in the presence of magnetized plasma can be utilized in manufacturing wide frequency range devices
Directory of Open Access Journals (Sweden)
Hongbo Liu
2015-11-01
Full Text Available The electrocaloric (EC effect has been paid great attentions recently for applications on cooling or electricity generation. However, the directly commercial measurement equipment for the effect is still unavailable. Here we report a novel method to predict EC effect by non-linear behaviors of dielectric permittivity under temperature and electric fields. According to the method, the analytical equations of EC temperature change ΔT are directly given for normal ferroelectrics and relaxor. The calculations have been performed on several materials and it is shown that the method is suitable for both inorganic and organic ferroelectrics, and relaxor.
Luo, Zhaochu; Xiong, Chengyue; Zhang, Xu; Guo, Zhen-Gang; Cai, Jianwang; Zhang, Xiaozhong
2016-04-13
The anomalous Hall effect of a magnetic material is coupled to the nonlinear transport effect of a semiconductor material in a simple structure to achieve a large geometric magnetoresistance (MR) based on a diode-assisted mechanism. An extremely large MR (>10(4) %) at low magnetic fields (1 mT) is observed at room temperature. This MR device shows potential for use as a logic gate for the four basic Boolean logic operations. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2017-12-01
We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to the nonlinear scale (rδrδL>0.5 for k ≲1 h /Mpc ) with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully nonlinear fields, potentially substantially expanding the baryon acoustic oscillations and redshift space distortions information content of dense large scale structure surveys, including for example SDSS main sample and 21 cm intensity mapping initiatives.
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)
Kasapoglu, E., E-mail: ekasap@cumhuriyet.edu.tr [Department of Physics, Cumhuriyet University, 58140 Sivas (Turkey); Duque, C.A. [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia-UdeA, Calle 70 No. 52-21, Medellín (Colombia); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos (Mexico); Restrepo, R.L. [Department of Physics, Cumhuriyet University, 58140 Sivas (Turkey); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia-UdeA, Calle 70 No. 52-21, Medellín (Colombia); Escuela de Ingeniería de Antioquia-EIA, Medellín (Colombia); Ungan, F.; Yesilgul, U.; Sari, H. [Department of Physics, Cumhuriyet University, 58140 Sivas (Turkey); Sökmen, I. [Department of Physics, Dokuz Eylül University, 35160 Buca, İzmir (Turkey)
2015-03-15
In the present work, the effects of the intense laser field on total optical absorption coefficient (the linear and third-order nonlinear) and total refractive index change for transition between two lower-lying electronic levels in the step-like GaAs/Ga{sub 1−x}Al{sub x}As quantum well under external electric and magnetic fields are investigated. The calculations were performed within the compact density-matrix formalism with the use of the effective mass and parabolic band approximations. The obtained results show that both total absorption coefficient and refractive index change are sensitive to the well dimensions and the effects of external fields. By changing the intensities of the electric, magnetic and non-resonant intense laser fields together with the well dimensions, we can obtain the blue or red shift, without the need for the growth of many different samples. - Highlights: • Augmentation of laser-field results in red shift in total AC spectra. • Magnetic field induces a blue-shift in the resonant peak. • Resonant peak position shifts to red with effect of electric field. • Resonant peak of total AC shifts to the higher photon energies with increasing well width.
International Nuclear Information System (INIS)
Kasapoglu, E.; Duque, C.A.; Mora-Ramos, M.E.; Restrepo, R.L.; Ungan, F.; Yesilgul, U.; Sari, H.; Sökmen, I.
2015-01-01
In the present work, the effects of the intense laser field on total optical absorption coefficient (the linear and third-order nonlinear) and total refractive index change for transition between two lower-lying electronic levels in the step-like GaAs/Ga 1−x Al x As quantum well under external electric and magnetic fields are investigated. The calculations were performed within the compact density-matrix formalism with the use of the effective mass and parabolic band approximations. The obtained results show that both total absorption coefficient and refractive index change are sensitive to the well dimensions and the effects of external fields. By changing the intensities of the electric, magnetic and non-resonant intense laser fields together with the well dimensions, we can obtain the blue or red shift, without the need for the growth of many different samples. - Highlights: • Augmentation of laser-field results in red shift in total AC spectra. • Magnetic field induces a blue-shift in the resonant peak. • Resonant peak position shifts to red with effect of electric field. • Resonant peak of total AC shifts to the higher photon energies with increasing well width
Non-linear Springing Excitation Due to a Bidirectional Wave Field
DEFF Research Database (Denmark)
Vidic-Perunovic, Jelena; Jensen, Jørgen Juncher
2005-01-01
Significant springing vibrations in ships have recently been measured in a large ocean-going bulk carrier. So far calculations using various linear and non-linear hydrodynamic procedures have not been able to predict the measured responses. In the present paper it is shown that the springing...... response depends strongly on second order (sum frequency) terms involving cross-coupling terms from the combined wind- and swell-driven wave system. The calculations are based on the second order strip theory formulation and thus no three-dimensional effects are accounted for. The agreement with measured...
Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field
International Nuclear Information System (INIS)
Hyman, J.M.; Rosenau, P.
1984-01-01
We analyse the evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma. The solutions's behavior, due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite dimensional space. These conclusions are backed by extensive numerical experimentation
International Nuclear Information System (INIS)
Pfirsch, D.; Sudan, R.N.
1996-01-01
It is observed that the recently developed magnetic flux-averaged magnetohydrodynamics (AMHD) [Phys. Plasmas 1, 2488 (1994)] is incompatible with Taylor close-quote s theorem, which states that the lowest-energy state of force-free equilibria based on the conservation of the helicity integral is absolutely stable for vanishingly small resistivity. By a modification of the Lagrangian from which AMHD is derived, a modified version of AMHD that is compatible with Taylor close-quote s theorem is obtained. It also provides an energy principle for examining the linear instability of resistive equilibria, which has a great advantage over resistive MHD. copyright 1996 American Institute of Physics
Lacoste-Collin, Laetitia; Castiella, Marion; Franceries, Xavier; Cassol, Emmanuelle; Vieillevigne, Laure; Pereda, Veronica; Bardies, Manuel; Courtade-Saïdi, Monique
2015-01-01
The study of cell survival following exposure to nonuniform radiation fields is taking on particular interest because of the increasing evidence of a nonlinear relationship at low doses. We conducted in vitro experiments using the MCF7 breast cancer cell line. A 2.4 × 2.4 cm(2) square area of a T25 flask was irradiated by a Varian Novalis accelerator delivering 6 MV photons. Cell survival inside the irradiation field, in the dose gradient zone and in the peripheral zone, was determined using a clonogenic assay for different radiation doses at the isocenter. Increased cell survival was observed inside the irradiation area for doses of 2, 10, and 20 Gy when nonirradiated cells were present at the periphery, while the cells at the periphery showed decreased survival compared to controls. Increased survival was also observed at the edge of the dose gradient zone for cells receiving 0.02 to 0.01 Gy when compared with cells at the periphery of the same flask, whatever the isocenter dose. These data are the first to report cell survival in the dose gradient zone. Radiotherapists must be aware of this nonlinearity in dose response.
Electric-field induced nonlinear ferromagnetic resonance in a CoFeB/MgO magnetic tunnel junction
Hirayama, E.; Kanai, S.; Ohe, J.; Sato, H.; Matsukura, F.; Ohno, H.
2015-09-01
We investigate the rf power dependence of homodyne-detected ferromagnetic resonance (FMR) spectra of a nanoscale CoFeB/MgO magnetic tunnel junction, in which the FMR is induced by the electric-field modulation of the magnetic anisotropy. The increase of the rf power changes the spectral lineshape and decreases characteristic frequency, at which drastic change in spectrum is observed. The behavior is consistent with nonlinear magnetization precession with a large precessional angle at high powers. From the rf power dependence of FMR spectra, we determine electric-field modulation ratio of magnetic anisotropy energy density to be 78 fJ/Vm, which is in agreement with the reported values.
Directory of Open Access Journals (Sweden)
E. M. Dubinin
2002-01-01
Full Text Available We investigate the nature of nonlinear waves propagating transverse to the magnetic field in a bi-ion plasma including plasma pressure. By using the conservation laws derived from the multi-ion fluid equations the system may be described by a single order differential equation whose properties control the structure of the flow and the magnetic field. Compressive solitons exist in specific ranges of the characteristic Mach numbers. Various features of solitons differ in different existence "windows". For example, there are solitons that contain a strong proton rarefaction core embedded in the main compressional structure. Compressive solitons are found in a wide range of flow parameters. Finite ion pressure introduces critical Mach numbers. In contrast to a plasma consisting only of protons and electrons these singular points are reached where a specific combination of ion and electron speeds lies on particular locii, in multi-parameter space, which corresponds to the generalized "sonic point" of the compound system.
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...... implementation for a simple single mode soliton propagation example. As opposed to the standard implementation, the new implementation is able to reproduce pulsed four wave mixing observed experimentally in a higher order mode fiber....
Directory of Open Access Journals (Sweden)
M. H. Liao
2013-08-01
Full Text Available The thermo-elastic strain is induced by through silicon vias (TSV due to the difference of thermal expansion coefficients between the copper (∼18 ppm/ °C and silicon (∼2.8 ppm/ °C when the structure is exposed to a thermal ramp budget in the three dimensional integrated circuit (3DIC process. These thermal expansion stresses are high enough to introduce the delamination on the interfaces between the copper, silicon, and isolated dielectric. A compact analytic model for the strain field induced by different layouts of thermal copper filled TSVs with the linear superposition principle is found to have large errors due to the strong stress interaction between TSVs. In this work, a nonlinear stress analytic model with different TSV layouts is demonstrated by the finite element method and the analysis of the Mohr's circle. The characteristics of stress are also measured by the atomic force microscope-raman technique with nanometer level space resolution. The change of the electron mobility with the consideration of this nonlinear stress model for the strong interactions between TSVs is ∼2–6% smaller in comparison with those from the consideration of the linear stress superposition principle only.
Wójcik, J; Kujawska, T; Nowicki, A; Lewin, P A
2008-12-01
The primary goal of this work was to verify experimentally the applicability of the recently introduced time-averaged wave envelope (TAWE) method [J. Wójcik, A. Nowicki, P.A. Lewin, P.E. Bloomfield, T. Kujawska, L. Filipczyński, Wave envelopes method for description of nonlinear acoustic wave propagation, Ultrasonics 44 (2006) 310-329.] as a tool for fast prediction of four dimensional (4D) pulsed nonlinear pressure fields from arbitrarily shaped acoustic sources in attenuating media. The experiments were performed in water at the fundamental frequency of 2.8 MHz for spherically focused (focal length F=80 mm) square (20 x 20 mm) and rectangular (10 x 25mm) sources similar to those used in the design of 1D linear arrays operating with ultrasonic imaging systems. The experimental results obtained with 10-cycle tone bursts at three different excitation levels corresponding to linear, moderately nonlinear and highly nonlinear propagation conditions (0.045, 0.225 and 0.45 MPa on-source pressure amplitude, respectively) were compared with those yielded using the TAWE approach [J. Wójcik, A. Nowicki, P.A. Lewin, P.E. Bloomfield, T. Kujawska, L. Filipczyński, Wave envelopes method for description of nonlinear acoustic wave propagation, Ultrasonics 44 (2006) 310-329.]. The comparison of the experimental results and numerical simulations has shown that the TAWE approach is well suited to predict (to within+/-1 dB) both the spatial-temporal and spatial-spectral pressure variations in the pulsed nonlinear acoustic beams. The obtained results indicated that implementation of the TAWE approach enabled shortening of computation time in comparison with the time needed for prediction of the full 4D pulsed nonlinear acoustic fields using a conventional (Fourier-series) approach [P.T. Christopher, K.J. Parker, New approaches to nonlinear diffractive field propagation, J. Acoust. Soc. Am. 90 (1) (1991) 488-499.]. The reduction in computation time depends on several parameters
Directory of Open Access Journals (Sweden)
Teresa D'Aprile
2000-11-01
Full Text Available In this paper we study the existence of concentrated solutions of the nonlinear field equation $$ -h^{2}Delta v+V(xv-h^{p}Delta_{p}v+ W'(v=0,, $$ where $v:{mathbb R}^{N}o{mathbb R}^{N+1}$, $Ngeq 3$, $p>N$, the potential $V$ is positive and radial, and $W$ is an appropriate singular function satisfying a suitable symmetric property. Provided that $h$ is sufficiently small, we are able to find solutions with a certain spherical symmetry which exhibit a concentration behaviour near a circle centered at zero as $ho 0^{+}$. Such solutions are obtained as critical points for the associated energy functional; the proofs of the results are variational and the arguments rely on topological tools. Furthermore a penalization-type method is developed for the identification of the desired solutions.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed
Infinite sets of conservation laws for linear and non-linear field equations
International Nuclear Information System (INIS)
Niederle, J.
1984-01-01
The work was motivated by a desire to understand group theoretically the existence of an infinite set of conservation laws for non-interacting fields and to carry over these conservation laws to the case of interacting fields. The relation between an infinite set of conservation laws of a linear field equation and the enveloping algebra of its space-time symmetry group was established. It is shown that in the case of the Korteweg-de Vries (KdV) equation to each symmetry of the corresponding linear equation delta sub(o)uxxx=u sub() determined by an element of the enveloping algebra of the space translation algebra, there corresponds a symmetry of the full KdV equation
Near-field nonlinear optical spectroscopy of Langmuir-Blodgett films
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Geisler, T.
1998-01-01
Using an uncoated fiber tip as a light source and a multilayer Langmuir-Blodgett film of 2-docosylamino-5-nitropyridine as a sample, we obtain near-field images at the fundamental-harmonic (FH) and second-harmonic (SH) wavelengths for different polarizations and wavelengths of the pump light...
Anisotropy of susceptibility in rocks that are magnetically non-linear even in weak fields
Czech Academy of Sciences Publication Activity Database
Chadima, Martin; Ježek, J.; Hrouda, F.
2017-01-01
Roč. 19, EGU General Assembly 2017 (2017) ISSN 1029-7006. [European Geosciences Union General Assembly. 23.04.2017-28.04.2017, Vienna] Institutional support: RVO:67985831 Keywords : anisotropy of magnetic susceptibility * field-dependent susceptibility * second-rank tensor Subject RIV: DE - Earth Magnetism, Geodesy, Geography http://meetingorganizer.copernicus.org/EGU2017/EGU2017-7210-1.pdf
External confinement and surface modes in magnetized force-free jets
Sobacchi, E.; Lyubarsky, Y. E.
2018-01-01
In the paradigm of magnetic launching of astrophysical jets, instabilities in the magnetohydrodynamic (MHD) flow are a good candidate to convert the Poynting flux into the kinetic energy of the plasma. If the magnetized plasma fills the almost entire space, the jet is unstable to helical perturbations of its body. However, the growth rate of these modes is suppressed when the poloidal component of the magnetic field has a vanishing gradient, which may be the actual case for a realistic configuration. Here we show that, if the magnetized plasma is confined into a limited region by the pressure of some external medium, the velocity shear at the contact surface excites unstable modes which can affect a significant fraction of the jet's body. We find that when the Lorentz factor of the jet is Γ ∼ 10 (Γ ∼ 100), these perturbations typically develop after propagating along the jet for tens (hundreds) of jet's radii. Surface modes may therefore play an important role in converting the energy of the jet from the Poynting flux to the kinetic energy of the plasma, particularly in active galactic nuclei. The scaling of the dispersion relation with (i) the angular velocity of the field lines and (ii) the sound speed in the confining gas is discussed.
A filament supported by different magnetic field configurations
Guo, Y.; Schmieder, B.; Démoulin, P.; Wiegelmann, T.; Aulanier, G.; Török, T.; Bommier, V.
2011-08-01
A nonlinear force-free magnetic field extrapolation of vector magnetogram data obtained by THEMIS/MTR on 2005 May 27 suggests the simultaneous existence of different magnetic configurations within one active region filament: one part of the filament is supported by field line dips within a flux rope, while the other part is located in dips within an arcade structure. Although the axial field chirality (dextral) and the magnetic helicity (negative) are the same along the whole filament, the chiralities of the filament barbs at different sections are opposite, i.e., right-bearing in the flux rope part and left-bearing in the arcade part. This argues against past suggestions that different barb chiralities imply different signs of helicity of the underlying magnetic field. This new finding about the chirality of filaments will be useful to associate eruptive filaments and magnetic cloud using the helicity parameter in the Space Weather Science.
Directory of Open Access Journals (Sweden)
S. Valipour
2016-03-01
Full Text Available In this paper, two types of frequency amplitude formulation method are initially utilized to obtain frequency–amplitude relationship of nonlinear vibration of a punctual charge in the electric field of a charged ring. In order to obtain the nonlinear natural frequency of the considered system, Reng-Gui and Geng-Cai modified methods are implemented. A table is also prepared to provide a brief review of recent development of nonlinear differential equations. The correctness of the obtained results is compared with those obtained from harmonic balance method (HBM and energy balance method (EBM. A numerical simulation is carried out to investigate the accuracy of the used methods. In accordance with it, the relative errors of the employed approaches are numerically and analytically found based on the exact numerical solutions. It is exposed that the exerted approaches are very reliable and applicable for solving the nonlinear differential equations.
Energy Technology Data Exchange (ETDEWEB)
Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; East, William E.; Blandford, Roger D. [Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, 2575 Sand Hill Road M/S 29, Menlo Park, CA 94025 (United States)
2016-09-10
Many powerful and variable gamma-ray sources, including pulsar wind nebulae, active galactic nuclei and gamma-ray bursts, seem capable of accelerating particles to gamma-ray emitting energies efficiently over very short timescales. These are likely due to the rapid dissipation of electromagnetic energy in a highly magnetized, relativistic plasma. In order to understand the generic features of such processes, we have investigated simple models based on the relaxation of unstable force-free magnetostatic equilibria. In this work, we make the connection between the corresponding plasma dynamics and the expected radiation signal, using 2D particle-in-cell simulations that self-consistently include synchrotron radiation reactions. We focus on the lowest order unstable force-free equilibrium in a 2D periodic box. We find that rapid variability, with modest apparent radiation efficiency as perceived by a fixed observer, can be produced during the evolution of the instability. The “flares” are accompanied by an increased polarization degree in the high energy band, with rapid variation in the polarization angle. Furthermore, the separation between the acceleration sites and the synchrotron radiation sites for the highest energy particles facilitates acceleration beyond the synchrotron radiation reaction limit. We also discuss the dynamical consequences of the radiation reaction, and some astrophysical applications of this model. Our current simulations with numerically tractable parameters are not yet able to reproduce the most dramatic gamma-ray flares, e.g., from the Crab Nebula. Higher magnetization studies are promising and will be carried out in the future.
