Nonlinear Force-Free Field Extrapolation of NOAA AR 0696
NASA Astrophysics Data System (ADS)
Thalmann, J. K.; Wiegelmann, T.
2007-12-01
We investigate the 3D coronal magnetic field structure of NOAA AR 0696 in the period of November 09-11, 2004, before and after an X2.5 flare (occurring around 02:13 UT on November 10, 2004). The coronal magnetic field dominates the structure of the solar corona and consequently plays a key role for the understanding of the initiation of flares. The most accurate presently available method to derive the coronal magnetic field is currently the nonlinear force-free field extrapolation from measurements of the photospheric magnetic field vector. These vector-magnetograms were processed from stokes I, Q, U, and V measurements of the Big Bear Solar Observatory and extrapolated into the corona with the nonlinear force-free optimization code developed by Wiegelmann (2004). We analyze the corresponding time series of coronal equilibria regarding topology changes of the 3D coronal magnetic field during the flare. Furthermore, quantities such as the temporal evolution of the magnetic energy and helicity are computed.
Nonlinear force-free magnetic fields. [quasi-steady state evolution of astrophysical fields
NASA Technical Reports Server (NTRS)
Low, B. C.
1982-01-01
The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current.
On the numerical computation of nonlinear force-free magnetic fields. [from solar photosphere
NASA Technical Reports Server (NTRS)
Wu, S. T.; Sun, M. T.; Chang, H. M.; Hagyard, M. J.; Gary, G. A.
1990-01-01
An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from the photosphere, given the proper boundary conditions. This paper presents the results of this work, describing the mathematical formalism that was developed, the numerical techniques employed, and comments on the stability criteria and accuracy developed for these numerical schemes. An analytical solution is used for a benchmark test; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent (less than 5 percent). This newly developed scheme was applied to analyze a solar vector magnetogram, and the results were compared with the results deduced from the classical potential field method. The comparison shows that additional physical features of the vector magnetogram were revealed in the nonlinear force-free case.
On the numerical computation of nonlinear force-free magnetic fields
NASA Technical Reports Server (NTRS)
Wu, S. T.; Chang, H. M.; Hagyard, M. J.
1985-01-01
An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from a source surface, given the proper boundary conditions. The results of this work; describing the mathematical formalism that was developed, the numerical techniques employed, and the stability criteria developed for these numerical schemes are presented. An analytical solution is used for a test case; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent ( 5%).
Error analysis regarding the calculation of nonlinear force-free field
NASA Astrophysics Data System (ADS)
Liu, S.; Zhang, H. Q.; Su, J. T.
2012-02-01
Magnetic field extrapolation is an alternative method to study chromospheric and coronal magnetic fields. In this paper, two semi-analytical solutions of force-free fields (Low and Lou in Astrophys. J. 352:343, 1990) have been used to study the errors of nonlinear force-free (NLFF) fields based on force-free factor α. Three NLFF fields are extrapolated by approximate vertical integration (AVI) Song et al. (Astrophys. J. 649:1084, 2006), boundary integral equation (BIE) Yan and Sakurai (Sol. Phys. 195:89, 2000) and optimization (Opt.) Wiegelmann (Sol. Phys. 219:87, 2004) methods. Compared with the first semi-analytical field, it is found that the mean values of absolute relative standard deviations (RSD) of α along field lines are about 0.96-1.19, 0.63-1.07 and 0.43-0.72 for AVI, BIE and Opt. fields, respectively. While for the second semi-analytical field, they are about 0.80-1.02, 0.67-1.34 and 0.33-0.55 for AVI, BIE and Opt. fields, respectively. As for the analytical field, the calculation error of <| RSD|> is about 0.1˜0.2. It is also found that RSD does not apparently depend on the length of field line. These provide the basic estimation on the deviation of extrapolated field obtained by proposed methods from the real force-free field.
A NEW CODE FOR NONLINEAR FORCE-FREE FIELD EXTRAPOLATION OF THE GLOBAL CORONA
Jiang Chaowei; Feng Xueshang; Xiang Changqing
2012-08-10
Reliable measurements of the solar magnetic field are still restricted to the photosphere, and our present knowledge of the three-dimensional coronal magnetic field is largely based on extrapolations from photospheric magnetograms using physical models, e.g., the nonlinear force-free field (NLFFF) model that is usually adopted. Most of the currently available NLFFF codes have been developed with computational volume such as a Cartesian box or a spherical wedge, while a global full-sphere extrapolation is still under development. A high-performance global extrapolation code is in particular urgently needed considering that the Solar Dynamics Observatory can provide a full-disk magnetogram with resolution up to 4096 Multiplication-Sign 4096. In this work, we present a new parallelized code for global NLFFF extrapolation with the photosphere magnetogram as input. The method is based on the magnetohydrodynamics relaxation approach, the CESE-MHD numerical scheme, and a Yin-Yang spherical grid that is used to overcome the polar problems of the standard spherical grid. The code is validated by two full-sphere force-free solutions from Low and Lou's semi-analytic force-free field model. The code shows high accuracy and fast convergence, and can be ready for future practical application if combined with an adaptive mesh refinement technique.
Concerning the extrapolation of solar nonlinear force-free magnetic fields
NASA Technical Reports Server (NTRS)
Gary, G. Allen
1990-01-01
This paper contains a review and discussion of the mathematical basis of the extrapolation techniques involved in using photospheric vector magnetograms to obtain the coronal field above the surface. The two basic techniques employing the Cauchy initial value problem and the variational techniques are reviewed in terms of the mathematical and practical applications. A short review is presented of the current research on numerical modeling techniques in the area of extrapolating vector magnetograms; specifically, algorithms to extrapolate nonlinear force-free magnetic fields from the photosphere are considered.
NASA Technical Reports Server (NTRS)
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.
Study on Two Methods for Nonlinear Force-Free Extrapolation Based on Semi-Analytical Field
NASA Astrophysics Data System (ADS)
Liu, S.; Zhang, H. Q.; Su, J. T.; Song, M. T.
2011-03-01
In this paper, two semi-analytical solutions of force-free fields (Low and Lou, Astrophys. J. 352, 343, 1990) have been used to test two nonlinear force-free extrapolation methods. One is the boundary integral equation (BIE) method developed by Yan and Sakurai ( Solar Phys. 195, 89, 2000), and the other is the approximate vertical integration (AVI) method developed by Song et al. ( Astrophys. J. 649, 1084, 2006). Some improvements have been made to the AVI method to avoid the singular points in the process of calculation. It is found that the correlation coefficients between the first semi-analytical field and extrapolated field using the BIE method, and also that obtained by the improved AVI method, are greater than 90% below a height 10 of the 64×64 lower boundary. For the second semi-analytical field, these correlation coefficients are greater than 80% below the same relative height. Although differences between the semi-analytical solutions and the extrapolated fields exist for both the BIE and AVI methods, these two methods can give reliable results for heights of about 15% of the extent of the lower boundary.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
Lerche, I.; Low, B. C.
2014-10-15
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4/3 as
Inoue, S.; Magara, T.; Choe, G. S.; Kim, K. S.; Pandey, V. S.; Shiota, D.; Kusano, K.
2014-01-01
We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.
Nonlinear Force-Free Magnetic Field Modeling of AR 10953: A Critical Assessment
NASA Astrophysics Data System (ADS)
De Rosa, Marc L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; Amari, T.; Canou, A.; McTiernan, J. M.; Régnier, S.; Thalmann, J. K.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M. C. M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2009-05-01
Nonlinear force-free field (NLFFF) modeling seeks to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have failed to arrive at consistent solutions when applied to (thus far, two) cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not available). One issue is that NLFFF models require consistent, force-free vector magnetic boundary data, and vector magnetogram data sampling the photosphere do not satisfy this requirement. Consequently, several problems have arisen that are believed to affect such modeling efforts. We use AR 10953 to illustrate these problems, namely: (1) some of the far-reaching, current-carrying connections are exterior to the observational field of view, (2) the solution algorithms do not (yet) incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is needed to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
NONLINEAR FORCE-FREE MAGNETIC FIELD FITTING TO CORONAL LOOPS WITH AND WITHOUT STEREOSCOPY
Aschwanden, Markus J.
2013-02-15
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 {mu}{sub 2} = 2. Degree-Sign 7 {+-} 1. Degree-Sign 3 between the model field lines and observed loops, and an accuracy of Almost-Equal-To 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.
Magneto-frictional Modeling of Coronal Nonlinear Force-free Fields. II. Application to Observations
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.
2016-09-01
A magneto-frictional module has been implemented and tested in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) in the first paper of this series. Here, we apply the magneto-frictional method to observations to demonstrate its applicability in both Cartesian and spherical coordinates, and in uniform and block-adaptive octree grids. We first reconstruct a nonlinear force-free field (NLFFF) on a uniform grid of 1803 cells in Cartesian coordinates, with boundary conditions provided by the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) at 06:00 UT on 2010 November 11 in active region NOAA 11123. The reconstructed NLFFF successfully reproduces the sheared and twisted field lines and magnetic null points. Next, we adopt a three-level block-adaptive grid to model the same active region with a higher spatial resolution on the bottom boundary and a coarser treatment of regions higher up. The force-free and divergence-free metrics obtained are comparable to the run with a uniform grid, and the reconstructed field topology is also very similar. Finally, a group of active regions, including NOAA 11401, 11402, 11405, and 11407, observed at 03:00 UT on 2012 January 23 by SDO/HMI is modeled with a five-level block-adaptive grid in spherical coordinates, where we reach a local resolution of 0\\buildrel{\\circ}\\over{.} 06 pixel‑1 in an area of 790 Mm × 604 Mm. Local high spatial resolution and a large field of view in NLFFF modeling can be achieved simultaneously in parallel and block-adaptive magneto-frictional relaxations.
Magneto-frictional Modeling of Coronal Nonlinear Force-free Fields. II. Application to Observations
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.
2016-09-01
A magneto-frictional module has been implemented and tested in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC) in the first paper of this series. Here, we apply the magneto-frictional method to observations to demonstrate its applicability in both Cartesian and spherical coordinates, and in uniform and block-adaptive octree grids. We first reconstruct a nonlinear force-free field (NLFFF) on a uniform grid of 1803 cells in Cartesian coordinates, with boundary conditions provided by the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) at 06:00 UT on 2010 November 11 in active region NOAA 11123. The reconstructed NLFFF successfully reproduces the sheared and twisted field lines and magnetic null points. Next, we adopt a three-level block-adaptive grid to model the same active region with a higher spatial resolution on the bottom boundary and a coarser treatment of regions higher up. The force-free and divergence-free metrics obtained are comparable to the run with a uniform grid, and the reconstructed field topology is also very similar. Finally, a group of active regions, including NOAA 11401, 11402, 11405, and 11407, observed at 03:00 UT on 2012 January 23 by SDO/HMI is modeled with a five-level block-adaptive grid in spherical coordinates, where we reach a local resolution of 0\\buildrel{\\circ}\\over{.} 06 pixel-1 in an area of 790 Mm × 604 Mm. Local high spatial resolution and a large field of view in NLFFF modeling can be achieved simultaneously in parallel and block-adaptive magneto-frictional relaxations.
Nonlinear Force-Free Magnetic Field Modeling of the Solar Corona: A Critical Assessment
NASA Astrophysics Data System (ADS)
De Rosa, M. L.; Schrijver, C. J.; Barnes, G.; Leka, K. D.; Lites, B. W.; Aschwanden, M. J.; McTiernan, J. M.; Régnier, S.; Thalmann, J.; Valori, G.; Wheatland, M. S.; Wiegelmann, T.; Cheung, M.; Conlon, P. A.; Fuhrmann, M.; Inhester, B.; Tadesse, T.
2008-12-01
Nonlinear force-free field (NLFFF) modeling promises to provide accurate representations of the structure of the magnetic field above solar active regions, from which estimates of physical quantities of interest (e.g., free energy and helicity) can be made. However, the suite of NLFFF algorithms have so far failed to arrive at consistent solutions when applied to cases using the highest-available-resolution vector magnetogram data from Hinode/SOT-SP (in the region of the modeling area of interest) and line-of-sight magnetograms from SOHO/MDI (where vector data were not been available). It is our view that the lack of robust results indicates an endemic problem with the NLFFF modeling process, and that this process will likely continue to fail until (1) more of the far-reaching, current-carrying connections are within the observational field of view, (2) the solution algorithms incorporate the measurement uncertainties in the vector magnetogram data, and/or (3) a better way is found to account for the Lorentz forces within the layer between the photosphere and coronal base. In light of these issues, we conclude that it remains difficult to derive useful and significant estimates of physical quantities from NLFFF models.
Nonlinear force-free magnetic fields: Calculation and applicatin to astrophysics. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Yang, Wei-Hong
1987-01-01
The problem concerned in this work is that of calculating magnetic field configurations in which the Lorentz force (vector)j x (vector)B is everywhere zero, subject to specified boundary conditions. The magnetic field is represented in terms of Clebsch variables in the form (vector)B = del alpha x del beta. These variables are constant on any field line. The most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. It is proposed that the field lines move in the direction of local Lorentz force and relax towards a force-free field configuration. This concept leads to an iteration procedure for modifying the variables alpha and beta that tends asymptotically towards the force-free state. This method is first applied to a simple problem in two rectangular dimensions; the calculation shows that the convergence of magnetic field energy to a minimum state (force-free) is close to exponential. This method is then applied to study some astrophysical force-free magnetic fields, such as the structures and evolution of magnetic fields of rotating sunspots and accretion disks. The implication of the results, as related to the mechanisms of solar flares, extragalactic radio sources and radio jets, are discussed.
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.; Valori, G.
2016-09-01
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov-Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax-Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
NASA Astrophysics Data System (ADS)
Guo, Y.; Xia, C.; Keppens, R.; Valori, G.
2016-09-01
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov–Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax–Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
NASA Astrophysics Data System (ADS)
Inoue, S.; Hayashi, K.; Kusano, K.
2016-02-01
We analyze a three-dimensional (3D) magnetic structure and its stability in large solar active region (AR) 12192, using the 3D coronal magnetic field constructed under a nonlinear force-free field (NLFFF) approximation. In particular, we focus on the magnetic structure that produced an X3.1-class flare, which is one of the X-class flares observed in AR 12192. According to our analysis, the AR contains a multiple-flux-tube system, e.g., a large flux tube, with footpoints that are anchored to the large bipole field, under which other tubes exist close to a polarity inversion line (PIL). These various flux tubes of different sizes and shapes coexist there. In particular, the latter are embedded along the PIL, which produces a favorable shape for the tether-cutting reconnection and is related to the X-class solar flare. We further found that most of magnetic twists are not released even after the flare, which is consistent with the fact that no observational evidence for major eruptions was found. On the other hand, the upper part of the flux tube is beyond a critical decay index, essential for the excitation of torus instability before the flare, even though no coronal mass ejections were observed. We discuss the stability of the complicated flux tube system and suggest the reason for the existence of the stable flux tube. In addition, we further point out a possibility for tracing the shape of flare ribbons, on the basis of a detailed structural analysis of the NLFFF before a flare.
NASA Astrophysics Data System (ADS)
Jiang, Chaowei; Wu, S. T.; Feng, Xueshang; Hu, Qiang
2014-01-01
We present a comprehensive study of the formation and eruption of an active region (AR) sigmoid in AR 11283. To follow the quasi-static evolution of the coronal magnetic field, we reconstruct a time sequence of static fields using a recently developed nonlinear force-free field model constrained by vector magnetograms. A detailed analysis of the fields compared with observations suggests the following scenario for the evolution of the region. Initially, a new bipole emerges into the negative polarity of a preexisting bipolar AR, forming a null-point topology between the two flux systems. A weakly twisted flux rope (FR) is then built up slowly in the embedded core region, largely through flux cancellation, forming a bald patch separatrix surface (BPSS). The FR grows gradually until its axis runs into a torus instability (TI) domain, and the BPSS also develops a full S-shape. The combined effects of the TI-driven expansion of the FR and the line tying at the BP tear the FR into two parts with the upper portion freely expelled and the lower portion remaining behind the postflare arcades. This process dynamically perturbs the BPSS and results in the enhanced heating of the sigmoid and the rope. The accelerated expansion of the upper-portion rope strongly pushes its envelope flux near the null point and triggers breakout reconnection at the null, which further drives the eruption. We discuss the important implications of these results for the formation and disruption of the sigmoid region with an FR.
Jiang, Chaowei; Feng, Xueshang; Wu, S. T.; Hu, Qiang E-mail: fengx@spaceweather.ac.cn E-mail: qh0001@uah.edu
2014-01-01
We present a comprehensive study of the formation and eruption of an active region (AR) sigmoid in AR 11283. To follow the quasi-static evolution of the coronal magnetic field, we reconstruct a time sequence of static fields using a recently developed nonlinear force-free field model constrained by vector magnetograms. A detailed analysis of the fields compared with observations suggests the following scenario for the evolution of the region. Initially, a new bipole emerges into the negative polarity of a preexisting bipolar AR, forming a null-point topology between the two flux systems. A weakly twisted flux rope (FR) is then built up slowly in the embedded core region, largely through flux cancellation, forming a bald patch separatrix surface (BPSS). The FR grows gradually until its axis runs into a torus instability (TI) domain, and the BPSS also develops a full S-shape. The combined effects of the TI-driven expansion of the FR and the line tying at the BP tear the FR into two parts with the upper portion freely expelled and the lower portion remaining behind the postflare arcades. This process dynamically perturbs the BPSS and results in the enhanced heating of the sigmoid and the rope. The accelerated expansion of the upper-portion rope strongly pushes its envelope flux near the null point and triggers breakout reconnection at the null, which further drives the eruption. We discuss the important implications of these results for the formation and disruption of the sigmoid region with an FR.
Jing, Ju; Liu, Chang; Lee, Jeongwoo; Wang, Shuo; Xu, Yan; Wang, Haimin; Wiegelmann, Thomas
2014-03-20
Dynamic phenomena indicative of slipping reconnection and magnetic implosion were found in a time series of nonlinear force-free field (NLFFF) extrapolations for the active region 11515, which underwent significant changes in the photospheric fields and produced five C-class flares and one M-class flare over five hours on 2012 July 2. NLFFF extrapolation was performed for the uninterrupted 5 hour period from the 12 minute cadence vector magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. According to the time-dependent NLFFF model, there was an elongated, highly sheared magnetic flux rope structure that aligns well with an Hα filament. This long filament splits sideways into two shorter segments, which further separate from each other over time at a speed of 1-4 km s{sup –1}, much faster than that of the footpoint motion of the magnetic field. During the separation, the magnetic arcade arching over the initial flux rope significantly decreases in height from ∼4.5 Mm to less than 0.5 Mm. We discuss the reality of this modeled magnetic restructuring by relating it to the observations of the magnetic cancellation, flares, a filament eruption, a penumbra formation, and magnetic flows around the magnetic polarity inversion line.
Nonlinear Force-Free Field Modeling of a Three-Dimensional X-ray Sigmoid Observed on the Sun
NASA Astrophysics Data System (ADS)
Inoue, S.; Magara, T.; Watari, S.
2011-12-01
Three-dimensional (3D) structure of X-ray sigmoid has not been well understood in spite of many 2D observations obtained by satellites. Because a sigmoid is considered as a precursor causing huge solar flares, the 3D structure is a key issue to understand a trigger process for the solar flares. In this paper, we will report a 3D structure of an X-ray sigmoid of the solar active region NOAA 10930 using the Nonlinear Force-Free Field (NLFFF) modeling. Especially, we compare the X-ray emission with field-aligned current in the chromosphere and the twist of the magnetic field line estimated from the NLFFF. According to our analysis, the sigmoid is composed of field lines with a wide range of twist (0< |Tn| < 1.5) that satisfy a stable condition against Kink mode instability (|Tn| > 1.75 from Torok et al. 2004). The strong electric current is distributed on the strong X-ray intensity region corresponding to the central part of the sigmoid even though the twist of field lines is weak in this region. On the other hand, the highly twisted field lines with the weak X-ray emission occupy the outer region corresponding to elbow parts of sigmoid. The twist of these field lines is estimated as 0.75 < |Tn| < 1.5. This result is similar to the result obtained from a flux emergence simulation by Magara 2004. Magara 2004 showed that the weak twist occupies the central part of sigmoid. Our result supports a scenario that sigmoidal structure is formed by flux emergence.
NASA Astrophysics Data System (ADS)
Petrie, G. J. D.; Canou, A.; Amari, T.
2011-12-01
Between 24 March 2008 and 2 April 2008, the three active regions (ARs) NOAA 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliosphere Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer-belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.
2016-06-01
In this work we provide an updated description of the Vertical-Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) code, which is designed to measure the evolution of the potential, non-potential, free energies, and the dissipated magnetic energies during solar flares. This code provides a complementary and alternative method to existing traditional NLFFF codes. The chief advantages of the VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free photosphere in the magnetic field extrapolation method, the capability to minimize the misalignment angles between observed coronal loops (or chromospheric fibril structures) and theoretical model field lines, as well as computational speed. In performance tests of the VCA-NLFFF code, by comparing with the NLFFF code of Wiegelmann, we find agreement in the potential, non-potential, and free energy within a factor of ≲ 1.3, but the Wiegelmann code yields in the average a factor of 2 lower flare energies. The VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven twisting and untwisting of the magnetic field is an adequate model to quantify the storage of magnetic energies in active regions and their dissipation during flares. The VCA-NLFFF code is also publicly available in the Solar SoftWare.
Jiang, Chaowei; Wu, S. T.; Hu, Qiang; Feng, Xueshang E-mail: wus@uah.edu E-mail: fengx@spaceweather.ac.cn
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.
Chitta, L. P.; Kariyappa, R.; Van Ballegooijen, A. A.; DeLuca, E. E.; Solanki, S. K.
2014-10-01
In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet that continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory, and the Imaging Magnetograph eXperiment instrument on the Sunrise balloon-borne observatory, as time-dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce a time series of three-dimensional nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.
Cosmic Ray Acceleration in Force Free Fields
NASA Astrophysics Data System (ADS)
Colgate, Stirling; Li, Hui; Kronberg, Philipp
2002-11-01
Galactic, extragalactic, and cluster magnetic fields are in apparent pressure equilibrium with the in-fall pressure of matter from the external medium, IGM, onto the Galaxies and clusters, and from the voids onto the galaxy sheets, (walls), implying fields of 5 , 0.5, & 20 μG respectively. Equipartition or minimum energy, implies β_CR=n_CRm_pc^2/(B^2/8π)˜= 1. The total energy in field and CRs is then ˜= 10^55 ergs Galactic and ˜= 4 ot 10^60 ergs per galaxy in the IGM and less within clusters, e.g., radio lobes, synchrotron "glow" in the IGM (Kronberg), and the UHECRs spectrum, Γ =-2.6. CRs escape from the Galaxy to the IGM, τ˜=10^7y, and similarly from the walls to the voids, ˜=10^8y, less than the GZK cut-off time provided B_galaxy>B_IGM>B_voids. The free energy of black hole formation, The Los Alamos model, is just sufficient. The lack of shocks at the boundaries of over pressured radio lobes and the need for high acceleration efficiency suggests eE_allel˜= eη_reconJ_allel, acceleration by reconnection of these force-free fields.
On the resistive diffusion of force-free magnetic fields
NASA Technical Reports Server (NTRS)
Low, B. C.
1980-01-01
Reid and Laing (1979) conjectured on the general behavior of resistive force-free magnetic fields in a slab model following a numerical study. However, the basic properties of resistive force-free magnetic fields had been established previously. Some results from the previous work are extended to show that the conjecture of Reid and Laing is incorrect. A general analytic treatment of the problem provides the correct physical properties that Reid and Laing were unable to deduce from their numerical solutions. A criticism is also given of the results presented in another numerical study treating cylindrical resistive force-free magnetic fields, by the same authors.
Linear force-free fields in the lower corona
NASA Technical Reports Server (NTRS)
Barbosa, D. D.
1978-01-01
Boundary conditions are imposed on the normal component of B on two parallel planes which delineate the force-free volume of linear magnetic fields in low coronal levels of the solar atmosphere. Green's function is employed to ensure that equations for the magnetic field energy remain bounded and smooth. Field line tracings of a simple bipolar source distribution are developed and compared with empirical data obtained from visual observations in H(alpha), EUV, and X-rays.
Magnetic clouds and force-free fields with constant alpha
NASA Technical Reports Server (NTRS)
Burlaga, L. F.