Non-linear diffusion of charged particles due to stochastic electromagnetic fields
International Nuclear Information System (INIS)
Martins, A.M.; Balescu, R.; Mendonca, J.T.
1989-01-01
It is well known that the energy confinement times observed in tokamak cannot be explained by the classical or neo-classical transport theory. The alternative explanations are based on the existence of various kinds of micro-instabilities, or on the stochastic destruction of the magnetic surfaces, due to the interaction of magnetic islands of different helicities. In the absence of a well established theory of anomalous transport it is perhaps important to study in some detail the diffusion coefficient of single charged particles in the presence of electromagnetic fluctuation, because it can provide the physical grounds for more complete and self-consistent calculations. In the present work we derive a general expression for the transverse diffusion coefficient of electrons and ions in a constant magnetic field and in the presence of space and time dependent electromagnetic fluctuation. We neglect macroscopic drifts due to inhomogeneity and field curvatures, but retain finite Larmor radius effects. (author) 3 refs
Casting the Coronal Magnetic Field Reconstruction Tools in 3D Using the MHD Bifrost Model
Energy Technology Data Exchange (ETDEWEB)
Fleishman, Gregory D.; Loukitcheva, Maria [Physics Department, Center for Solar-Terrestrial Research, New Jersey Institute of Technology Newark, NJ, 07102-1982 (United States); Anfinogentov, Sergey; Mysh’yakov, Ivan [Institute of Solar-Terrestrial Physics (ISZF), Lermontov st., 126a, Irkutsk, 664033 (Russian Federation); Stupishin, Alexey [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034 (Russian Federation)
2017-04-10
Quantifying the coronal magnetic field remains a central problem in solar physics. Nowadays, the coronal magnetic field is often modeled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as π -disambiguation, photospheric field preprocessing, and volume reconstruction methods, using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model, we know the magnetic field vector in the entire 3D domain, which enables us to perform a “voxel-by-voxel” comparison of the restored and the true magnetic fields in the 3D model volume. Our tests show that the available π -disambiguation methods often fail in the quiet-Sun areas dominated by small-scale magnetic elements, while they work well in the active region (AR) photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although it does produce a more force-free boundary condition, also results in some effective “elevation” of the magnetic field components. This “elevation” height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from the actual AR photospheric magnetogram are free from this systematic error, while other metrics are comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results than those from a photospheric boundary.
The classical wormhole solution and wormhole wavefunction with a nonlinear Born-Infeld scalar field
Lu, H. Q.; Shen, L. M.; Ji, P.; Ji, G. F.; Sun, N. J.
2002-01-01
On this paper we consider the classical wormhole solution of the Born-Infeld scalar field. The corresponding classical wormhole solution can be obtained analytically for both very small and large $\\dot{\\phi}$. At the extreme limits of small $\\dot{\\phi}$ the wormhole solution has the same format as one obtained by Giddings and Strominger[10]. At the extreme limits of large $\\dot{\\phi}$ the wormhole solution is a new one. The wormhole wavefunctions can also be obtained for both very small and l...
Nonlinear theory of a free electron laser with a helical wiggler and an axial guide magnetic field
Directory of Open Access Journals (Sweden)
N. S. Ginzburg
2013-09-01
Full Text Available A 1D nonlinear theory of a free electron laser (FEL with a helical wiggler and an axial guide magnetic field is developed based on averaged equations of the electron motion. By averaging we separated two different cases of the e-beam/rf-wave interaction. The first one corresponds to the traditional wiggler synchronism (resonance of rf wave with the electrons moving along stationary helical trajectories. The second one corresponds to combination resonances distinguishing by excitation of oscillation of the electrons near the stationary helical trajectory. Comparative analysis of the FEL operation in different regimes has been studied under the traditional wiggler synchronism condition. It was shown that FELs operated far from cyclotron resonance (including a reversed guide field orientation possess low sensitivity to the initial velocity spread in the driving beam resulting in high electron efficiency. In contrast, under the weak guide field (the gyrofrequency is less than the bounce frequency of a conventional orientation, the FEL efficiency is restricted by a significant increase in the transverse velocity of the electrons during the interaction with the rf wave that results in violation of the synchronism conditions and is accompanied by electron current losses. An additional mechanism of FEL efficiency enhancement under the conventional guide field orientation in the conditions when the gyrofrequency is higher than the bounce frequency, based on the dependence of the effective mass of the oscillating electrons on their energy, was demonstrated. Results of the theoretical analysis are compared with the results of experimental studies of FEL oscillators. The specific features of energy extraction from the electron beam under condition of an abnormal Doppler effect in the case of the combination resonance are described. This regime is beneficial to increase radiation frequency keeping wiggler period and electron energies.
Orel, V E; Dziatkovs'ka, I I; Nikolov, M O; Romanov, A V; Mel'nyk, Iu H; Dziatkovs'ka, N M
2010-07-01
While local hyperthermia application the intratumoral blood flow is enhancing, leading to oxygenation and vascular permeability for antitumoral medicines. The work objective was to investigate the dependence of the development kinetics in carcinoma Gereni (CG) from combined action of doxorubicin (DR) and the kind of thermal impact, a contact one--due to a contact delivery of heat from a water heater and without contact - due to the tumor electromagnetic irradiation (EMI) using heterogenous electromagnetic field (EMF). DR was injected to the animals in a mass concentration of 1,5 mg on 1 kg of their body mass. The DR injection, a contact heating and EMI were started on the 8th day after the tumor reinoculation and kept on conducting once a 2 days. The course had included 5 injections and/or 5 seances of a contact heating and/or EMF. The combined action of DR and EMI, using spatially heterogenous EMF of applicator in environment of physiological hyperthermia, have had influenced mostly the inhibition of a nonlinear dynamics in CG development. Antitumoral action of DR in the animals with CG was influenced by thermal and nonthermal effects, which were initiated by spatially heterogenous EMF. Nonlinear dynamics of a CG development in animals did not depend from horizontal direction of isolines of a spatially heterogenous EMF of inductive applicator towards the tumor and duration of the irradiation procedure (15 or 30 minutes) after DR injection. The data obtained were exploited in clinical practice for the inductothermy optimal regimes elaboration while conducting complex treatment of patients, suffering oncological diseases.
Rath, N.; Onofri, M.; Barnes, D.; Romero, J.; the TAE Team
2015-11-01
The C-2U device has recently demonstrated sustainment of an advanced, beam-driven FRC over time scales longer than the characteristic times for confinement, fast ion slow-down, and wall current decay. In anticipation of further advances in plasma lifetime, we are developing feedback control techniques for major FRC parameters and resistive instabilities. The LamyRidge code solves the time-dependent extended MHD equations in axisymmetric geometry. In the Q2D code, LamyRidge is combined with a 3-D kinetic code that tracks fast ions and runs in parallel with LamyRidge. Periodically, the background fields in the kinetic code are updated from the MHD simulation and the averaged fast particle distribution is integrated into the fluid equations. Recently, we have added the capability to run Q2D simulations as subordinate processes in Simulink, giving us the ability to run non-linear, closed-loop simulations using control algorithms developed in Simulink. The same Simulink models can be exported to real-time targets (CPU or FPGA) to perform feedback control in experiments. We present closed-loop simulations of beam-driven FRCs under magnetically-actuated feedback control. Results for positionally unstable FRCs are compared with the predictions of a linearized rigid-plasma model. Plasmas predicted to be passively stabilized by the linear model are found to exhibit Alfvenic growth in several cases. Feedback gains predicted to be stabilizing in the linear model are generally found to be insufficient in non-linear simulations, and vice versa. Control of separatrix geometry is demonstrated.
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.
Terahertz semiconductor nonlinear optics
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias
2013-01-01
In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz nonlinear...
International Nuclear Information System (INIS)
Koterov, V.N.; Shcheprov, A.V.
1991-01-01
The study of the electron distribution function in weakly ionized gases is necessary for a detailed treatment of the processes in gas discharges which are presently used in a variety of industrial applications. Here, approximate equations are derived for the electron energy spectrum in a gas-discharge plasma. These are applicable both in the case of a nearly isotropic elect distribution function, when the Lorentz approximation is valid, and when the distribution is highly anisotropic. The practical applicability of the proposed technique is verified by solving the problem of the spatially nonequilibrium transport of electrons in the cathode sheath of a glow discharge in helium, assuming that the electric field profile is given
Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field
Chen, J.; Palmadesso, P. J.
1986-01-01
The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.
Morelli, Maria Sole; Valenza, Gaetano; Greco, Alberto; Giannoni, Alberto; Passino, Claudio; Emdin, Michele; Scilingo, Enzo Pasquale; Vanello, Nicola
2016-08-01
Brain activations underlying control of breathing are not completely known. Furthermore, the coupling between neural and respiratory dynamics is usually estimated through linear correlation measures, thus totally disregarding possible underlying nonlinear interactions. To overcome these limitations, in this preliminary study we propose a nonlinear coupling analysis of simultaneous recordings of electroencephalographic (EEG) and respiratory signals at rest and after variation of carbon dioxide (CO2) level. Specifically, a CO2 increase was induced by a voluntary breath hold task. EEG global field power (GFP) in different frequency bands and end-tidal CO2 (PETCO2) were estimated in both conditions. The maximum information coefficient (MIC) and MIC-ρ2 (where ρ represents the Pearson's correlation coefficient) between the two signals were calculated to identify generic associations (i.e. linear and nonlinear correlations) and nonlinear correlations, respectively. With respect to a free breathing state, our results suggest that a breath hold state is characterized by an increased coupling between respiration activity and specific EEG oscillations, mainly involving linear and nonlinear interactions in the delta band (1-4 Hz), and prevalent nonlinear interactions in the alpha band (8-13 Hz).
Field verification of linear and nonlinear hybrid wave models for offshore tower response prediction
Energy Technology Data Exchange (ETDEWEB)
Couch, A.T. [Hudson Engineering, Houston, TX (United States). Offshore Structural Div.; Conte, J.P. [Rice Univ., Houston, TX (United States). Dept. of Civil Engineering
1996-12-31
Accuracy of the prediction of the dynamic response of deepwater fixed offshore platforms to irregular sea waves depends very much on the theory used to determine water kinematics from the mudline to the free surface. A common industry practice consists of using linear wave theory, which assumes infinitesimal wave steepness, in conjunction with empirical wave stretching techniques to provide a more realistic representation of near surface kinematics. The current velocity field is then added to the wave-induced fluid velocity field and the wave-and-current forces acting on the structure are computed via Morrison`s equation. The first objective of this study is to compare the predicted responses of Cognac, a deepwater fixed platform, obtained from various empirically stretched linear wave models with the response of Cognac predicted based on the Hybrid Wave Model. The latter is a recently developed higher-order, and therefore more accurate, wave model which satisfies, up to the second-order in wave steepness, the local mass conservation and the free surface boundary conditions up to the free surface. The second objective of this study consists of comparing the various analytical response predictions with the measured response of the Cognac platform. Availability of a set of oceanographic and structural vibration data for Cognac provides a unique opportunity to evaluate the prediction ability of traditional analytical models used in designing such structures. The results of this study indicate that (1) the use of the Hybrid Wave Model provides a predicted platform response which is in closer agreement with the measured response than the predictions based on the various stretched linear wave models; and (2) the Wheeler stretching technique produces platform response results which are more accurate than those obtained by using the other stretching schemes considered here.
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 the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...
Donoso, Guillermo; Ladera, Celso L.
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
Kilpatrick, Zachary P.
2010-06-01
We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather. © 2010 Elsevier B.V. All rights reserved.
Guasp, J.; Pastor, I.; Álvarez-Estrada, R. F.; Castejón, F.
2015-02-01
Analytical results obtained recently of the ab-initio classical incoherent Thomson Scattering (TS) spectrum from a single-electron (Alvarez-Estrada et al 2012 Phys. Plasmas 19 062302) have been numerically implemented in a paralelized code to efficiently compute the TS emission from a given electron distribution function, irrespective of its characteristics and/or the intensity of the incoming radiation. These analytical results display certain differences, when compared with other authors, in the general case of incoming linearly and circularly polarized radiation and electrons with arbitrary initial directions. We regard such discrepancies and the ubiquitous interest in TS as motivations for this work. Here, we implement some analytical advances (like generalized Bessel functions for incoming linearly polarized radiation) in TS. The bulk of this work reports on the efficient computation of TS spectra (based upon our analytical approach), for an electron population having an essentially arbitrary distribution function and for both incoming linearly and circularly polarized radiation. A detailed comparison between the present approach and a previous Monte Carlo one (Pastor et al 2011 Nuclear Fusion 51 043011), dealing with the ab-initio computation of TS spectra, is reported. Both approaches are shown to fully agree with each other. As key computational improvements, the analytical technique yields a × 30 to × 100 gain in computation time and is a very flexible tool to compute the scattered spectrum and eventually the scattered electromagnetic fields in the time domain. The latter are computed explicitly here for the first time, as far as we know. Scaling laws for the power integrated over frequency versus initial kinetic energy are studied for the case of isotropic and monoenergetic electron distribution functions and their potential application as diagnostic tools for high-energy populations is briefly discussed. Finally, we discuss the application of these
De Conti, Alberto; Silveira, Fernando H.; Visacro, Silvério
2014-05-01
This paper investigates the influence of corona on currents and electromagnetic fields predicted by a return-stroke model that represents the lightning channel as a nonuniform transmission line with time-varying (nonlinear) resistance. The corona model used in this paper allows the calculation of corona currents as a function of the radial electric field in the vicinity of the channel. A parametric study is presented to investigate the influence of corona parameters, such as the breakdown electric field and the critical electric field for the stable propagation of streamers, on predicted currents and electromagnetic fields. The results show that, regardless of the assumed corona parameters, the incorporation of corona into the nonuniform and nonlinear transmission line model under investigation modifies the model predictions so that they consistently reproduce most of the typical features of experimentally observed lightning electromagnetic fields and return-stroke speed profiles. In particular, it is shown that the proposed model leads to close vertical electric fields presenting waveforms, amplitudes, and decay with distance in good agreement with dart leader electric field changes measured in triggered lightning experiments. A comparison with popular engineering return-stroke models further confirms the model's ability to predict consistent electric field waveforms in the close vicinity of the channel. Some differences observed in the field amplitudes calculated with the different models can be related to the fact that current distortion, while present in the proposed model, is ultimately neglected in the considered engineering return-stroke models.
International Nuclear Information System (INIS)
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ''sawtooth oscillations,'' have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma
Energy Technology Data Exchange (ETDEWEB)
Kasapoglu, E., E-mail: ekasap@cumhuriyet.edu.tr [Department of Physics, Cumhuriyet University, 58140 Sivas (Turkey); Duque, C.A. [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Mora-Ramos, M.E. [Centro de Investigación en Ciencias, Instituto de Ciencias Básicas y Aplicadas, Universidad Autóonoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos (Mexico); Sökmen, I. [Department of Physics, Dokuz Eylül University, 35160 Buca, İzmir (Turkey)
2015-10-01
In the present work, the effects of the intense laser field on total optical absorption coefficient (the linear and third-order nonlinear) and total refractive index change (the linear and third-order nonlinear) for transitions between different intersubbands in the Ga{sub 1−x}Al{sub x}As/GaAs cylindrical quantum dot under external electric field are investigated. The calculations were performed within the compact density-matrix formalism with the use of the effective mass approximation. The obtained results show that both total absorption coefficient and refractive index change are sensitive to the electric and intense laser fields. By changing the intensities of the electric and laser fields, we can obtain the blue or red shift, without the need for the growth of many different samples. - Highlights: • The effects of the non-resonant intense laser field and electric field on the nonlinear optical properties of cylindrical quantum dot are investigated. • The both total absorption coefficient and refractive index change are sensitive to dot dimensions and the effects of external fields. • By changing the external fields together with dot dimensions a blue or red shift can be obtained.
International Nuclear Information System (INIS)
Zelenyj, L.M.; Kuznetsova, M.M.
1989-01-01
Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed
International Nuclear Information System (INIS)
Donoso, Guillermo; Ladera, Celso L
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring–magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet–coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels. (paper)
Energy Technology Data Exchange (ETDEWEB)
Pashitskii, E. A., E-mail: pashitsk@iop.kiev.ua; Pentegov, V. I., E-mail: pentegov@iop.kiev.ua [National Academy of Sciences of Ukraine, Institute of Physics (Ukraine)
2017-03-15
We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a{sub 0} ≫ l{sub P} (where l{sub P} is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n{sub F}) to energy density ε(n{sub F}) dependent on the number density of fermions n{sub F}. As the early Universe expands, the dimensionless quantity ν(n{sub F}) = P(n{sub F})/ε(n{sub F}) decreases with decreasing n{sub F} from its maximum value ν{sub max} = 1 for n{sub F} → ∞ to zero for n{sub F} → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n{sub F})–ε(n{sub F})–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R{sub c} =–μ{sup 2}/ξ and radius a{sub c} ≫ a{sub 0}. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G{sub N}.
International Nuclear Information System (INIS)
Liu Guanghui; Guo Kangxian; Wang Chao
2012-01-01
The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A faster and accurate semianalytical formulation with a robust optimization solution for estimating the splice loss of graded-index fibers has been proposed. The semianalytical optimization of modal parameters has been carried out by Nelder-Mead method of nonlinear unconstrained minimization suitable for functions which are uncertain, noisy, or even discontinuous. Instead of normally used Gaussian function, as the trial field for the fundamental mode of graded-index optical fiber a novel sinc...
Nonlinear Approaches in Engineering Applications
Jazar, Reza
2012-01-01
Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...
Ooi, Kelvin J. A.; Tan, Dawn T. H.
2017-10-01
The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.
Sierra-Pérez, Julián; Torres-Arredondo, M.-A.; Alvarez-Montoya, Joham
2018-01-01
Structural health monitoring consists of using sensors integrated within structures together with algorithms to perform load monitoring, damage detection, damage location, damage size and severity, and prognosis. One possibility is to use strain sensors to infer structural integrity by comparing patterns in the strain field between the pristine and damaged conditions. In previous works, the authors have demonstrated that it is possible to detect small defects based on strain field pattern recognition by using robust machine learning techniques. They have focused on methodologies based on principal component analysis (PCA) and on the development of several unfolding and standardization techniques, which allow dealing with multiple load conditions. However, before a real implementation of this approach in engineering structures, changes in the strain field due to conditions different from damage occurrence need to be isolated. Since load conditions may vary in most engineering structures and promote significant changes in the strain field, it is necessary to implement novel techniques for uncoupling such changes from those produced by damage occurrence. A damage detection methodology based on optimal baseline selection (OBS) by means of clustering techniques is presented. The methodology includes the use of hierarchical nonlinear PCA as a nonlinear modeling technique in conjunction with Q and nonlinear-T 2 damage indices. The methodology is experimentally validated using strain measurements obtained by 32 fiber Bragg grating sensors bonded to an aluminum beam under dynamic bending loads and simultaneously submitted to variations in its pitch angle. The results demonstrated the capability of the methodology for clustering data according to 13 different load conditions (pitch angles), performing the OBS and detecting six different damages induced in a cumulative way. The proposed methodology showed a true positive rate of 100% and a false positive rate of 1.28% for a
Kono, Mitsuo
2010-01-01
A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Chen, Wei
2004-06-01
Experimental results are presented to show that a pulsed, intensive membrane potential can reduce intra membrane, nonlinear charge movement currents, which are the voltage-sensors in the voltage-dependent membrane proteins and in the excitation-contraction coupling of skeletal muscle fibers. The results indicate a possible mechanism involved in electrical injury: dysfunctions of the voltage-dependent membrane proteins caused by electroconformational damages in their voltage-sensors.
International Nuclear Information System (INIS)
Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.
2009-01-01
Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.
International Nuclear Information System (INIS)
Ketov, S.V.
1996-01-01
The simplest free-field realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G 2 affine currents, respectively, are investigated. Both the N=8 and N=7 algebras are found to admit unitary and highest-weight irreducible representations in terms of a single free boson and free fermions in 8 of Spin(7) or 7 of G 2 , respectively, at level k=1 and the corresponding central charges c 8 =26/5 and c 7 =5. (orig.)
Nonlinear Optics and Applications
Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)
2007-01-01
Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.
[Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile
Energy Technology Data Exchange (ETDEWEB)
Davidson, R.C. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Chen, C. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Science and Fusion Center
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
Directory of Open Access Journals (Sweden)
E. L. Verde
2012-09-01
Full Text Available Further advances in magnetic hyperthermia might be limited by biological constraints, such as using sufficiently low frequencies and low field amplitudes to inhibit harmful eddy currents inside the patient's body. These incite the need to optimize the heating efficiency of the nanoparticles, referred to as the specific absorption rate (SAR. Among the several properties currently under research, one of particular importance is the transition from the linear to the non-linear regime that takes place as the field amplitude is increased, an aspect where the magnetic anisotropy is expected to play a fundamental role. In this paper we investigate the heating properties of cobalt ferrite and maghemite nanoparticles under the influence of a 500 kHz sinusoidal magnetic field with varying amplitude, up to 134 Oe. The particles were characterized by TEM, XRD, FMR and VSM, from which most relevant morphological, structural and magnetic properties were inferred. Both materials have similar size distributions and saturation magnetization, but strikingly different magnetic anisotropies. From magnetic hyperthermia experiments we found that, while at low fields maghemite is the best nanomaterial for hyperthermia applications, above a critical field, close to the transition from the linear to the non-linear regime, cobalt ferrite becomes more efficient. The results were also analyzed with respect to the energy conversion efficiency and compared with dynamic hysteresis simulations. Additional analysis with nickel, zinc and copper-ferrite nanoparticles of similar sizes confirmed the importance of the magnetic anisotropy and the damping factor. Further, the analysis of the characterization parameters suggested core-shell nanostructures, probably due to a surface passivation process during the nanoparticle synthesis. Finally, we discussed the effect of particle-particle interactions and its consequences, in particular regarding discrepancies between estimated
Energy Technology Data Exchange (ETDEWEB)
Karzova, M., E-mail: masha@acs366.phys.msu.ru [Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 36 Avenue Guy de Collongue, 69134 Ecully (France); Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Cunitz, B.; Kreider, W.; Bailey, M. [Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, 1013 NE 40" t" h Street, Seattle, WA 98105 (United States); Yuldashev, P.; Andriyakhina, Y. [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation); Sapozhnikov, O.; Khokhlova, V. [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 40" t" h Street, Seattle, WA 98105 (United States)
2015-10-28
Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher intensity at the focus to provide stronger pushing force; however, nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match the focal geometry of the beam as measured at a low power output. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging.
Karzova, M.; Cunitz, B.; Yuldashev, P.; Andriyakhina, Y.; Kreider, W.; Sapozhnikov, O.; Bailey, M.; Khokhlova, V.
2015-10-01
Newer imaging and therapeutic ultrasound technologies require higher in situ pressure levels compared to conventional diagnostic values. One example is the recently developed use of focused ultrasonic radiation force to move kidney stones and residual fragments out of the urinary collecting system. A commercial diagnostic 2.3 MHz C5-2 array probe is used to deliver the acoustic pushing pulses. The probe comprises 128 elements equally spaced at the 55 mm long convex cylindrical surface with 38 mm radius of curvature. The efficacy of the treatment can be increased by using higher intensity at the focus to provide stronger pushing force; however, nonlinear acoustic saturation can be a limiting factor. In this work nonlinear propagation effects were analyzed for the C5-2 transducer using a combined measurement and modeling approach. Simulations were based on the 3D Westervelt equation; the boundary condition was set to match the focal geometry of the beam as measured at a low power output. Focal waveforms simulated for increased output power levels were compared with the fiber-optic hydrophone measurements and were found in good agreement. It was shown that saturation effects do limit the acoustic pressure in the focal region of the transducer. This work has application to standard diagnostic probes and imaging.
Directory of Open Access Journals (Sweden)
Bég Anwar O.
2014-01-01
Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease
Gongora, J. S. Totero
2016-08-29
By employing ab-initio simulations of Maxwell-Bloch equations with a source of quantum noise, we study a new laser concept based on photonic dark-matter nanostructures that emit only in the near-field, with no far-field radiation pattern
A non-linear theory for the bubble regime of plasma wake fields in tailored plasma channels
Thomas, Johannes
2016-01-01
We introduce a first full analytical bubble and blow-out model for a radially inhomogeneous plasma in a quasi-static approximation. For both cases we calculate the accelerating and the focusing fields. In our model we also assume a thin electron layer that surrounds the wake field and calculate the field configuration within. Our theory holds for arbitrary radial density profiles and reduces to known models in the limit of a homogeneous plasma. From a previous study of hollow plasma channels with smooth boundaries for laser-driven electron acceleration in the bubble regime we know that pancake-like laser pulses lead to highest electron energies [Pukhov et al, PRL 113, 245003 (2014)]. As it was shown, the bubble fields can be adjusted to balance the laser depletion and dephasing lengths by varying the plasma density profile inside a deep channel. Now we show why the radial fields in the vacuum part of a channel become defocussing.
Nonlinear optics and photonics
He, Guang S
2015-01-01
This book provides a comprehensive presentation on most of the major topics in nonlinear optics and photonics, with equal emphasis on principles, experiments, techniques, and applications. It covers many major new topics including optical solitons, multi-photon effects, nonlinear photoelectric effects, fast and slow light , and Terahertz photonics. Chapters 1-10 present the fundamentals of modern nonlinear optics, and could be used as a textbook with problems provided at the end of each chapter. Chapters 11-17 cover the more advanced topics of techniques and applications of nonlinear optics and photonics, serving as a highly informative reference for researchers and experts working in related areas. There are also 16 pages of color photographs to illustrate the visual appearances of some typical nonlinear optical effects and phenomena. The book could be adopted as a textbook for both undergraduates and graduate students, and serve as a useful reference work for researchers and experts in the fields of physics...
International Nuclear Information System (INIS)
Krommes, J.A.
2009-01-01
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-? theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Krommes, J. A.
2009-05-01
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Energy Technology Data Exchange (ETDEWEB)
J.A. Krommes
2009-05-19
Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed. An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.
Ghorbanpour Arani, A.; Sabzeali, M.; BabaAkbar Zarei, H.
2017-12-01
In this study, the nonlinear thermo-electro vibrations of double-walled boron nitride nanopeapods (DWBNNPPs) and double-walled carbon nanopeapods (DWCNPPs) under magnetic field embedded in an elastic medium is investigated. DWBNNPPs are made of piezoelectric and smart materials therefore, electric field is effective on them; meanwhile, DWCNPPs are made of carbon thus, magnetic field can be useful to control them. The Pasternak model is used to simulate the effects of elastic medium which surrounds the system. Nanotubes are modeled with assumption of the Euler-Bernoulli beam (EBB) theory and the surface effects are considered to achieve accurate response of the system. Moreover, interaction between two layers is modeled by van der Waals (vdW) forces. The equations of motion are derived using the energy method and the Hamilton principle. Then the governing equations are solved by using Galerkin's method and incremental harmonic balance method (IHBM). The influences of various parameters such as the magnetic field, different types of DWCNPPs and DWBNNPPs, elastic medium, existence of fullerene and surface effect on the vibration behavior of the system are investigated. The results demonstrate that DWBNNPPs have more influence on the frequency of the system than DWCNPPs. In addition, the presence of fullerene in nanotubes has a negative impact on the frequency behavior of revisionthe system.
International Nuclear Information System (INIS)
Lalousis, P.
1984-01-01
Nonthermal direct electrodynamic interaction between laser energy and a fully ionized plasma was studied. The particular emphasis is on the action of nonlinear forces, in which the optical electromagnetic fields act on the plasma electrons which then transfer their energy to the ions electrostatically. Instead of the usual single fluid model, the plasma is treated as two separate conducting fluids for electrons and ions, coupled by momentum and Coulomb interactions. The equations governing the two fluids are derived from first principles, and numerical algorithms for computing these equations are developed, enabling the plasma oscillatons to be resolved and studied. Fully ionized plasma expansion without laser irradiation is studied first numerically. Remarkable damping mechanisms by coupling to ion oscillations have been observed. Inhomogeneities in densities of the two fluids result in large electrostatic fields and double layers are generated. There is quite close agreement between numerically calculated electrostatic fields and analytical solutions. Laser interaction with fully ionized plasma is also studied numerically. The generation of cavitons is numerically observed, and it is inferred that laser plasma interactions produce very high electrostatic fields in the vicinity of cavitons. It is further shown that charge neutrality is not necessarily maintained in a caviton
Directory of Open Access Journals (Sweden)
Xujian Shu
2018-03-01
Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.
Energy Technology Data Exchange (ETDEWEB)
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
Blanloeuil , Philippe; Meziane , Anissa; Norris , Andrew N.; Renier , Mathieu; Veidt , Martin
2014-01-01
International audience; The directivity patterns of the higher harmonics generated by the interaction between a bulk wave and a closed crack are obtained in the far field. A Finite Element (FE) model gives the near field solution which is then analytically propagated with expressions based on Hankel functions. The crack is modeled by an interface of unilateral contact with CoulombÕs friction which takes into account a compression pre-stress s0 that closes the crack. The mode conversion occurr...
Czech Academy of Sciences Publication Activity Database
Doležel, Ivo; Kropík, P.; Ulrych, B.
2013-01-01
Roč. 219, č. 13 (2013), s. 7159-7169 ISSN 0096-3003 R&D Projects: GA ČR GA102/09/1305 Grant - others:GA MŠk(CZ) MEB051041 Institutional support: RVO:61388998 Keywords : induction heating * electric field * temperature field Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.600, year: 2013 http://www.sciencedirect.com/science/article/pii/S0096300311010824
Pazur, Alexander
2004-01-01
Background Previous reports indicate altered metabolism and enzyme kinetics for various organisms, as well as changes of neuronal functions and behaviour of higher animals, when they were exposed to specific combinations of weak static and alternating low frequency electromagnetic fields. Field strengths and frequencies, as well as properties of involved ions were related by a linear equation, known as the formula of ion cyclotron resonance (ICR, abbreviation mentioned first by Liboff). Under...
Ceroici, Chris; Zemp, Roger J
2017-07-01
Capacitive micromachined ultrasonic transducers (CMUTs) promise many advantages over traditional piezoelectric transducers such as the potential to construct large, cost-effective 2-D arrays. To avoid wiring congestion issues associated with fully wired arrays, top-orthogonal-to-bottom electrode (TOBE) CMUT array architectures have proven to be a more practical alternative, using only 2N wires for an N ×N array. Optimally designing a TOBE CMUT array is a significant challenge due to the range of parameters from the device level up to the operating conditions of the entire array. Since testing many design variations can be prohibitively expensive, a simulation approach accounting for both the small and large-scale array characteristics of TOBE arrays is essential. In this paper, we demonstrate large-scale TOBE CMUT array simulations using a nonlinear CMUT lumped-circuit model. We investigate the performance of the array with different CMUT design parameters and array operating conditions. These simulated results are then compared with measurements of TOBE arrays fabricated using a sacrificial release process.
Non-Force-Free Magnetic Flux Ropes with Minimum Complexity in anAmbient Medium: A Parameter Study
2012-10-16
nonzero (Chen 2012, henceforth referred to as Paper 1). The work is formulated using standard magnetohydrodynamics ( MHD ) and develops a new physical...embedded in a plasma medium of pressure pa. The method presented in Paper 1 self-consistently solves the basic one-dimensional (1D) MHD equation subject...channel of electric current and the magnetic field arising from this current. An analytic method has been developed to obtain one-dimensional equilibrium
Directory of Open Access Journals (Sweden)
Raja Roy Choudhury
2013-01-01
Full Text Available A faster and accurate semianalytical formulation with a robust optimization solution for estimating the splice loss of graded-index fibers has been proposed. The semianalytical optimization of modal parameters has been carried out by Nelder-Mead method of nonlinear unconstrained minimization suitable for functions which are uncertain, noisy, or even discontinuous. Instead of normally used Gaussian function, as the trial field for the fundamental mode of graded-index optical fiber a novel sinc function with exponentially and R-3/2 (R is the normalized radius of the optical fiber decaying trailing edge has been used. Due to inclusion of three parameters in the optimization of fundamental modal solution and application of an efficient optimization technique with simple analytical expressions for various modal parameters, the results are found to be accurate and computationally easier to find than the standard numerical method solution.
Directory of Open Access Journals (Sweden)
I.L. Animasaun
2016-06-01
Full Text Available This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.
International Nuclear Information System (INIS)
Aschwanden, Markus J.; Sun, Xudong; Liu, Yang
2014-01-01
We developed a coronal nonlinear force-free field (COR-NLFFF) forward-fitting code that fits an approximate nonlinear force-free field (NLFFF) solution to the observed geometry of automatically traced coronal loops. In contrast to photospheric NLFFF codes, which calculate a magnetic field solution from the constraints of the transverse photospheric field, this new code uses coronal constraints instead, and this way provides important information on systematic errors of each magnetic field calculation method, as well as on the non-force-freeness in the lower chromosphere. In this study we applied the COR-NLFFF code to NOAA Active Region 11158, during the time interval of 2011 February 12-17, which includes an X2.2 GOES-class flare plus 35 M- and C-class flares. We calculated the free magnetic energy with a 6 minute cadence over 5 days. We find good agreement between the two types of codes for the total nonpotential E N and potential energy E P but find up to a factor of 4 discrepancy in the free energy E free = E N – E P and up to a factor of 10 discrepancy in the decrease of the free energy ΔE free during flares. The coronal NLFFF code exhibits a larger time variability and yields a decrease of free energy during the flare that is sufficient to satisfy the flare energy budget, while the photospheric NLFFF code shows much less time variability and an order of magnitude less free-energy decrease during flares. The discrepancy may partly be due to the preprocessing of photospheric vector data but more likely is due to the non-force-freeness in the lower chromosphere. We conclude that the coronal field cannot be correctly calculated on the basis of photospheric data alone and requires additional information on coronal loop geometries.
Directory of Open Access Journals (Sweden)
R. N. Bhowmik
2015-06-01
Full Text Available We have studied current-voltage (I-V characteristics of α-Fe1.64Ga0.36O3, a typical canted ferromagnetic semiconductor. The sample showed a transformation of the I-V curves from linear to non-linear character with the increase of bias voltage. The I-V curves showed irreversible features with hysteresis loop and bi-stable electronic states for up and down modes of voltage sweep. We report positive magnetoresistance and magnetic field induced negative differential resistance as the first time observed phenomena in metal doped hematite system. The magnitudes of critical voltage at which I-V curve showed peak and corresponding peak current are affected by magnetic field cycling. The shift of the peak voltage with magnetic field showed a step-wise jump between two discrete voltage levels with least gap (ΔVP 0.345(± 0.001 V. The magnetic spin dependent electronic charge transport in this new class of magnetic semiconductor opens a wide scope for tuning large electroresistance (∼500-700%, magnetoresistance (70-135 % and charge-spin dependent conductivity under suitable control of electric and magnetic fields. The electric and magnetic field controlled charge-spin transport is interesting for applications of the magnetic materials in spintronics, e.g., magnetic sensor, memory devices and digital switching.