1988-01-01
Magnetic clouds observed at 1 AU are modeled as cylindrically symmetric, constant alpha force-free magnetic fields. The model satisfactorily explains the types of variations of the magnetic field direction that are observed as a magnetic cloud moves past a spacecraft in terms of the possible orientations of the axis of a magnetic cloud. The model also explains why the magnetic field strength is observed to be higher inside a magnetic cloud than near its boundaries. However, the model predicts that the magnetic field strength profile should be symmetric with respect to the axis of the magnetic cloud, whereas observations show that this is not generally the case.
Energy buildup in sheared force-free magnetic fields
NASA Technical Reports Server (NTRS)
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.
Force-free fields in thin coronal loops
NASA Technical Reports Server (NTRS)
Emslie, A. Gordon; Wilkinson, L. K.
1994-01-01
We solve the force-free equation J x B = 0 for fields which are toroidally symmetric. The technique utilizes an expansion about a cylindrical field and is therefore valid or tori with a large aspect ratio such as long, thin, coronal loops. The calculation is performed in spatial toroidal coordinates, rather than in the flux coordinates used by previous authors; this allows direct calculation of the loci of flux surfaces and of surfaces of constant magnetic pressure. Our solutions differ significantly from toroidal fields in laboratories, which are in general not force-free. They are characterized by field lines whose projections in the poloidal planes are circles with centers displaced by varying distances from the axis of the torus. In general, flux surfaces do not correspond to surfaces of constant magnetic pressure. We have examined solutions corresponding to simple analytic zero-order cylindrical fields. For moderate twists in the zero-order (cylindrical) field, the magnetic pressure is larger on the inner toroidal radius. However, this effect diminishes with twist angle and in fact, for extreme initial twists, the magnetic pressure can be larger on the outer radius. We compare our results with previous work utilizing flux coordinates.
ON THE FORCE-FREE NATURE OF PHOTOSPHERIC SUNSPOT MAGNETIC FIELDS AS OBSERVED FROM HINODE (SOT/SP)
Tiwari, Sanjiv Kumar
2012-01-01
A magnetic field is force-free if there is no interaction between it and the plasma in the surrounding atmosphere, i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of various magnetic parameters, such as magnetic energy (using the virial theorem), gradient of twist of sunspot magnetic fields (computed from the force-free parameter {alpha}), and any kind of extrapolation, heavily hinges on the force-free approximation of the photospheric sunspot magnetic fields. Thus, it is of vital importance to inspect the force-free behavior of sunspot magnetic fields. The force-free nature of sunspot magnetic fields has been examined earlier by some researchers, ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. For this purpose, we use several vector magnetograms of high spatial resolution obtained from the Solar Optical Telescope/Spectro-Polarimeter on board Hinode. Both the necessary and sufficient conditions for force-free nature are examined by checking the global and local nature of equilibrium magnetic forces over sunspots. We find that sunspot magnetic fields are not very far from the force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free field behavior. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we do not find a systematic relationship between the nature of sunspot magnetic fields and the associated flare activity. Further, we examine whether the fields at the photosphere follow linear or nonlinear force-free conditions. After examining this in various complex and simple sunspots, we conclude that
Non-force-free solar magnetic fields in magnetohydrostatic equilibrium
NASA Technical Reports Server (NTRS)
Comfort, R. H.; Tandberg-Hanssen, E.; Wu, S. T.
1979-01-01
The objective of the paper is to examine a class of non-force-free fields analytically. Specifically, magnetic fields in magnetohydrostatic equilibrium with a plasma in a gravitational field are treated in an approximation of two independent variables but three vector components. Spherical coordinates are emphasized, although the formal results for cylindrical and Cartesian coordinates are presented in the appendices. Formal solutions for the magnetic-field components are obtained in terms of the plasma variables, and field line equations are derived. A final equation governing the plasma variables is then obtained. Procedures are developed for analyzing this equation and obtaining sets of self-consistent particular solutions to the governing equations; a number of such sets of solutions are presented. As an example, one solution set is examined, illustrating the application of the results to the analysis of solar observational data.
Force-free magnetic fields - Generating functions and footpoint displacements
NASA Technical Reports Server (NTRS)
Wolfson, Richard; Verma, Ritu
1991-01-01
This paper presents analytic and numerical calculations that explore equilibrium sequences of bipolar force-free magnetic fields in relation to displacments of their magnetic footpoints. It is shown that the appearance of magnetic islands - sometimes interpreted as marking the loss of equilibrium in models of the solar atmosphere - is likely associated only with physically unrealistic footpoint displacements such as infinite separation or 'tearing' of the model photosphere. The work suggests that the loss of equilibrium in bipolar configurations, sometimes proposed as a mechanism for eruptive solar events, probably requires either fully three-dimensional field configurations or nonzero plasma pressure. The results apply only to fields that are strictly bipolar, and do not rule out equilibrium loss in more complex structures such as quadrupolar fields.
Force-free magnetic fields - The magneto-frictional method
NASA Technical Reports Server (NTRS)
Yang, W. H.; Sturrock, P. A.; Antiochos, S. K.
1986-01-01
The problem under discussion is that of calculating magnetic field configurations in which the Lorentz force j x B is everywhere zero, subject to specified boundary conditions. We choose to represent the magnetic field in terms of Clebsch variables in the form B = grad alpha x grad beta. These variables are constant on any field line so that each field line is labeled by the corresponding values of alpha and beta. When the field is described in this way, the most appropriate choice of boundary conditions is to specify the values of alpha and beta on the bounding surface. We show that such field configurations may be calculated by a magneto-frictional method. We imagine that the field lines move through a stationary medium, and that each element of magnetic field is subject to a frictional force parallel to and opposing the velocity of the field line. This concept leads to an iteration procedure for modifying the variables alpha and beta, that tends asymptotically towards the force-free state. We apply the method first to a simple problem in two rectangular dimensions, and then to a problem of cylindrical symmetry that was previously discussed by Barnes and Sturrock (1972). In one important respect, our new results differ from the earlier results of Barnes and Sturrock, and we conclude that the earlier article was in error.
Linear force-free magnetic fields for solar extrapolation and interpretation
NASA Technical Reports Server (NTRS)
Gary, G. Allen
1989-01-01
This paper discusses the interconnection of the various linear force-free magnetic field formulations, the specific phenomenological and topological parameters of these formulations, and their usefulness. Particularly, the limitations and usefulness of linear force-free fields are discussed. Specific field configurations are related to magnetographic interpretation. The relationship of the integral and Fourier procedures is shown explicitly. The physical interpretation of linear force-free fields is shown by analytic models and from the Marshall Space Flight Center solar vector magnetograms.
NASA Astrophysics Data System (ADS)
Liu, Suo; Zhang, Hongqi; Su, Jiangtao; Song, Mutao
2013-07-01
In this paper, the availability, applicability and deviation of nonlinear force-free (NLFF) fields extrapolated by Approximate Vertical Integration (AVI), Boundary Integral Equation (BIE) and Optimization (Opt.) methods are studied based on the comparison with two semi-analytical fields (Low & Lou 1990). These NLFF extrapolations based on the observational vector magnetograms are used to study the spatial magnetic field in the quiet Sun.
Topological constraints and the existence of force-free fields
NASA Technical Reports Server (NTRS)
Antiochos, S. K.
1986-01-01
A fundamental problem in plasma theory is the question of the existence of MHD equilibria. The issue of topological constraints is of crucial importance for the problem of the existence of equilibria. Heuristic methods are used to discuss the coronal wrapping pattern. It is concluded that for a given set of footpoint positions the wrapping pattern in the corona is completely fixed. The topological constraints are included in the boundary conditions on the Euler potentials and impost no additional restrictions on possible equilibria. Although this does not prove that equilibria always exist, it does show that the force-free problem is not overdetermined and that existence of equilibria is still an open question.
The exterior source surface for force-free fields. [solar atmosphere magnetic field model
NASA Technical Reports Server (NTRS)
Barbosa, D. D.
1978-01-01
Consideration is given to the exterior source surface for force-free fields. The spherical harmonic expansion is presented for boundary values on two concentric spheres. An upper limit on a constant which measures the strength of coronal currents is found to be a function of the lowest multipole moment of the prescribed boundary values. The solar atmosphere is in the class of magnetic fields for which the study is applicable.
MAGNETIC HELICITY OF SELF-SIMILAR AXISYMMETRIC FORCE-FREE FIELDS
Zhang Mei; Flyer, Natasha; Low, Boon Chye
2012-08-10
In this paper, we continue our theoretical studies addressing the possible consequences of magnetic helicity accumulation in the solar corona. Our previous studies suggest that coronal mass ejections (CMEs) are natural products of coronal evolution as a consequence of magnetic helicity accumulation and that the triggering of CMEs by surface processes such as flux emergence also have their origin in magnetic helicity accumulation. Here, we use the same mathematical approach to study the magnetic helicity of axisymmetric power-law force-free fields but focus on a family whose surface flux distributions are defined by self-similar force-free fields. The semi-analytical solutions of the axisymmetric self-similar force-free fields enable us to discuss the properties of force-free fields possessing a huge amount of accumulated magnetic helicity. Our study suggests that there may be an absolute upper bound on the total magnetic helicity of all bipolar axisymmetric force-free fields. With the increase of accumulated magnetic helicity, the force-free field approaches being fully opened up with Parker-spiral-like structures present around a current-sheet layer as evidence of magnetic helicity in the interplanetary space. It is also found that among the axisymmetric force-free fields having the same boundary flux distribution, the one that is self-similar is the one possessing the maximum amount of total magnetic helicity. This gives a possible physical reason why self-similar fields are often found in astrophysical bodies, where magnetic helicity accumulation is presumably also taking place.
Global constant-alpha force-free magnetic fields and coronal structures
NASA Technical Reports Server (NTRS)
Nakagawa, Y.; Wu, S. T.; Tandberg-Hanssen, E.
1978-01-01
Nakagawa's (1973) general formulation of constant-alpha global force-free magnetic fields is used to examine the topological characteristics of axisymmetric constant-alpha fields with specific reference to solar EUV, XUV, and X-ray structures observed from Skylab. The theoretical formulation is briefly summarized, and topological characteristics of the field lines are analyzed. The results are compared with X-ray observations of a large coronal arch and white-light observations of a coronal transient. It is concluded that global-scale force-free magnetic fields are present in the solar atmosphere and that their topological characteristics differ significantly from those of potential fields.
Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland, M. S.; Gilchrist, S. A.
2012-09-10
At present, many models of the coronal magnetic field rely on photospheric vector magnetograms, but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that is not at present used as constraints in the computational domain, directly influencing the evolution of the model. This is in part due to the mathematical complications of incorporating such input into numerical models. Projection effects, confusion due to overlapping loops (the coronal plasma is optically thin), and the limited number of usable loops further complicate the use of information from coronal images. We develop and test a new algorithm to use images of coronal loops in the modeling of the solar coronal magnetic field. We first fit projected field lines with those of constant-{alpha} force-free fields to approximate the three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like iterative technique, which uses these trajectories as volume constraints on the values of {alpha}, to obtain a volume-filling nonlinear force-free model of the magnetic field, modifying a code and method presented by Wheatland. We thoroughly test the technique on known analytical and solar-like model magnetic fields previously used for comparing different extrapolation techniques and compare the results with those obtained by currently available methods relying only on the photospheric data. We conclude that we have developed a functioning method of modeling the coronal magnetic field by combining the line-of-sight component of the photospheric magnetic field with information from coronal images. Whereas we focus on the use of coronal loop information in combination with line-of-sight magnetograms, the method is readily extended to
Asymptotic analysis of force-free magnetic fields of cylindrical symmetry
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Roumeliotis, G.
1995-01-01
It is known from computer calculations that if a force-free magnetic-field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution, and, in the process, the energy of the field increases progressively. Analysis of a simple model of force-free fields of cylindrical symmetry leads to simple asymptotic expressions for the extent and energy of such a configuration. The analysis is carried through for both spherical and planar source surfaces. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T.
2013-05-20
Photospheric magnetic vector maps from two different instruments are used to model the nonlinear force-free coronal magnetic field above an active region. We use vector maps inferred from polarization measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI) and the Solar Optical Telescope's Spectropolarimeter (SP) on board Hinode. Besides basing our model calculations on HMI data, we use both SP data of original resolution and scaled down to the resolution of HMI. This allows us to compare the model results based on data from different instruments and to investigate how a binning of high-resolution data affects the model outcome. The resulting three-dimensional magnetic fields are compared in terms of magnetic energy content and magnetic topology. We find stronger magnetic fields in the SP data, translating into a higher total magnetic energy of the SP models. The net Lorentz forces of the HMI and SP lower boundaries verify their force-free compatibility. We find substantial differences in the absolute estimates of the magnetic field energy but similar relative estimates, e.g., the fraction of excess energy and of the flux shared by distinct areas. The location and extension of neighboring connectivity domains differ and the SP model fields tend to be higher and more vertical. Hence, conclusions about the magnetic connectivity based on force-free field models are to be drawn with caution. We find that the deviations of the model solution when based on the lower-resolution SP data are small compared to the differences of the solutions based on data from different instruments.
NASA Technical Reports Server (NTRS)
Sheeley, N. R., Jr.; Harvey, J. W.
1975-01-01
This paper presents particularly simple mathematical formulas for the calculation of force-free fields of constant alpha from the distribution of discrete sources on a flat surface. The advantage of these formulas lies in their physical simplicity and the fact that they can be easily used in practice to calculate the fields. The disadvantage is that they are limited to fields of 'sufficiently small alpha'. These formulas may be useful in the study of chromospheric magnetic fields by the comparison of high-resolution H-alpha photographs and photospheric magnetograms.
On some properties of force-free magnetic fields in infinite regions of space
NASA Technical Reports Server (NTRS)
Aly, J. J.
1984-01-01
Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.
Temporal and Spatial Relationship of Flare Signatures and the Force-free Coronal Magnetic Field
NASA Astrophysics Data System (ADS)
Thalmann, J. K.; Veronig, A.; Su, Y.
2016-08-01
We investigate the plasma and magnetic environment of active region NOAA 11261 on 2011 August 2 around a GOES M1.4 flare/CME (SOL2011-08-02T06:19). We compare coronal emission at the (extreme) ultraviolet and X-ray wavelengths, using SDO AIA and RHESSI images, in order to identify the relative timing and locations of reconnection-related sources. We trace flare ribbon signatures at ultraviolet wavelengths in order to pin down the intersection of previously reconnected flaring loops in the lower solar atmosphere. These locations are used to calculate field lines from three-dimensional (3D) nonlinear force-free magnetic field models, established on the basis of SDO HMI photospheric vector magnetic field maps. Using this procedure, we analyze the quasi-static time evolution of the coronal model magnetic field previously involved in magnetic reconnection. This allows us, for the first time, to estimate the elevation speed of the current sheet’s lower tip during an on-disk observed flare as a few kilometers per second. A comparison to post-flare loops observed later above the limb in STEREO EUVI images supports this velocity estimate. Furthermore, we provide evidence for an implosion of parts of the flaring coronal model magnetic field, and identify the corresponding coronal sub-volumes associated with the loss of magnetic energy. Finally, we spatially relate the build up of magnetic energy in the 3D models to highly sheared fields, established due to the dynamic relative motions of polarity patches within the active region.
The stability properties of cylindrical force-free fields - Effect of an external potential field
NASA Technical Reports Server (NTRS)
Chiuderi, C.; Einaudi, G.; Ma, S. S.; Van Hoven, G.
1980-01-01
A large-scale potential field with an embedded smaller-scale force-free structure gradient x B equals alpha B is studied in cylindrical geometry. Cases in which alpha goes continuously from a constant value alpha 0 on the axis to zero at large r are considered. Such a choice of alpha (r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of k space are calculated, showing time-scales much shorter than the resistive decay time.
A long-lived coronal X-ray arcade. [force-free magnetic field analysis
NASA Technical Reports Server (NTRS)
Mcguire, J. P.; Tandberg-Hanssen, E.; Krall, K. R.; Wu, S. T.; Smith, J. B., Jr.; Speich, D. M.
1977-01-01
A large, long-lived, soft X-ray emitting arch system observed during a Skylab mission is analyzed. The supposition is that these arches owe their stability to the stable coronal magnetic-field configuration. A global constant alpha force-free magnetic field analysis, is used to describe the arches which stayed in the same approximate position for several solar rotations. A marked resemblance is noted between the theoretical magnetic field configuration and the observed X-ray emmitting feature.
Quasi-static evolution of sheared force-free fields and the solar flare problem
NASA Technical Reports Server (NTRS)
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.
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Antiochos, S. K.; Klinchuk, J. A.; Roumeliotis, G.
1994-01-01
It is known from computer calculations that if a force-free magnetic field configuration is stressed progressively by footpoint displacements, the configuration expands and approaches the open configuration with the same surface flux distribution and the energy of the field increases progressively. For configurations of translationalsymmetry, it has been found empirically that the energy tends asymptotically to a certain functional form. It is here shown that analysis of a simple model of the asymptotic form of force-free fields of translational symmetry leads to and therefore justifies this functional form. According to this model, the field evolves in a well-behaved manner with no indication of instability or loss of equilibrium.
Dilation of force-free magnetic flux tubes. [solar magnetic field profiles
NASA Technical Reports Server (NTRS)
Frankenthal, S.
1977-01-01
A general study is presented of the mapping functions which relate the magnetic-field profiles across a force-free rope in segments subjected to various external pressures. The results reveal that if the external pressure falls below a certain critical level (dependent on the flux-current relation which defines the tube), the magnetic profile consists of an invariant core sheathed in a layer permeated by an azimuthal magnetic field.
Turbulent relaxation to a force-free field-reversed state
NASA Technical Reports Server (NTRS)
Dahlburg, J. P.; Montgomery, D.; Doolen, G. D.; Turner, L.
1986-01-01
The evolution of nonequilibrium initial conditions of an incompressible magnetohydrodynamic Z pinch is described by a three-dimensional, pseudospectral numerical code. Magnetohydrodynamic turbulence develops in the resistive, nonviscous magnetofluid, resulting in the selective decay of the energy relative to the magnetic helicity, at Lundquist numbers of only a few hundred. An interior force-free region grows with time and achieves spontaneous reversal of the toroidal magnetic field at the wall, without the necessity of an external electric field.
NASA Technical Reports Server (NTRS)
Low, B. C.
1980-01-01
The paper considers whether a neighboring magnetostatic equilibrium exists to allow a magnetic field initially in a force-free configuration to accommodate any imposed weak pressure. The following problem is treated. The foot points of the field are fixed and the plasma is frozen into the field lines under the approximation of infinite electrical conductivity. A weak pressure is introduced. It is determined infinitesimal plasma displacements exist to adjust the field lines to a new equilibrium without changing the field line connectivity. The analysis is carried out for the bipolar force-free fields forming one of two evolutionary sequences modeling the development of the preflare stage. It was found that for the force-free field corresponding to the quasi-static stage of evolution, the neighboring magnetostatic equilibrium always exists and the imposed gas pressure can be accommodated with a slight departure of the field from being exactly force free.
Force-free magnetic fields - Is there a 'loss of equilibrium'?
NASA Technical Reports Server (NTRS)
Klimchuk, J. A.; Sturrock, P. A.
1989-01-01
This paper examines concept in solar physics that is known as loss of equilibrium in which a sequence of force-free magnetic fields, said to represent a possible quasi-static evolution of solar magnetic fields, reaches a critical configuration beyond which no acceptable solution of the prescribed form exists. This concept is used to explain eruptive phenomena ranging from solar flares to coronal mass ejections. Certain sequences of force-free configurations are discussed that exhibit a loss of equilibrium, and it is argued that the concept is devoid of physical significance since each sequence is defined a way that does not represent an acceptable thought experiment. For example, the sequence may be defined in terms of a global constraint on the boundary conditions, or the evolution of the sequence may require the creation of mgnetic flux that is not connected to the photosphere and is not present in the original configuration. The global constraints typically occur in using the so-called generating function method. An acceptance thought experiment is proposed to specify the field configuration in terms of photospheric boundary conditions comprising the normal component of the field and the field-line connectivity. Consider a magnetic-field sequence that, when described in terms of a generating function, exhibits a loss of equilibrium and show that, when one instead defines the sequence in terms of the corresponding boundary conditions, the sequence is well behaved.
Mean-field Ohm's law and coaxial helicity injection in force-free plasmas
Weening, R. H.
2011-12-15
A theoretical analysis of steady-state coaxial helicity injection (CHI) in force-free plasmas is presented using a parallel mean-field Ohm's law that includes resistivity {eta} and hyper-resistivity {Lambda} terms. Using Boozer coordinates, a partial differential equation is derived for the time evolution of the mean-field poloidal magnetic flux, or magnetic Hamiltonian function, from the parallel mean-field Ohm's law. A general expression is obtained from the mean-field theory for the efficiency of CHI current drive in force-free plasmas. Inductances of internal energy, magnetic helicity, and poloidal magnetic flux are used to characterize axisymmetric plasma equilibria that have a model current profile. Using the model current profile, a method is suggested to determine the level of magnetohydrodynamic activity at the magnetic axis and the consequent deviation from the completely relaxed Taylor state. The mean-field Ohm's law model suggests that steady-state CHI can be viewed most simply as a boundary layer problem.
Embedding Circular Force-Free Flux Ropes in Potential Magnetic Fields
NASA Astrophysics Data System (ADS)
Titov, V. S.; Torok, T.; Mikic, Z.; Linker, J.
2013-12-01
We propose a method for constructing approximate force-free equilibria in active regions that locally have a potential bipolar-type magnetic field with a thin force-free flux rope embedded inside it. The flux rope has a circular-arc axis and circular cross-section in which the interior magnetic field is predominantly toroidal (axial). Its magnetic pressure is balanced outside by that of the poloidal (azimuthal) field created at the boundary by the electric current sheathing the flux rope. To facilitate the implementation of the method in our numerical magnetohydrodynamic (MHD) code, the entire solution is described in terms of the vector potential of the magnetic field. The parameters of the flux rope can be chosen so that a subsequent MHD relaxation of the constructed configuration under line-tied conditions at the boundary provides a numerically exact equilibrium. Such equilibria are an approximation for the magnetic configuration preceding solar eruptions, which can be triggered in our model by imposing suitable photospheric flows beneath the flux rope. The proposed method is a useful tool for constructing pre-eruption magnetic fields in data-driven simulations of solar active events. Research supported by NASA's Heliophysics Theory and LWS Programs, and NSF/SHINE and NSF/FESD.
Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields
NASA Technical Reports Server (NTRS)
Rasband, S. N.; Turner, L.
1981-01-01
It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.
A method for embedding circular force-free flux ropes in potential magnetic fields
Titov, V. S.; Török, T.; Mikic, Z.; Linker, J. A.
2014-08-01
We propose a method for constructing approximate force-free equilibria in pre-eruptive configurations in which a thin force-free flux rope is embedded into a locally bipolar-type potential magnetic field. The flux rope is assumed to have a circular-arc axis, a circular cross-section, and electric current that is either concentrated in a thin layer at the boundary of the rope or smoothly distributed across it with a maximum of the current density at the center. The entire solution is described in terms of the magnetic vector potential in order to facilitate the implementation of the method in numerical magnetohydrodynamic (MHD) codes that evolve the vector potential rather than the magnetic field itself. The parameters of the flux rope can be chosen so that its subsequent MHD relaxation under photospheric line-tied boundary conditions leads to nearly exact numerical equilibria. To show the capabilities of our method, we apply it to several cases with different ambient magnetic fields and internal flux-rope structures. These examples demonstrate that the proposed method is a useful tool for initializing data-driven simulations of solar eruptions.
Kumar, Dinesh; Bhattacharyya, R.; Smolarkiewicz, P. K.
2013-11-15
In ideal magnetohydrodynamics characterized by an infinite electrical conductivity, the magnetic flux across an arbitrary fluid surface is conserved in time. The magnetofluid then can be partitioned into contiguous subvolumes of fluid, each of which entraps its own subsystem of magnetic flux. During dynamical evolution of the magnetofluid, these subvolumes press into each other; and in the process, two such subvolumes may come into direct contact while ejecting a third interstitial subvolume. Depending on the orientations of magnetic fields of the two interacting subvolumes, the magnetic field at the common surface of interaction may become discontinuous and a current sheet is formed there. This process of current sheet formation and their subsequent decay is believed to be a plausible mechanism for coronal heating and may also be responsible for various eruptive phenomena at the solar corona. In this work, we explore this theoretical concept through numerical simulations of a viscous, incompressible magnetofluid characterized by infinite electrical conductivity. In particular, we show that if the initial magnetic field is prescribed by superposition of two linear force-free fields with different torsion coefficients, then formation of current sheets are numerically realizable in the neighborhood of magnetic nulls.