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
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
Pazur, Alexander
2004-01-01
Background Previous reports indicate altered metabolism and enzyme kinetics for various organisms, as well as changes of neuronal functions and behaviour of higher animals, when they were exposed to specific combinations of weak static and alternating low frequency electromagnetic fields. Field strengths and frequencies, as well as properties of involved ions were related by a linear equation, known as the formula of ion cyclotron resonance (ICR, abbreviation mentioned first by Liboff). Under certain conditions already a aqueous solution of the amino acid and neurotransmitter glutamate shows this effect. Methods An aqueous solution of glutamate was exposed to a combination of a static magnetic field of 40 μT and a sinusoidal electromagnetic magnetic field (EMF) with variable frequency (2–7 Hz) and an amplitude of 50 nT. The electric conductivity and dielectric properties of the solution were investigated by voltammetric techniques in combination with non linear dielectric spectroscopy (NLDS), which allow the examination of the dielectric properties of macromolecules and molecular aggregates in water. The experiments target to elucidate the biological relevance of the observed EMF effect on molecular level. Results An ion cyclotron resonance (ICR) effect of glutamate previously reported by the Fesenko laboratory 1998 could be confirmed. Frequency resolution of the sample currents was possible by NLDS techniques. The spectrum peaks when the conditions for ion cyclotron resonance (ICR) of glutamate are matched. Furthermore, the NLDS spectra are different under ICR- and non-ICR conditions: NLDS measurements with rising control voltages from 100–1100 mV show different courses of the intensities of the low order harmonics, which could possibly indicate "intensity windows". Furthermore, the observed magnetic field effects are pH dependent with a narrow optimum around pH 2.85. Conclusions Data will be discussed in the context with recent published models for the
Audenino, A. L.; Calderale, P. M.
1996-12-01
The specific damping capacity of metallic materials is not linear and depends upon temperature, strain and strain rate. To evaluate the strain influence on material damping, homogeneous strain fields are recommended; these homogenous fields generally are not realized in damping measurement. In this paper the development of an automated experimental procedure is presented; the procedure is based on an improved method able to evaluate the material damping by sinusoidally exciting the specimen in uniaxal traction or compression with a frequency from 60 to 300 Hz. The test machine is a high frequency Amsler vibrofore and the experimental method is based on the acquisition of the decay signal when the machine excitation force has been removed. Signals are acquired by means of an A/D board installed in a personal computer; dedicated software has been created which performs complete analysis and directly provides graphic results. The method can discriminate between material damping and damping of the machine and fixtures. The resulting curves of the loss factor as a function of strain amplitude for three steels and two cast irons are presented.
Particle simulation study of collisionless driven reconnection in a sheared magnetic field
International Nuclear Information System (INIS)
Horiuchi, Ritoku; Sato, Tetsuya.
1996-08-01
Nonlinear development of collisionless driven reconnection and the consequent energy conversion process between the field and particles in a sheared magnetic field are investigated by means of a two-and-a-half-dimensional particle simulation. Magnetic reconnection takes place in two steps irrespective of a longitudinal magnetic field, but the growth rate of reconnection field varies in proportion to the E x B drift velocity at an input boundary. It is clearly observed that the triggering mechanism of collisionless driven reconnection for the fast growing phase changes from an electron meandering dominance in a weak longitudinal field to an electron inertia dominance in a strong field. The electron acceleration and heating take place in the reconnection area under the influence of reconnection electric field, while the electron energy is converted to the ion energy through the action of electrostatic (ambipolar) field excited by magnetic compression in the downstream. It is also found that, in the presence of a longitudinal magnetic field, the electron acceleration by the reconnection field takes place effectively and the generated force-free current is maintained for a long period while forming an asymmetric spatial profile of current layer. (author)
Agrawal, Govind
2012-01-01
Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o
National Research Council Canada - National Science Library
Rassias, Themistocles M
1987-01-01
... known that nonlinear partial differential equations can not be treated in the same systematic way as linear ones and this volume provides, among other things, proofs of existence and uniqueness theorems for nonlinear differential equations of a global nature. However, the basic techniques which have proven to be efficient in dealing with li...
Topology optimization of nonlinear optical devices
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2011-01-01
This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...
Lie Symmetries and Solitons in Nonlinear Systems with Spatially Inhomogeneous Nonlinearities
International Nuclear Information System (INIS)
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Torres, Pedro J.
2007-01-01
Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schroedinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves
Nonlinear Analysis and Variational Problems
Pardalos, Panos M
2010-01-01
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization. "Nonlinear Analysis and Variational Problems" is organized into two parts. Part I, Nonlinear Analysis, centers on stability issues for functional equations, fixed point
Palazzo, S; Murari, A; Vagliasindi, G; Arena, P; Mazon, D; De Maack, A
2010-08-01
In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN-unlike software CNN implementations.
Energy Technology Data Exchange (ETDEWEB)
Palazzo, S.; Vagliasindi, G.; Arena, P. [Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Universita degli Studi di Catania, 95125 Catania (Italy); Murari, A. [Consorzio RFX-Associazione EURATOM ENEA per la Fusione, I-35127 Padova (Italy); Mazon, D. [Association EURATOM-CEA, CEA Cadarache, 13108 Saint-Paul-lez-Durance (France); De Maack, A. [Arts et Metiers Paris Tech Engineering College (ENSAM), 13100 Aix-en-Provence (France); Collaboration: JET-EFDA Contributors
2010-08-15
In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496x560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN - unlike software CNN implementations.
Palazzo, S.; Murari, A.; Vagliasindi, G.; Arena, P.; Mazon, D.; de Maack, A.; Jet-Efda Contributors
2010-08-01
In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496×560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN—unlike software CNN implementations.
International Nuclear Information System (INIS)
Palazzo, S.; Vagliasindi, G.; Arena, P.; Murari, A.; Mazon, D.; De Maack, A.
2010-01-01
In the past years cameras have become increasingly common tools in scientific applications. They are now quite systematically used in magnetic confinement fusion, to the point that infrared imaging is starting to be used systematically for real-time machine protection in major devices. However, in order to guarantee that the control system can always react rapidly in case of critical situations, the time required for the processing of the images must be as predictable as possible. The approach described in this paper combines the new computational paradigm of cellular nonlinear networks (CNNs) with field-programmable gate arrays and has been tested in an application for the detection of hot spots on the plasma facing components in JET. The developed system is able to perform real-time hot spot recognition, by processing the image stream captured by JET wide angle infrared camera, with the guarantee that computational time is constant and deterministic. The statistical results obtained from a quite extensive set of examples show that this solution approximates very well an ad hoc serial software algorithm, with no false or missed alarms and an almost perfect overlapping of alarm intervals. The computational time can be reduced to a millisecond time scale for 8 bit 496x560-sized images. Moreover, in our implementation, the computational time, besides being deterministic, is practically independent of the number of iterations performed by the CNN - unlike software CNN implementations.
Non-potential Field Formation in the X-shaped Quadrupole Magnetic Field Configuration
Energy Technology Data Exchange (ETDEWEB)
Kawabata, Y.; Shimizu, T. [Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Inoue, S., E-mail: kawabata.yusuke@ac.jaxa.jp [Max-Planck-Institute for Solar System Research, Justus-von-Liebig-Weg 3 D-37077 Göttingen (Germany)
2017-06-20
Some types of solar flares are observed in X-shaped quadrupolar field configuration. To understand the magnetic energy storage in such a region, we studied non-potential field formation in an X-shaped quadrupolar field region formed in the active region NOAA 11967, which produced three X-shaped M-class flares on 2014 February 2. Nonlinear force-free field modeling was applied to a time series of vector magnetic field maps from the Solar Optical Telescope on board Hinode and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory . Our analysis of the temporal three-dimensional magnetic field evolution shows that the sufficient free energy had already been stored more than 10 hr before the occurrence of the first M-class flare and that the storage was observed in a localized region. In this localized region, quasi-separatrix layers (QSLs) started to develop gradually from 9 hr before the first M-class flare. One of the flare ribbons that appeared in the first M-class flare was co-spatial with the location of the QSLs, suggesting that the formation of the QSLs is important in the process of energy release. These QSLs do not appear in the potential field calculation, indicating that they were created by the non-potential field. The formation of the QSLs was associated with the transverse photospheric motion of the pre-emerged flux and the emergence of a new flux. This observation indicates that the occurrence of the flares requires the formation of QSLs in the non-potential field in which free magnetic energy is stored in advance.
Gasinski, Leszek
2005-01-01
Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.
Set Your Creative Forces Free!
DEFF Research Database (Denmark)
Meier Sørensen, Bent; Villadsen, Kaspar
eccentric Managing Director. At first glance the essential message to the employees may be read as ‘set Your creative forces and potentials free!; a statement which activates a semantics of liberation of artistic creativeness and rebellious transgression of conventions. It is suggested, however......, that the manager’s bodily comportment activate and oscillates between a more complex web of managerial rationalities including sovereignty, discipline and pastoral care. It is further suggested that this managerial hybridity renders difficult, or even closes off, conventional forms of contestation and resistance...
Set Your Creative Forces Free!
DEFF Research Database (Denmark)
Meier Sørensen, Bent; Villadsen, Kaspar
eccentric Managing Director. At first glance the essential message to the employees may be read as ‘set Your creative forces and potentials free!; a statement which activates a semantics of liberation of artistic creativeness and rebellious transgression of conventions. It is suggested, however......-hierarchical’ and aestheticized managerial practice reconfigures power relations within a creative industry. The key problematic is ‘governmental’ in the sense suggested by Michel Foucault in as far as the manager’s ethical self-practice—which involves expressive and ‘liberated’ bodily comportment—is used as a means for culture...
2016-07-01
architectures , practical nonlinearities, nonlinear dynamics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT: SAR 8. NUMBER OF PAGES...performers from Mesodynamic Architectures (MESO) and uPNT all to include devices in these runs. This cost-sharing was planned, and is necessary for...contributions to the performance of MEMS gyroscopes. In particular, we have demonstrated for the first time that Parametric Amplification can improve the
International Nuclear Information System (INIS)
Karabulut, I.; Mora-Ramos, M.E.; Duque, C.A.
2011-01-01
The intersubband electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga 1-x Al x As asymmetric double quantum wells are studied, under the influence of combined or independent applied electric and magnetic fields as well as hydrostatic pressure. The outcome of the density matrix formalism and the effective mass, and parabolic-band approximations have been considered as main theoretical tools for the description. It is obtained that under particular geometrical conditions, with or without electric and/or magnetic field strength, the optical rectification is null and, simultaneously, in such circumstances the optical absorption has a relative maximum. It is also detected that the influence of the hydrostatic pressure leads to increasing or decreasing behaviors of the nonlinear optical absorption in dependence of the particular regime of pressure values considered, with significant distinction of the cases of opposite electric field orientations. - Highlights: → Maxima of the NOA correspond to zero in the NOR. → Electric fields can couple the double quantum wells. → Hydrostatic pressure can couple the double quantum wells. → NOA can increase/decrease with hydrostatic pressure. → Overlap between wave functions depends on the magnetic field.
Directory of Open Access Journals (Sweden)
Yukun Ren
2018-02-01
Full Text Available Induced-charge electroosmosis has attracted lots of attention from the microfluidic community over the past decade. Most previous researches on this subject focused on induced-charge electroosmosis (ICEO vortex streaming actuated on ideally polarizable surfaces immersed in electrolyte solutions. Starting from this point, we conduct herein a linear asymptotic analysis on nonlinear electroosmotic flow next to leaky dielectric blocks of arbitrary electrical conductivity and dielectric permittivity in harmonic AC electric fields, and theoretically demonstrate that observable ICEO fluid motion can be generated at high field frequencies in the vicinity of nearly insulating semiconductors, a very low electrical conductivity, of which can evidently increase the double-layer relaxation frequency (inversely proportional to the solid permittivity to be much higher than the typical reciprocal RC time constant for induced double-layer charging on ideally polarizable surfaces. A computational model is developed to study the feasibility of this high-frequency vortex flow field of ICEO for sample mixing in microfluidics, in which the usage of AC voltage signal at high field frequencies may be beneficial to suppress electrochemical reactions to some extent. The influence of various parameters for developing an efficient mixer is investigated, and an integrated arrangement of semiconductor block array is suggested for achieving a reliable mixing performance at relatively high sample fluxes. Our physical demonstration with high-frequency ICEO next to leaky dielectric blocks using a simple channel structure offers valuable insights into the design of high-throughput micromixers for a variety of lab-on-a-chip applications.
Nonlinear evolution of drift instabilities
International Nuclear Information System (INIS)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation
Fundamentals of nonlinear optics
Powers, Peter E
2011-01-01
Peter Powers's rigorous but simple description of a difficult field keeps the reader's attention throughout. … All chapters contain a list of references and large numbers of practice examples to be worked through. … By carefully working through the proposed problems, students will develop a sound understanding of the fundamental principles and applications. … the book serves perfectly for an introductory-level course for second- and third-order nonlinear optical phenomena. The author's writing style is refreshing and original. I expect that Fundamentals of Nonlinear Optics will fast become pop
Multidimensional nonlinear descriptive analysis
Nishisato, Shizuhiko
2006-01-01
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...
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.
International Conference on Applications in Nonlinear Dynamics
Longhini, Patrick; Palacios, Antonio
2017-01-01
This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.
International Nuclear Information System (INIS)
Nalegaev, S S; Petrov, N V; Bespalov, V G
2014-01-01
A numerical reconstruction of spatial distributions of optical radiation propagating through a volume of nonlinear medium at input and output planes of the medium was demonstrated using a scheme of digital holography. A nonlinear Schrodinger equation with Fourier Split-Step method was used as a tool to propagate wavefront in the volume of the medium. Time dependence of the refractive index change was not taken into account.
Nonlinear fiber optics formerly quantum electronics
Agrawal, Govind
1995-01-01
The field of nonlinear fiber optics has grown substantially since the First Edition of Nonlinear Fiber Optics, published in 1989. Like the First Edition, this Second Edition is a comprehensive, tutorial, and up-to-date account of nonlinear optical phenomena in fiber optics. It synthesizes widely scattered research material and presents it in an accessible manner for students and researchers already engaged in or wishing to enter the field of nonlinear fiber optics. Particular attention is paid to the importance of nonlinear effects in the design of optical fiber communication systems. This is
Nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Nonlinear chiral transport phenomena
Chen, Jiunn-Wei; Ishii, Takeaki; Pu, Shi; Yamamoto, Naoki
2016-06-01
We study the nonlinear responses of relativistic chiral matter to the external fields such as the electric field E , gradients of temperature and chemical potential, ∇T and ∇μ . Using the kinetic theory with Berry curvature corrections under the relaxation time approximation, we compute the transport coefficients of possible new electric currents that are forbidden in usual chirally symmetric matter but are allowed in chirally asymmetric matter by parity. In particular, we find a new type of electric current proportional to ∇μ ×E due to the interplay between the effects of the Berry curvature and collisions. We also derive an analog of the "Wiedemann-Franz" law specific for anomalous nonlinear transport in relativistic chiral matter.
Directory of Open Access Journals (Sweden)
Orlando Soriano-Vargas
2016-12-01
Full Text Available Spinodal decomposition was studied during aging of Fe-Cr alloys by means of the numerical solution of the linear and nonlinear Cahn-Hilliard differential partial equations using the explicit finite difference method. Results of the numerical simulation permitted to describe appropriately the mechanism, morphology and kinetics of phase decomposition during the isothermal aging of these alloys. The growth kinetics of phase decomposition was observed to occur very slowly during the early stages of aging and it increased considerably as the aging progressed. The nonlinear equation was observed to be more suitable for describing the early stages of spinodal decomposition than the linear one.
Energy Technology Data Exchange (ETDEWEB)
Soriano-Vargas, O.; Lopez-Hirata, V.M.; Avila-Davila, E.O.; Saucedo-MuNoz, M.L.; Cayetano-Castro, N.
2016-07-01
Spinodal decomposition was studied during aging of Fe-Cr alloys by means of the numerical solution of the linear and nonlinear Cahn-Hilliard differential partial equations using the explicit finite difference method. Results of the numerical simulation permitted to describe appropriately the mechanism, morphology and kinetics of phase decomposition during the isothermal aging of these alloys. The growth kinetics of phase decomposition was observed to occur very slowly during the early stages of aging and it increased considerably as the aging progressed. The nonlinear equation was observed to be more suitable for describing the early stages of spinodal decomposition than the linear one. (Author)
Extreme Nonlinear Optics An Introduction
Wegener, Martin
2005-01-01
Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...
Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.
2017-09-01
Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.
Nonlinear gyrokinetic tokamak physics
International Nuclear Information System (INIS)
Brizard, A.J.
1990-01-01
The gyrokinetic reduced description of low-frequency and small-perpendicular-wavelength nonlinear tokamak dynamics is presented in three different versions: the reduced dynamical description of test particles moving in electromagnetic fields; the reduced gyrokinetic description of the self-consistent interaction of particles and fields through the Maxwell-Vlasov equations; and the reduced description of nonlinear fluid motion. The unperturbed tokamak plasma is described in terms of a noncanonical Hamiltonian guiding-center theory. The unperturbed guiding-center tokamak plasma is then perturbed by gyrokinetic electromagnetic fields and consequently the perturbed guiding-center dynamical system acquires new gyrophase dependence. The perturbation analysis that follows makes extensive use of Lie-transform perturbation techniques. Because the electromagnetic perturbations affect both the Hamiltonian and the Poisson-bracket structure, the Phase-space Lagrangian Lie perturbation method is used. The description of the reduced test-particle dynamics is given in terms of a non-canonical Hamiltonian gyrocenter theory. The description of the reduced kinetic dynamics is concerned with the self consistent response of the guiding-center plasma and is described in terms of the nonlinear gyrokinetic Maxwell-Vlasov equations. It is also shown that the gyrokinetic Maxwell-Vlasov system possesses a gyrokinetic energy adiabatic invariant and that, in both the linear and nonlinear (quadratic) approximations, the corresponding energy invariants are exact. The description of the reduced fluid dynamics is concerned with the derivation of a closed set of reduced fluid equations. Three generations of reduced fluid models are presented: the reduced MHD equations; the reduced FLR-MHD equations; and the gyrofluid equations
Sharykin, I. N.; Kuznetsov, A. A.; Myshyakov, I. I.
2018-02-01
This work demonstrates the possibility of magnetic-field topology investigations using microwave polarimetric observations. We study a solar flare of GOES M1.7 class that occurred on 11 February, 2014. This flare revealed a clear signature of spatial inversion of the radio-emission polarization sign. We show that the observed polarization pattern can be explained by nonthermal gyrosynchrotron emission from the twisted magnetic structure. Using observations of the Reuven Ramaty High Energy Solar Spectroscopic Imager, Nobeyama Radio Observatory, Radio Solar Telescope Network, and Solar Dynamics Observatory, we have determined the parameters of nonthermal electrons and thermal plasma and identified the magnetic structure where the flare energy release occurred. To reconstruct the coronal magnetic field, we use nonlinear force-free field (NLFFF) and potential magnetic-field approaches. Radio emission of nonthermal electrons is simulated by the GX Simulator code using the extrapolated magnetic field and the parameters of nonthermal electrons and thermal plasma inferred from the observations; the model radio maps and spectra are compared with observations. We have found that the potential-magnetic-field approach fails to explain the observed circular polarization pattern; on the other hand, the Stokes-V map is successfully explained by assuming nonthermal electrons to be distributed along the twisted magnetic structure determined by the NLFFF extrapolation approach. Thus, we show that the radio-polarization maps can be used for diagnosing the topology of the flare magnetic structures where nonthermal electrons are injected.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
Cheng, Heming; Huang, Xieqing; Fan, Jiang; Wang, Honggang
1999-10-01
The calculation of a temperature field has a great influence upon the analysis of thermal stresses and stains during quenching. In this paper, a 42CrMo steel cylinder was used an example for investigation. From the TTT diagram of the 42CrMo steel, the CCT diagram was simulated by mathematical transformation, and the volume fraction of phase constituents was calculated. The thermal physical properties were treated as functions of temperature and the volume fraction of phase constituents. The rational approximation was applied to the finite element method. The temperature field with phase transformation and non-linear surface heat-transfer coefficients was calculated using this technique, which can effectively avoid oscillationin the numerical solution for a small time step. The experimental results of the temperature field calculation coincide with the numerical solutions.
Directory of Open Access Journals (Sweden)
Koneri L. Krupalakshmi
Full Text Available A numerical investigation of two-dimensional MHD boundary layer flow and thermal characteristics of an electrically conducting dusty non-Newtonian fluid over a convectively heated stretching sheet has been considered. The effects of nonlinear thermal radiation, heat source or sink and viscous dissipation are also taken into the account. The Rosseland approximation is used to model the nonlinear thermal radiation. Suitable similarity transformations are used to transform the flow governing equations into a set of nonlinear differential equations of one independent variable. The Shooting method is adopted to solve transformed equations. The effects of various material parameters on the flow and heat transfer in terms of velocity and temperature distributions are drawn in the form of graphs and are briefly discussed. The numerical computations for the Nusselt number and skin friction drag are also carried out for the emerging parameters of interest in the problem. The obtained numerical results show the good agreement with the existing one for limiting case.
Nonlinear terahertz superconducting plasmonics
Energy Technology Data Exchange (ETDEWEB)
Wu, Jingbo; Liang, Lanju; Jin, Biaobing, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn; Kang, Lin; Xu, Weiwei; Chen, Jian; Wu, Peiheng, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn [Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University, Nanjing 210093 (China); Zhang, Caihong; Kawayama, Iwao; Murakami, Hironaru; Tonouchi, Masayoshi, E-mail: bbjin@nju.edu.cn, E-mail: tonouchi@ile.osaka-u.ac.jp, E-mail: phwu@nju.edu.cn [Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871 (Japan); Wang, Huabing [Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University, Nanjing 210093 (China); National Institute for Materials Science, Tsukuba 305-0047 (Japan)
2014-10-20
Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.
Nonlinear Photonics 2014: introduction.
Akhmediev, N; Kartashov, Yaroslav
2015-01-12
International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
Energy Technology Data Exchange (ETDEWEB)
Rodríguez-Magdaleno, K.A.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I. [Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calz. Solidaridad Esq. Paseo a La Bufa S/N. C.P. 98060 Zacatecas (Mexico); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos (Mexico); Física Teórica y Aplicada, Escuela de Ingeniería de Antioquia, AA 7516 Medellín (Colombia); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)
2014-03-15
In this work, the conduction band electron states and the associated intersubband-related linear and nonlinear optical absorption coefficient and relative refractive index change are calculated for an asymmetric double n-type δ-doped quantum well in a GaAs-matrix. The effects of an external applied static electric field are included. Values of the two-dimensional impurities density (N{sub 2d}) of each single δ-doped quantum well are taken to vary within the range of 1.0×10{sup 12} to 7.0×10{sup 12} cm{sup −2}, consistent with the experimental data growth regime. The optical responses are reported as a function of the δ-doped impurities density and the applied electric field. It is shown that single electron states and the related optical quantities are significantly affected by the structural asymmetry of the double δ-doped quantum well system. In addition, a brief comparison with the free-carrier-related optical response is presented. -- Highlights: • Nonlinear optics in asymmetric double n-type δ-doped quantum well in a GaAs-matrix. • The system is considered under external applied electric field in growth direction. • The 2D impurity density is consistent with the experimental data growth regime. • The optical quantities are significantly affected by the structural asymmetry of the system.
International Nuclear Information System (INIS)
Rodríguez-Magdaleno, K.A.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I.; Mora-Ramos, M.E.; Duque, C.A.
2014-01-01
In this work, the conduction band electron states and the associated intersubband-related linear and nonlinear optical absorption coefficient and relative refractive index change are calculated for an asymmetric double n-type δ-doped quantum well in a GaAs-matrix. The effects of an external applied static electric field are included. Values of the two-dimensional impurities density (N 2d ) of each single δ-doped quantum well are taken to vary within the range of 1.0×10 12 to 7.0×10 12 cm −2 , consistent with the experimental data growth regime. The optical responses are reported as a function of the δ-doped impurities density and the applied electric field. It is shown that single electron states and the related optical quantities are significantly affected by the structural asymmetry of the double δ-doped quantum well system. In addition, a brief comparison with the free-carrier-related optical response is presented. -- Highlights: • Nonlinear optics in asymmetric double n-type δ-doped quantum well in a GaAs-matrix. • The system is considered under external applied electric field in growth direction. • The 2D impurity density is consistent with the experimental data growth regime. • The optical quantities are significantly affected by the structural asymmetry of the system
Wiegelmann, Thomas; Petrie, Gordon J. D.; Riley, Pete
2017-09-01
Coronal magnetic field models use photospheric field measurements as boundary condition to model the solar corona. We review in this paper the most common model assumptions, starting from MHD-models, magnetohydrostatics, force-free and finally potential field models. Each model in this list is somewhat less complex than the previous one and makes more restrictive assumptions by neglecting physical effects. The magnetohydrostatic approach neglects time-dependent phenomena and plasma flows, the force-free approach neglects additionally the gradient of the plasma pressure and the gravity force. This leads to the assumption of a vanishing Lorentz force and electric currents are parallel (or anti-parallel) to the magnetic field lines. Finally, the potential field approach neglects also these currents. We outline the main assumptions, benefits and limitations of these models both from a theoretical (how realistic are the models?) and a practical viewpoint (which computer resources to we need?). Finally we address the important problem of noisy and inconsistent photospheric boundary conditions and the possibility of using chromospheric and coronal observations to improve the models.
International Nuclear Information System (INIS)
Monk, P.
1993-01-01
The use of acoustic waves as probes to determine otherwise inaccessible properties of a medium is extremely widespread. Applications include sonar, medical imaging and non-destructive testing. Despite the importance of the applications, there is as yet no acceptable method for solving the full non-linear problem at resonance frequencies (frequencies at which the size of the features under investigations are approximately the wavelength of the incident acoustic field). The medical imaging problem, which consists in trying to determine the sound speed, density and absorption properties of a bounded inhomogeneous medium from scattered acoustic waves is the motivaiton for the investigation described in this paper. We shall present a solution technique for a standard model inverse acoustic scattering problem which consists of reconstructing the refractive index of an inhomogeneity from given far field data (far field data is essentially the measured scattered field at considerable distance from the inhomogeneity). This model inverse problem simplifies the inhomogeneity by neglecting density and absorption but includes two important features of the real problem: nonlinearity and illposedness. Furthermore the method we present can easily by extended to more general problems
Nonlinear optics principles and applications
Rottwitt, Karsten
2014-01-01
IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...
Overview of magnetic nonlinear beam dynamics in the RHIC
International Nuclear Information System (INIS)
Luo, Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, F.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, G.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-01-01
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed
Overview of magnetic nonlinear beam dynamics in the RHIC
Energy Technology Data Exchange (ETDEWEB)
Luo,Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, f.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, g.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.
2009-05-04
In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed.
Optical Computing With Nonlinear Optics
Khitrova, Galina; Gibbs, Hyatt; Peyghambarian, Nasser
1987-01-01
Nonlinear optics is becoming a new thrust in the field of optical computing and signal processing.14 Optical nonlinearity makes the device's transmission intensity dependent, so one can obtain the thresholding needed for logic decisionmaking. Thresholding is essential to digital optical computing, neural nets, and associative memories. GaAs etalons exhibit many of the characteristics desirable for the nonlinear devices including high speed (picosecond) and diode-laser compatability. However, demonstrations of the use of nonlinear decisionmaking for optical computing have used ZnS or ZnSe interference filters. They are slow (millisecond), but they can be used with the visible 514.5-nm output of an argon laser. We have used such filters to demonstrate all-optical logic operations, one-bit addition by symbolic substitution, and recognition of a three-spot pattern in an arbitrary 2 x 8 array of input beams. The application to associative memories is under study.
Nonlinear optics principles and applications
Li, Chunfei
2017-01-01
This book reflects the latest advances in nonlinear optics. Besides the simple, strict mathematical deduction, it also discusses the experimental verification and possible future applications, such as the all-optical switches. It consistently uses the practical unit system throughout. It employs simple physical images, such as "light waves" and "photons" to systematically explain the main principles of nonlinear optical effects. It uses the first-order nonlinear wave equation in frequency domain under the condition of “slowly varying amplitude approximation" and the classical model of the interaction between the light and electric dipole. At the same time, it also uses the rate equations based on the energy-level transition of particle systems excited by photons and the energy and momentum conservation principles to explain the nonlinear optical phenomenon. The book is intended for researchers, engineers and graduate students in the field of the optics, optoelectronics, fiber communication, information tech...
Nonlinear Optics: Principles and Applications
DEFF Research Database (Denmark)
Rottwitt, Karsten; Tidemand-Lichtenberg, Peter
As nonlinear optics further develops as a field of research in electromagnetic wave propagation, its state-of-the-art technologies will continue to strongly impact real-world applications in a variety of fields useful to the practicing scientist and engineer. From basic principles to examples...... of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...
Rajasekar, Shanmuganathan
2016-01-01
This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...
Nonlinear susceptibility magnitude imaging of magnetic nanoparticles
International Nuclear Information System (INIS)
Ficko, Bradley W.; Giacometti, Paolo; Diamond, Solomon G.
2015-01-01
This study demonstrates a method for improving the resolution of susceptibility magnitude imaging (SMI) using spatial information that arises from the nonlinear magnetization characteristics of magnetic nanoparticles (mNPs). In this proof-of-concept study of nonlinear SMI, a pair of drive coils and several permanent magnets generate applied magnetic fields and a coil is used as a magnetic field sensor. Sinusoidal alternating current (AC) in the drive coils results in linear mNP magnetization responses at primary frequencies, and nonlinear responses at harmonic frequencies and intermodulation frequencies. The spatial information content of the nonlinear responses is evaluated by reconstructing tomographic images with sequentially increasing voxel counts using the combined linear and nonlinear data. Using the linear data alone it is not possible to accurately reconstruct more than 2 voxels with a pair of drive coils and a single sensor. However, nonlinear SMI is found to accurately reconstruct 12 voxels (R 2 =0.99, CNR=84.9) using the same physical configuration. Several time-multiplexing methods are then explored to determine if additional spatial information can be obtained by varying the amplitude, phase and frequency of the applied magnetic fields from the two drive coils. Asynchronous phase modulation, amplitude modulation, intermodulation phase modulation, and frequency modulation all resulted in accurate reconstruction of 6 voxels (R 2 >0.9) indicating that time multiplexing is a valid approach to further increase the resolution of nonlinear SMI. The spatial information content of nonlinear mNP responses and the potential for resolution enhancement with time multiplexing demonstrate the concept and advantages of nonlinear SMI. - Highlights: • Development of a nonlinear susceptibility magnitude imaging model • Demonstration of nonlinear SMI with primary and harmonic frequencies • Demonstration of nonlinear SMI with primary and intermodulation frequencies
Dimensional Reduction of Nonlinear Gauge Theories
Ikeda, Noriaki; Izawa, K.-I.
2004-09-01
We extend 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional two-form gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a model, which provides a realization of Courant algebroid by 2D nonlinear gauge theory. We see that the reduction of the base structure generically results in a modification of the target (algebroid) structure.
Energy Technology Data Exchange (ETDEWEB)
Lewis, Jennifer
2012-10-15
This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. The goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.
DEFF Research Database (Denmark)
Mosekilde, Erik
Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Nonlinear surface electromagnetic phenomena
Ponath, H-E
1991-01-01
In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are
Oscillators from nonlinear realizations
Kozyrev, N.; Krivonos, S.
2018-02-01
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.
Energy Technology Data Exchange (ETDEWEB)
Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in
2016-12-15
Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two dimensions involving interacting fields. The Yang–Baxter integrability is proved for the model by finding a new kind of commutation rule for its basic fields, representing nonstandard scalar fields along the transverse direction. In spite of a close link with the quantum Landau–Lifshitz equation, the present model differs widely from it, in its content and the result obtained. Using further the algebraic Bethe ansatz we solve exactly the eigenvalue problem of this quantum field model for all its higher conserved operators. The idea presented here should instigate the construction of a novel class of integrable field and lattice models and exploration of a new type of underlying algebras.
4th International Conference on Structural Nonlinear Dynamics and Diagnosis
2018-01-01
This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...
Primordial fluctuations from nonlinear couplings
International Nuclear Information System (INIS)
Calzetta, E.A.; Gonorazky, S.
1997-01-01
We study the spectrum of primordial fluctuations in theories where the inflaton field is nonlinearly coupled to massless fields and/or to itself. Conformally invariant theories generically predict a scale-invariant spectrum. Scales entering the theory through infrared divergences cause logarithmic corrections to the spectrum, tilting it towards the blue. We discuss in some detail whether these fluctuations are quantum or classical in nature. copyright 1997 The American Physical Society
Chaos and Structures in Nonlinear Plasmas
Chen, James
In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
Artificial Nonlinearity Generated from Electromagnetic Coupling Metamolecule
Wen, Yongzheng; Zhou, Ji
2017-04-01
A purely artificial mechanism for optical nonlinearity is proposed based on a metamaterial route. The mechanism is derived from classical electromagnetic interaction in a metamolecule consisting of a cut-wire meta-atom nested within a split-ring meta-atom. Induced by the localized magnetic field in the split-ring meta-atom, the magnetic force drives an anharmonic oscillation of free electrons in the cut-wire meta-atom, generating an intrinsically nonlinear electromagnetic response. An explicit physical process of a second-order nonlinear behavior is adequately described, which is perfectly demonstrated with a series of numerical simulations. Instead of "borrowing" from natural nonlinear materials, this novel mechanism of optical nonlinearity is artificially dominated by the metamolecule geometry and possesses unprecedented design freedom, offering fascinating possibilities to the research and application of nonlinear optics.
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Metamaterial-Enhanced Nonlinear Terahertz Spectroscopy
Directory of Open Access Journals (Sweden)
Zhang X.
2013-03-01
Full Text Available We demonstrate large nonlinear terahertz responses in the gaps of metamaterial split ring resonators in several materials and use nonlinear THz transmission and THz-pump/THz-probe spectroscopy to study the nonlinear responses and dynamics. We use the field enhancement in the SRR gaps to initiate high-field phenomena at lower incident fields. In vanadium dioxide, we drive the insulator-to-metal phase transition with high-field THz radiation. The film conductivity increases by over two orders of magnitude and the phase transition occurs on a several picosecond timescale. In gallium arsenide, we observe high-field transport phenomena, including mobility saturation and impact ionization. The carrier density increases by up to ten orders of magnitude at high fields. At the highest fields, we demonstrate THz-induced damage in both vanadium dioxide and gallium arsenide.
Non-Linear Algebra and Bogolubov's Recursion
Morozov, A.; Serbyn, M.
2007-01-01
Numerous examples are given of application of Bogolubov's forest formula to iterative solutions of various non-linear equations: one and the same formula describes everything, from ordinary quadratic equation to renormalization in quantum field theory.
Stochastic effects on the nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Flessas, G P; Leach, P G L; Yannacopoulos, A N
2004-01-01
The aim of this article is to provide a brief review of recent advances in the field of stochastic effects on the nonlinear Schroedinger equation. The article reviews rigorous and perturbative results. (review article)
SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS
Desmal, Abdulla
2015-07-29
A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.
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.
A procedure to construct exact solutions of nonlinear evolution ...
Indian Academy of Sciences (India)
Exact solutions; the functional variable method; nonlinear wave equations. PACS Nos 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg. 1. Introduction. The theory of nonlinear dispersive and dissipative wave motion has recently undergone much research. Phenomena in physics and other fields are often described by nonlinear.
Nonlinearities in reservoir engineering: Enhancing quantum correlations
Hu, Xiangming; Hu, Qingping; Li, Lingchao; Huang, Chen; Rao, Shi
2017-12-01
There are two decisive factors for quantum correlations in reservoir engineering, but they are strongly reversely dependent on the atom-field nonlinearities. One is the squeezing parameter for the Bogoliubov modes-mediated collective interactions, while the other is the dissipative rates for the engineered collective dissipations. Exemplifying two-level atomic ensembles, we show that the moderate nonlinearities can compromise these two factors and thus enhance remarkably two-mode squeezing and entanglement of different spin atomic ensembles or different optical fields. This suggests that the moderate nonlinearities of the two-level systems are more advantageous for applications in quantum networks associated with reservoir engineering.
Experimental verification of transient nonlinear acoustical holography.
Jing, Yun; Cannata, Jonathan; Wang, Tianren
2013-05-01
This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm.
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...