NASA Astrophysics Data System (ADS)
Farrugia, Charles; Moestl, Christian; Leitner, Martin; Galvin, Antoinette; Lugaz, Noé; Yu, Wenyuan
2016-07-01
This work is about modeling of those small solar wind transients (STs) which have a flux rope geometry. The two models used are: (i) the linear force free solution of Lundquist in terms of Bessel functions, and (ii) the non-linear Gold-Hoyle solution describing a uniformly-twisted flux tube. The first has been used almost exclusively in modeling of both large and small flux ropes in the solar wind. The second was applied to one small transient. In recent work there have been claims that variant (ii) is more appropriate than (i) for large transients, i.e. magnetic clouds. We select by eye six flux rope STs from STEREO and Wind data, chosen purely on the basis of having a large and smooth rotation. We also choose these during solar maximum activity conditions since our current work shows that only then are these models appropriate.
Current sheet formation in a sheared force-free-magnetic field. [in sun
NASA Technical Reports Server (NTRS)
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.
Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona
Thalmann, J. K.
2014-01-01
The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region (AR) corona has only recently been substantiated by high-resolution observations. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We deliver estimates of the free magnetic energy associated with a braided coronal structure. Our model results suggest (∼100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the AR corona being heated by field line braiding. We were able to appropriately assess the coronal free energy by using vector field measurements and we attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase in the overall twist of a flare-related flux rope that was noted by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within 12 minutes. Unlike another method to which we compare our results, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal three-dimensional field line geometry. To our knowledge, this is done for the first time here.
NASA Astrophysics Data System (ADS)
Ram, Abhay K.; Dasgupta, Brahmananda; Krishnamurthy, V.; Mitra, Dhrubaditya
2014-07-01
The cosmic magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free in the sense that the Lorentz force vanishes. The three-dimensional Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical magnetic field. In fluid dynamics, ABC flows are steady state solutions of the Euler equation. The ABC magnetic field lines exhibit a complex and varied structure that is a mix of regular and chaotic trajectories in phase space. The characteristic features of field line trajectories are illustrated through the phase space distribution of finite-distance and asymptotic-distance Lyapunov exponents. In regions of chaotic trajectories, an ensemble-averaged variance of the distance between field lines reveals anomalous diffusion—in fact, superdiffusion—of the field lines. The motion of charged particles in the force-free ABC magnetic fields is different from the flow of passive scalars in ABC flows. The particles do not necessarily follow the field lines and display a variety of dynamical behavior depending on their energy, and their initial pitch-angle. There is an overlap, in space, of the regions in which the field lines and the particle orbits are chaotic. The time evolution of an ensemble of particles, in such regions, can be divided into three categories. For short times, the motion of the particles is essentially ballistic; the ensemble-averaged, mean square displacement is approximately proportional to t2, where t is the time of evolution. The intermediate time region is defined by a decay of the velocity autocorrelation function—this being a measure of the time after which the collective dynamics is independent of the initial conditions. For longer times, the particles undergo superdiffusion—the mean square displacement is proportional to tα, where α > 1, and is weakly dependent on the energy of the particles. These super-diffusive characteristics, both of magnetic
Ram, Abhay K.; Dasgupta, Brahmananda; Krishnamurthy, V.; Mitra, Dhrubaditya
2014-07-15
The cosmic magnetic fields in regions of low plasma pressure and large currents, such as in interstellar space and gaseous nebulae, are force-free in the sense that the Lorentz force vanishes. The three-dimensional Arnold-Beltrami-Childress (ABC) field is an example of a force-free, helical magnetic field. In fluid dynamics, ABC flows are steady state solutions of the Euler equation. The ABC magnetic field lines exhibit a complex and varied structure that is a mix of regular and chaotic trajectories in phase space. The characteristic features of field line trajectories are illustrated through the phase space distribution of finite-distance and asymptotic-distance Lyapunov exponents. In regions of chaotic trajectories, an ensemble-averaged variance of the distance between field lines reveals anomalous diffusion—in fact, superdiffusion—of the field lines. The motion of charged particles in the force-free ABC magnetic fields is different from the flow of passive scalars in ABC flows. The particles do not necessarily follow the field lines and display a variety of dynamical behavior depending on their energy, and their initial pitch-angle. There is an overlap, in space, of the regions in which the field lines and the particle orbits are chaotic. The time evolution of an ensemble of particles, in such regions, can be divided into three categories. For short times, the motion of the particles is essentially ballistic; the ensemble-averaged, mean square displacement is approximately proportional to t{sup 2}, where t is the time of evolution. The intermediate time region is defined by a decay of the velocity autocorrelation function—this being a measure of the time after which the collective dynamics is independent of the initial conditions. For longer times, the particles undergo superdiffusion—the mean square displacement is proportional to t{sup α}, where α > 1, and is weakly dependent on the energy of the particles. These super-diffusive characteristics
NASA Technical Reports Server (NTRS)
Parker, E. N.
1990-01-01
Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.
NASA Astrophysics Data System (ADS)
Rudenko, George; Myshyakov, Ivan; Anfinogentov, Sergey
A possibility for satisfactory removing of azimuthal ambiguity in the transverse field of vector magnetograms and the extrapolation of magnetic fields independently of the region position on the solar disk is shown. It is demonstrated an exact correspondence between the calculated field and the nonpotential loop structure in a near-limb region. The new technique of azimuthal ambiguity removing consists of the following parts: -translation of data in the form of artificial Stokes parameters into the working "quasi-spherical" coordinate system with subsequent smoothing to reduce noise component of the transverse field and with the inverse transformation to the vector form; -FFT extrapolation of the boundary potential field with constant direction of the oblique derivative corresponding to the observed line-of-sight component in the "quasi-spherical" coordinate system; -modification of the Metropolis's minimum energy method to spherical geometry with no need for data grid uniformity. Based on a version of the optimization method from Rudenko and Myshyakov (2009, Solar Phys. V. 257, 28), we use magnetograms corrected with modification of the Metropolis's method as boundary conditions for magnetic field extrapolation in the nonlinear force-free approximation.
Quasi-static evolution of force-free magnetic fields and a model for two-ribbon solar flares
NASA Technical Reports Server (NTRS)
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.
Effect of Polarimetric Noise on the Estimation of Twist and Magnetic Energy of Force-Free Fields
NASA Astrophysics Data System (ADS)
Tiwari, Sanjiv Kumar; Venkatakrishnan, P.; Gosain, Sanjay; Joshi, Jayant
2009-07-01
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.
EFFECT OF POLARIMETRIC NOISE ON THE ESTIMATION OF TWIST AND MAGNETIC ENERGY OF FORCE-FREE FIELDS
Tiwari, Sanjiv Kumar; Venkatakrishnan, P.; Gosain, Sanjay; Joshi, Jayant E-mail: pvk@prl.res.in E-mail: jayant@prl.res.in
2009-07-20
The force-free parameter {alpha}, 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 {alpha} 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 {alpha} 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 {alpha} 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{sup -3} of the continuum intensity (I {sub 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 {alpha} and magnetic energy values. The results show that (1) the sign of {alpha} 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.
Comparative study of a constant-alpha force-free field and its approximations in an ideal toroid
NASA Astrophysics Data System (ADS)
Vandas, M.; Romashets, E.
2015-08-01
Aims: Magnetic clouds in the solar wind are large, loop-like interplanetary flux ropes and may be locally approximated by a toroidal flux rope. We compare approximate constant-alpha force-free fields in an ideal toroid, used in magnetic cloud analysis, with the exact solution, and examine their validity for low aspect ratios, which can be found in magnetic clouds. The approximate toroidal solutions were originally derived under the assumption of large aspect ratios. Methods: Three analytic simple approximate constant-alpha force-free solutions and the exact analytic solution are compared with respect to magnetic field profiles, magnetic field magnitude distributions, and magnetic helicity, with moderate (2-3) and very low (<2) aspect ratios. Results: The Miller & Turner (1981, Phys. Fluids, 24, 363) field and its modification (to satisfy exact solenoidality) match the position of the magnetic axis in the toroidal flux rope well even for very low aspect ratios. The same can be said for the modified field and the position of the magnetic field maximum. When calculating helicity of the toroidal flux rope, the Miller & Turner field yields better results. A simple formula for magnetic helicity derived from the Miller & Turner solution is valid with a good accuracy even for very low aspect ratios. Conclusions: The Miller & Turner solution is a reasonable substitute for the exact solution even for low aspect ratios (≈2).
Aschwanden, Markus J.; Wuelser, Jean-Pierre; Nitta, Nariaki V.; Lemen, James R.; DeRosa, Marc L.; Malanushenko, Anna
2012-09-10
The three-dimensional coordinates of stereoscopically triangulated loops provide strong constraints for magnetic field models of active regions in the solar corona. Here, we use STEREO/A and B data from some 500 stereoscopically triangulated loops observed in four active regions (2007 April 30, May 9, May 19, and December 11), together with SOHO/MDI line-of-sight magnetograms. We measure the average misalignment angle between the stereoscopic loops and theoretical magnetic field models, finding a mismatch of {mu} = 19 Degree-Sign -46 Degree-Sign for a potential field model, which is reduced to {mu} 14 Degree-Sign -19 Degree-Sign for a non-potential field model parameterized by twist parameters. The residual error is commensurable with stereoscopic measurement errors ({mu}{sub SE} Almost-Equal-To 8 Degree-Sign -12 Degree-Sign ). We developed a potential field code that deconvolves a line-of-sight magnetogram into three magnetic field components (B{sub x} , B{sub y} , B{sub z} ), as well as a non-potential field forward-fitting code that determines the full length of twisted loops (L Almost-Equal-To 50-300 Mm), the number of twist turns (median N{sub twist} = 0.06), the nonlinear force-free {alpha}-parameter (median {alpha} Almost-Equal-To 4 Multiplication-Sign 10{sup -11} cm{sup -1}), and the current density (median j{sub z} Almost-Equal-To 1500 Mx cm{sup -2} s{sup -1}). All twisted loops are found to be far below the critical value for kink instability, and Joule dissipation of their currents is found to be far below the coronal heating requirement. The algorithm developed here, based on an analytical solution of nonlinear force-free fields that is accurate to second order (in the force-free parameter {alpha}), represents the first code that enables fast forward fitting to photospheric magnetograms and stereoscopically triangulated loops in the solar corona.
NASA Technical Reports Server (NTRS)
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.
The topology of force-free magnetic fields and its implications for coronal activity
NASA Technical Reports Server (NTRS)
Antiochos, Spiro K.
1987-01-01
The topological constraints on coronal magnetic fields are considered. For a field that is initially well-behaved and undergoes deformation by well-behaved ideal MHD motions, it is shown that the topology of the field lines in the corona can be determined at all times solely from the footpoint positions on the photospheric boundary. This result implies that the topology and, consequently, the history of the footpoint motions impose no further constraints on the field beyond those already included in the connectivity boundary conditions, so that there is no reason to expect a lack of equilibrium for fields that are initially well-behaved and evolve by ideal MHD. On the other hand, nonideal processes such as reconnection are bound to occur in the solar corona, and these may lead to magnetic topologies that have no well-bahaved Euler potentials. Hence Parker's hypothesis that footpoint motions lead to the formation of current sheets is still likely to be correct, but only if nonideal processes are included. The effects of reconnection on magnetic topology and the implications for coronal activity are discussed.
The galactic dynamo, the helical force free field and the emissions of AGN
Colgate, S.; Li, Hui
1997-05-01
We present a theory relating the central galactic black hole (BH) formation to the galactic dynamo through an accretion disk. The associated AGN emissions and the collimated radio sources are then a result of the dynamo process. A unified theory of quasar and BL-Lac formation (hereafter AGN) starts with the collapse of damped Lyman-alpha clouds, presumably proto-galaxies, which then evolve to a central disk and black hole, (BH). An alpha - omega dynamo forms in this accretion disk where the augmentation of the poloidal field from the toroidal field depends upon star disk collisions. The winding number of the inner most orbit of the disk is so large, tilde 10 to the 11th power that the total gain of the dynamo is semi-infinite, and the original seed field of no consequence. The total magnetic flux produced is tilde 10000 times that of the galaxy, sufficient to explain the much larger flux of clusters. The semi-infinite gain of the dynamo implies that the field saturates at the dynamic stress so that most of the free energy of formation of the BH is carried off as magnetic energy in the form of a magnetic helix. The dissipation of this magnetic energy leads to the unique emission spectrum of AGN as well as the equally startling collimated radio and optical sources.
Spacetime approach to force-free magnetospheres
NASA Astrophysics Data System (ADS)
Gralla, Samuel E.; Jacobson, Ted
2014-12-01
Force-free electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this paper, we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus), we cover (1) the basics of the theory, (2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), (3) the behaviour of current sheets, (4) the general theory of stationary, axisymmetric magnetospheres, and (5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify, and generalize known aspects of the physics of force-free magnetospheres, while also introducing several new results.
NASA Astrophysics Data System (ADS)
Nandy, Dibyendu; Calhoun, A.; Windschitl, J.; Canfield, R. C.; Linton, M. G.
2007-05-01
The twist component of magnetic helicity in solar active regions is known to be an important indicator of sub-photospheric flux tube dynamics and solar eruptive activity. Traditionally, estimates of the parameter alpha -- appearing in the force-free-field equation -- has been used to infer the twist of photospheric active regions. However, the photosphere is not force-free and this has lead to recent concerns on the validity of using the alpha parameter for determining photospheric active region twist. We have devised a new flux-tube-fitting technique for determining the twist of active regions without recourse to the force-free-field equation. This method assumes that the underlying active region flux system is cylindrically symmetric and uniformly twisted. By using this new technique, on a statistically compelling number of photospheric active region vector magnetograms, we re-confirm the hemispheric helicity rule independent of the force-free-field assumption. This research has been supported in parts by a NASA Living With a Star grant NNG05GE47G. A.C. and J.W. were supported by a NSF Research Experience for Undergraduates grant ATM-0243923 to Montana State University. M.G.L. acknowledges support from NASA and the Office of Naval Research.
NASA Technical Reports Server (NTRS)
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.
NASA Technical Reports Server (NTRS)
Meyer, R. X.; Mayfield, E. B.; Underwood, J. H.; Mckenzie, D. L.; Milligan, J. E.; De Loach, A. C.; Hoover, R. B.
1974-01-01
Data obtained from the S-056 X-ray experiment on Skylab/ATM have been analyzed based on the assumption that the magnetic fields in the chromosphere and lower corona are force-free. Underlying the analysis is the hypothesis that the observed X-ray filaments coincide with magnetic field lines. The photographic recording of the filaments can then be compared with the projection along the line of sight of the computed magnetic field lines of the model. Ground-based observations of the longitudinal magnetic field component complement the X-ray data and are used in the theoretical interpretation.
NASA Technical Reports Server (NTRS)
Low, B. C.
1974-01-01
A one-dimensional model is considered in which an increasingly large electric field is induced by a rapidly evolving magnetic field. In the case of solar flares, energies are estimated to which protons and electrons may be directly accelerated by such an induced electric field.
An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta
Allanson, O. Neukirch, T. Wilson, F. Troscheit, S.
2015-10-15
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Zhang, Haocheng; Deng, Wei; Li, Hui; Bottcher, Markus
2016-01-20
The optical radiation and polarization signatures in blazars are known to be highly variable during flaring activities. It is frequently argued that shocks are the main driver of the flaring events. However, the spectral variability modelings generally lack detailed considerations of the self-consistent magnetic field evolution modeling; thus, so far the associated optical polarization signatures are poorly understood. We present the first simultaneous modeling of the optical radiation and polarization signatures based on 3D magnetohydrodynamic simulations of relativistic shocks in the blazar emission environment, with the simplest physical assumptions. By comparing the results with observations, we find that shocks inmore » a weakly magnetized environment will largely lead to significant changes in the optical polarization signatures, which are seldom seen in observations. Hence an emission region with relatively strong magnetization is preferred. In such an environment, slow shocks may produce minor flares with either erratic polarization fluctuations or considerable polarization variations, depending on the parameters; fast shocks can produce major flares with smooth polarization angle rotations. In addition, the magnetic fields in both cases are observed to actively revert to the original topology after the shocks. In addition, all these features are consistent with observations. Future observations of the radiation and polarization signatures will further constrain the flaring mechanism and the blazar emission environment.« less
Stability of force-free magnetospheres
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan
2014-11-01
We analyze the dynamical evolution of a perturbed force-free magnetosphere of a rotating black hole, which is described by the Blandford-Znajek solution in the stationary limit. We find that the electromagnetic field perturbations can be classified into two categories: "trapped modes" and "traveling waves." The trapped modes are analogous to the vacuum (without plasma) electromagnetic quasinormal modes in rotating black hole spacetimes, but with different eigenfrequencies and wave functions, due to their coupling with the background electromagnetic field and current. The traveling waves propagate freely to infinity or the black hole horizon along specific null directions, and they are closely related to the no-scattering Poynting flux solutions discovered by Brennan, Gralla and Jacobson. Our results suggest that the Blandford-Znajek solution is mode stable, and more importantly we expect this study to illuminate the dynamical behavior of force-free magnetospheres as well as to shed light on the path to new exact solutions.
Force-Free Black Hole Magnetospheres
NASA Astrophysics Data System (ADS)
Okamoto, Isao
2009-10-01
It is argued that a force-free degenerate electrodynamic (FFDE) magnetosphere of a Kerr black hole with 0 < ΩF < ΩH consists of the outer classical and inner general-relativistic domains. This is described by a simple DC dual-circuit model, with dissipative membranes as two loads at a ``force-free infinity surface'' (Sff∞) with ω = 0 and at a ``force-free horizon surface'' (SffH) with ω = ΩH, where ω, ΩH, and ΩF, are the frame-dragging, the horizon and the field line angular frequencies. It is beneath upper null surface, SN, at ω = ΩF between the two domains that dual unipolar batteries (double EMF's) exist back-to-back, oppositely directed, with a pair-creation gap between. The total energy flux boldsymbol{S}E is a linear sum of the two fluxes: the hole's outward spin-down energy flux boldsymbol{S}SD originating at SffH and the Poynting flux boldsymbol{S}EM emitted at SN in both the outward and inward directions, with boldsymbol{S}E being proportional to ΩF, boldsymbol{S}SD to ω and boldsymbol{S}EM to (ΩF - ω) along each field line. Applying a perturbation method for a split-monopolar field with a spin-parameter h ≪ 1, the analytic solution of the stream equation is given, and the double eigenvalue problem due to the `criticality condition' at the outer/inner fast surfaces SoF/SiF and the `boundary condition' at SN is solved to yield the final eigenvalue ΩF, in terms of ΩH and ≥H = 0.5676. The ratio of the output power reaching Sff∞ to to the dissipation on SffH is ɛ = 1 + (4/5) (1-≥H)h².
Force-free Jacobian equilibria for Vlasov-Maxwell plasmas
Abraham-Shrauner, B.
2013-10-15
New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.
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.
Gauge fields, nonlinear realizations, supersymmetry
NASA Astrophysics Data System (ADS)
Ivanov, E. A.
2016-07-01
This is a brief survey of the all-years research activity in the Sector "Supersymmetry" (the former Markov Group) at the Bogoliubov Laboratory of Theoretical Physics. The focus is on the issues related to gauge fields, spontaneously broken symmetries in the nonlinear realizations approach, and diverse aspects of supersymmetry.
Separable solutions of force-free spheres and applications to solar active regions
Prasad, A.; Mangalam, A.; Ravindra, B. E-mail: mangalam@iiap.res.in
2014-05-10
We present a systematic study of the force-free field equation for simple axisymmetric configurations in spherical geometry and apply it to the solar active regions. The condition of separability of solutions in the radial and angular variables leads to two classes of solutions: linear and nonlinear force-free fields (NLFF). We have studied these linear solutions and extended the nonlinear solutions for the radial power law index to the irreducible rational form n = p/q, which is allowed for all cases of odd p and cases of q > p for even p, where the poloidal flux ψ∝1/r{sup n} and the field B∝1/r {sup n+2}. We apply these solutions to simulate photospheric vector magnetograms obtained using the spectropolarimeter on board Hinode. The effectiveness of our search strategy is first demonstrated on test inputs of dipolar, axisymmetric, and nonaxisymmetric linear force-free fields. Using the best fit, we build three-dimensional axisymmetric field configurations and calculate the energy and relative helicity with two independent methods, which are in agreement. We have analyzed five magnetograms for AR 10930 spanning a period of three days during which two X-class flares occurred and found the free energy and relative helicity of the active region before and after the flare; our analysis indicates a peak in these quantities before the flare events, which is consistent with the other results. We also analyzed single-polarity regions AR 10923 and 10933, which showed very good fits to potential fields. This method provides useful reconstruction of NLFF and input fields for other numerical techniques.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Magnetospheres of black hole systems in force-free plasma
Palenzuela, Carlos; Garrett, Travis; Lehner, Luis; Liebling, Steven L.
2010-08-15
The interaction of black holes with ambient magnetic fields is important for a variety of highly energetic astrophysical phenomena. We study this interaction within the force-free approximation in which a tenuous plasma is assumed to have zero inertia. Blandford and Znajek used this approach to demonstrate the conversion of some of the black hole's energy into electromagnetic Poynting flux in stationary and axisymmetric single black hole systems. We adopt this approach and extend it to examine asymmetric and, most importantly, dynamical systems by implementing the fully nonlinear field equations of general relativity coupled to Maxwell's equations. For single black holes, we study, in particular, the dependence of the Poynting flux and show that, even for misalignments between the black hole spin and the direction of the asymptotic magnetic field, a Poynting flux is generated with a luminosity dependent on such misalignment. For binary black hole systems, we show both in the head-on and orbiting cases that the moving black holes generate a Poynting flux.
Shaping the nonlinear near field.
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Shaping the nonlinear near field
NASA Astrophysics Data System (ADS)
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states.
Shaping the nonlinear near field
Wolf, Daniela; Schumacher, Thorsten; Lippitz, Markus
2016-01-01
Light scattering at plasmonic nanoparticles and their assemblies has led to a wealth of applications in metamaterials and nano-optics. Although shaping of fields around nanostructures is widely studied, the influence of the field inside the nanostructures is often overlooked. The linear field distribution inside the structure taken to the third power causes third-harmonic generation, a nonlinear optical response of matter. Here we demonstrate by a far field Fourier imaging method how this simple fact can be used to shape complex fields around a single particle alone. We employ this scheme to switch the third-harmonic emission from a single point source to two spatially separated but coherent sources, as in Young's double-slit assembly. We envision applications as diverse as coherently feeding antenna arrays and optical spectroscopy of spatially extended electronic states. PMID:26762487
Freely Decaying Turbulence in Force-free Electrodynamics
NASA Astrophysics Data System (ADS)
Zrake, Jonathan; East, William E.
2016-02-01
Freely decaying, relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two- and three-dimensional periodic domains in both helical and nonhelical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings and in three dimensions to have a magnetic energy spectrum consistent with the Kolmogorov 5/3 power law. Three-dimensional relaxations also obey the Taylor hypothesis; they settle promptly into the lowest-energy configuration allowed by conservation of the total magnetic helicity. However, in two dimensions, the relaxed state is a force-free equilibrium whose energy greatly exceeds the Taylor minimum and that contains persistent force-free current layers and isolated flux tubes. We explain this behavior in terms of additional topological invariants that exist only in two dimensions, namely the helicity enclosed within each level surface of the magnetic potential function. The speed and completeness of turbulent magnetic free-energy discharge could help account for rapidly variable gamma-ray emission from the Crab Nebula, gamma-ray bursts, blazars, and radio galaxies.
Force-free coil principles applied to high-temperature superconducting materials
Furth, H.P.; Jardin, S.C.; Montgomery, D.B.
1987-11-01
Force-free magnetic-field configurations, where the current flows parallel to the magnetic field vector, have the potential to raise the critical magnetic field and current-density limits for high-temperature superconductors. 10 refs., 3 figs.
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. PMID:11102074
ON THE GLOBAL STRUCTURE OF PULSAR FORCE-FREE MAGNETOSPHERE
Petrova, S. A.
2013-02-20
The dipolar magnetic field structure of a neutron star is modified by the plasma originating in the pulsar magnetosphere. In the simplest case of a stationary axisymmetric force-free magnetosphere, a self-consistent description of the fields and currents is given by the well-known pulsar equation. Here we revise the commonly used boundary conditions of the problem in order to incorporate the plasma-producing gaps and to provide a framework for a truly self-consistent treatment of the pulsar magnetosphere. A generalized multipolar solution of the pulsar equation is found, which, as compared to the customary split monopole solution, is suggested to better represent the character of the dipolar force-free field at large distances. In particular, the outer gap location entirely inside the light cylinder implies that beyond the light cylinder the null and critical lines should be aligned and become parallel to the equator at a certain altitude. Our scheme of the pulsar force-free magnetosphere, which will hopefully be followed by extensive analytic and numerical studies, may have numerous implications for different fields of pulsar research.
Nonlinear model of elastic field sources
NASA Astrophysics Data System (ADS)
Lev, B. I.; Zagorodny, A. G.
2016-09-01
A general concept of the long-range elastic interactions in continuous medium is proposed. The interaction is determined as a consequence of symmetry breaking of the elastic field distribution produced by the topological defect as isolated inclusions. It is proposed to treat topological defects as the source of elastic field that can be described in terms of this field. The source is considered as a nonlinear object which determines the effective charge of the field at large distances in the linear theory. The models of the nonlinear source are proposed.
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D.
2013-10-15
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Scattering of force-free electrodynamic waves by spacetime curvature
NASA Astrophysics Data System (ADS)
Zhang, Fan; McWilliams, Sean
2014-03-01
The electromagnetic fields E and B are vectors that couple to spacetime curvatures via Ricci identities, and so force-free electrodynamic waves will in general be scattered. However, Brennan, Gralla and Jacobson found a family of exact solutions that escape scattering. We analytically and numerically study these solutions and their alterations, in order to provide more details as to what features allow them to possess this property. We hope our results will be useful when searching for other solutions of this type. We also provide physical intuition for some commonly encountered theoretical constructs.
The Force-Free Magnetosphere of a Rotating Black Hole
NASA Technical Reports Server (NTRS)
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."
THE FORCE-FREE MAGNETOSPHERE OF A ROTATING BLACK HOLE
Contopoulos, Ioannis; Kazanas, Demosthenes
2013-03-10
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 {omega} and the poloidal electric current I. 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''.
Primordial magnetic fields and nonlinear electrodynamics
Kunze, Kerstin E.
2008-01-15
The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the subsequent radiation dominated stage are unaltered. The nonlinear regime of electrodynamics is described by Lagrangians having a power-law dependence on one of the invariants of the electromagnetic field. It is found that there is a range of parameters for which primordial magnetic fields of cosmologically interesting strengths can be created.
New approaches to nonlinear diffractive field propagation.
Christopher, P T; Parker, K J
1991-07-01
In many domains of acoustic field propagation, such as medical ultrasound imaging, lithotripsy shock treatment, and underwater sonar, a realistic calculation of beam patterns requires treatment of the effects of diffraction from finite sources. Also, the mechanisms of loss and nonlinear effects within the medium are typically nonnegligible. The combination of diffraction, attenuation, and nonlinear effects has been treated by a number of formulations and numerical techniques. A novel model that incrementally propagates the field of baffled planar sources with substeps that account for the physics of diffraction, attenuation, and nonlinearity is presented. The model accounts for the effect of refraction and reflection (but not multiple reflections) in the case of propagation through multiple, parallel layers of fluid medium. An implementation of the model for axis symmetric sources has been developed. In one substep of the implementation, a new discrete Hankel transform is used with spatial transform techniques to propagate the field over a short distance with diffraction and attenuation. In the other substep, the temporal frequency domain solution to Burgers' equation is implemented to account for the nonlinear accretion and depletion of harmonics. This approach yields a computationally efficient procedure for calculating beam patterns from a baffled planar, axially symmetric source under conditions ranging from quasilinear through shock. The model is not restricted by the usual parabolic wave approximation and the field's directionality is explicitly accounted for at each point. Useage of a harmonic-limiting scheme allows the model to propagate some previously intractable high-intensity nonlinear fields. Results of the model are shown to be in excellent agreement with measurements performed on the nonlinear field of an unfocused 2.25-MHz piston source, even in the near field where the established parabolic wave approximation model fails. Next, the model is used to
Three-dimensional force-free looplike magnetohydrodynamic equilibria
NASA Technical Reports Server (NTRS)
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.
Imbalanced relativistic force-free magnetohydrodynamic turbulence
Cho, Jungyeon; Lazarian, A.
2014-01-01
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfvénic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper, we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., b{sub +}{sup 2}/b{sub −}{sup 2}∝(ϵ{sub +}/ϵ{sub −}){sup n} with n > 2). These results are consistent with those obtained for imbalanced non-relativistic Alfvénic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.
Solar coronal loops as non force-free minimum energy relaxed states
Kumar, Dinesh; Bhattacharyya, R.
2011-08-15
In this work, the well established two-fluid relaxation model based on the minimum energy principle is extended to include open systems like the solar corona. The Euler-Lagrange equations obtained are of double curl in nature and support non-zero plasma-{beta} along with mass flow of the magnetofluid. These equations are solved in Cartesian coordinates utilizing a geometry relevant to the solar atmosphere, and a basic comparative study of the non force-free, force-free, and potential magnetic field obtained as solutions of the same Euler-Lagrange equations is presented.
NASA Astrophysics Data System (ADS)
He, Xiaokai; Cao, Zhoujian
2016-01-01
The Hertz potential is a powerful tool for the source-free electrodynamics. Especially for the algebraically special spacetime background, the Hertz potential formalism simplifies the Maxwell equations quite much. In astrophysics, strong electric-magnetic field is very common. Force-free electrodynamics is a good approximation for strong enough electric-magnetic field compared to the inertial energy of the involved plasma. For example, the force-free model has been extensively used to describe the magnetosphere of stars in the universe. In this paper, we extend the Hertz potential formalism to the force-free electrodynamics. The Hertz potential formalism simplifies the force-free dynamical equations as much as that in the source-free case. As an application, we use the Hertz potential formalism to the Schwarzschild background. And the Brennan-Gralla-Jacobson solutions are recovered straightforwardly.
Stability of force-free plasma--vacuum equilibria
Lortz, D.; Spies, G.O. )
1994-02-01
The magnetohydrodynamic stability of force-free plasma--vacuum systems (curl [bold B]=[mu][bold B] in the plasma, with constant [mu]) is studied in circular cylinders with identified ends (topological torus). A necessary stability criterion is derived by considering large poloidal mode numbers. This takes a simple form (the magnetic rotation numbers at the axis and plasma--vacuum interface must have opposite signs) if the magnetic field lines in the interface are not closed. If they are closed, then violation of this simple condition does not imply instability unless the aspect ratio exceeds some value which depends on both the numerator and denominator of the rational magnetic rotation number at the interface. For aspect ratios greater than unity, combination with the criterion for stability to internal kinks implies that the inhomogeneity parameter [vert bar][mu][vert bar] must be above the threshold for reversal of the toroidal current density, but below that for reversal of the poloidal one. This condition is independent of the wall radius, in contrast to the well-known necessary and sufficient stability criterion in the limit of infinite aspect ratio, which remains sufficient for arbitrary aspect ratios, and which requires that [vert bar][mu][vert bar] be in a smaller interval that does depend on the wall radius.
The force-free twisted magnetosphere of a neutron star
NASA Astrophysics Data System (ADS)
Akgün, T.; Miralles, J. A.; Pons, J. A.; Cerdá-Durán, P.
2016-10-01
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to 40 per cent with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to 25 per cent, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist (ϕmax ≲ 1.5 rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution.
NASA Astrophysics Data System (ADS)
Rapoport, Yu G.; Boardman, A. D.; Grimalsky, V. V.; Ivchenko, V. M.; Kalinich, N.
2014-05-01
The idea of nonlinear ‘transformation optics-inspired’ [1-6] electromagnetic cylindrical field concentrators has been taken up in a preliminary manner in a number of conference reports [7-9]. Such a concentrator includes both external linear region with a dielectric constant increased towards the centre and internal region with nonlinearity characterized by constant coefficients. Then, in the process of farther investigations we realized the following factors considered neither in [7-9] nor in the recent paper [10]: saturation of nonlinearity, nonlinear losses, linear gain, numerical convergence, when nonlinear effect becomes very strong and formation of ‘hotspots’ starts. It is clearly demonstrated here that such a strongly nonlinear process starts when the nonlinear amplitude of any incident beam(s) exceeds some ‘threshold’ value. Moreover, it is shown that the formation of hotspots may start as the result of any of the following processes: an increase of the input amplitude, increasing the linear amplification in the central nonlinear region, decreasing the nonlinear losses, a decrease in the saturation of the nonlinearity. Therefore, a tendency to a formation of ‘hotspots’ is a rather universal feature of the strongly nonlinear behaviour of the ‘nonlinear resonator’ system, while at the same time the system is not sensitive to the ‘prehistory’ of approaching nonlinear threshold intensity (amplitude). The new proposed method includes a full-wave nonlinear solution analysis (in the nonlinear region), a new form of complex geometric optics (in the linear inhomogeneous external cylinder), and new boundary conditions, matching both solutions. The observed nonlinear phenomena will have a positive impact upon socially and environmentally important devices of the future. Although a graded-index concentrator is used here, it is a direct outcome of transformation optics. Numerical evaluations show that for known materials these nonlinear effects
EFFECT OF SOLAR CHROMOSPHERIC NEUTRALS ON EQUILIBRIUM FIELD STRUCTURES
Arber, T. D.; Botha, G. J. J.; Brady, C. S. E-mail: G.J.J.Botha@warwick.ac.u
2009-11-10
Solar coronal equilibrium fields are often constructed by nonlinear force-free field (NLFFF) extrapolation from photospheric magnetograms. It is well known that the photospheric field is not force-free and the correct lower boundary for NLFFF construction ought to be the top of the chromosphere. To compensate for this, pre-filtering algorithms are often applied to the photospheric data to remove the non-force-free components. Such pre-filtering models, while physically constrained, do not address the mechanisms that may be responsible for the field becoming force-free. The chromospheric field can change through, for example, field expansion due to gravitational stratification, reconnection, or flux emergence. In this paper, we study and quantify the effect of the chromospheric neutrals on equilibrium field structures. It is shown that, depending on the degree to which the photospheric field is not force-free, the chromosphere will change the structure of the equilibrium field. This is quantified to give an estimate of the change in alpha profiles one might expect due to neutrals in the chromosphere. Simple scaling of the decay time of non-force-free components of the magnetic field due to chromospheric neutrals is also derived. This is used to quantify the rate at which, or equivalent at which height, the chromosphere is expected to become force-free.
Field Measurement of the Acoustic Nonlinearity Parameter in Turbine Blades
NASA Technical Reports Server (NTRS)
Hinton, Yolanda L.; Na, Jeong K.; Yost, William T.; Kessel, Gregory L.
2000-01-01
Nonlinear acoustics techniques were used to measure fatigue in turbine blades in a power generation plant. The measurements were made in the field using a reference based measurement technique, and a reference sample previously measured in the laboratory. The acoustic nonlinearity parameter showed significant increase with fatigue in the blades, as indicated by service age and areas of increased stress. The technique shows promise for effectively measuring fatigue in field applications and predicting subsequent failures.
NASA Astrophysics Data System (ADS)
Yu, Cong
2011-03-01
The force-free (or low inertia) limit of magnetohydrodynamics (MHD) can be applied to many astrophysical objects, including black holes, neutron stars and accretion discs, where the electromagnetic field is so strong that the inertia and pressure of the plasma can be ignored. This is difficult to achieve with the standard MHD numerical methods because they still have to deal with plasma inertial terms even when these terms are much smaller than the electromagnetic terms. Under the force-free approximation, the plasma dynamics is entirely determined by the magnetic field. The plasma provides the currents and charge densities required by the dynamics of electromagnetic fields, but these currents carry no inertia. We present a high-order Godunov scheme to study such force-free electrodynamics. We have implemented weighted essentially non-oscillatory (WENO) spatial interpolations in our scheme. An exact Riemann solver is implemented, which requires spectral decomposition into characteristic waves. We advance the magnetic field with the constrained transport (CT) scheme to preserve the divergence-free condition to machine round-off error. We apply the third-order total variation diminishing (TVD) Runge-Kutta scheme for the temporal integration. The mapping from face-centred variables to volume-centred variables is carefully considered. Extensive testing are performed to demonstrate the ability of our scheme to address force-free electrodynamics correctly. We finally apply the scheme to study relativistic magnetically dominated tearing instabilities and neutron star magnetospheres.
Gamma-Ray Pulsar Light Curves in Vacuum and Force-Free Geometry
NASA Technical Reports Server (NTRS)
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.
Seismological Field Observation of Mesoscopic Nonlinearity
NASA Astrophysics Data System (ADS)
Sens-Schönfelder, Christoph; Gassenmeier, Martina; Eulenfeld, Tom; Tilmann, Frederik; Korn, Michael; Niederleithinger, Ernst
2016-04-01
of events associated with separately inverted parameters. As the local ground acceleration is not correlated to static stress changes we can exclude static stress changes as causative process. The shaking sensitivity and healing process is well known from laboratory experiments in composite materials as mesoscopic nonlinearity. The sensitive behavior at this station is related to the particular near surface material that is a conglomerate cemented with gypsum - so called gypcrete. However, mesoscopic nonlinearity with different parameters might be a key to understand velocity changes also at other sites.
Nonlinear transmission of an intense terahertz field through monolayer graphene
Hafez, H. A.; Ibrahim, A.; Ozaki, T.; Al-Naib, I.; Dignam, M. M.; Oguri, K.; Sekine, Y.; Hibino, H.; Cooke, D. G.; Tanaka, S.; Komori, F.
2014-11-15
We report nonlinear terahertz (THz) effects in monolayer graphene, giving rise to transmission enhancement of a single-cycle THz pulse when the incident THz peak electric field is increased. This transmission enhancement is attributed to reduced photoconductivity, due to saturation effects in the field-induced current and increased intraband scattering rates arising from transient heating of electrons. We have developed a tight-binding model of the response using the length gauge interaction Hamiltonian that provides good qualitative agreement. The model fully accounts for the nonlinear response arising from the linear dispersion energy spectrum in graphene. The results reveal a strong dependence of the scattering time on the THz field, which is at the heart of the observed nonlinear response.
Nonlinear Bubble Interactions in Acoustic Pressure Fields
NASA Technical Reports Server (NTRS)
Barbat, Tiberiu; Ashgriz, Nasser; Liu, Ching-Shi
1996-01-01
The systems consisting of a two-phase mixture, as clouds of bubbles or drops, have shown many common features in their responses to different external force fields. One of particular interest is the effect of an unsteady pressure field applied to these systems, case in which the coupling of the vibrations induced in two neighboring components (two drops or two bubbles) may result in an interaction force between them. This behavior was explained by Bjerknes by postulating that every body that is moving in an accelerating fluid is subjected to a 'kinetic buoyancy' equal with the product of the acceleration of the fluid multiplied by the mass of the fluid displaced by the body. The external sound wave applied to a system of drops/bubbles triggers secondary sound waves from each component of the system. These secondary pressure fields integrated over the surface of the neighboring drop/bubble may result in a force additional to the effect of the primary sound wave on each component of the system. In certain conditions, the magnitude of these secondary forces may result in significant changes in the dynamics of each component, thus in the behavior of the entire system. In a system containing bubbles, the sound wave radiated by one bubble at the location of a neighboring one is dominated by the volume oscillation mode and its effects can be important for a large range of frequencies. The interaction forces in a system consisting of drops are much smaller than those consisting of bubbles. Therefore, as a first step towards the understanding of the drop-drop interaction subject to external pressure fluctuations, it is more convenient to study the bubble interactions. This paper presents experimental results and theoretical predictions concerning the interaction and the motion of two levitated air bubbles in water in the presence of an acoustic field at high frequencies (22-23 KHz).
Nonlinear electromagnetic fields as a source of universe acceleration
NASA Astrophysics Data System (ADS)
Kruglov, S. I.
2016-04-01
A model of nonlinear electromagnetic fields with a dimensional parameter β is proposed. From PVLAS experiment the bound on the parameter β was obtained. Electromagnetic fields are coupled with the gravitation field and we show that the universe accelerates due to nonlinear electromagnetic fields. The magnetic universe is considered and the stochastic magnetic field is a background. After inflation the universe decelerates and approaches to the radiation era. The range of the scale factor, when the causality of the model and a classical stability take place, was obtained. The spectral index, the tensor-to-scalar ratio, and the running of the spectral index were estimated which are in approximate agreement with the Planck, WMAP, and BICEP2 data.
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described. PMID:10829672
Nonlinear electron acoustic waves in presence of shear magnetic field
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Chakrabarti, Nikhil
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
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. PMID:26497312
High field optical nonlinearity and the Kramers-Kronig relations.
Wahlstrand, J K; Cheng, Y-H; Milchberg, H M
2012-09-14
The nonlinear optical response to high fields is absolutely measured for the noble gas atoms He, Ne, Ar, Kr, and Xe. We find that the response is quadratic in the laser field magnitude up to the ionization threshold of each gas. Its size and quadratic dependence are well predicted by a Kramers-Kronig analysis employing known ionization probabilities, and the results are consistent with calculations using the time-dependent Schrödinger equation.
Spectral investigation of nonlinear local field effects in Ag nanoparticles
Sato, Rodrigo Takeda, Yoshihiko; Ohnuma, Masato; Oyoshi, Keiji
2015-03-21
The capability of Ag nanoparticles to modulate their optical resonance condition, by optical nonlinearity, without an external feedback system was experimentally demonstrated. These optical nonlinearities were studied in the vicinity of the localized surface plasmon resonance (LSPR), using femtosecond pump-and-probe spectroscopy with a white-light continuum probe. Transient transmission changes ΔT/T exhibited strong photon energy and particle size dependence and showed a complex and non-monotonic change with increasing pump light intensity. Peak position and change of sign redshift with increasing pump light intensity demonstrate the modulation of the LSPR. These features are discussed in terms of the intrinsic feedback via local field enhancement.
Stochastic acceleration of charged particle in nonlinear wave field
NASA Astrophysics Data System (ADS)
He, Kaifen
2003-04-01
Possibility of stochastic acceleration of charged particle by nonlinear waves is investigated. Spatially regular (SR) and spatiotemporal chaotic (STC) wave solutions evolving from saddle steady wave are tested as the fields. In the non-steady SR field the particle is finally trapped by the wave and averagely gains its group velocity, while in the STC field the particle motion displays trapped-free phases with its averaged velocity larger or smaller than the group velocity depending on the charge sign. A simplified model is established to investigate the acceleration mechanism. By analogy with motor protein, it is found that the virtual pattern of saddle steady wave plays a role of asymmetric potential, which and the nonlinear varying perturbation wave are the two sufficient ingredients for the acceleration in our case.
Formation of sub-ion scale filamentary force-free structures in the vicinity of reconnection region
NASA Astrophysics Data System (ADS)
Zelenyi, L. M.; Frank, A. G.; Artemyev, A. V.; Petrukovich, A. A.; Nakamura, R.
2016-05-01
In this paper we review the results of spacecraft observations of current sheets (CSs) of sub-ion spatial scales in the Earth’s magnetotail as well as experiments with these structures in laboratory devices. We demonstrate that such sub-ion CSs having a thickness less than the ion gyroradius are usually formed in the vicinity of the magnetic reconnection region and are supported by strong electron currents flowing along magnetic field lines. The magnetic field configuration of sub-ion CSs is close to the force-free configuration, with a strong shear magnetic field component in the CS central region. Spacecraft observations suggest that parallel electron currents are generated by electron beams (pronounced enhancement of the phase space density for electrons with small pitch angles and energies ∼1–3 keV). We discuss several models describing such force-free sub-ion CSs.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1976-01-01
An investigation is conducted of five relativistic plane nonlinear waves, taking into account circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. It is found that a large-amplitude superluminous wave determines the average plasma properties, and not vice versa. Attention is given to the implications of the obtained results for the acceleration of cosmic rays in pulsar magnetospheres.
Gravity Dual for Reggeon Field Theory and Nonlinear Quantum Finance
NASA Astrophysics Data System (ADS)
Nakayama, Yu
We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Relativistic nonlinear plasma waves in a magnetic field
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Pellat, R.
1975-01-01
Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
Nonlinear electric field structures in the inner magnetosphere
Malaspina, D. M.; Andersson, L.; Ergun, R. E.; Wygant, J. R.; Bonnell, J. W.; Kletzing, C.; Reeves, G. D.; Skoug, R. M.; Larsen, B. A.
2014-08-28
Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combinedmore » with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.« less
Nonlinear electric field structures in the inner magnetosphere
Malaspina, D. M.; Andersson, L.; Ergun, R. E.; Wygant, J. R.; Bonnell, J. W.; Kletzing, C.; Reeves, G. D.; Skoug, R. M.; Larsen, B. A.
2014-08-28
Recent observations by the Van Allen Probes spacecraft have demonstrated that a variety of electric field structures and nonlinear waves frequently occur in the inner terrestrial magnetosphere, including phase space holes, kinetic field-line resonances, nonlinear whistler-mode waves, and several types of double layer. However, it is nuclear whether such structures and waves have a significant impact on the dynamics of the inner magnetosphere, including the radiation belts and ring current. To make progress toward quantifying their importance, this study statistically evaluates the correlation of such structures and waves with plasma boundaries. A strong correlation is found. These statistical results, combined with observations of electric field activity at propagating plasma boundaries, are consistent with the identification of these boundaries as the source of free energy responsible for generating the electric field structures and nonlinear waves of interest. Therefore, the ability of these structures and waves to influence plasma in the inner magnetosphere is governed by the spatial extent and dynamics of macroscopic plasma boundaries in that region.
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. PMID:20364986
Nonlinear response of electric fields at a neutral point
NASA Astrophysics Data System (ADS)
Berkovsky, Mikhail; Dufty, James W.; Calisti, Annette; Stamm, Roland; Talin, Bernard
1995-05-01
The complex dynamics of electric fields at a neutral point in a plasma is studied via a model of noninteracting ``quasiparticles.'' The simplicity of the model allows the reduction of the many-body problem to an effective single-particle analysis-all properties of interest can be reduced to quadratures. Still, the final calculations to extract a quantitative or even qualitative understanding of the field dynamics can be difficult. Attention here is focused on the dynamics of the conditional electric field: the field value at time t for a given initial value of the field. In addition to the relevant linear response function (electric field time correlation function), this property provides the complete nonlinear response of the electric field to arbitrary initial field perturbations. The static properties (distribution of electric fields and field time derivatives) and the electric field time correlation function have been known for some time for this model. We compare these results and the present result for the conditional electric field with molecular dynamics simulations including interactions. The comparisons suggest that the model provides a quantitative representation of electric field dynamics in real plasmas, except at strong coupling. The exact theoretical results are compared also with those obtained by modeling the electric field as a stochastic variable obeying a kangaroo process. The latter can be constructed to yield both the exact stationary distribution and the exact electric field time correlation function. However, we find that the conditional field is never well approximated by this process. An alternative representation of the joint distribution for electric fields, consistent with the exact stationary distribution, field correlation function, and conditional electric field, is suggested.
On the pressure field of nonlinear standing water waves
NASA Technical Reports Server (NTRS)
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.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
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.
Malanushenko, A.; Longcope, D. W.; McKenzie, D. E.
2009-12-20
Nonlinear force-free fields are the most general case of force-free fields, but the hardest to model as well. There are numerous methods of computing such fields by extrapolating vector magnetograms from the photosphere, but very few attempts have so far made quantitative use of coronal morphology. We present a method to make such quantitative use of X-ray and EUV images of coronal loops. Each individual loop is fit to a field line of a linear force-free field, allowing the estimation of the field line's twist, three-dimensional geometry, and the field strength along it. We assess the validity of such a reconstruction since the actual corona is probably not a linear force-free field, and that the superposition of linear force-free fields is generally not itself a force-free field. To do so, we perform a series of tests on nonlinear force-free fields, described in Low and Lou. For model loops we project field lines onto the photosphere. We compare several results of the method with the original field, in particular the three-dimensional loop shapes, local twist (coronal alpha), distribution of twist in the model photosphere, and strength of the magnetic field. We find that (1) for these trial fields, the method reconstructs twist with a mean absolute deviation of at most 15% of the range of photospheric twist, (2) heights of the loops are reconstructed with a mean absolute deviation of at most 5% of the range of trial heights, and (3) the magnitude of non-potential contribution to a photospheric field is reconstructed with a mean absolute deviation of at most 10% of the maximal value.