Optimization for nonlinear inverse problem
International Nuclear Information System (INIS)
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
Gradiometer Based on Nonlinear Magneto-Optic Rotation, Phase I
National Aeronautics and Space Administration — This Phase I SBIR project will demonstrate sensitive measurements of magnetic field gradients by nonlinear atomic spectroscopy. The gradients are determined by...
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-06-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering
Natural Poisson structures of nonlinear plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
Hamiltonian field theories, for models of nonlinear plasma dynamics, require a Poisson bracket structure for functionals of the field variables. These are presented, applied, and derived for several sets of field variables: coherent waves, incoherent waves, particle distributions, and multifluid electrodynamics. Parametric coupling of waves and plasma yields concise expressions for ponderomotive effects (in kinetic and fluid models) and for induced scattering. (Auth.)
Study of nonlinear resonance effect in Paul trap.
Zhou, Xiaoyu; Xiong, Caiqiao; Zhang, Shuo; Zhang, Ning; Nie, Zongxiu
2013-05-01
In this article, we investigated the nonlinear resonance effect in the Paul trap with a superimposed hexapole field, which was assumed as a perturbation to the quadrupole field. On the basis of the Poincare-Lighthill-Kuo (PLK) perturbation method, ion motional equation, known as nonlinear Mathieu equation (NME) was expressed as the addition of approximation equations in terms of perturbation order. We discussed the frequency characteristics of ion axial-radial (z-r) coupled motion in the nonlinear field, derived the expressions of ion trajectories and nonlinear resonance conditions, and found that the mechanism of nonlinear resonance is similar to the normal resonance. The frequency spectrum of ion motion in nonlinear field includes not only the natural frequency series but also nonlinear introduced frequency series, which provide the driving force for the nonlinear resonance. The nonlinear field and the nonlinear effects are inevitable in practical ion trap experiments. Our method provides better understanding of these nonlinear effects and would be helpful for the instrumentation for ion trap mass spectrometers.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Mothersill, Carmel; Seymour, Colin
2012-07-01
Our recent data suggest there is a physical component to the bystander signal induced by radiation exposure and that alternative medicine techniques such as Reiki and acupuncture or exposures to weak EM fields alter the response of cells to direct irradiation and either altered bystander signal production or altered the response of cells receiving bystander signals. Our proposed mechanism to explain these findings is that perturbation of electromagnetic (EM) fields is central to the induction of low radiation dose responses especially non-targeted bystander effects. In this presentation we review the alternative medicine data and other data sets from our laboratory which test our hypothesis that perturbation of bio-fields will modulate radiation response in the low dose region. The other data sets include exposure to MRI, shielding using lead and or Faraday cages, the use of physical barriers to bystander signal transmission and the use of membrane channel blockers. The data taken together strongly suggest that EM field perturbation can modulate low dose response and that in fact the EM field rather than the targeted deposition of ionizing energy in the DNA may be the key determinant of dose response in a cell or organism The results also lead us to suspect that at least when chemical transmission is blocked, bystander signals can be transmitted by other means. Our recent experiments suggest light signals and volatiles are not likely. We conclude that alternative medicine and other techniques involving electromagnetic perturbations can modify the response of cells to low doses of ionizing radiation and can induce bystander effects similar to those seen in medium transfer experiments. In addition to the obvious implications for mechanistic studies of low dose effects, this could perhaps provide a novel target to exploit in space radiation protection and in optimizing therapeutic gain during radiotherapy.
L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control
Schaft, A.J. van der
1992-01-01
Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. Based upon these results a nonlinear analog
L@#2@#-gain analysis of nonlinear systems and nonlinear state feedback Hl control
van der Schaft, Arjan
1992-01-01
Previously obtained results on L2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear
Nonlinear elliptic differential equations with multivalued nonlinearities
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Nonlinear elliptic differential equations with multivalued ... has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth .... A is upper semicontinuous (as a set-valued map) from every finite dimensional subspace of X into ...
Perspectives on Nonlinear Filtering
Law, Kody
2015-01-07
The solution to the problem of nonlinear filtering may be given either as an estimate of the signal (and ideally some measure of concentration), or as a full posterior distribution. Similarly, one may evaluate the fidelity of the filter either by its ability to track the signal or its proximity to the posterior filtering distribution. Hence, the field enjoys a lively symbiosis between probability and control theory, and there are plenty of applications which benefit from algorithmic advances, from signal processing, to econometrics, to large-scale ocean, atmosphere, and climate modeling. This talk will survey some recent theoretical results involving accurate signal tracking with noise-free (degenerate) dynamics in high-dimensions (infinite, in principle, but say d between 103 and 108 , depending on the size of your application and your computer), and high-fidelity approximations of the filtering distribution in low dimensions (say d between 1 and several 10s).
On Poisson Nonlinear Transformations
Directory of Open Access Journals (Sweden)
Nasir Ganikhodjaev
2014-01-01
Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.
Nonlinear Microwave Optomechanics
Shevchuk, O.
2017-01-01
The nonlinearity is essential for creation of non-classical states of the cavity or mechanical resonator such as squeezed or cat states. A microwave cavity can be made nonlinear by, for instance, adding Josephson junctions. The mechanical resonator is inherently nonlinear. The radiation pressure
Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong
2015-01-01
This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.
Dynamics and vibrations progress in nonlinear analysis
Kachapi, Seyed Habibollah Hashemi
2014-01-01
Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding
Desmal, Abdulla
2015-04-13
A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.
Analytical study of a reversed-field pinch with rectangular cross section
International Nuclear Information System (INIS)
Zhang Peng
1990-01-01
An analyic solution of the force-free equation for a toroidal configuration of rectangular cross section is presented. It is shown that the critical value of contraction ratio for the appearance of a reversed field as well as of the ohmic current increases as the elongation of the cross section increases
Holographic paramagnetism–ferromagnetism phase transition with the nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Zhang, Cheng-Yuan; Wu, Ya-Bo, E-mail: ybwu61@163.com; Zhang, Ya-Nan; Wang, Huan-Yu; Wu, Meng-Meng
2017-01-15
In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism–ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born–Infeld nonlinear electrodynamics which has been presented in Ref. , we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.
Holographic paramagnetism–ferromagnetism phase transition with the nonlinear electrodynamics
Directory of Open Access Journals (Sweden)
Cheng-Yuan Zhang
2017-01-01
Full Text Available In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism–ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born–Infeld nonlinear electrodynamics which has been presented in Ref. [55], we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder form in the case without external field. Furthermore, the increase of nonlinear parameter b will result in extending the period of the external magnetic field. Especially, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noticeable.
Enhanced Nonlinear Effects in Metamaterials and Plasmonics
Directory of Open Access Journals (Sweden)
C. Argyropoulos
2012-07-01
Full Text Available In this paper we provide an overview of the anomalous and enhanced nonlinear effects available when optical nonlinear materials are combined inside plasmonic waveguide structures. Broad, bistable and all-optical switching responses are exhibited at the cut-off frequency of these waveguides, characterized by reduced Q-factor resonances. These phenomena are due to the large field enhancement obtained inside specific plasmonic gratings, which ensures a significant boosting of the nonlinear operation. Several exciting applications are proposed, which may potentially lead to new optical components and add to the optical nanocircuit paradigm.
Nonlinear single-spin spectrum analyzer.
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-15
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
Homogenized description and retrieval method of nonlinear metasurfaces
Liu, Xiaojun; Larouche, Stéphane; Smith, David R.
2018-03-01
A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry
Picosecond nonlinear optical properties of cuprous oxide with ...
Indian Academy of Sciences (India)
2014-02-08
Feb 8, 2014 ... various important applications in the field of material research. In brief, nanotechnology is one of the most active research areas which find useful applications in different fields of science. Intense research is also pursued to develop new nonlinear optical materials with high optical nonlinearities and fast ...
Fourth Order Nonlinear Intensity and the corresponding Refractive ...
African Journals Online (AJOL)
Nonlinear effects occur whenever the optical fields associated with one or more intense light such as from laser beams propagating in a crystal are large enough to produce polarization fields. This paper describes how the fourth order nonlinear intensity and the corresponding effective refractive index that is intensity ...
Nonlinear reconstruction of redshift space distortions
Zhu, Hong-Ming; Yu, Yu; Pen, Ue-Li
2018-02-01
We apply nonlinear reconstruction to the dark matter density field in redshift space and solve for the nonlinear mapping from the initial Lagrangian position to the final redshift space position. The reconstructed anisotropic field inferred from the nonlinear displacement correlates with the linear initial conditions to much smaller scales than the redshift space density field. The number of linear modes in the density field is improved by a factor of 30 - 40 after reconstruction. We thus expect this reconstruction approach to substantially expand the cosmological information including baryon acoustic oscillations and redshift space distortions for dense low-redshift large scale structure surveys including for example SDSS main sample, DESI BGS, and 21 cm intensity mapping surveys.
Nonlinear electromagnetic interactions in thermal QED
International Nuclear Information System (INIS)
Brandt, F.T.; Frenkel, J.
1995-01-01
We examine the behavior of the nonlinear interactions between electromagnetic fields at high temperature. It is shown that, in general, the ln(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T→∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action
PARTIAL ERUPTION OF A FILAMENT WITH TWISTING NON-UNIFORM FIELDS
International Nuclear Information System (INIS)
Bi, Yi; Jiang, Yunchun; Yang, Jiayan; Xiang, Yongyuan; Cai, Yunfang; Liu, Weiwei
2015-01-01
The eruption of a filament in a kinklike fashion is often regarded as a signature of kink instability. However, the kink instability threshold for the filament’s magnetic structure is not widely understood. Using Hα observations from the New Vacuum Solar Telescope, we present a partial eruptive filament. During the eruption, the filament thread appeared to split from its middle and to break out in a kinklike fashion. In this period, the remaining filament material stayed below and erupted without the kinking motion later on. The coronal magnetic field lines associated with the filament are obtained from nonlinear force-free field extrapolations using the twelve-minute-cadence vector magnetograms of the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory. We studied the extrapolated field lines passing through the magnetic dips which are in good agreement with the observed filament. The field lines are non-uniformly twisted and appear to be composed of two twisted flux ropes winding around each other. One of them has a higher twist than the other, and the flux rope with the higher twist has its dips aligned with the kinking eruptive thread at the beginning of its eruption. Before the eruption, moreover, the flux rope with the higher twist was found to expand with an approximately constant field twist. In addition, the helicity flux maps deduced from the HMI magnetograms show that some helicity is injected into the overlying magnetic arcade, but no significant helicity is injected into the flux ropes. Accordingly, we suggest that the highly twisted flux rope became kink unstable when the instability threshold declined with the expansion of the flux rope
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Stationary nonlinear Airy beams
International Nuclear Information System (INIS)
Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.
2011-01-01
We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Nonlinear optics at interfaces
International Nuclear Information System (INIS)
Chen, C.K.
1980-12-01
Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory
Nonlinear Interchange Modes in 3D
Bagaipo, Jupiter; Hassam, Adil
2012-10-01
We have shown previously that, in 2D, the ideal magnetohydrodynamic interchange mode stabilized by a constant transverse magnetic field is nonlinearly unstable if near marginal conditions. This study is extended to a 3D system where the mode is marginally stabilized by allowing for wavenumbers weakly transverse to an axial field. Two different boundary conditions are studied: periodic and line-tied in the axial direction. Periodic boundary conditions have applications in toroidal fusion devices while line-tied systems are common in the solar corona. We use reduced equations for a strong axial field to find an analytic solution as a function of the deviation from marginality. Using a systematic perturbation analysis we show that, to lowest order, there exists a secondary, quasistatic equilibrium with a critical field strength. Allowing for deviations from criticality yield a nonlinear time-evolution equation for the perturbation amplitude. The periodic case allows for two types of modes, and it is shown that the mode isomorphic to the earlier 2D problem is nonlinearly unstable, while the ``sausage''-type mode is nonlinearly stable. These modes are modes along a rational surface and ballooning type modes, respectively. The line-tied case is shown to always be nonlinearly stable.
Modelling Nonlinear Optics in the CERN SPS
Zimmermann, Frank; Faus-Golfe, A; Collier, Paul
2002-01-01
Nonlinear fields arising from eddy currents in the vac-uum chamber and remanent fields in the magnets of the CERN SPS vary with time and with the acceleration cycle. We describe a procedure of constructing a nonlinear op-tics model for the SPS, by considering sextupolar, octupo-lar, and decapolar field errors in the dipole and quadrupole magnets, respectively, whose strengths are adjusted so as to best reproduce the measured nonlinear chromaticities up to third order in the momentum deviation. Applying this procedure to SPS chromaticity measurements taken at 26 GeV/c, we have obtained a refined optics model. The tune shifts with the transverse amplitude predicted by this model are consistent with a direct measurement.
Saturation and stability of nonlinear photonic crystals
International Nuclear Information System (INIS)
Franco-Ortiz, M; Corella-Madueño, A; Rosas-Burgos, R A; Adrian Reyes, J; Avendaño, Carlos G
2017-01-01
We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions. (paper)
MAGNETIC FIELD RELAXATION AND CURRENT SHEETS IN AN IDEAL PLASMA
International Nuclear Information System (INIS)
Candelaresi, S.; Pontin, D. I.; Hornig, G.
2015-01-01
We investigate the existence of magnetohydrostatic equilibria for topologically complex magnetic fields. The approach employed is to perform ideal numerical relaxation experiments. We use a newly developed Lagrangian relaxation scheme that exactly preserves the magnetic field topology during the relaxation. Our configurations include both twisted and sheared fields, of which some fall into the category for which Parker predicted no force-free equilibrium. The first class of field considered contains no magnetic null points, and field lines connect between two perfectly conducting plates. In these cases, we observe only resolved current layers of finite thickness. In further numerical experiments, we confirm that magnetic null points are loci of singular currents
Nonlinear fractals: applications in physiology and ophthalmology
Directory of Open Access Journals (Sweden)
M. V. Zueva
2014-07-01
Full Text Available Fractal geometry and nonlinear dynamics have applications in the field of biology and medicine. Many complex structures of living systems reveal fractal-like geometry. Among them, nonlinearity of human anatomic structures and physiologic functions are of special interest. Here, we review several multidisciplinary studies that demonstrate multi-scale nonlinear complexity of physiological functions and fractal geometry of anatomical structures of a healthy human including retina. With ageing and diseases, these entities become simpler or more complex. Pathologic conditions contribute to highly periodic dynamics of processes that dominates on a time scale. Nonlinear dynamics application in ophthalmology and physiology of visual system can be promoted by the studies of fractal flickeringbackground and its impact on retina and visual cortex electrical activity. The next step will be the development of novel electrophysiological diagnostics and visual system impairment treatment
Design with Nonlinear Constraints
Tang, Chengcheng
2015-12-10
Most modern industrial and architectural designs need to satisfy the requirements of their targeted performance and respect the limitations of available fabrication technologies. At the same time, they should reflect the artistic considerations and personal taste of the designers, which cannot be simply formulated as optimization goals with single best solutions. This thesis aims at a general, flexible yet e cient computational framework for interactive creation, exploration and discovery of serviceable, constructible, and stylish designs. By formulating nonlinear engineering considerations as linear or quadratic expressions by introducing auxiliary variables, the constrained space could be e ciently accessed by the proposed algorithm Guided Projection, with the guidance of aesthetic formulations. The approach is introduced through applications in different scenarios, its effectiveness is demonstrated by examples that were difficult or even impossible to be computationally designed before. The first application is the design of meshes under both geometric and static constraints, including self-supporting polyhedral meshes that are not height fields. Then, with a formulation bridging mesh based and spline based representations, the application is extended to developable surfaces including origami with curved creases. Finally, general approaches to extend hard constraints and soft energies are discussed, followed by a concluding remark outlooking possible future studies.
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Lasers for nonlinear microscopy.
Wise, Frank
2013-03-01
Various versions of nonlinear microscopy are revolutionizing the life sciences, almost all of which are made possible because of the development of ultrafast lasers. In this article, the main properties and technical features of short-pulse lasers used in nonlinear microscopy are summarized. Recent research results on fiber lasers that will impact future instruments are also discussed.
High frequency non-linear electromagnetic excitation of sound in tungsten
International Nuclear Information System (INIS)
Korolyuk, A.P.; Khizhnyj, V.I.
1988-01-01
Nonlinear electromagnetic generation of the second harmonic of longitudinal sound was revealed under anomalous skin effect in tungsten. Nonmonotonous suppression of the effect of nonlinear sound generation was revealed in magnetic field, normal to the sample surface
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
Electromagnetic pulses at the boundary of a nonlinear plasma
International Nuclear Information System (INIS)
Satorius, E.H.
1975-01-01
An investigation was made of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collisionless, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma. Two cases are studied. First, the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered, i.e., a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma are considered. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found. In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found. (U.S.)
A nonlinear bounce kinetic equation for trapped electrons
International Nuclear Information System (INIS)
Gang, F.Y.
1990-03-01
A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
FIELD TOPOLOGY ANALYSIS OF A LONG-LASTING CORONAL SIGMOID
International Nuclear Information System (INIS)
Savcheva, A. S.; Van Ballegooijen, A. A.; DeLuca, E. E.
2012-01-01
We present the first field topology analysis based on nonlinear force-free field (NLFFF) models of a long-lasting coronal sigmoid observed in 2007 February with the X-Ray Telescope on Hinode. The NLFFF models are built with the flux rope insertion method and give the three-dimensional coronal magnetic field as constrained by observed coronal loop structures and photospheric magnetograms. Based on these models, we have computed horizontal maps of the current and the squashing factor Q for 25 different heights in the corona for all six days of the evolution of the region. We use the squashing factor to quantify the degree of change of the field line linkage and to identify prominent quasi-separatrix layers (QSLs). We discuss the major properties of these QSL maps and devise a way to pick out important QSLs since our calculation cannot reach high values of Q. The complexity in the QSL maps reflects the high degree of fragmentation of the photospheric field. We find main QSLs and current concentrations that outline the flux rope cavity and that become characteristically S-shaped during the evolution of the sigmoid. We note that, although intermittent bald patches exist along the length of the sigmoid during its whole evolution, the flux rope remains stable for several days. However, shortly after the topology of the field exhibits hyperbolic flux tubes (HFT) on February 7 and February 12 the sigmoid loses equilibrium and produces two B-class flares and associated coronal mass ejections (CMEs). The location of the most elevated part of the HFT in our model coincides with the inferred locations of the two flares. Therefore, we suggest that the presence of an HFT in a coronal magnetic configuration may be an indication that the system is ready to erupt. We offer a scenario in which magnetic reconnection at the HFT drives the system toward the marginally stable state. Once this state is reached, loss of equilibrium occurs via the torus instability, producing a CME.