Modeling magnetic field amplification in nonlinear diffusive shock acceleration
NASA Astrophysics Data System (ADS)
Vladimirov, Andrey
2009-02-01
This research was motivated by the recent observations indicating very strong magnetic fields at some supernova remnant shocks, which suggests in-situ generation of magnetic turbulence. The dissertation presents a numerical model of collisionless shocks with strong amplification of stochastic magnetic fields, self-consistently coupled to efficient shock acceleration of charged particles. Based on a Monte Carlo simulation of particle transport and acceleration in nonlinear shocks, the model describes magnetic field amplification using the state-of-the-art analytic models of instabilities in magnetized plasmas in the presence of non-thermal particle streaming. The results help one understand the complex nonlinear connections between the thermal plasma, the accelerated particles and the stochastic magnetic fields in strong collisionless shocks. Also, predictions regarding the efficiency of particle acceleration and magnetic field amplification, the impact of magnetic field amplification on the maximum energy of accelerated particles, and the compression and heating of the thermal plasma by the shocks are presented. Particle distribution functions and turbulence spectra derived with this model can be used to calculate the emission of observable nonthermal radiation.
Nonlinear spinor fields in Bianchi type-VI spacetime
NASA Astrophysics Data System (ADS)
Saha, Bijan
2016-05-01
Within the scope of Bianchi type-VI cosmological model we study the role of spinor field in the evolution of the Universe. It is found that due to the spinor affine connections the energy-momentum tensor of the spinor field possesses non-diagonal components. The non-triviality of non-diagonal components of the energy-momentum tensor imposes some severe restrictions either on the spinor field or on the metric functions or on both of them. But unlike in the cases of Bianchi type-I or VI_0 , in the case of Bianchi type-VI model, it does not lead to the elimination of spinor field nonlinearity or mass term in the spinor field Lagrangian. It is also found that depending on the sign of self-coupling constant the model can give rise to late time acceleration or generate oscillatory mode of evolution.
Nonlinear nanoprobes for characterizing ultrafast optical near field
NASA Astrophysics Data System (ADS)
Li, Haifeng
With the rapid development of ultrafast optics and nanophotonics, it is crucial to measure the spatiotemporal evolution of an ultrafast optical near field in nanometer spatial and femtosecond temporal resolution with minimal perturbation. Although near-field scanning optical microscopy (NSOM) can achieve nanoscale spatial resolution and various ultrashort pulse diagnostic tools can characterize femtosecond laser pulses, yet such capability to noninvasively characterize the nanoscale characteristics of femtosecond pulses in all three spatial dimensions remains elusive. In this dissertation, we developed different types of nonlinear optical probes to characterize ultrashort optical pulses. The nonlinear optical probe is composed of three parts, a silica fiber taper, a single nanowire bonded to the end of the fiber and nonlinear nanoparticles attached on the tip of the nanowire. The optical fiber taper can be readily mounted on a mechanical stage and served as a macroscopic interface for handling and positioning control. The single nanowire bridges the dimension gap between the nanocrystals and the fiber taper, and is critical for achieving large aspect ratio and hence minimizing optical scattering and perturbation. The nonlinear nanoparticles give rise to its capability to characterize ultrashort optical pulses. The unique fusion of nanoscale and nonlinear features in developed nonlinear optical probes provides the ability of probing ultrafast optical field in complex 3D microand nano- structures. The demonstration of such ability is crucial for understanding the interaction of ultrafast optical fields and nanoscale systems. The fabrication processes of the nonlinear optical probes are illustrated in detail and the optical properties of the probes are investigated. Two different types of nonlinear optical probes, two-photon fluorescent nanoprobes and Second HARmonic nanoProbes (SHARP), are fabricated. Interferometric autocorrelation measurements near the focal point
Multicomponent Nonlinear Systems of Bose-Fermi Fields: Exact Solutions
Kostov, Nikolay A.; Gerdjikov, Vladimir S.; Valchev, Tihomir I.
2011-04-07
We present families of stationary solutions for a multicomponent nonlinear system of two boson and N{sub f} fermion fields in terms of elliptic functions of modulus k. This system is an extention of models, describing Bose-Fermi mixtures in the mean field approximation. We also single out the particular cases when the quasiperiodic solutions become periodic ones. In the limit of sinusoidal external potential (k{yields}0) our solutions model periodic waves trapped in an optical lattice. The other limit k{yields}1 provides solutions expressed by hyperbolic functions (vector solitons). Thus we demonstrate that our system describes quasi-periodic and periodic waves, as well as solitons.
Nonlinear model for coherent electric field structures in the magnetosphere
Jovanovic; Shukla
2000-05-01
A new pseudo-three-dimensional electron hole in a magnetized plasma is possible when the low-frequency ion dynamics is taken into account. The newly found nonlinear Bernstein-Greene-Kruskal stationary solution, whose parallel phase velocity ranges between almost zero and the electron thermal speed, has the form of a cylinder that is tilted relative to the magnetic field. These structures are interpreted as three-dimensional electron holes coupled with hydrodynamic vortices, and provide a possible theoretical explanation for the POLAR and FAST satellite observations of coherent structures characterized by bipolar spikes of the parallel electric field and large perpendicular ion kinetic energies.
Probing electric fields within organic transistors by nonlinear optics
NASA Astrophysics Data System (ADS)
Miranda, Paulo B.; Motti, Silvia G.; Gomes, Douglas J. C.
2015-03-01
Organic field-effect transistors (OFETs) are important building blocks in many organic devices, but further improvements in their performance will require a detailed knowledge of their operation mechanism. Thus mapping the electric fields in OFETs, both in the active organic layer and inside the gate dielectric, will allow a direct comparison with theoretical OFET models and guide advances in device engineering. The nonlinear optical processes of sum-frequency generation (SFG) and second-harmonic generation (SHG) may be used to probe electric fields in OFETs. With a proper choice of pump wavelength, SHG can selectively probe the field component along the OFET channel, inside the organic semiconductor. In contrast, SFG may probe the field within any organic material by selecting a specific molecular vibration and monitoring the field-enhanced SFG signal. Here we investigate OFETs fabricated with a polythiophene derivative (P3HT) on silicon substrates and with the insulating polymer PMMA for the dielectric layer. Both the strength and sign of the electric field in PMMA can be determined, yielding a direct probe of charge accumulation along the OFET channel. An extension of this technique to map the spatial distribution of accumulated charge along the channel will also be discussed. Work funded by FAPESP and CNPq (Brazil).
Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature
NASA Astrophysics Data System (ADS)
Zhang, Fan; McWilliams, Sean T.; Pfeiffer, Harald P.
2015-07-01
Recently, a family of exact force-free electrodynamic (FFE) solutions was given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by Michel, Menon and Dermer, and other authors. These solutions have been proposed as useful models for describing the outer magnetosphere of conducting stars. As with any exact analytical solution that aspires to describe actual physical systems, it is vitally important that the solution possess the necessary stability. In this paper, we show via fully nonlinear numerical simulations that the aforementioned FFE solutions, despite being highly special in their properties, are nonetheless stable under small perturbations. Through this study, we also introduce a three-dimensional pseudospectral relativistic FFE code that achieves exponential convergence for smooth test cases, as well as two additional well-posed FFE evolution systems in the appendix that have desirable mathematical properties. Furthermore, we provide an explicit analysis that demonstrates how propagation along degenerate principal null directions of the spacetime curvature tensor simplifies scattering, thereby providing an intuitive understanding of why these exact solutions are tractable, i.e. why they are not backscattered by spacetime curvature.
Modeling field emitter arrays using nonlinear line charge distribution
NASA Astrophysics Data System (ADS)
Biswas, Debabrata; Singh, Gaurav; Kumar, Raghwendra
2016-09-01
Modeling high aspect ratio field emitter arrays is a computational challenge due to the enormity of the resources involved. The line charge model (LCM) provides an alternate semi-analytical tool that has been used to model both infinite as well as finite sized arrays. It is shown that the linearly varying charge density used in the LCM generically mimics ellipsoidal emitters rather than a Cylindrical-Post-with-an-Ellipsoidal-Tip (CPET) that is typical of nanowires. Furthermore, generalizing the charge density beyond the linear regime allows for modeling shapes that are closer to a CPET. Emitters with a fixed base radius and a fixed apex radius are studied with a view to understanding the effect of nonlinearity on the tip enhancement factor and the emitter current in each case. Furthermore, an infinite square array of the CPET emitters is studied using the nonlinear line charge model, each having a height h =1500 μm and a base radius b =1.5 μm . It is found that for moderate external field strengths ( 0.3 -0.4 V /μm ), the array current density falls sharply for lattice spacings smaller than 4/3 h . Beyond this value, the maximal array current density can be observed over a range of lattice spacings and falls gradually thereafter.
Analytic lyapunov exponents in a classical nonlinear field equation
Franzosi; Gatto; Pettini; Pettini
2000-04-01
It is shown that the nonlinear wave equation partial differential(2)(t)straight phi- partial differential2xstraight phi-&mgr;(0) partial differential(x)( partial differential(x)straight phi)(3)=0, which is the continuum limit of the Fermi-Pasta-Ulam beta model, has a positive Lyapunov exponent lambda(1), whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of lambda(1) for the FPU model within the framework of a Riemannian description of Hamiltonian chaos. We also discuss a difficulty of the statistical mechanical treatment of this classical field system, which is absent in the dynamical description.
NONLINEAR SIMULATION OF TURBULENT FIELD LINES: DISPERSAL STATISTICS
Ragot, B. R.
2010-11-10
A new method for the full nonlinear computation of sets of turbulent field lines is introduced that extends the sums of random numbers distribution method previously applied to the computation of individual field lines. With a multiscale variation of the phases consistent with in situ observations of intermittent solar wind (SW) turbulence, the new method allows inclusion of the equivalent of more than four decades of turbulent scales with a fully three-dimensional distribution of wavevectors. As a first application, pairs of magnetic field lines are computed in independent realizations of the turbulence, for spectra typical of the quiet slow SW near 1 AU. The statistics of field-line dispersal are then studied from the simulated pairs of magnetic field lines and compared to earlier theoretical predictions. It appears that while the earlier theoretical picture remains relatively accurate as long as the mean variation of separation logarithm {Lambda} is less than one, the qualitative picture is quickly altered as {Lambda} grows past one.
NASA Astrophysics Data System (ADS)
Verweij, Martin D.; Demi, Libertario; van Dongen, Koen W. A.
2012-09-01
The Iterative Nonlinear Contrast Source (INCS) method is a full-wave method for the accurate computation of wide-angle, pulsed, nonlinear ultrasound fields appearing in, e.g., medical echoscopy. The method is based on the Westervelt equation and considers the occurring nonlinear term as a distributed contrast source that operates in a linear background medium. This formulation leads to an integral equation, which is solved in an iterative way. The original INCS method uses a Neumann scheme to successively approximate the nonlinear wave field in homogeneous, lossless, nonlinear media. To cope with attenuative and/or inhomogeneous nonlinear media, additional contrast sources may be introduced. Since these deteriorate the convergence rate of the Neumann scheme, more advanced iterative solution schemes like Bi-CGSTAB are required. To overcome the difficulty that such schemes only apply to linear integral equations, the nonlinear contrast source is linearized, at the cost of a significant systematic error in the fourth and higher harmonics. In this paper, a strategy is proposed in which the relevant iterative solution scheme is restarted with an updated version of the linearized contrast source. Results demonstrate the effectiveness of this strategy in eliminating the systematic error. In addition, it is shown that the same approach also improves the convergence rate in case of nonlinear propagation in media with attenuation.
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. Because 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 indicatemore » 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. As a results this theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.« less
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. Because 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. As a results this theory yields a flat oblique spectrum and underestimates the growth of oblique modes in a similar manner to kinetic theory relative to kinetic simulations.
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
Nonlinear Dirac equation solitary waves in external fields.
Mertens, Franz G; Quintero, Niurka R; Cooper, Fred; Khare, Avinash; Saxena, Avadh
2012-10-01
We consider nonlinear Dirac equations (NLDE's) in the 1+1 dimension with scalar-scalar self-interaction g2/κ+1(Ψ[over ¯]Ψ)κ+1 in the presence of various external electromagnetic fields. We find exact solutions for special external fields and we study the behavior of solitary-wave solutions to the NLDE in the presence of a wide variety of fields in a variational approximation depending on collective coordinates which allows the position, width, and phase of these waves to vary in time. We find that in this approximation the position q(t) of the center of the solitary wave obeys the usual behavior of a relativistic point particle in an external field. For time-independent external fields, we find that the energy of the solitary wave is conserved but not the momentum, which becomes a function of time. We postulate that, similarly to the nonlinear Schrödinger equation (NLSE), a sufficient dynamical condition for instability to arise is that dP(t)/dq[over ̇](t)<0. Here P(t) is the momentum of the solitary wave, and q[over ̇] is the velocity of the center of the wave in the collective coordinate approximation. We found for our choices of external potentials that we always have dP(t)/dq[over ̇](t)>0, so, when instabilities do occur, they are due to a different source. We investigate the accuracy of our variational approximation using numerical simulations of the NLDE and find that, when the forcing term is small and we are in a regime where the solitary wave is stable, that the behavior of the solutions of the collective coordinate equations agrees very well with the numerical simulations. We found that the time evolution of the collective coordinates of the solitary wave in our numerical simulations, namely the position of the average charge density and the momentum of the solitary wave, provide good indicators for when the solitary wave first becomes unstable. When these variables stop being smooth functions of time (t), then the solitary wave starts to distort
PREPROCESSING MAGNETIC FIELDS WITH CHROMOSPHERIC LONGITUDINAL FIELDS
Yamamoto, Tetsuya T.; Kusano, K.
2012-06-20
Nonlinear force-free field (NLFFF) extrapolation is a powerful tool for the modeling of the magnetic field in the solar corona. However, since the photospheric magnetic field does not in general satisfy the force-free condition, some kind of processing is required to assimilate data into the model. In this paper, we report the results of new preprocessing for the NLFFF extrapolation. Through this preprocessing, we expect to obtain magnetic field data similar to those in the chromosphere. In our preprocessing, we add a new term concerning chromospheric longitudinal fields into the optimization function proposed by Wiegelmann et al. We perform a parameter survey of six free parameters to find minimum force- and torque-freeness with the simulated-annealing method. Analyzed data are a photospheric vector magnetogram of AR 10953 observed with the Hinode spectropolarimeter and a chromospheric longitudinal magnetogram observed with SOLIS spectropolarimeter. It is found that some preprocessed fields show the smallest force- and torque-freeness and are very similar to the chromospheric longitudinal fields. On the other hand, other preprocessed fields show noisy maps, although the force- and torque-freeness are of the same order. By analyzing preprocessed noisy maps in the wave number space, we found that small and large wave number components balance out on the force-free index. We also discuss our iteration limit of the simulated-annealing method and magnetic structure broadening in the chromosphere.
Thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime
Yano, Ryosuke; Suzuki, Kojiro; Kuroda, Hisayasu
2009-12-15
Thermally relativistic flows in the early Universe can be characterized by the emergence of flows induced by gravitational-force-free particle motion in curved spacetime as well as induced by the gravitational force. In this paper, thermally relativistic flows induced by gravitational-force-free particle motion in curved spacetime are discussed on the basis of the general relativistic Boltzmann equation. As an object of analysis, we consider the flow from the static state inside the Schwarzschild radius of a thermally relativistic stuffed black hole induced by such motion. Analytical results obtained using the collisionless, nongravitational general relativistic Boltzmann equation reveal that the initial cluster is induced by gravitational-force-free particle motion. Numerical results obtained using the nongravitational general relativistic Anderson-Witting model confirm the presence of an initial cluster inside the thermally relativistic stuffed black hole, which is induced by gravitational-force-free particle motion.
Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results
NASA Technical Reports Server (NTRS)
Lee, Nam C.; Parks, George K.
1992-01-01
A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.
Magnetic energy dissipation in force-free jets
NASA Technical Reports Server (NTRS)
Choudhuri, Arnab Rai; Konigl, Arieh
1986-01-01
It is shown that a magnetic pressure-dominated, supersonic jet which expands or contracts in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to occur, the effective reconnection time must be a fraction of the expansion time. The dissipation rate for the axisymmetric minimum-energy field configuration is analytically derived. The results indicate that the field relaxation process could be a viable mechanism for powering the synchrotron emission in extragalactic jets if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.
NASA Astrophysics Data System (ADS)
Fu, Yiming; Chen, Yang; Zhong, Jun
2014-10-01
The nonlinear dynamic response problems of fiber-metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber-metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-β method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.
Forced Field Extrapolation of the Magnetic Structure of the Hα fibrils in the Solar Chromosphere
NASA Astrophysics Data System (ADS)
Xiaoshuai, Zhu; Huaning, Wang; Zhanle, Du; Han, He
2016-07-01
We present a careful assessment of forced field extrapolation using the Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetogram. We use several metrics to check the convergence property. The extrapolated field lines below 3600 km appear to be aligned with most of the Hα fibrils observed by the New Vacuum Solar Telescope. In the region where magnetic energy is far larger than potential energy, the field lines computed by forced field extrapolation are still consistent with the patterns of Hα fibrils while the nonlinear force-free field results show a large misalignment. The horizontal average of the lorentz force ratio shows that the forced region where the force-free assumption fails can reach heights of 1400-1800 km. The non-force-free state of the chromosphere is also confirmed based on recent radiation magnetohydrodynamics simulations.
Forced Field Extrapolation of the Magnetic Structure of the Hα fibrils in the Solar Chromosphere
NASA Astrophysics Data System (ADS)
Xiaoshuai, Zhu; Huaning, Wang; Zhanle, Du; Han, He
2016-07-01
We present a careful assessment of forced field extrapolation using the Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetogram. We use several metrics to check the convergence property. The extrapolated field lines below 3600 km appear to be aligned with most of the Hα fibrils observed by the New Vacuum Solar Telescope. In the region where magnetic energy is far larger than potential energy, the field lines computed by forced field extrapolation are still consistent with the patterns of Hα fibrils while the nonlinear force-free field results show a large misalignment. The horizontal average of the lorentz force ratio shows that the forced region where the force-free assumption fails can reach heights of 1400–1800 km. The non-force-free state of the chromosphere is also confirmed based on recent radiation magnetohydrodynamics simulations.
Nonlinear phase field model for electrodeposition in electrochemical systems
Liang, Linyun; Chen, Long-Qing
2014-12-29
A nonlinear phase-field model has been developed for describing the electrodeposition process in electrochemical systems that are highly out of equilibrium. Main thermodynamic driving forces for the electrode-electrolyte interface (EEI) evolution are limited to local variations of overpotential and ion concentration. Application of the model to Li-ion batteries describes the electrode interface motion and morphology change caused by charge mass transfer in the electrolyte, an electrochemical reaction at the EEI and cation deposition on the electrode surface during the charging operation. The Li electrodeposition rate follows the classical Butler-Volmer kinetics with exponentially and linearly depending on local overpotential and cation concentration at the electrode surface, respectively. Simulation results show that the Li deposit forms a fiber-like shape and grows parallel to the electric field direction. The longer and thicker deposits are observed both for higher current density and larger rate constant where the surface reaction rate is expected to be high. The proposed diffuse interface model well captures the metal electrodeposition phenomena in plenty of non-equilibrium electrochemical systems.
Role of nonlinear refraction in the generation of terahertz field pulses by light fields
Zabolotskii, A. A.
2013-07-15
The generation of microwave (terahertz) pulses without any envelope in a four-level quasi-resonant medium is considered. Two intense quasi-monochromatic laser fields lead to a partial upper-level population. Microwave field pulses cause the transition between these levels. For appropriately chosen scales, the evolution of the fields is shown to be described by the pseudo-spin evolution equations in a microwave field with the inclusion of nonlinear refraction caused by an adiabatic upper-level population. The evolution of terahertz field pulses is described outside the scope of the slow-envelope approximation. When a number of standard approximations are taken into account, this system of equations is shown to be equivalent to an integrable version of the generalized reduced Maxwell-Bloch equations or to the generalized three-wave mixing equations. The soliton solution found by the inverse scattering transform method is used as an example to show that nonlinear refraction leads to a strong compression of the microwave (terahertz) field soliton.
Nonlinear response of superconductors to alternating fields and currents
McDonald, J.
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.
Zhou, Fushun; Huang, Can Lu, Quanming; Wang, Shui; Xie, Jinlin
2015-09-15
Two-dimensional particle-in-cell simulation is performed to investigate magnetic reconnection in a force-free current sheet. The results show that the evolution of the ion diffusion region has two different phases. In the first phase, the electrons flow toward the X line along one pair of separatrices and away from the X line along the other pair of separatrices. Therefore, in the ion diffusion region, a distorted quadrupole structure of the out-of-plane magnetic field is formed, which is similar to that of a typical guide field reconnection in the Harris current sheet. In the second phase, the electrons move toward the X line along the separatrices and then flow away from the X line at the inner side of the separatrices. In the ion diffusion region, the out-of-plane magnetic field exhibits a characteristic quadrupole pattern with a good symmetry, which is similar to that of antiparallel reconnection in the Harris current sheet.
RECONSTRUCTION OF THE CORONAL MAGNETIC FIELD USING THE CESE-MHD METHOD
Jiang Chaowei; Feng, Xueshang; Xiang, Changqing; Fan, Yuliang E-mail: fengx@spaceweather.ac.cn E-mail: fanyuliang@bao.ac.cn
2011-02-01
We present a new implementation of the MHD relaxation method for reconstruction of the nearly force-free coronal magnetic field from a photospheric vector magnetogram. A new numerical MHD scheme is proposed to solve the full MHD equations by using the spacetime conservation-element and solution-element method. The bottom boundary condition is prescribed in a similar way as in the stress-and-relax method, by changing the transverse field incrementally to match the magnetogram, and other boundaries of the computational box are set by the nonreflecting boundary conditions. Applications to the well-known benchmarks for nonlinear force-free-field reconstruction, the Low and Lou force-free equilibria, validate the method and confirm its capability for future practical application, with observed magnetograms as inputs.
NASA Astrophysics Data System (ADS)
Wan, W. M. V.; Lee, H. C.; Hui, P. M.; Yu, K. W.
1996-08-01
The effective response of random media consisting of two different kinds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-field relation of the form J=χ\\|E\\|βE. A simple self-consistent mean-field theory, which leads to a simple way in determining the average local electric field in each constituent, is introduced. Each component is assumed to have a conductivity depending on the averaged local electric field. The averaged local electric field is then determined self-consistently. Numerical simulations of the system are carried out on random nonlinear resistor networks. Theoretical results are compared with simulation data, and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Ponte Castaneda et al. [Phys. Rev. B 46, 4387 (1992)]. It is found that the present theory, at small contrasts of χ between the two components, gives a result identical to that of Ponte Castaneda et al. up to second order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.
Weakly nonlinear study of normal-field instability in confined ferrofluids.
Lira, Sérgio A; Miranda, José A
2011-07-01
Similar to the classic three-dimensional Rosensweig instability, a ferrofluid confined in a vertical Hele-Shaw cell subjected to an in-plane normal magnetic field develops a periodic array of peaked interfacial structures. We perform a weakly nonlinear analysis that is able to reproduce the morphology of such pattern formation phenomenon at lowest nonlinear order. A mode-coupling theory is applied to compare the early nonlinear evolution of the interface with static shapes obtained when relevant forces equilibrate. Our nonlinear results indicate that the time-evolving shapes tend to approach stable stationary solutions. PMID:21867300
Nonlinear Generation of shear flows and large scale magnetic fields by small scale
NASA Astrophysics Data System (ADS)
Aburjania, G.
2009-04-01
EGU2009-233 Nonlinear Generation of shear flows and large scale magnetic fields by small scale turbulence in the ionosphere by G. Aburjania Contact: George Aburjania, g.aburjania@gmail.com,aburj@mymail.ge
Nonlinear waves on the free surface of a dielectric liquid in an oblique electric field
Gashkov, M. A.; Zubarev, N. M. Kochurin, E. A.
2015-09-15
The nonlinear dynamics of the free surface of an ideal dielectric liquid that is exposed to an external oblique electric field has been studied theoretically. In the framework of the Hamiltonian formalism, a system of nonlinear integro-differential equations has been derived that describes the dynamics of nonlinear waves in the small-angle approximation. It is established that for a liquid with high dielectric permittivity, these equations have a solution in the form of plane waves of arbitrary shape that propagate without distortion in the direction of the horizontal component of the external field.
NASA Astrophysics Data System (ADS)
Mukai, Y.; Hirori, H.; Yamamoto, T.; Kageyama, H.; Tanaka, K.
2016-01-01
We report on the nonlinear magnetization dynamics of a HoFeO3 crystal induced by a strong terahertz magnetic field resonantly enhanced with a split ring resonator and measured with magneto-optical Kerr effect microscopy. The terahertz magnetic field induces a large change (˜40%) in the spontaneous magnetization. The frequency of the antiferromagnetic resonance decreases in proportion to the square of the magnetization change. A modified Landau-Lifshitz-Gilbert equation with a phenomenological nonlinear damping term quantitatively reproduced the nonlinear dynamics.
NASA Astrophysics Data System (ADS)
Gong, Xiao-Bo; Liao, Yi; Xu, Zhao-Yi
2016-09-01
Based on the Lagrangian of the steady axisymmetric force-free magnetosphere (FFM) equation around Kerr black holes (KBHs), we find that the FFM equation can be rewritten in a new form as f,rr / (1 -μ2) +f,μμ / Δ + K (f (r , μ) , r , μ) = 0, where μ = - cos θ. With coordinate transformation, the above equation can be given as s,yy +s,zz + D (s (y , z) , y , z) = 0. Using this form, we prove that the Meissner effect is not possessed by a KBH-FFM with the condition dω / dAϕ ⩽ 0 and Hϕ (dHϕ / dAϕ) ⩾ 0, here Aϕ is the ϕ component of the vector potential A → , ω is the angular velocity of magnetic fields and Hϕ corresponds to twice the poloidal electric current.
Effect of nonlinear chirped Gaussian laser pulse on plasma wake field generation
Afhami, Saeedeh; Eslami, Esmaeil
2014-08-15
An ultrashort laser pulse propagating in plasma can excite a nonlinear plasma wake field which can accelerate charged particles up to GeV energies within a compact space compared to the conventional accelerator devices. In this paper, the effect of different kinds of nonlinear chirped Gaussian laser pulse on wake field generation is investigated. The numerical analysis of our results depicts that the excitation of plasma wave with large and highly amplitude can be accomplished by nonlinear chirped pulses. The maximum amplitude of excited wake in nonlinear chirped pulse is approximately three times more than that of linear chirped pulse. In order to achieve high wake field generation, chirp parameters and functions should be set to optimal values.
NASA Astrophysics Data System (ADS)
Lapert, M.; Tehini, R.; Turinici, G.; Sugny, D.
2008-08-01
We consider the optimal control of quantum systems interacting nonlinearly with an electromagnetic field. We propose monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a nonstandard choice of the cost, which is not quadratic in the field. These algorithms can be constructed for pure- and mixed-state quantum systems. The efficiency of the method is shown numerically for molecular orientation with a nonlinearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well approximated by pulses that could be implemented experimentally.
Effects of non-linearities on magnetic field generation
Nalson, Ellie; Malik, Karim A.; Christopherson, Adam J. E-mail: achristopherson@gmail.com
2014-09-01
Magnetic fields are present on all scales in the Universe. While we understand the processes which amplify the fields fairly well, we do not have a ''natural'' mechanism to generate the small initial seed fields. By using fully relativistic cosmological perturbation theory and going beyond the usual confines of linear theory we show analytically how magnetic fields are generated. This is the first analytical calculation of the magnetic field at second order, using gauge-invariant cosmological perturbation theory, and including all the source terms. To this end, we have rederived the full set of governing equations independently. Our results suggest that magnetic fields of the order of 10{sup -30}- 10{sup -27} G can be generated (although this depends on the small scale cut-off of the integral), which is largely in agreement with previous results that relied upon numerical calculations. These fields are likely too small to act as the primordial seed fields for dynamo mechanisms.
Nonlinear interactions between black holes and Proca fields
NASA Astrophysics Data System (ADS)
Zilhão, Miguel; Witek, Helvi; Cardoso, Vitor
2015-12-01
Physics beyond the standard model is an important candidate for dark matter, and an interesting testing ground for strong-field gravity: the equivalence principle ‘forces’ all forms of matter to fall in the same way, and it is therefore natural to look for imprints of these fields in regions with strong gravitational fields, such as compact stars or black holes (BHs). Here we study general relativity minimally coupled to a massive vector field, and how BHs in this theory lose ‘hair’. Our results indicate that BHs can sustain Proca field condensates for extremely long time-scales.
Stages: sub-Fourier dynamic shim updating using nonlinear magnetic field phase preparation.
Witschey, Walter R T; Littin, Sebastian; Cocosco, Chris A; Gallichan, Daniel; Schultz, Gerrit; Weber, Hans; Welz, Anna; Hennig, Jürgen; Zaitsev, Maxim
2014-01-01
Heterogeneity of the static magnetic field in magnetic resonance imaging may cause image artifacts and degradation in image quality. The field heterogeneity can be reduced by dynamically adjusting shim fields or dynamic shim updating, in which magnetic field homogeneity is optimized for each tomographic slice to improve image quality. A limitation of this approach is that a new magnetic field can be applied only once for each slice, otherwise image quality would improve somewhere to its detriment elsewhere in the slice. The motivation of this work is to overcome this limitation and develop a technique using nonlinear magnetic fields to dynamically shim the static magnetic field within a single Fourier-encoded volume or slice, called sub-Fourier dynamic shim updating. However, the nonlinear magnetic fields are not used as shim fields; instead, they impart a strong spatial dependence to the acquired MR signal by nonlinear phase preparation, which may be exploited to locally improve magnetic field homogeneity during acquisition. A theoretical description of the method is detailed, simulations and a proof-of-principle experiment are performed using a magnet coil with a known field geometry. The method is shown to remove artifacts associated with magnetic field homogeneity in balanced steady-state free-precession pulse sequences. We anticipate that this method will be useful to improve the quality of magnetic resonance images by removing deleterious artifacts associated with a heterogeneous static magnetic field.
Magnetic-field generation by the ablative nonlinear Rayleigh–Taylor instability
Nilson, P. M.; Gao, L.; Igumenshchev, I. V.; Fiksel, G.; Yan, R.; Davies, J. R.; Martinez, D.; Smalyuk, V. A.; Haines, M. G.; Blackman, E. G.; Froula, D. H.; Betti, R.; Meyerhofer, D. D.
2015-04-01
Experiments reporting magnetic-field generation by the ablative nonlinear Rayleigh–Taylor (RT) instability are reviewed. The experiments show how large-scale magnetic fields can, under certain circumstances, emerge and persist in strongly driven laboratory and astrophysical flows at drive pressures exceeding one million times atmospheric pressure.
Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation
Gerstner, Wulfram
2016-01-01
The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities. PMID:27690349
Nonlinear energy dissipation of magnetic nanoparticles in oscillating magnetic fields
NASA Astrophysics Data System (ADS)
Soto-Aquino, D.; Rinaldi, C.
2015-11-01
The heating of magnetic nanoparticle suspensions subjected to alternating magnetic fields enables a variety of emerging applications such as magnetic fluid hyperthermia and triggered drug release. Rosensweig (2002) [25] obtained a model for the heat dissipation rate of a collection of non-interacting particles. However, the assumptions made in this analysis make it rigorously valid only in the limit of small applied magnetic field amplitude and frequency (i.e., values of the Langevin parameter that are much less than unity and frequencies below the inverse relaxation time). In this contribution we approach the problem from an alternative point of view by solving the phenomenological magnetization relaxation equation exactly for the case of arbitrary magnetic field amplitude and frequency and by solving a more accurate magnetization relaxation equation numerically. We also use rotational Brownian dynamics simulations of non-interacting magnetic nanoparticles subjected to an alternating magnetic field to estimate the rate of energy dissipation and compare the results of the phenomenological theories to the particle-scale simulations. The results are summarized in terms of a normalized energy dissipation rate and show that Rosensweig's expression provides an upper bound on the energy dissipation rate achieved at high field frequency and amplitude. Estimates of the predicted dependence of energy dissipation rate, quantified as specific absorption rate (SAR), on magnetic field amplitude and frequency, and particle core and hydrodynamic diameter, are also given.
Nonlinear spatial integration in the receptive field surround of retinal ganglion cells.
Takeshita, Daisuke; Gollisch, Tim
2014-05-28
Throughout different sensory systems, individual neurons integrate incoming signals over their receptive fields. The characteristics of this signal integration are crucial determinants for the neurons' functions. For ganglion cells in the vertebrate retina, receptive fields are characterized by the well-known center-surround structure and, although several studies have addressed spatial integration in the receptive field center, little is known about how visual signals are integrated in the surround. Therefore, we set out here to characterize signal integration and to identify relevant nonlinearities in the receptive field surround of ganglion cells in the isolated salamander retina by recording spiking activity with extracellular electrodes under visual stimulation of the center and surround. To quantify nonlinearities of spatial integration independently of subsequent nonlinearities of spike generation, we applied the technique of iso-response measurements as follows: using closed-loop experiments, we searched for different stimulus patterns in the surround that all reduced the center-evoked spiking activity by the same amount. The identified iso-response stimuli revealed strongly nonlinear spatial integration in the receptive field surrounds of all recorded cells. Furthermore, cell types that had been shown previously to have different nonlinearities in receptive field centers showed similar surround nonlinearities but differed systematically in the adaptive characteristics of the surround. Finally, we found that there is an optimal spatial scale of surround suppression; suppression was most effective when surround stimulation was organized into subregions of several hundred micrometers in diameter, indicating that the surround is composed of subunits that have strong center-surround organization themselves. PMID:24872559
NASA Astrophysics Data System (ADS)
Kapuria, S.; Yaqoob Yasin, M.
2013-05-01
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.
Non-linear vacuum polarization in strong fields
Gyulassy, M.
1981-07-01
The Wichmann-Kroll formalism for calculating the vacuum polarization density to first order in ..cap alpha.. but to all orders in Z..cap alpha.. is derived. The most essential quantity is shown to be the electrons Green's function in these calculations. The method of constructing that Green's function in the field of finite radius nuclei is then presented.
Blumenfeld, I.; Clayton, C.E.; Decker, F.J.; Hogan, M.J.; Huang, C.; Ischebeck, R.; Iverson, R.H.; Joshi, C.; Katsouleas, T.; Kirby, N.; Lu, W.; Marsh, K.A.; Mori, W.B.; Muggli, P.; Oz, E.; Siemann, R.H.; Walz, D.R.; Zhou, M.; /UCLA
2012-06-12
The scaling of the two important figures of merit, the transformer ratio T and the longitudinal electric field E{sub z}, with the peak drive-bunch current I{sub p}, in a nonlinear plasma wakefield accelerator is presented for the first time. The longitudinal field scales as I{sub P}{sup 0.623{+-}0.007}, in good agreement with nonlinear wakefield theory ({approx}I{sub P}{sup 0.5}), while the unloaded transformer ratio is shown to be greater than unity and scales weakly with the bunch current. The effect of bunch head erosion on both parameters is also discussed.
Force-free swimming of a model helical flagellum in viscoelastic fluids
Liu, Bin; Powers, Thomas R.; Breuer, Kenneth S.
2011-01-01
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. PMID:22106263
Varying self-inductance and energy storage in a sheared force-free arcade. [of coronal loops
NASA Technical Reports Server (NTRS)
Zuccarello, F.; Burm, H.; Kuperus, M.; Raadu, M.; Spicer, D. S.
1987-01-01
An electric circuit analogy is used to model the build-up and storage of magnetic energy in the coronal loops known to exist in the atmosphere of the sun. The present parameterization of magnetic energy storage in an electric circuit analog uses a bulk current I flowing in the circuit and a self-inductance L. Because the self-inductance is determined by the geometry of the magnetic configuration any change in its dimensions will change L. If L is increased, the amount of magnetic energy stored and the rate at which magnetic energy is stored are both increased. One way of increasing L is to shear the magnetic field lines and increase their effective geometrical length. Using the force-free field approximation for a magnetic arcade whose field lines are sheared by photospheric motions, it is demonstrated that the increase of magnetic energy is initially due to the increase of the current intensity I and later mainly due to the increase of the self-inductance.
Nonlinear dependence of complex plasma parameters on applied electric field
Sodha, M. S.; Mishra, S. K.; Misra, Shikha
2011-02-15
This paper presents an analysis of the effect of an applied static or alternating electric field on the electron density and temperature, charge on the particles, the electron collision frequency, the electronic conductivity, and the coefficient of electron diffusion in a complex plasma (i) when not illuminated by light, which can cause photoelectric emission from the particles, and (ii) when so illuminated. A parametric analysis based on computations for some typical sets of parameters has also been made. The significance of this work to (i) the disappearance of a polar mesospheric summer echoes structure by radio wave and (ii) magneto-hydrodynamic (MHD) power generation has also been indicated. The time dependence of the various parameters after the application of the electric field has also been discussed.
Holomorphic normal form of nonlinear perturbations of nilpotent vector fields
NASA Astrophysics Data System (ADS)
Stolovitch, Laurent; Verstringe, Freek
2016-07-01
We consider germs of holomorphic vector fields at a fixed point having a nilpotent linear part at that point, in dimension n ≥ 3. Based on Belitskii's work, we know that such a vector field is formally conjugate to a (formal) normal form. We give a condition on that normal form which ensures that the normalizing transformation is holomorphic at the fixed point.We shall show that this sufficient condition is a nilpotent version of Bruno's condition (A). In dimension 2, no condition is required since, according to Stróżyna-Żołladek, each such germ is holomorphically conjugate to a Takens normal form. Our proof is based on Newton's method and sl2(C)-representations.
HELICITY CONSERVATION IN NONLINEAR MEAN-FIELD SOLAR DYNAMO
Pipin, V. V.; Sokoloff, D. D.; Zhang, H.; Kuzanyan, K. M.
2013-05-01
It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 10{sup 6}. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock-Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 10{sup 6}.
Nonlinear deformation of a ferrofluid droplet in a uniform magnetic field.
Zhu, Gui-Ping; Nguyen, Nam-Trung; Ramanujan, R V; Huang, Xiao-Yang
2011-12-20
This paper reports experimental and numerical results of the deformation of a ferrofluid droplet on a superhydrophobic surface under the effect of a uniform magnetic field. A water-based ferrofluid droplet surrounded by immiscible mineral oil was stretched by a magnetic field parallel to the substrate surface. The results show that an increasing flux density increases the droplet width and decreases the droplet height. A numerical model was established to study the equilibrium shape of the ferrofluid droplet. The governing equations for physical fields, including the magnetic field, are solved by the finite volume method. The interface between the two immiscible liquids was tracked by the level-set method. Nonlinear magnetization was implemented in the model. Comparison between experimental and numerical results shows that the numerical model can predict well the nonlinear deformation of a ferrofluid droplet in a uniform magnetic field. PMID:22044246
High-order optical processes in intense laser field: Towards nonperturbative nonlinear optics
NASA Astrophysics Data System (ADS)
Strelkov, V. V.
2016-05-01
We develop an approach describing nonlinear-optical processes in the strong-field domain characterized by the nonperturbative field-with-matter interaction. The polarization of an isolated atom in the external field calculated via the numerical solution of the time-dependent Schrödinger equation agrees with our analytical findings. For the practically important case of one strong laser field and several weaker fields, we derive and analytically solve propagation equations describing high-order (HO) wave mixing, HO parametric amplification, and HO stimulated scattering. These processes provide a way of efficient coherent xuv generation. Some properties of HO processes are new in nonlinear optics: essentially complex values of the coefficients in the propagation equations, the superexponential (hyperbolic) growing solutions, etc. Finally, we suggest conditions for the practical realization of these processes and discuss published numerical and experimental results where such processes could have been observed.
But, D. B.; Drexler, C.; Ganichev, S. D.; Sakhno, M. V.; Sizov, F. F.; Dyakonova, N.; Drachenko, O.; Gutin, A.; Knap, W.
2014-04-28
Terahertz power dependence of the photoresponse of field effect transistors, operating at frequencies from 0.1 to 3 THz for incident radiation power density up to 100 kW/cm{sup 2} was studied for Si metal–oxide–semiconductor field-effect transistors and InGaAs high electron mobility transistors. The photoresponse increased linearly with increasing radiation intensity up to the kW/cm{sup 2} range. Nonlinearity followed by saturation of the photoresponse was observed for all investigated field effect transistors for intensities above several kW/cm{sup 2}. The observed photoresponse nonlinearity is explained by nonlinearity and saturation of the transistor channel current. A theoretical model of terahertz field effect transistor photoresponse at high intensity was developed. The model explains quantitative experimental data both in linear and nonlinear regions. Our results show that dynamic range of field effect transistors is very high and can extend over more than six orders of magnitudes of power densities (from ∼0.5 mW/cm{sup 2} to ∼5 kW/cm{sup 2})
Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien; Tasinato, Gianmassimo
2009-01-01
We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbation on uniform density hypersurfaces, showing that on large scales it is sourced only by the nonlinear version of the entropy perturbation. We then expand these equations to second order in the perturbations, using a coordinate based formalism. Our results are relatively compact and elegant and enable one to identify the new effects coming from the non-canonical structure of the scalar fields Lagrangian. We also explain how to analyze, in our formalism, the interesting scenario of multi-field Dirac-Born-Infeld inflation.
NASA Astrophysics Data System (ADS)
Elhefnawy, Abdel R. F.
1993-05-01
A weakly nonlinear evolution of two dimensional wave packets on the surface of a magnetic fluid in the presence of an uniform magnetic field is presented, taking into account the surface tension. The method used is that of multiple scales to derive two partial differential equations. These differential equations can be combined to yield two alternate nonlinear Schroedinger equations. The first equation is valid near the cutoff wavenumber while the second equation is used to show that stability of uniform wave trains depends on the wavenumber, the density, the surface tension and the magnetic field. At the critical point, a generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. From the latter equation, the various stability criteria are obtained.
Detecting non-linearities in neuro-electrical signals: A study of synchronous local field potentials
NASA Astrophysics Data System (ADS)
Müller-Gerking, Johannes; Martinerie, Jacques; Neuenschwander, Sergio; Pezard, Laurent; Renault, Bernard; Varela, Francisco J.
The question of the presence and detection of non-linear dynamics and possibly low-dimensional chaos in the brain is still an open question, with recent results indicating that initial claims for low dimensionality were faulted by incomplete statistical testing. To make some progress on this question, our approach was to use stringent data analysis of precisely controlled and behaviorally significant neuroelectric data. There are strong indications that functional brain activity is correlated with synchronous local field potentials. We examine here such synchronous episodes in data recorded from the visual system of behaving cats and pigeons. Our purpose was to examine under these ideal conditions whether the time series showed any evidence of non-linearity concommitantly with the arising of synchrony. To test for non-linearity we have used surrogate sets for non-linear forecasting, the false nearest strands method, and an examination of deterministic vs stochastic modeling. Our results indicate that the time series under examination do show evidence for traces of non-linear dynamics but weakly, since they are not robust under changes of parameters. We conclude that low-dimensional chaos is unlikely to be found in the brain, and that a robust detection and characterization of higher-dimensional non-linear dynamics is beyond the reach of current analytical tools.
On the generation of nonlinear travelling waves in confined geometries using electric fields
Cimpeanu, R; Papageorgiou, D. T
2014-01-01
We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid–surface–structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid–fluid interface and study the characteristics of the generated velocity field inside the channel. PMID:24936019
On the generation of nonlinear travelling waves in confined geometries using electric fields.
Cimpeanu, R; Papageorgiou, D T
2014-07-28
We investigate electrostatically induced interfacial instabilities and subsequent generation of nonlinear coherent structures in immiscible, viscous, dielectric multi-layer stratified flows confined in small-scale channels. Vertical electric fields are imposed across the channel to produce interfacial instabilities that would normally be absent in such flows. In situations when the imposed vertical fields are constant, interfacial instabilities emerge due to the presence of electrostatic forces, and we follow the nonlinear dynamics via direct numerical simulations. We also propose and illustrate a novel pumping mechanism in microfluidic devices that does not use moving parts. This is achieved by first inducing interfacial instabilities using constant background electric fields to obtain fully nonlinear deformations. The second step involves the manipulation of the imposed voltage on the lower electrode (channel wall) to produce a spatio-temporally varying voltage there, in the form of a travelling wave with pre-determined properties. Such travelling wave dielectrophoresis methods are shown to generate intricate fluid-surface-structure interactions that can be of practical value since they produce net mass flux along the channel and thus are candidates for microfluidic pumps without moving parts. We show via extensive direct numerical simulations that this pumping phenomenon is a result of an externally induced nonlinear travelling wave that forms at the fluid-fluid interface and study the characteristics of the generated velocity field inside the channel. PMID:24936019
Exactly solvable model for nonlinear light-matter interaction in an arbitrary time-dependent field
Brown, J. M.; Lotti, A.; Teleki, A.; Kolesik, M.
2011-12-15
Exact analytic expressions are derived for the dipole moment and nonlinear current of a one-dimensional quantum particle subject to a short-range attractive potential and an arbitrary time-dependent electric field. An efficient algorithm for the current evaluation is described and a robust implementation suitable for numerical simulations is demonstrated.
String solutions in the S/sup 2/ nonlinear sigma-model with a gauge field
Rybakov, Yu.P.; Khalder, A.L.
1986-11-01
A variant of the S/sup 2/ nonlinear sigma-model of Faddeev with an Abelian gauge field is considered. By using a direct variational method the authors demonstrate the existence of string-like solutions in this model and they establish the regularity of these solutions.
Kinetic model of force-free current sheets with non-uniform temperature
Kolotkov, D. Y.; Nakariakov, V. M.; Vasko, I. Y.
2015-11-15
The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed.
Kinetic model of force-free current sheets with non-uniform temperature
NASA Astrophysics Data System (ADS)
Kolotkov, D. Y.; Vasko, I. Y.; Nakariakov, V. M.
2015-11-01
The kinetic model of a one-dimensional force-free current sheet (CS) developed recently by Harrison and Neukirch [Phys. Rev. Lett. 102(13), 135003 (2009)] predicts uniform distributions of the plasma temperature and density across the CS. However, in realistic physical systems, inhomogeneities of these plasma parameters may arise quite naturally due to the boundary conditions or local plasma heating. Moreover, as the CS spatial scale becomes larger than the characteristic kinetic scales (the regime often referred to as the MHD limit), it should be possible to set arbitrary density and temperature profiles. Thus, an advanced model has to allow for inhomogeneities of the macroscopic plasma parameters across the CS, to be consistent with the MHD limit. In this paper, we generalise the kinetic model of a force-free current sheet, taking into account the inhomogeneity of the density and temperature across the CS. In the developed model, the density may either be enhanced or depleted in the CS central region. The temperature profile is prescribed by the density profile, keeping the plasma pressure uniform across the CS. All macroscopic parameters, as well as the distribution functions for the protons and electrons, are determined analytically. Applications of the developed model to current sheets observed in space plasmas are discussed.
Time-dependent Force-free Pulsar Magnetospheres: Axisymmetric and Oblique Rotators
Spitkovsky, Anatoly; /KIPAC, Menlo Park
2006-04-10
Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or ''force-free'') limit of MHD. We present a new numerical method for solution of equations of force-free relativistic MHD based on the finite-difference time-domain (FDTD) approach with a prescription for handling spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. For the aligned rotator we confirm the general properties of the time-independent solution of Contopoulos et al. (1999). For the oblique rotator we present the 3D structure of the magnetosphere and compute, for the first time, the spindown power of pulsars as a function of inclination of the magnetic axis. We find the pulsar spindown luminosity to be L {approx} ({mu}{sup 2}{Omega}{sub *}{sup 4}/c{sup 3})(1 + sin{sup 2}{alpha}) for a star with the dipole moment {mu}, rotation frequency {Omega}{sub *}, and magnetic inclination angle {alpha}. We also discuss the effects of current sheet resistivity and reconnection on the structure and evolution of the magnetosphere.
Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range
NASA Astrophysics Data System (ADS)
Acosta, V.; Ledbetter, M. P.; Rochester, S. M.; Budker, D.; Jackson Kimball, D. F.; Hovde, D. C.; Gawlik, W.; Pustelny, S.; Zachorowski, J.; Yashchuk, V. V.
2006-05-01
Recent work investigating resonant nonlinear magneto-optical rotation (NMOR) related to long-lived (τrel˜1s) ground-state atomic coherences has demonstrated potential magnetometric sensitivities exceeding 10-11G/Hz for small (≲1μG ) magnetic fields. In the present work, NMOR using frequency-modulated light (FM NMOR) is studied in the regime where the longitudinal magnetic field is in the geophysical range (˜500mG) , of particular interest for many applications. In this regime a splitting of the FM NMOR resonance due to the nonlinear Zeeman effect is observed. At sufficiently high light intensities, there is also a splitting of the FM NMOR resonances due to ac Stark shifts induced by the optical field, as well as evidence of alignment-to-orientation conversion type processes. The consequences of these effects for FM-NMOR-based atomic magnetometry in the geophysical field range are considered.