Origin of soft limits from nonlinear supersymmetry in Volkov-Akulov theory
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata; Karlsson, Anna; Murli, Divyanshu [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94305 (United States)
2017-03-15
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
A search for integrable four-dimensional nonlinear accelerator lattices
Energy Technology Data Exchange (ETDEWEB)
Nagaitsev, S.; /Fermilab; Danilov, V.; /SNS Project, Oak Ridge
2010-05-01
Integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and/or electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents two examples of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.
Initial evolution of nonlinear magnetic islands in high temperature plasmas
International Nuclear Information System (INIS)
Kotschenreuther, M.
1988-06-01
The evolution of nonlinear magnetic islands is computed in the kinetic collisionality regime called the semicollisional regime, which is appropriate to present fusion confinement devices. Realistic effects are included, such as the presence of small external field errors, radial electric fields, and omega. When present simultaneously, these effects can greatly change the stability of small amplitude nonlinear islands. Islands with Δ' > O can sometimes be prevented from growing to macroscopic size; it is also possible to produce moderate mode-number nonlinear instabilities in the plasma edge. Furthermore, island growth can be prevented by application of external fields with suitably chosen amplitude and frequency
Hagedorn, Peter
1982-01-01
Thoroughly revised and updated, the second edition of this concise text provides an engineer's view of non-linear oscillations, explaining the most important phenomena and solution methods. Non-linear descriptions are important because under certain conditions there occur large deviations from the behaviors predicted by linear differential equations. In some cases, completely new phenomena arise that are not possible in purely linear systems. The theory of non-linear oscillations thus has important applications in classical mechanics, electronics, communications, biology, and many other branches of science. In addition to many other changes, this edition has a new section on bifurcation theory, including Hopf's theorem.
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Nonlinear Cyclotron absorption of a hole doppleron in cadmium
Energy Technology Data Exchange (ETDEWEB)
Voloshin, I.F.; Bugal' ter, G.A.; Demikhovskii, V.Y.; Fisher, L.M.; Yudin, V.A.
1977-10-01
We investigated experimentally the nonlinear behavior of the impedance of a cadmium plate in the region of existence of the hole doppleron. It is shown theoretically that this phenomenon can be attributed to nonlinear cyclotron absorption of the wave in the metal. A theory of nonlinear cyclotron absorption of a hole doppleron in cadmium is constructed. The nonlinearity is due to the influence of the wave magnetic field H that alters the trajectories of the resonant electrons responsible for the cyclotron asorption. The Lorentz force connected with the field H modulates the particle velocity along the magnetic field at a characteristic frequency ..omega../sub 0/ proportional to the square root of the wave amplitude. The modulation of the longitudinal particle velocity leads to violation of the condition of their resonant interaction with the wave, as a result of which the absorption coefficient decreases. The nonlinearity is significant when the frequency ..omega../sub 0/ is large compared with the electron-collision frequency. A decrease of the cyclotron absorption changes radically the picture of the surface-impedance oscillations of the plate in the magnetic field. We studied in the experiment the influence of the temperature, of the angle of inclination of the magnetic field, and of the frequency on the nonlinear-effect threshold field that separates the regions of linear and nonlinear behavior of the sample impedance. The measurement results are in qualitative agreement with the conclusions of the theory.
New analytical solutions for nonlinear physical models of the ...
Indian Academy of Sciences (India)
2016-10-18
Oct 18, 2016 ... Abstract. In this article, a variety of solitary wave solutions are found for some nonlinear equations. In math- ematical physics, we studied two complex systems, the Maccari system and the coupled Higgs field equation. We construct sufficient exact solutions for nonlinear evolution equations. To study ...
Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes
DEFF Research Database (Denmark)
Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan
2013-01-01
The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...
parametric nonlinear quasivariational inequalities
Directory of Open Access Journals (Sweden)
Zeqing Liu
2005-01-01
uniqueness results and sensitivity analysis of solutions are also established for the system of generalized nonlinear parametric quasivariational inequalities and some convergence results of iterative sequence generated by the algorithm with errors are proved.
DEFF Research Database (Denmark)
Nguyen-Duy, Khiem
and remains the prime source of energy in non-terrestrial applications such as those in sky-explorers. However, a renewable energy source is expensive, bulky, and its performance is weather dependent, which make testing of downstream converters very difficult. As a result, a nonlinear source emulator (NSE...... of a proposed NSE system with high dynamic performance. The goal of the work is to achieve a state-of-the art transient time of 10 µs. In order to produce the arbitrary nonlinear curve, the exponential function of a typical diode is used, but the diode can be replaced by other nonlinear curve reference...... simulation of nonlinear source systems with higher output power. In this work, a module will consist of two fundamental units: an isolated power supply and an NSE. The isolated power supply has to possess a very low circuit input-to-output capacitance (very low Cio) in order to reduce the effect...
2013-01-01
filter, Bayesian decision theory, Generalized Likelihood Ratio Test (GLRT), and constant false alarm rate ( CFAR ) processing (31). Once the...Abbreviations, and Acronyms CFAR constant false alarm rate CNR cognitive nonlinear radar EM electromagnetic FCC Federal Communications Comission
Nonlinear Optical Terahertz Technology
National Aeronautics and Space Administration — We develop a new approach to generation of THz radiation. Our method relies on mixing two optical frequency beams in a nonlinear crystalline Whispering Gallery Mode...
Nonlinear differential equations
Struble, Raimond A
2017-01-01
Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.
Nonlinear ambipolar diffusion waves
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T.; Rowlands, G.
1985-07-01
The evolution of a plasma perturbation in a neutral gas is considered using the ambipolar diffusion approximation. A nonlinear diffusion equation is derived and, in the one-dimensional case, exact solutions of shock type are obtained.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
Crossing a Nonlinear Resonance
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 9. Crossing a Nonlinear Resonance: Adiabatic Invariants and the Melnikov-Arnold Integral. Sudhir R Jain. General Article Volume 19 Issue 9 September 2014 pp 797-813 ...
Introduction to nonlinear science
Nicolis, G
1995-01-01
One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...
Spectral theory and nonlinear analysis with applications to spatial ecology
Cano-Casanova, S; Mora-Corral , C
2005-01-01
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.
Digital Communications Using Chaos and Nonlinear Dynamics
Larson, Lawrence E; Liu, Jia-Ming
2006-01-01
This book introduces readers to a new and exciting cross-disciplinary field of digital communications with chaos. This field was born around 15 years ago, when it was first demonstrated that nonlinear systems which produce complex non-periodic noise-like chaotic signals, can be synchronized and modulated to carry useful information. Thus, chaotic signals can be used instead of pseudo-random digital sequences for spread-spectrum and private communication applications. This deceptively simple idea spun hundreds of research papers, and many novel communication schemes based on chaotic signals have been proposed. However, only very recently researchers have begun to make a transition from academic studies toward practical implementation issues, and many "promising" schemes had to be discarded or re-formulated. This book describes the state of the art (both theoretical and experimental) of this novel field. The book is written by leading experts in the fields of Nonlinear Dynamics and Electrical Engineering who pa...
Nonlinear Multiantenna Detection Methods
Directory of Open Access Journals (Sweden)
Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Energy Technology Data Exchange (ETDEWEB)
Vemareddy, P. [Udaipur Solar Observatory, Physical Research Laboratory, Udaipur 313 001 (India); Wiegelmann, T., E-mail: vema@prl.res.in, E-mail: wiegelmann@mps.mpg.de [Max-Planck-Institut für Sonnensystemforschung, D-37077 Göttingen (Germany)
2014-09-01
We study the quasi-static evolution of coronal magnetic fields constructed from the non-linear force-free field (NLFFF) approximation aiming to understand the relation between the magnetic field topology and ribbon emission during an X1.5 flare in active region (AR) NOAA 11166. The flare with a quasi-elliptical and two remote ribbons occurred on 2011 March 9 at 23:13 UT over a positive flux region surrounded by negative flux at the center of the bipolar AR. Our analysis of the coronal magnetic structure with potential and NLFFF solutions unveiled the existence of a single magnetic null point associated with a fan-spine topology and is co-spatial with the hard X-ray source. The footpoints of the fan separatrix surface agree with the inner edge of the quasi-elliptical ribbon and the outer spine is linked to one of the remote ribbons. During the evolution, the slow footpoint motions stressed the field lines along the polarity inversion line and caused electric current layers in the corona around the fan separatrix surface. These current layers trigger magnetic reconnection as a consequence of dissipating currents, which are visible as cusp-shaped structures at lower heights. The reconnection process reorganized the magnetic field topology whose signatures are observed at the separatrices/quasi-separatrix layer structure in both the photosphere and the corona during the pre-to-post flare evolution. In agreement with previous numerical studies, our results suggest that the line-tied footpoint motions perturb the fan-spine system and cause null point reconnection, which eventually causes the flare emission at the footpoints of the field lines.
Atom lasers and nonlinear atom optics
International Nuclear Information System (INIS)
Deng Lu
2000-01-01
Two recent experimental breakthroughs in the field of atomic physics are reported: the realization of a well-collimated, widely tunable, quasi-continuous wave atom laser, and the generation of matter waves via coherent multi-wave mixing. The former is a critical step towards a continuous wave, high brightness atom laser while the latter has opened a new field of research: nonlinear atom optics
Nonlinear, tunable and active metamaterials
Lapine, Mikhail; Kivshar, Yuri
2015-01-01
Metamaterials, artificial electromagnetic media achieved by structuring on the subwave-length-scale were initially suggested for the negative index and superlensing. They became a paradigm for engineering electromagnetic space and controlling propagation of waves. The research agenda is now shifting on achieving tuneable, switchable, nonlinear and sensing functionalities. The time has come to talk about the emerging research field of metadevices employing active and tunable metamaterials with unique functionalities achieved by structuring of functional matter on the subwave-length scale. This book presents the first systematic and comprehensive summary of the reviews written by the pioneers and top-class experts in the field of metamaterials. It addresses many grand challenges of the cutting edge research for creating smaller and more efficient photonic structures and devices.
Fundamentals of nonlinear optical materials
Indian Academy of Sciences (India)
Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.
Hickman, J. E.; Palm, C.
2011-12-01
Over the last several decades, agricultural soils in many parts of sub-Saharan Africa have become depleted of nitrogen (N) and other nutrients, creating challenges to achieving food security in many countries. At only 7 kg N ha-1 yr-1, average fertilizer application rates in the region are an order of magnitude lower than typical rates in the United States, and well below optimal levels. Increased use of nutrient inputs is a centerpiece of most African Green Revolution strategies, making it important to quantify the impacts of this change in practices as farmers begin moving towards 50-80 kg N ha-1 yr-1. Increased N inputs are invariably accompanied by losses of trace N gases to the atmosphere, including the greenhouse gas nitrous oxide (N2O), and nitric oxide (NO), a precursor to tropospheric ozone pollution. Several investigations of greenhouse gas emissions and one investigation of NO emissions from sub-Saharan agricultural systems have been conducted over the last 20 years, but they are few in number and were not designed to identify potentially important thresholds in the response of trace gas emissions to fertilization rate. Here we examine the response function of NO and N2O emissions to 6 different levels of inorganic fertilizer additions in a maize field in Yala, Kenya during the 2011 long rainy season. We used a randomized complete block design incorporating inorganic fertilizer treatments of 0, 50, 75, 100, 150, and 200 kg N ha-1 in 4 blocks. After each of 2 fertilizer applications, we measured trace gas fluxes daily, and conducted weekly measurements until trace gas emissions subsided to control levels. We fit the data to linear and exponential models relating N gas emissions to N input levels, and conducted a model comparison using AIC. Preliminary analysis suggests that NO emissions do respond in a non-linear fashion over the course of 67 days, as has been found in several commercial agroecosystems for N2O. Although N2O emissions responded linearly
Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals
Ivancevic, Vladimir G
2008-01-01
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...
Advanced in Nonlinear Optics and Laser Research and Development
International Nuclear Information System (INIS)
Jackel, S.; Kotler, Z; Lavi, R.; Sternklar, S.
1996-01-01
The Nonlinear Optics Group (NLOG) at Soreq NRC is engaged in the development of fundamental and applied technology in the related fields of nonlinear optics and laser development. Our work in nonlinear optics started with the goal of improving laser performance. These efforts were successful and opened the way for R and D in nonlinear optics for other applications. Today we use nonlinear optics to enable continuous tunability of lasers, control the path of light beams, modulate a light signal rapidly, provide optical data storage, and supply new means of microscopically probing biological and inorganic samples. Technology maturation and interaction with users will show which aspects of nonlinear optics will make the most impact
Nonlinear Fabry-Perot filled with CS2 and nitrobenzene
International Nuclear Information System (INIS)
Bischofberger, T.; Shen, Y.R.
1979-01-01
We have studied the characteristics of nonlinear Fabry-Perot filled with Kerr liquids CS 2 and nitorbenzene and found excellent agreement between theory and experiment. The transient behavior due to cavity-field buildup is discussed
Network science, nonlinear science and infrastructure systems
2007-01-01
Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .
Nonlinear stage of Z-pinch instability
International Nuclear Information System (INIS)
Garanin, S.F.; Chernyshev, Yu.D.
1987-01-01
Nonlinear development of MHD instability of constriction type for Z-pinch with completely skinned current is considered. The two-dimensional numerical calculations of the constriction show that its development enters the stage described by automodel solution, when the constriction length is fixed and plasma compression takes place in an isentropic way. At the perturbation wave length small, as compared with pinch radius, the stage is preceded by a stage reduced to nonlinear Rayleigh-Taylor instability. For that case dynamics of the motion of magnetic field ''bubbles'' and plasma ''jets'' is considered. It is shown that plasma jets escaping from the pinch region do not close the pinch from current source
Advanced Research Workshop on Nonlinear Hyperbolic Problems
Serre, Denis; Raviart, Pierre-Arnaud
1987-01-01
The field of nonlinear hyperbolic problems has been expanding very fast over the past few years, and has applications - actual and potential - in aerodynamics, multifluid flows, combustion, detonics amongst other. The difficulties that arise in application are of theoretical as well as numerical nature. In fact, the papers in this volume of proceedings deal to a greater extent with theoretical problems emerging in the resolution of nonlinear hyperbolic systems than with numerical methods. The volume provides an excellent up-to-date review of the current research trends in this area.
Laser beam propagation in nonlinear optical media
Guha, Shekhar
2013-01-01
""This is very unique and promises to be an extremely useful guide to a host of workers in the field. They have given a generalized presentation likely to cover most if not all situations to be encountered in the laboratory, yet also highlight several specific examples that clearly illustrate the methods. They have provided an admirable contribution to the community. If someone makes their living by designing lasers, optical parametric oscillators or other devices employing nonlinear crystals, or designing experiments incorporating laser beam propagation through linear or nonlinear media, then
International Nuclear Information System (INIS)
Shen Yuanrang
2011-01-01
This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)
Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors
Schöll, Eckehard
2005-08-01
Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Nonlinear optical response in narrow graphene nanoribbons
Karimi, Farhad; Knezevic, Irena
We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.
Modeling of Local Magnetic Field Enhancements within Solar Flux Ropes
Romashets, E; Vandas, M; Poedts, Stefaan
2010-01-01
To model and study local magnetic-field enhancements in a solar flux rope we consider the magnetic field in its interior as a superposition of two linear (constant alpha) force-free magnetic-field distributions, viz. a global one, which is locally similar to a part of the cylinder, and a local torus-shaped magnetic distribution. The newly derived solution for a toroid with an aspect ratio close to unity is applied. The symmetry axis of the toroid and that of the cylinder may or may not coinci...
Probing nonlinear electrodynamics in slowly rotating spacetimes through neutrino astrophysics
Cuesta, Herman J. Mosquera; Lambiase, Gaetano; Pereira, Jonas P.
2017-01-01
Huge electromagnetic fields are known to be present during the late stages of the dynamics of supernovae. Thus, when dealing with electrodynamics in this context, the possibility may arise to probe nonlinear theories (generalizations of the Maxwellian electromagnetism). We firstly solve Einstein field equations minimally coupled to an arbitrary (current-free) nonlinear Lagrangian of electrodynamics (NLED) in the slow rotation regime $a\\ll M$ (black hole's mass), up to first order in $a/M$. We...
Nonlinear theory of electroelastic and magnetoelastic interactions
Dorfmann, Luis
2014-01-01
This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.
Nonlinear Optics with 2D Layered Materials.
Autere, Anton; Jussila, Henri; Dai, Yunyun; Wang, Yadong; Lipsanen, Harri; Sun, Zhipei
2018-03-25
2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Quantum Nonlinear Optics in Optomechanical Nanoscale Waveguides.
Zoubi, Hashem; Hammerer, Klemens
2017-09-22
We show that strong nonlinearities at the few photon level can be achieved in optomechanical nanoscale waveguides. We consider the propagation of photons in cm-scale one-dimensional nanophotonic structures where stimulated Brillouin scattering (SBS) is strongly enhanced by radiation pressure coupling. We introduce a configuration that allows slowing down photons by several orders of magnitude via SBS from sound waves using two pump fields. Slowly propagating photons can then experience strong nonlinear interactions through virtual off-resonant exchange of dispersionless phonons. As a benchmark we identify requirements for achieving a large cross-phase modulation among two counterpropagating photons applicable for photonic quantum gates. Our results indicate that strongly nonlinear quantum optics is possible in continuum optomechanical systems realized in nanophotonic structures.
Nonlinear (super)symmetries and amplitudes
Energy Technology Data Exchange (ETDEWEB)
Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)
2017-03-07
There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.
Nonlinear principal component analysis and its applications
Mori, Yuichi; Makino, Naomichi
2016-01-01
This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed...