NASA Astrophysics Data System (ADS)
Titov, Serguey V.; Déjardin, Pierre-Michel; El Mrabti, Halim; Kalmykov, Yuri P.
2010-09-01
The nonlinear ac response of the magnetization M(t) of a uniaxially anisotropic superparamagnetic nanoparticle subjected to both ac and dc bias magnetic fields of arbitrary strengths and orientations is determined by averaging Gilbert’s equation augmented by a random field with Gaussian white-noise properties in order to calculate exactly the relevant statistical averages. It is shown that the magnetization dynamics of the uniaxial particle driven by a strong ac field applied at an angle to the easy axis of the particle (so that the axial symmetry is broken) alters drastically leading to different nonlinear effects due to coupling of the thermally activated magnetization reversal mode with the precessional modes of M(t) via the driving ac field.
Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites
NASA Astrophysics Data System (ADS)
Sarychev, Andrey K.; Shalaev, Vladimir M.
2000-09-01
A scaling theory of local field fluctuations and optical nonlinearities is developed for random metal-dielectric composites near a percolation threshold. The theory predicts that in the optical and infrared spectral ranges the local fields are very inhomogeneous and consist of sharp peaks representing localized surface plasmons (s.p.). The localization maps the Anderson localization problem described by the random Hamiltonian with both on- and off-diagonal disorder. The local fields exceed the applied field by several orders of magnitudes resulting in giant enhancements of various optical phenomena. A new numerical method based on the developed theory is suggested. This method is employed to calculate the giant field fluctuations and enhancement of various optical processes in 2D metal-dielectric composites - semicontinuous metal films. The local field fluctuations appear to be highly correlated in space. These fluctuations result in dramatically enhanced Rayleigh and Raman light scattering. The scaling analysis is performed to describe the giant light scattering in a vicinity of the percolation threshold. The developed theory describes quantitatively enhancement of various nonlinear optical processes in percolation composites. It is shown that enhancement depends strongly on whether nonlinear multiphoton scattering includes an act of photon subtraction (annihilation). The magnitudes and spectral dependencies of enhancements in optical processes with photon subtraction, such as Raman and hyper-Raman scattering, Kerr refraction and four-wave mixing, are dramatically different from those processes without photon subtraction, such as sum-frequency and high-harmonic generation. Electromagnetic properties of metal-dielectric crystals and composites beyond the quasistatic approximation are also studied. Equations of macroscopic electromagnetism are presented for these systems. Both linear and nonlinear optical responses are considered in the case of a strong skin effect
Sub transitional and supersonic travelling field response in nonlinear viscoelastic media
NASA Technical Reports Server (NTRS)
Padovan, Joe
1989-01-01
This paper considers the problem of traveling fields in nonlinearly elastic and viscoelastic media. By introducing the appropriate hierarchical partitioning, the governing equations of motion are shown to be a continuum analogy of Duffing's equation. Through the use of a constrained perturbation procedure, the response behavior is obtained in sub, transitional as well as supersonic ranges of disturbance speed. Due to the generality of the approach taken, the effects of damping can be handled. To quantify the effects of material nonlinearity, strain softening and hardening are considered. Such behavior is quantified in general example problems.
Effect of nonlinear absorption on electric field applied lead chloride by Z-scan technique
Rejeena, I.; Lillibai,; Nampoori, V. P. N.; Radhakrishnan, P.; Rahimkutty, M. H.
2014-10-15
The preparation, spectral response and optical nonlinearity of gel grown lead chloride single crystals subjected to electric field of 20V using parallel plate arrangements have been investigated. Optical band gap of the samples were determined using linear absorption spectra. Open aperture z-scan was employed for the determination of nonlinear absorption coefficient of PbCl{sub 2} solution. The normalized transmittance curve exhibits a valley shows reverse saturable absorption. The non linear absorption at different input fluences were recorded using a single Gaussian laser beam in tight focus geometry. The RSA nature of the sample makes it suitable for optical limiting applications.
Jiménez-Aquino, J I; Romero-Bastida, M
2011-07-01
The detection of weak signals through nonlinear relaxation times for a Brownian particle in an electromagnetic field is studied in the dynamical relaxation of the unstable state, characterized by a two-dimensional bistable potential. The detection process depends on a dimensionless quantity referred to as the receiver output, calculated as a function of the nonlinear relaxation time and being a characteristic time scale of our system. The latter characterizes the complete dynamical relaxation of the Brownian particle as it relaxes from the initial unstable state of the bistable potential to its corresponding steady state. The one-dimensional problem is also studied to complement the description.
Effect of nonlinear absorption on electric field applied lead chloride by Z-scan technique
NASA Astrophysics Data System (ADS)
Rejeena, I.; Lillibai, Rahimkutty, M. H.; Nampoori, V. P. N.; Radhakrishnan, P.
2014-10-01
The preparation, spectral response and optical nonlinearity of gel grown lead chloride single crystals subjected to electric field of 20V using parallel plate arrangements have been investigated. Optical band gap of the samples were determined using linear absorption spectra. Open aperture z-scan was employed for the determination of nonlinear absorption coefficient of PbCl2 solution. The normalized transmittance curve exhibits a valley shows reverse saturable absorption. The non linear absorption at different input fluences were recorded using a single Gaussian laser beam in tight focus geometry. The RSA nature of the sample makes it suitable for optical limiting applications.
Nonlinear dynamical law governs magnetic field induced changes in lymphoid phenotype.
Marino, A A; Wolcott, R M; Chervenak, R; Jourd'heuil, F; Nilsen, E; Frilot, C
2001-12-01
The results of many different types of animal and human studies dealing with the biological effects of exposure to low frequency electromagnetic fields (EMFs) have consistently been both positive and negative. We addressed the question of why this pattern had occurred so commonly in biological studies involving exposure to EMFs and hypothesized that it stemmed from the prevalent use of a linear model to characterize what are inherently nonlinear input-output relationships. The hypothesis was tested by analyzing biological data using a novel statistical procedure that could be adjusted to detect either nonlinear or linear effects. The reliability of the procedure was established using positive and negative controls and by comparison with the results obtained from sampling a known nonlinear system. In four independent experiments, male and female mice were exposed continuously to 0.1 or 0.5 mT, 60 Hz, for 175 days, and the effect on 20 immune parameters was measured using flow cytometry and functional assays. In each experiment, EMF exposure resulted in statistically significant changes in lymphoid phenotype when and only when the response of the animals to the fields was analyzed as if it were governed by nonlinear laws. Our results suggest that the pattern of inconsistency in the EMF bioeffects studies is an artifact resulting from an incorrect choice of the conceptual model for the relation between the field and the biological effect it causally determines. PMID:11748671
NASA Astrophysics Data System (ADS)
Samal, M. K.; Seshu, P.
2009-06-01
Piezoceramic materials exhibit different types of nonlinearities depending upon the magnitude of the mechanical and electric field strength in the continuum. Some of the nonlinearities observed under weak electric fields are: presence of superharmonics in the response spectra and jump phenomena etc. especially if the system is excited near resonance. In this paper, an analytical solution (in 2D plane stress domain) for the nonlinear response of a rectangular piezoceramic slab has been obtained by use of Rayleigh-Ritz method and perturbation technique. The eigenfunction obtained from solution of the differential equation of the linear problem has been used as the shape function in the Rayleigh-Ritz method. Forced vibration experiments have been conducted on a rectangular piezoceramic slab by applying varying electric field strengths across the thickness and the results have been compared with those of analytical solution. The analytical solutions compare well with those of experimental results. These solutions should serve as a method to validate the FE formulations as well as help in the determination of nonlinear material property coefficients for these materials.
Nonlinear optics response of semiconductor quantum wells under high magnetic fields
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 {yields} {infinity}. 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.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity
NASA Astrophysics Data System (ADS)
Clayton, C. E.; Adli, E.; Allen, J.; An, W.; Clarke, C. I.; Corde, S.; Frederico, J.; Gessner, S.; Green, S. Z.; Hogan, M. J.; Joshi, C.; Litos, M.; Lu, W.; Marsh, K. A.; Mori, W. B.; Vafaei-Najafabadi, N.; Xu, X.; Yakimenko, V.
2016-08-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within +/-3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m-1 to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity.
Gang, Noa; Persinger, Michael A
2011-12-01
There have been multiple claims that exposing water to a static magnetic field affects its properties which influence living systems. To test this hypothesis, planarian subsequent to dissection were maintained in spring water that had been previously exposed for only one day to one of three (16, 160, or 1,600 G) intensity static magnetic fields or to a reference condition. Although there was no significant difference in regeneration rates over the subsequent seven-day period, there was a statistically significant nonlinear effect for planarian mobility and diffusion rates. Both mobility rates and diffusion velocity of a liquid within the water that had been exposed to the 16 G field was about twice that for water exposed to the other intensities. These results imply that nonlinear biophysical effects may emerge under specific conditions of intensity ranges for particular volumes of water.
Quantum plasmonics: nonlinear effects in the field enhancement of a plasmonic nanoparticle dimer.
Marinica, D C; Kazansky, A K; Nordlander, P; Aizpurua, J; Borisov, A G
2012-03-14
A fully quantum mechanical investigation using time-dependent density functional theory reveals that the field enhancement in a coupled nanoparticle dimer can be strongly affected by nonlinear effects. We show that both classical as well as linear quantum mechanical descriptions of the system fail even for moderate incident light intensities. An interparticle current resulting from the strong field photoemission tends to neutralize the plasmon-induced surface charge densities on the opposite sides of the nanoparticle junction. Thus, the coupling between the two nanoparticles and the field enhancement is reduced as compared to linear theory. A substantial nonlinear effect is revealed already at incident powers of 10(9) W/cm(2) for interparticle separation distances as large as 1 nm and down to the touching limit.
Nonlinear Faraday effect in CdS semiconductor in an ultrahigh magnetic field
Druzhinin, V.V.; Tatsenko, O.M.; Bykov, A.I.
1994-08-01
A significant nonlinearity in the angle of rotation polarization plane was observed in CdS at wavelengths of 494 in the presence of high magnetic fields (0.5-5 MG). The onset significant nonlinearity also depended on sample temperature. An absorption study with probe wavelength of {approximately} 494 nm revealed an increase in optical transmission associated with a splitting of the conduction band. Dispersion, field and temperature curves indicate a low conduction electron mass m{sub e} = 0.3 m{sub o}. A numerical calculation and interpretation of the observed effects was carried out using band theory. The optical and magnetooptical properties of semiconducting crystals of CdS were studied, reviews of which are presented in [1,2]. This article describes joint American-Russian experiments to study the optical and magnetooptical properties of CdS in ultrahigh fields to {approximately} 7 MG.
Sela, I.; Watkins, D.E.; Laurich, B.K.; Smith, D.L. ); Subbanna, S.; Kroemer, H. )
1991-02-18
The nonlinear optical properties of a new class of strained-layer superlattices (intrinsic Stark effect superlattices) have been investigated. Specifically, we have compared the nonlinear transmission of Ga{sub 1{minus}{ital x}}In{sub {ital x}}As-GaAs strained-layer superlattices grown along the (211) axis to identical superlattices grown along the (100) axis, and found that the optical nonlinearity in the (211) sample is about one order of magnitude greater than in the (100) sample. A blue shift of the exciton resonance and an increase in the exciton absorption strength in the (211) sample with increasing light intensity was observed (attributed to screening of the intrinsic Stark effect fields by photogenerated carriers), resulting in the stronger optical nonlinearity. The maximum of the nonlinear absorption index, {vert bar}{alpha}{sub 2}{vert bar}, in the (211) sample was 54 cm/W ({vert bar}Im {chi}{sup 3}{vert bar}=0.33 esu) whereas in the (100) sample the maximum of {vert bar}{alpha}{sub 2}{vert bar} was 6.9 cm/W ({vert bar}Im {chi}{sup 3}{vert bar}=0.042 esu). The measured carrier recovery time in both samples was 2 ns.
Nano-imaging collagen by atomic force, near-field and nonlinear microscope
NASA Astrophysics Data System (ADS)
Lim, Ken Choong; Tang, Jinkai; Li, Hao; Ng, Boon Ping; Kok, Shaw Wei; Wang, Qijie; Zhang, Ying
2015-03-01
As the most abundant protein in the human body, collagen has a very important role in vast numbers of bio-medical applications. The unique second order nonlinear properties of fibrillar collagen make it a very important index in nonlinear optical imaging based disease diagnosis of the brain, skin, liver, colon, kidney, bone, heart and other organs in the human body. The second-order nonlinear susceptibility of collagen has been explored at the macroscopic level and was explained as a volume-averaged molecular hyperpolarizability. However, details about the origin of optical second harmonic signals from collagen fibrils at the molecular level are still not clear. Such information is necessary for accurate interpolation of bio-information from nonlinear optical imaging techniques. The later has shown great potential in collagen based disease diagnosis methodologies. In this paper, we report our work using an atomic force microscope (AFM), near field (SNOM) and nonlinear laser scanning microscope (NLSM) to study the structure of collagen fibrils and other pro-collagen structures.
DC magnetic field sensing based on the nonlinear magnetoelectric effect in magnetic heterostructures
NASA Astrophysics Data System (ADS)
Burdin, Dmitrii; Chashin, Dmitrii; Ekonomov, Nikolai; Fetisov, Leonid; Fetisov, Yuri; Shamonin, Mikhail
2016-09-01
Recently, highly sensitive magnetic field sensors using the magnetoelectric effect in composite ferromagnetic-piezoelectric layered structures have been demonstrated. However, most of the proposed concepts are not useful for measuring dc magnetic fields, because the conductivity of piezoelectric layers results in a strong decline of the sensor’s sensitivity at low frequencies. In this paper, a novel functional principle of magnetoelectric sensors for dc magnetic field measurements is described. The sensor employs the nonlinear effect of voltage harmonic generation in a composite magnetoelectric structure under the simultaneous influence of a strong imposed ac magnetic field and a weak dc magnetic field to be measured. This physical effect arises due to the nonlinear dependence of the magnetostriction in the ferromagnetic layer on the magnetic field. A sensor prototype comprising of a piezoelectric fibre transducer sandwiched between two layers of the amorphous ferromagnetic Metglas® alloy was fabricated. The specifications regarding the magnetic field range, frequency characteristics, and noise level were studied experimentally. The prototype showed the responsivity of 2.5 V mT-1 and permitted the measurement of dc magnetic fields in the range of ~10 nT to about 0.4 mT. Although sensor operation is based on the nonlinear effect, the sensor response can be made linear with respect to the measured magnetic field in a broad dynamic range extending over 5 orders of magnitude. The underlying physics is explained through a simplified theory for the proposed sensor. The functionality, differences and advantages of the magnetoelectric sensor compare well with fluxgate magnetometers. The ways to enhance the sensor performance are considered.
DC magnetic field sensing based on the nonlinear magnetoelectric effect in magnetic heterostructures
NASA Astrophysics Data System (ADS)
Burdin, Dmitrii; Chashin, Dmitrii; Ekonomov, Nikolai; Fetisov, Leonid; Fetisov, Yuri; Shamonin, Mikhail
2016-09-01
Recently, highly sensitive magnetic field sensors using the magnetoelectric effect in composite ferromagnetic-piezoelectric layered structures have been demonstrated. However, most of the proposed concepts are not useful for measuring dc magnetic fields, because the conductivity of piezoelectric layers results in a strong decline of the sensor’s sensitivity at low frequencies. In this paper, a novel functional principle of magnetoelectric sensors for dc magnetic field measurements is described. The sensor employs the nonlinear effect of voltage harmonic generation in a composite magnetoelectric structure under the simultaneous influence of a strong imposed ac magnetic field and a weak dc magnetic field to be measured. This physical effect arises due to the nonlinear dependence of the magnetostriction in the ferromagnetic layer on the magnetic field. A sensor prototype comprising of a piezoelectric fibre transducer sandwiched between two layers of the amorphous ferromagnetic Metglas® alloy was fabricated. The specifications regarding the magnetic field range, frequency characteristics, and noise level were studied experimentally. The prototype showed the responsivity of 2.5 V mT‑1 and permitted the measurement of dc magnetic fields in the range of ~10 nT to about 0.4 mT. Although sensor operation is based on the nonlinear effect, the sensor response can be made linear with respect to the measured magnetic field in a broad dynamic range extending over 5 orders of magnitude. The underlying physics is explained through a simplified theory for the proposed sensor. The functionality, differences and advantages of the magnetoelectric sensor compare well with fluxgate magnetometers. The ways to enhance the sensor performance are considered.
ON THE STABILITY OF NON-FORCE-FREE MAGNETIC EQUILIBRIA IN STARS
Duez, V.; Braithwaite, J.; Mathis, S.
2010-11-20
The existence of stable magnetic configurations in white dwarfs, neutron stars, and various non-convective stellar regions is now well recognized. It has recently been shown numerically that various families of equilibria, including axisymmetric mixed poloidal-toroidal configurations, are stable. Here we test the stability of an analytically derived non-force-free magnetic equilibrium resulting from an initial relaxation (self-organization) process, using three-dimensional magnetohydrodynamic simulations: the obtained mixed configuration is compared with the dynamical evolution of its purely poloidal and purely toroidal components, both known to be unstable. The mixed equilibrium shows no sign of instability under white noise perturbations. This configuration therefore provides a good description of magnetic equilibrium topology inside non-convective stellar objects and will be useful to initialize magneto-rotational transport in stellar evolution codes and in multi-dimensional magnetohydrodynamic simulations.
Light bending by nonlinear electrodynamics under strong electric and magnetic field
Kim, Jin Young; Lee, Taekoon E-mail: tlee@kunsan.ac.kr
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.
Nonlinear spinor field in isotropic space-time and dark energy models
NASA Astrophysics Data System (ADS)
Saha, Bijan
2016-07-01
Within the scope of the isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not possess nontrivial non-diagonal components of energy-momentum tensor, consequently it does not impose any additional restrictions on the components of the spinor field or metric function. The spinor description of different matter was given and the evolution of the Universe corresponding to these sources is illustrated. In the framework of a three-fluid system the utility of spinor description of matter is established.
Spata, Michael
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 and extra-classical receptive field properties and the statistics of natural scenes.
Zetzsche, C; Röhrbein, F
2001-08-01
-stopping, complex-cell properties and extra-classical receptive field properties, but the 'ideal' complex cells seem only to occur with PCA. Thus, a combination of ON/OFF nonlinearities with an integrated PCA-ICA strategy seems necessary to exploit the statistical properties of natural images. PMID:11563533
Effect of Transverse Magnetic Fields on Cold-Atom Nonlinear Magneto-Optical Rotation
NASA Astrophysics Data System (ADS)
Meyer, David; Kunz, Paul; Fatemi, Fredrik; Quraishi, Qudsia
2016-05-01
We investigate nonlinear magneto-optical rotation (NMOR) in cold atoms in the presence of a transverse magnetic field where alignment-to-orientation conversion (AOC) dominates. The AOC mechanism, which relies on AC-Stark shifts generated by a strong, off-resonant probe beam, significantly alters the NMOR resonance. When an additional magnetic field is present, parallel to the electric field of the light, a nested feature within this NMOR resonance manifests. Unlike similar features observed with lower optical power in warm vapors, attributed to optical pumping through nearby hyperfine levels, this feature is due solely to the AOC mechanism. Using numerical simulations, a perturbative solution, and experimental observations we characterize the feature with respect to optical power, optical polarization, magnetic field strength, and magnetic field direction. These results shed further light on the AOC mechanism common to NMOR-based experiments and we demonstrate a potential application to measure transverse DC magnetic fields and spatial gradients.
Contributions of the substrate electric field to the molecular adsorbate optical nonlinearities
Zouari, M.; Villaeys, A.A.
2005-10-15
The nonlinear optical response of an adsorbate, whose structure is altered by the inhomogeneous electrostatic field of the substrate, has been evaluated with a particular emphasis on the sum-frequency generation process. In the limiting case of an homogeneous electrostatic field, besides the contributions associated with the induced dipole moments, we have additional contributions which only exist if the adsorbed molecule has permanent dipole moments. Also, the Franck-Condon factors of the unperturbed molecule weight the internal couplings induced by the electrostatic field. For the more general inhomogeneous electrostatic field case, while the main observations remain valid, the Franck-Condon factors are modified by the molecular structure changes induced by the electrostatic field. In addition, we have a strong redistribution of the vibronic couplings resulting from the analytical Q dependence of the partial charge distribution which is a signature of the field inhomogeneities.
Tensor of the nonlinear polarizability of anisotropic medium and ``local'' field method
NASA Astrophysics Data System (ADS)
Lavric, V. V.; Ovander, L. N.; Shunyakov, V. T.
1983-08-01
The nonlinear polarizability tensor (NPT) for a molecular crystal of arbitrary symmetry has been obtained within the framework of polariton theory. Use of the Göppert-Mayer unitary transformation for the Hamiltonian of the crystal plus quantized electromagnetic field system made it possible to represent finally the result for the NPT in a compact form and to compare with results of semiphenomenological calculation of the NPT and to go out of the framework of the Gaitler-London approximation.
The hysteresis-free negative capacitance field effect transistors using non-linear poly capacitance
NASA Astrophysics Data System (ADS)
Fan, S.-T.; Yan, J.-Y.; Lai, D.-C.; Liu, C. W.
2016-08-01
A gate structure design for negative capacitance field effect transistors (NCFETs) is proposed. The hysteresis loop in current-voltage performances is eliminated by the nonlinear C-V dependence of polysilicon in the gate dielectrics. Design considerations and optimizations to achieve the low SS and hysteresis-free transfer were elaborated. The effects of gate-to-source/drain overlap, channel length scaling, interface trap states and temperature impact on SS are also investigated.
NASA Astrophysics Data System (ADS)
Gong, Jiao-Li; Liu, Jin-Song; Chu, Zheng; Yang, Zhen-Gang; Wang, Ke-Jia; Yao, Jian-Quan
2016-10-01
The nonlinear radiation responses of two different n-doped bulk semiconductors: indium antimonide (InSb) and indium arsenide (InAs) in an intense terahertz (THz) field are studied by using the method of ensemble Monte Carlo (EMC) at room temperature. The results show that the radiations of two materials generate about 2-THz periodic regular spectrum distributions under a high field of 100 kV/cm at 1-THz center frequency. The center frequencies are enhanced to about 7 THz in InSb, and only 5 THz in InAs, respectively. The electron valley occupancy and the percentage of new electrons excited by impact ionization are also calculated. We find that the band nonparabolicity and impact ionization promote the generation of nonlinear high frequency radiation, while intervalley scattering has the opposite effect. Moreover, the impact ionization dominates in InSb, while impact ionization and intervalley scattering work together in InAs. These characteristics have potential applications in up-convension of THz wave and THz nonlinear frequency multiplication field. Project supported by the National Natural Science Foundation of China (Grant Nos. 11574105 and 61177095), the Natural Science Foundation of Hubei Province, China (Grant Nos. 2012FFA074 and 2013BAA002), the Wuhan Municipal Applied Basic Research Project, China (Grant No. 20140101010009), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2013KXYQ004 and 2014ZZGH021).
ANALYSIS OF HIGH FIELD NON-LINEAR LOSSES ON SRF SURFACES DUE TO SPECIFIC TOPOGRAPHIC ROUGHNESS
Chen Xu,Charles Reece,Michael Kelley
2012-07-01
The high-field performance of SRF cavities will eventually be limited by the realization of fundamental material limits, whether it is Hc1 or Hsh, or some derivative thereof, at which the superconductivity is lost. Before reaching this fundamental field limit at the macro level, it must be encountered at localized, perhaps microscopic, sites of field enhancement due to local topography. If such sites are small enough, they may produce thermally stabilized normal-conducting regions which contribute non-linear losses when viewed from the macro resonant field perspective, and thus produce degradation in Q0. We have undertaken a calculation of local surface magnetic field enhancement from specific fine topographic structure by conformal mapping method and numerically. A solution of the resulting normal conducting volume has been derived and the corresponding RF Ohmic loss simulated.