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
Nonlinear dynamics and quantum chaos an introduction
Wimberger, Sandro
2014-01-01
The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.
Nonlinear control of magnetic signatures
Niemoczynski, Bogdan
Magnetic properties of ferrite structures are known to cause fluctuations in Earth's magnetic field around the object. These fluctuations are known as the object's magnetic signature and are unique based on the object's geometry and material. It is a common practice to neutralize magnetic signatures periodically after certain time intervals, however there is a growing interest to develop real time degaussing systems for various applications. Development of real time degaussing system is a challenging problem because of magnetic hysteresis and difficulties in measurement or estimation of near-field flux data. The goal of this research is to develop a real time feedback control system that can be used to minimize magnetic signatures for ferrite structures. Experimental work on controlling the magnetic signature of a cylindrical steel shell structure with a magnetic disturbance provided evidence that the control process substantially increased the interior magnetic flux. This means near field estimation using interior sensor data is likely to be inaccurate. Follow up numerical work for rectangular and cylindrical cross sections investigated variations in shell wall flux density under a variety of ambient excitation and applied disturbances. Results showed magnetic disturbances could corrupt interior sensor data and magnetic shielding due to the shell walls makes the interior very sensitive to noise. The magnetic flux inside the shell wall showed little variation due to inner disturbances and its high base value makes it less susceptible to noise. This research proceeds to describe a nonlinear controller to use the shell wall data as an input. A nonlinear plant model of magnetics is developed using a constant tau to represent domain rotation lag and a gain function k to describe the magnetic hysteresis curve for the shell wall. The model is justified by producing hysteresis curves for multiple materials, matching experimental data using a particle swarm algorithm, and
Finite-temperature Casimir effect in the presence of nonlinear dielectrics
DEFF Research Database (Denmark)
Kheirandish, Fardin; Amooghorban, Ehsan; Soltani, Morteza
2011-01-01
Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations to coupl......Starting from a Lagrangian, the electromagnetic field in the presence of a nonlinear dielectric medium is quantized using path-integral techniques, and correlation functions of different fields are calculated. The susceptibilities of the nonlinear medium are obtained, and their relations...
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Field theory of the Eulerian perfect fluid
Ariki, Taketo; Morales, Pablo A.
2018-01-01
The Eulerian perfect-fluid theory is reformulated from its action principle in a pure field-theoretic manner. Conservation of the convective current is no longer imposed by Lin’s constraints, but rather adopted as the central idea of the theory. Our formulation, for the first time, successfully reduces redundant degrees of freedom promoting one half of the Clebsch variables to true dynamical fields. Interactions on these fields allow for the exchange of the convective current of quantities such as mass and charge, which are uniformly understood as the breaking of the underlying symmetry of the force-free fluid. The Clebsch fields play the essential role of exchanging angular momentum with the force field producing vorticity.
Final report. [Nonlinear magnetohydrodynamics
International Nuclear Information System (INIS)
Montgomery, D.C.
1998-01-01
This is a final report on the research activities carried out under the above grant at Dartmouth. During the period considered, the grant was identified as being for nonlinear magnetohydrodynamics, considered as the most tractable theoretical framework in which the plasma problems associated with magnetic confinement of fusion plasmas could be studied. During the first part of the grant's lifetime, the author was associated with Los Alamos National Laboratory as a consultant and the work was motivated by the reversed-field pinch. Later, when that program was killed at Los Alamos, the problems became ones that could be motivated by their relation to tokamaks. Throughout the work, the interest was always on questions that were as fundamental as possible, compatible with those motivations. The intent was always to contribute to plasma physics as a science, as well as to the understanding of mission-oriented confined fusion plasmas. Twelve Ph.D. theses were supervised during this period and a comparable number of postdoctoral research associates were temporarily supported. Many of these have gone on to distinguished careers, though few have done so in the context of the controlled fusion program. Their work was a combination of theory and numerical computation, in gradually less and less idealized settings, moving from rectangular periodic boundary conditions in two dimensions, through periodic straight cylinders and eventually, before the grant was withdrawn, to toroids, with a gradually more prominent role for electrical and mechanical boundary conditions. The author never had access to a situation where he could initiate experiments and relate directly to the laboratory data he wanted. Computers were the laboratory. Most of the work was reported in referred publications in the open literature, copies of which were transmitted one by one to DOE at the time they appeared. The Appendix to this report is a bibliography of published work which was carried out under the
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
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...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...
Nonlinearity in nanomechanical cantilevers
DEFF Research Database (Denmark)
Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.
2013-01-01
predictions deviate strongly from our measurements for the nonlinearity of the fundamental flexural mode, which show a systematic dependence on aspect ratio (length/width) together with random scatter. This contrasts with the second mode, which is always found to be in good agreement with theory....... 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...
Nonlinear plasmonic imaging techniques and their biological applications
Deka, Gitanjal; Sun, Chi-Kuang; Fujita, Katsumasa; Chu, Shi-Wei
2017-01-01
Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics), as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.
Nonlinear plasmonic imaging techniques and their biological applications
Directory of Open Access Journals (Sweden)
Deka Gitanjal
2016-07-01
Full Text Available Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics, as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.
Propagation of nonlinear reactive contaminants in porous media
Serrano, Sergio E.
2003-08-01
A study on the effect of nonlinear reactions on the space and time distribution of contaminant plumes governed by the advective-dispersive equation in porous media was conducted. Several models of nonlinear reactions were considered: the irreversible nonlinear first-order kinetic sorption model, the nonlinear Freundlich sorption isotherm model, the nonlinear Langmuir sorption isotherm model, and the reversible nonlinear kinetic sorption model. Each of these models was coupled with the advective-dispersive equation with dimensionless concentration and an approximate analytical series solutions was obtained. Comparison between linear and nonlinear plumes indicated that nonlinear reactions may have a significant effect on the shape and spatial distribution of a contaminant at a given time and in certain cases may explain quantitatively the occurrence of scaled (e.g., concentration change while preserving shape), retarded, and nonsymmetric plumes as well as the presence of back tails and sharp front ends usually observed in the field. By adopting a nonlinear model of contaminant migration a more realistic representation of contaminant propagation is possible than that obtained with a linear model.
International Nuclear Information System (INIS)
Aly, J. J.; Amari, T.
2010-01-01
Janse and Low have most recently addressed the following question. Consider a cylindrical domain containing a simple topology potential magnetic field threading its lower and upper horizontal faces, and a perfectly conducting plasma. Suppose that this domain is made to slowly contract or expand in the vertical direction, so driving the field into a quasi-static evolution through a series of force-free configurations. Then are these configurations smooth, or do they contain current sheets (CSs)? We reexamine here their three-step argument leading to the conclusion that CSs form most generally. We prove analytically that the field has to evolve through 'topologically untwisted' and 'nonpotential' configurations, thus confirming the first two steps. However, we find the third step-leading to the conclusion that a smooth untwisted force-free field is necessarily potential-to be very disputable.
Nonlinear cyclotron absorption and stimulated scattering
International Nuclear Information System (INIS)
Chung, T.H.
1986-01-01
In electron cyclotron resonance heating (ECRH), wave sources heating a plasma linearly with respect to intensity; but as the intensity of ECRH gets larger, there might appear nonlinear effects that would result in cutoff of net absorption. This thesis uses quantum mechanical theory to derive a threshold microwave intensity for nonlinear absorption. The quantum mechanical theory estimates that the threshold microwave intensity for nonlinear absorption is about 10 5 watts/cm 2 for a microwave heating experiment (T/sub e/ = 100 ev, λ = 3,783 cm, B = 2.5 kG). This value seems large considering the present power capabilities of microwave sources (10 2 ∼ 10 3 watts/cm 2 ), but for a low temperature plasma, this threshold will go down. There is another nonlinear phenomenon called stimulated cyclotron scattering that enhances photon scattering by electrons gyrating in a magnetic field. This is expected to prevent incoming photons from arriving at the central region of the fusion plasma, where absorption mainly takes place. Theory based on a photon transport model predicts that the threshold intensity for the stimulated cyclotron scattering is about 10 4 watts/cm 2 for the plasma parameters mentioned above. This value seems large also, but a longer wavelength of microwaves and a larger magnitude magnetic field, which will be the case in reactor type facilities, will lower the threshold intensity to levels comparable with the currently developed microwave sources
Gorban, A. N.; Karlin, I. V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Nonlinear fractional relaxation
Indian Academy of Sciences (India)
Abstract. We define a nonlinear model for fractional relaxation phenomena. We use ε-expansion method to analyse this model. By studying the fundamental solutions of this model we find that when t → 0 the model exhibits a fast decay rate and when t → ∞ the model exhibits a power-law decay. By analysing the frequency ...
Directory of Open Access Journals (Sweden)
Jaydeep Jesur
2000-01-01
and features are added such a way that it can be also used for design of nonlinear control systems to achieve desired performance. It is very simple to learn this tool. One can easily use it with preliminary knowledge of DF and PPT methods.
Nonlinear collisionless magnetic reconnection
Ottaviani, M.; Porcelli, F.
1993-12-01
Collisionless magnetic reconnection in regimes where the mode structure is characterized by global convection cells is found to exhibit a quasiexplosive time behavior in the early nonlinear stage where the fluid displacement is smaller than the equilibrium scale length. This process is accompanied by the formation of a current density sublayer narrower than the skin depth. This sublayer keeps shrinking with time.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
Nonlinearity and disorder: Classification and stability of nonlinear impurity modes
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...
Fluctuating nonlinear hydrodynamics of flocking
Yadav, Sunil Kumar; Das, Shankar P.
2018-03-01
Starting from a microscopic model, the continuum field theoretic description of the dynamics of a system of active ingredients or "particles" is presented. The equations of motion for the respective collective densities of mass and momentum follow exactly from that of a single element in the flock. The single-particle dynamics has noise and anomalous momentum dependence in its frictional terms. The equations for the collective densities are averaged over a local equilibrium distribution to obtain the corresponding coarse grained equations of fluctuating nonlinear hydrodynamics (FNH). The latter are the equations used frequently for describing active systems on the basis of intuitive arguments. The transport coefficients which appear in the macroscopic FNH equations are determined in terms of the parameters of the microscopic dynamics.
Hidden acoustic information revealed by intentional nonlinearity
Dowling, David R.
2017-11-01
Acoustic waves are omnipresent in modern life and are well described by the linearized equations of fluid dynamics. Once generated, acoustic waves carry and collect information about their source and the environment through which they propagate, respectively, and this information may be retrieved by analyzing recordings of these waves. Because of this, acoustics is the primary means for observation, surveillance, reconnaissance, and remote sensing in otherwise opaque environments, such as the Earth's oceans and crust, and the interior of the human body. For such information-retrieval tasks, acoustic fields are nearly always interrogated within their recorded frequency range or bandwidth. However, this frequency-range restriction is not general; acoustic fields may also carry (hidden) information at frequencies outside their bandwidth. Although such a claim may seem counter intuitive, hidden acoustic-field information can be revealed by re-introducing a marquee trait of fluid dynamics: nonlinearity. In particular, an intentional quadratic nonlinearity - a form of intra-signal heterodyning - can be used to obtain acoustic field information at frequencies outside a recorded acoustic field's bandwidth. This quadratic nonlinearity enables a variety of acoustic remote sensing applications that were long thought to be impossible. In particular, it allows the detrimental effects of sparse recordings and random scattering to be suppressed when the original acoustic field has sufficient bandwidth. In this presentation, the topic is developed heuristically, with a just brief exposition of the relevant mathematics. Hidden acoustic field information is then revealed from simulated and measured acoustic fields in simple and complicated acoustic environments involving frequencies from a few Hertz to more than 100 kHz, and propagation distances from tens of centimeters to hundreds of kilometers. Sponsored by ONR, NAVSEA, and NSF.
Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging
Desmal, Abdulla
2016-03-01
Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using
Stochastic inflation and nonlinear gravity
International Nuclear Information System (INIS)
Salopek, D.S.; Bond, J.R.
1991-01-01
We show how nonlinear effects of the metric and scalar fields may be included in stochastic inflation. Our formalism can be applied to non-Gaussian fluctuation models for galaxy formation. Fluctuations with wavelengths larger than the horizon length are governed by a network of Langevin equations for the physical fields. Stochastic noise terms arise from quantum fluctuations that are assumed to become classical at horizon crossing and that then contribute to the background. Using Hamilton-Jacobi methods, we solve the Arnowitt-Deser-Misner constraint equations which allows us to separate the growing modes from the decaying ones in the drift phase following each stochastic impulse. We argue that the most reasonable choice of time hypersurfaces for the Langevin system during inflation is T=ln(Ha), where H and a are the local values of the Hubble parameter and the scale factor, since T is the natural time for evolving the short-wavelength scalar field fluctuations in an inhomogeneous background
Magnetic field reconnexion in a sheared field
International Nuclear Information System (INIS)
Ugai, M.
1981-01-01
A nonlinear development of the Petschek mode in a sheared magnetic field where there is a field component Bsub(z) along an X line is numerically studied. It is found that finite-amplitude intermediate waves, adjacent to the slow shock, may eventually stand in the quasi-steady configuration; on the other hand, the fundamental characteristics of the Petschek-mode development are scarcely influenced, either qualitatively or quantitatively, by the Bsub(z) field. (author)
On nonlinear Fourier transform: towards the nonlinear superposition
Saksida, Pavle
2017-01-01
In the paper we consider the nonlinear Fourier transform associated to the AKNSZS systems. In particular, we discuss the construction of the nonlinear Fourier modes of this transform by means of a perturbation scheme. The linearization of the AKNS-ZS nonlinear Fourier transform is the usual, linear Fourier transform and the linearization of a nonlinear Fourier mode of frequency d is the linear Fourier mode of the same frequency. We show that the first non-trivial term in the perturbation expression of any nonlinear Fourier mode is given by the dilogarithm function.
Nonlinearity, Conservation Law and Shocks
Indian Academy of Sciences (India)
Nonlinearity, Conservation Law and Shocks. Part I : Genuine Nonlinearity and Discontinuous Solutions. Phoolan Prasad is with the. Department of. Mathematics, Indian. Institute of Science and has been working in the area of nonlinear waves and hyperbolic partial differential equations. He is deeply interested in.
Terahertz Nonlinear Optics in Semiconductors
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.
2013-01-01
We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...... breathing of a single-cycle THz pulse in a semiconductor....
FRF decoupling of nonlinear systems
Kalaycıoğlu, Taner; Özgüven, H. Nevzat
2018-03-01
Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based o...
Nonlinear charge transport in bipolar semiconductors due to electron heating
Energy Technology Data Exchange (ETDEWEB)
Molina-Valdovinos, S., E-mail: sergiom@fisica.uaz.edu.mx [Universidad Autónoma de Zacatecas, Unidad Académica de Física, Calzada Solidaridad esq. Paseo, La Bufa s/n, CP 98060, Zacatecas, Zac, México (Mexico); Gurevich, Yu.G. [Centro de Investigación y de Estudios Avanzados del IPN, Departamento de Física, Av. IPN 2508, México D.F., CP 07360, México (Mexico)
2016-05-27
It is known that when strong electric field is applied to a semiconductor sample, the current voltage characteristic deviates from the linear response. In this letter, we propose a new point of view of nonlinearity in semiconductors which is associated with the electron temperature dependence on the recombination rate. The heating of the charge carriers breaks the balance between generation and recombination, giving rise to nonequilibrium charge carriers concentration and nonlinearity. - Highlights: • A new mechanism of nonlinearity of current-voltage characteristic (CVC) is proposed. • The hot electron temperature violates the equilibrium between electrons and holes. • This violation gives rise to nonequilibrium concentration of electrons and holes. • This leads to nonlinear CVC (along with the heating nonlinearity).
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Transfer and scattering of wave packets by a nonlinear trap.
Li, Kai; Kevrekidis, P G; Malomed, Boris A; Frantzeskakis, D J
2011-11-01
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers," as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "radiation." A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, which may be dragged by a nonlinear trap moving at a constant acceleration, are briefly considered too.
Non-linear conductivity in Coulomb glasses
Energy Technology Data Exchange (ETDEWEB)
Voje, A.; Bergli, J. [Department of Physics, University of Oslo, P. O. Box 1048 Blindern, 0316 Oslo (Norway); Ortuno, M.; Somoza, A.M. [Departamento de Fisica - CIOyN, Universidad de Murcia, Murcia 30.071 (Spain); Caravaca, M.
2009-12-15
We have studied the nonlinear conductivity of two-dimensional Coulomb glasses. We have used a Monte Carlo algorithm to simulate the dynamic of the system under an applied electric field E. We have compared results for two different models: a regular square lattice with only diagonal disorder and a random array of sites with diagonal and off-diagonal disorder. We have found that for moderate fields the logarithm of the conductivity is proportional to {radical}(E)/T{sup 2}, reproducing experimental results. We have also found that in the nonlinear regime the site occupancy in the Coulomb gap follows a Fermi-Dirac distribution with an effective temperature T{sub eff} higher than the phonon bath temperature T. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Progress in nonlinear nano-optics
Lienau, Christoph; Grunwald, Rüdiger
2015-01-01
This book presents the state of the art in nonlinear nanostructures for ultrafast laser applications. Most recent results in two emerging fields are presented: (i) generation of laser-induced nanostructures in materials like metals, metal oxides and semiconductors, and (ii) ultrafast excitation and energy transfer in nanoscale physical, chemical and hybrid systems. Particular emphasis is laid on the up-to-date controversially discussed mechanisms of sub-wavelength ripple formation including models of self-organized material transport and multiphoton excitation channels, nonlinear optics of plasmonic structures (nanotips, nanowires, 3D-metamaterials), and energy localization and transport on ultrafast time scale and spatial nanoscale. High-resolution spectroscopy, simulation and characterization techniques are reported. New applications of ultrashort-pulsed lasers for materials processing and the use of nanostructured materials for characterizing laser fields and laser-matter-interactions are discussed.
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Generalized nonlinear Proca equation and its free-particle solutions
Nobre, F. D.; Plastino, A. R.
2016-06-01
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schrödinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ ^{μ }(ěc {x},t), involves an additional field Φ ^{μ }(ěc {x},t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E2 = p2c2 + m2c4 for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed.
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)