Local-field enhancement of optical nonlinearities in the AGZO nano-triangle array
NASA Astrophysics Data System (ADS)
Long, Hua; Bao, Lijiao; Wang, Kai; Liu, Shuhui; Wang, Bing
2016-10-01
Enhancement of the third order optical nonlinearities in Ga and Al co-doped ZnO (AGZO) nano-triangle array was investigated by performing a Z-scan method with a femtosecond laser (800 nm, 40 fs). The AGZO nano-triangle array was fabricated on silica substrates by nanosphere lithography (NSL) method, showing a surface plasmon resonance (SPR) peak around 3 μm. The two photon absorption (TPA) coefficient and nonlinear refractive index of the AGZO nano-triangle array were determined to be 340 cm/GW and 3.22 × 10-2 cm2/GW under an excitation intensity of 26 GW/cm2. It shows a 3.4-fold enhancement of the nonlinear refraction in the AGZO array with respect to that in the AGZO film, which attributes to the local field enhancement effect. The finite-difference time-domain (FDTD) simulation was in agreement with the experimental results. It indicates that the AGZO nano-triangle arrays have potential applications for nonlinear optical devices like all-optical switching, optical limiting and other types of signal processing.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1. PMID:27575123
NASA Astrophysics Data System (ADS)
Toida, Mieko
2016-07-01
The electric field parallel to the magnetic field in nonlinear magnetosonic waves in three component plasmas (two-ion-species plasma and electron-positron-ion plasma) is theoretically studied based on a three-fluid model. In a two-ion-species plasma, a magnetosonic mode has two branches, high-frequency mode and low-frequency mode. The parallel electric field E ∥ and its integral along the magnetic field, F = - ∫ E ∥ d s , in the two modes propagating quasiperpendicular to the magnetic field are derived as functions of the wave amplitude ɛ and the density ratio and cyclotron frequency ratio of the two ion species. The theory shows that the magnitude of F in the high-frequency-mode pulse is much greater than that in the low-frequency-mode pulse. Theoretical expressions for E ∥ and F in nonlinear magnetosonic pulses in an electron-positron-ion plasma are also obtained under the assumption that the wave amplitudes are in the range of ( m e / m i ) 1 / 2 < ɛ < 1 , where m e / m i is the electron to ion mass ratio.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators
NASA Astrophysics Data System (ADS)
Driben, R.; Konotop, V. V.; Malomed, B. A.; Meier, T.
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3 +3 harmonic-oscillator p -wave eigenfunctions with orbital and magnetic quantum numbers l =1 and m =1 , 0, -1 . The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l =1 .
Measurements of Nonlinear Hall-Driven Reconnection in the Reversed Field Pinch
NASA Astrophysics Data System (ADS)
Tharp, T. D.; Almagri, A. F.; Miller, M. C.; Mirnov, V. V.; Prager, S. C.; Sarff, J. S.; Kim, C. C.
2010-11-01
Previous measurements have established that reversed field pinch (RFP) sawtooth relaxation is characterized by spontaneous reconnection occurring simultaneously at multiple sites. Here, we report measurements of the magnetic fields and terms in Ohm's law associated with reconnection in the edge region of MST plasmas. The magnetic field structure is measured by probes and compared with theoretical predictions computed in both toroidal and cylindrical geometry. The composite magnetic structure from modes with toroidal mode numbers n=1-4 resonant at the toroidal field reversal surface reveals a complex but still coherent edge structure. Key terms of Ohm's law for the dominant mode (n=1) are accessible from magnetic field measurements and reveal the ordering (1neJxB >> E>ηJ), clearly indicating that single fluid physics is not sufficient to explain this reconnection. In particular, nonlinear three-wave coupling through the Hall term acts as a driving mechanism for this linearly stable mode. The observed coherent structures and strong nonlinear interaction terms highlight the substantial role of collective mode phase matching during sawtooth events.
Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.
Driben, R; Konotop, V V; Malomed, B A; Meier, T
2016-07-01
The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p-wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of noncoaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled-field equations agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l=1.
Guo, Dapeng; Wang, Yonghuan; Li, Lingfeng; Wang, Xiaozhi; Luo, Jikui
2015-01-01
High-field asymmetric waveform ion mobility spectrometry (FAIMS) separates ions by utilizing the characteristics of nonlinear ion mobility at high and low electric fields. Accurate ion discrimination depends on the precise solution of nonlinear relationships and is essential for accurate identification of ion species for applications. So far, all the nonlinear relationships of ion mobility obtained are based at low electric fields (E/N <65 Td). Microchip FAIMS (μ-FAIMS) with small dimensions has high electric field up to E/N = 250 Td, making the approximation methods and conclusions for nonlinear relationships inappropriate for these systems. In this paper, we deduced nonlinear functions based on the first principle and a general model. Furthermore we considered the hydrodynamics of gas flow through microchannels. We then calculated the specific alpha coefficients for cocaine, morphine, HMX, TNT and RDX, respectively, based on their FAIMS spectra measured by μ-FAIMS system at ultra-high fields up to 250 Td. The results show that there is no difference in nonlinear alpha functions obtained by the approximation and new method at low field (<120 Td), but the error induced by using approximation method increases monotonically with the increase in field, and could be as much as 30% at a field of 250 Td.
Nonlinear electron acoustic cyclotron waves in presence of uniform magnetic field
Dutta, Manjistha; Khan, Manoranjan; Ghosh, Samiran; Roychoudhury, Rajkumar; Chakrabarti, Nikhil
2013-04-15
Nonlinear electron acoustic cyclotron waves (EACW) are studied in a quasineutral plasma in presence of uniform magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary charge neutral inhomogeneous background. In long wavelength limit, it is shown that the linear electron acoustic wave is modified by the uniform magnetic field similar to that of electrostatic ion cyclotron wave. Nonlinear equations for these waves are solved by using Lagrangian variables. Results show that the spatial solitary wave-like structures are formed due to nonlinearities and dispersions. These structures transiently grow to larger amplitude unless dispersive effect is actively operative and able to arrest this growth. We have found that the wave dispersion originated from the equilibrium inhomogeneity through collective effect and is responsible for spatiotemporal structures. Weak dispersion is not able to stop the wave collapse and singular structures of EACW are formed. Relevance of the results in the context of laboratory and space plasmas is discussed.
Gurevich, A
2014-08-22
A theory of dissipative nonlinear conductivity, σ(1)(ω,H), of s-wave superconductors under strong electromagnetic fields at low temperatures is proposed. Closed-form expressions for σ(1)(H) and the surface resistance R(s)(ω,H) are obtained in the nonequilibrium dirty limit for which σ(1)(H) has a significant minimum as a function of a low-frequency (ħω ≪ k(B)T) magnetic field H. The calculated microwave suppression of R(s)(H) is in good agreement with recent experiments on alloyed Nb resonator cavities. It is shown that superimposed dc and ac fields, H = H(0) + H(a)cosωt, can be used to reduce ac dissipation in thin film nanostructures by tuning σ(1)(H(0)) with the dc field. PMID:25192119
Analytical Predictions of Field and Plasma Dynamics during Nonlinear Weibel-Mediated Flow Collisions
NASA Astrophysics Data System (ADS)
Ruyer, C.; Gremillet, L.; Bonnaud, G.; Riconda, C.
2016-08-01
The formation of collisionless shocks mediated by the ion Weibel instability is addressed theoretically and numerically in the nonrelativistic limit. First, the model developed in C. Ruyer et al., Phys. Plasmas 22, 032102 (2015) for the weakly nonlinear ion Weibel instability in a symmetric two-stream system is shown to be consistent with recent experimental and simulation results. Large-scale kinetic simulations are then performed to clarify the spatiotemporal evolution of the magnetic-field and plasma properties in the subsequent strongly nonlinear phase leading to shock formation. A simple analytical model is proposed which captures the simulation results up to a point close to ion isotropization. Electron screening effects are found important in the instability dynamics, so that numerical simulations using a nonphysical electron mass should be considered with caution.
Ruyer, C; Gremillet, L; Bonnaud, G; Riconda, C
2016-08-01
The formation of collisionless shocks mediated by the ion Weibel instability is addressed theoretically and numerically in the nonrelativistic limit. First, the model developed in C. Ruyer et al., Phys. Plasmas 22, 032102 (2015) for the weakly nonlinear ion Weibel instability in a symmetric two-stream system is shown to be consistent with recent experimental and simulation results. Large-scale kinetic simulations are then performed to clarify the spatiotemporal evolution of the magnetic-field and plasma properties in the subsequent strongly nonlinear phase leading to shock formation. A simple analytical model is proposed which captures the simulation results up to a point close to ion isotropization. Electron screening effects are found important in the instability dynamics, so that numerical simulations using a nonphysical electron mass should be considered with caution. PMID:27541468
Fully non-linear cosmological perturbations of multicomponent fluid and field systems
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim; Park, Chan-Gyung
2016-09-01
We present fully non-linear and exact cosmological perturbation equations in the presence of multiple components of fluids and minimally coupled scalar fields. We ignore the tensor-type perturbation. The equations are presented without taking the temporal gauge condition in the Friedmann background with general curvature and the cosmological constant. We include the anisotropic stress. Even in the absence of anisotropic stress of individual component, the multiple component nature introduces the anisotropic stress in the collective fluid quantities. We prove the Newtonian limit of multiple fluids in the zero-shear gauge and the uniform-expansion gauge conditions, present the Newtonian hydrodynamic equations in the presence of general relativistic pressure in the zero-shear gauge, and present the fully non-linear equations and the third-order perturbation equations of the non-relativistic pressure fluids in the CDM-comoving gauge.
Turbulence Dissipation in Non-Linear Diffusive Shock Acceleration with Magnetic Field Amplification
NASA Astrophysics Data System (ADS)
Ellison, Donald C.; Vladimirov, A.
2008-03-01
High Mach number shocks in young supernova remnants (SNRs) are believed to simultaneously place a large fraction of the supernova explosion energy in relativistic particles and amplify the ambient magnetic field by large factors. Continuing our efforts to model this strongly nonlinear process with a Monte Carlo simulation, we have incorporated the effects of the dissipation of the self-generated turbulence on the shock structure and thermal particle injection rate. We find that the heating of the thermal gas in the upstream shock precursor by the turbulence damping significantly impacts the acceleration process in our thermal pool injection model. This precursor heating may also have observational consequences. In this preliminary work, we parameterize the turbulence damping rate and lay the groundwork for incorporating more realistic physical models of turbulence generation and dissipation in nonlinear DSA. This work was support in part by NASA ATP grant NNX07AG79G.
NASA Astrophysics Data System (ADS)
Nan, Fan; Xie, Fang-Ming; Liang, Shan; Ma, Liang; Yang, Da-Jie; Liu, Xiao-Li; Wang, Jia-Hong; Cheng, Zi-Qiang; Yu, Xue-Feng; Zhou, Li; Wang, Qu-Quan; Zeng, Jie
2016-06-01
This paper describes a facile method for the synthesis of Au/AuAg/Ag2S/PbS core-multishell nanorods with double trapping layers. The synthesis, in sequence, involved deposition of Ag shells onto the surfaces of Au nanorod seeds, formation of AuAg shells by a galvanic replacement reaction, and overgrowth of the Ag2S shells and PbS shells. The resulting core-multishell nanorod possesses an air gap between the Au core and the AuAg shell. Together with the Ag2S shell, the air gap can efficiently trap light, causing strong field confinement and nonlinear enhancement. The as-prepared Au/AuAg/Ag2S/PbS core-multishell nanorods display distinct localized surface plasmon resonance and nonlinear optical properties, demonstrating an effective pathway for maneuvering the optical properties of nanocavities.This paper describes a facile method for the synthesis of Au/AuAg/Ag2S/PbS core-multishell nanorods with double trapping layers. The synthesis, in sequence, involved deposition of Ag shells onto the surfaces of Au nanorod seeds, formation of AuAg shells by a galvanic replacement reaction, and overgrowth of the Ag2S shells and PbS shells. The resulting core-multishell nanorod possesses an air gap between the Au core and the AuAg shell. Together with the Ag2S shell, the air gap can efficiently trap light, causing strong field confinement and nonlinear enhancement. The as-prepared Au/AuAg/Ag2S/PbS core-multishell nanorods display distinct localized surface plasmon resonance and nonlinear optical properties, demonstrating an effective pathway for maneuvering the optical properties of nanocavities. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr09151a
NASA Astrophysics Data System (ADS)
Ucuncuoglu, Suleyman; Schneider, David A.; Dunlap, David; Finzi, Laura
2014-03-01
RNA Polymerase I (Pol I) conducts more than 60% of all the transcriptional activity in cells and also is responsible for synthesizing the RNA structure of the ribosome in eukaryotic cells. It is evident in many studies that Pol I transcription is affected by tumor suppressors and oncogenes which makes Pol I as a target for the anticancer therapeutics. The mechanistic pathways and kinetics of the Pol I transcription needs to be understood more precisely. Even though previous bulk studies measured the kinetics of the Pol I transcription, the results may hinder the intermediate states such as processivity and pausing during elongation. Here we used the single molecule approach to show that Pol I pauses more than Pol II during elongation step by using a novel single molecule instrument, multiplexed tethered particle motion microscopy (TPM). Our in-house developed TPM equipment is able to concurrently observe hundreds of single molecules. TPM technique has a major advantage to observe pausing under force-free condition unlike other single molecule techniques such as magnetic tweezers and optical tweezers. We also report that the processivity of Pol I is very low where only one out of fifteen transcription event reached the run-off site. We anticipate that our single molecule assays paved the way for observing more sophisticated aspects of Pol I transcription and it's relation with initiation and transcriptional factors.
Li, Yue; Ho, Janet; Wang, Jianchuan; Li, Zhong-Ming; Zhong, Gan-Ji; Zhu, Lei
2016-01-13
Understanding nonlinear dielectric behavior in polar polymers is crucial to their potential application as next generation high energy density and low loss dielectrics. In this work, we studied nonlinear dielectric properties of a biaxially oriented poly(vinylidene fluoride) (BOPVDF) film under both low and high electric fields. For fundamental nonlinear dielectric constants at low fields (<30 MV/m), Novocontrol high-voltage broadband dielectric spectroscopy (HVBDS) was accurate enough to measure up to the third harmonics. It was observed that the low-field dielectric nonlinearity for the BOPVDF disappeared above 10 Hz at room temperature, suggesting that the low-field dielectric nonlinearity originated from ionic migration of impurity ions rather than dipolar relaxation of the amorphous segments. Above the coercive field (EC ≈ 70 MV/m), bipolar electric displacement-electric field (D-E) loop tests were used to extract the nonlinear behavior for pure PVDF crystals, which had a clear origin of ferroelectric switching of polar crystalline dipoles and domains and nonpolar-to-polar (α → δ → β) phase transformations. By using HVBDS, it was observed that the ferroelectric switching of polar crystalline dipoles and domains in BOPVDF above the EC always took place between 20 and 500 Hz regardless of a broad range of temperature from -30 to 100 °C. This behavior was drastically different from that of the amorphous PVDF dipoles, which had a strong dependence on frequency over orders of magnitude.
Li, Yue; Ho, Janet; Wang, Jianchuan; Li, Zhong-Ming; Zhong, Gan-Ji; Zhu, Lei
2016-01-13
Understanding nonlinear dielectric behavior in polar polymers is crucial to their potential application as next generation high energy density and low loss dielectrics. In this work, we studied nonlinear dielectric properties of a biaxially oriented poly(vinylidene fluoride) (BOPVDF) film under both low and high electric fields. For fundamental nonlinear dielectric constants at low fields (<30 MV/m), Novocontrol high-voltage broadband dielectric spectroscopy (HVBDS) was accurate enough to measure up to the third harmonics. It was observed that the low-field dielectric nonlinearity for the BOPVDF disappeared above 10 Hz at room temperature, suggesting that the low-field dielectric nonlinearity originated from ionic migration of impurity ions rather than dipolar relaxation of the amorphous segments. Above the coercive field (EC ≈ 70 MV/m), bipolar electric displacement-electric field (D-E) loop tests were used to extract the nonlinear behavior for pure PVDF crystals, which had a clear origin of ferroelectric switching of polar crystalline dipoles and domains and nonpolar-to-polar (α → δ → β) phase transformations. By using HVBDS, it was observed that the ferroelectric switching of polar crystalline dipoles and domains in BOPVDF above the EC always took place between 20 and 500 Hz regardless of a broad range of temperature from -30 to 100 °C. This behavior was drastically different from that of the amorphous PVDF dipoles, which had a strong dependence on frequency over orders of magnitude. PMID:26698912
Mean Field Strategies Induce Unrealistic Non-Linearities in Calcium Puffs
Solovey, Guillermo; Fraiman, Daniel; Dawson, Silvina Ponce
2011-01-01
Mean field models are often useful approximations to biological systems, but sometimes, they can yield misleading results. In this work, we compare mean field approaches with stochastic models of intracellular calcium release. In particular, we concentrate on calcium signals generated by the concerted opening of several clustered channels (calcium puffs). To this end we simulate calcium puffs numerically and then try to reproduce features of the resulting calcium distribution using mean field models were all the channels open and close simultaneously. We show that an unrealistic non-linear relationship between the current and the number of open channels is needed to reproduce the simulated puffs. Furthermore, a single channel current which is five times smaller than the one of the stochastic simulations is also needed. Our study sheds light on the importance of the stochastic kinetics of the calcium release channel activity to estimate the release fluxes. PMID:21869877
Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony; Bingham, Robert; Clarke, Robert; Churazov, Eugene; Crowston, Robert; Doyle, Hugo; Drake, R Paul; Heathcote, Robert; Koenig, Michel; Kuramitsu, Yasuhiro; Kuranz, Carolyn; Lee, Dongwook; MacDonald, Michael; Murphy, Christopher; Notley, Margaret; Park, Hye-Sook; Pelka, Alexander; Ravasio, Alessandra; Reville, Brian; Sakawa, Youichi; Wan, Willow; Woolsey, Nigel; Yurchak, Roman; Miniati, Francesco; Schekochihin, Alexander; Lamb, Don; Gregori, Gianluca
2015-07-01
The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.
Non-linear transport by solitons in nanofibers of polymers in high magnetic field
NASA Astrophysics Data System (ADS)
Kirova, N.; Brazovskii, S.; Choi, A.; Park, Y. W.
2012-06-01
Nonlinear local excitations like solitons, polarons, and bipolarons are known to be responsible for physical properties of conducting polymers. Recent experiments on nano-fibers in high electric and magnetic fields provide a further insight by demonstrating an effect of vanishing magnetoconductance (MC) in the polyacetylene (PA)-in contrast to other polymers. Here we present new experimental data and describe the theoretical model based on notion of solitons-dimerization kinks which can carry either the spin or the charge; they are allowed only in the PA with its degenerate ground state. The solitons experience a confinement force due to the interchange coupling which is erased by the electric field and disappears above critical field strength. The unbinding by tunneling allows for the transport of individual solitons, which sweeps off the spins residing at electronic intragap states associated with polarons, hence the vanishing MC.
Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony; Bingham, Robert; Clarke, Robert; Churazov, Eugene; Crowston, Robert; Doyle, Hugo; Drake, R Paul; Heathcote, Robert; Koenig, Michel; Kuramitsu, Yasuhiro; Kuranz, Carolyn; Lee, Dongwook; MacDonald, Michael; Murphy, Christopher; Notley, Margaret; Park, Hye-Sook; Pelka, Alexander; Ravasio, Alessandra; Reville, Brian; Sakawa, Youichi; Wan, Willow; Woolsey, Nigel; Yurchak, Roman; Miniati, Francesco; Schekochihin, Alexander; Lamb, Don; Gregori, Gianluca
2015-07-01
The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe. PMID:26100873
Meinecke, Jena; Tzeferacos, Petros; Bell, Anthony; Bingham, Robert; Clarke, Robert; Churazov, Eugene; Crowston, Robert; Doyle, Hugo; Drake, R. Paul; Heathcote, Robert; Koenig, Michel; Kuramitsu, Yasuhiro; Kuranz, Carolyn; Lee, Dongwook; MacDonald, Michael; Murphy, Christopher; Notley, Margaret; Park, Hye-Sook; Pelka, Alexander; Ravasio, Alessandra; Reville, Brian; Sakawa, Youichi; Wan, Willow; Woolsey, Nigel; Yurchak, Roman; Miniati, Francesco; Schekochihin, Alexander; Lamb, Don; Gregori, Gianluca
2015-01-01
The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe. PMID:26100873
Nonlinear evolution of cosmic magnetic fields and cosmic microwave background anisotropies
NASA Astrophysics Data System (ADS)
Tashiro, Hiroyuki; Sugiyama, Naoshi; Banerjee, Robi
2006-01-01
In this work we investigate the effects of primordial magnetic fields on cosmic microwave background anisotropies (CMB). Based on cosmological magneto-hydro dynamic (MHD) simulations [R. Banerjee and K. Jedamzik, Phys. Rev. DPRVDAQ0556-2821 70, 123003 (2004).10.1103/PhysRevD.70.123003] we calculate the CMB anisotropy spectra and polarization induced by fluid fluctuations (Alfvén modes) generated by primordial magnetic fields. The strongest effect on the CMB spectra comes from the transition epoch from a turbulent regime to a viscous regime. The balance between magnetic and kinetic energy until the onset of the viscous regime provides a one to one relation between the comoving coherence length L and the comoving magnetic field strength B, such as L˜30(B/10-9Gauss)3pc. The resulting CMB temperature and polarization anisotropies for the initial power law index of the magnetic fields n>3/2 are somewhat different from the ones previously obtained by using linear perturbation theory. In particular, differences can appear on intermediate scales l<2000 and small scales l>20000. On scales l<2000 the CMB anisotropy and polarization spectra are flat in the case of our nonlinear calculations whereas the spectra have a blue index calculated with linear perturbation theory if we assume the velocity fields of baryons induced by the magnetic fields achieved Alfvén velocity due to the turbulent motions on large scales in the early universe. Our calculation gives a constraint on the magnetic field strength in the intermediate scale of CMB observations. Upper limits are set by WMAP and BOOMERANG results for comoving magnetic field strength of B<28nGauss with a comoving coherence length of L>0.7Mpc for the most extreme case, or B<30nGauss and L>0.8Mpc for the most conservative case. We may also expect higher signals on large scales of the polarization spectra compared to linear calculations. The signal may even exceed the B-mode polarization from gravitational lensing depending on
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity.
Clayton, C E; Adli, E; Allen, J; An, W; Clarke, C I; Corde, S; Frederico, J; Gessner, S; Green, S Z; Hogan, M J; Joshi, C; Litos, M; Lu, W; Marsh, K A; Mori, W B; Vafaei-Najafabadi, N; Xu, X; Yakimenko, V
2016-01-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m(-1) to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity. PMID:27527569
NASA Astrophysics Data System (ADS)
Richert, Ranko
2016-03-01
A model of non-linear dielectric polarization is studied in which the field induced entropy change is the source of polarization dependent retardation time constants. Numerical solutions for the susceptibilities of the system are obtained for parameters that represent the dynamic and thermodynamic behavior of glycerol. The calculations for high amplitude sinusoidal fields show a significant enhancement of the steady state loss for frequencies below that of the low field loss peak. Also at relatively low frequencies, the third harmonic susceptibility spectrum shows a "hump," i.e., a maximum, with an amplitude that increases with decreasing temperature. Both of these non-linear effects are consistent with experimental evidence. While such features have been used to conclude on a temperature dependent number of dynamically correlated particles, Ncorr, the present result demonstrates that the third harmonic susceptibility display a peak with an amplitude that tracks the variation of the activation energy in a model that does not involve dynamical correlations or spatial scales.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity
Clayton, C. E.; Adli, E.; Allen, J.; An, W.; Clarke, C. I.; Corde, S.; Frederico, J.; Gessner, S.; Green, S. Z.; Hogan, M. J.; et al
2016-08-16
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.).more » Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m–1 to a similar degree of accuracy. Lastly, these results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity.« less
Rosnitskiy, P. Yuldashev, P. Khokhlova, V.
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.
Self-mapping the longitudinal field structure of a nonlinear plasma accelerator cavity
Clayton, C. E.; Adli, E.; Allen, J.; An, W.; Clarke, C. I.; Corde, S.; Frederico, J.; Gessner, S.; Green, S. Z.; Hogan, M. J.; Joshi, C.; Litos, M.; Lu, W.; Marsh, K. A.; Mori, W. B.; Vafaei-Najafabadi, N.; Xu, X.; Yakimenko, V.
2016-01-01
The preservation of emittance of the accelerating beam is the next challenge for plasma-based accelerators envisioned for future light sources and colliders. The field structure of a highly nonlinear plasma wake is potentially suitable for this purpose but has not been yet measured. Here we show that the longitudinal variation of the fields in a nonlinear plasma wakefield accelerator cavity produced by a relativistic electron bunch can be mapped using the bunch itself as a probe. We find that, for much of the cavity that is devoid of plasma electrons, the transverse force is constant longitudinally to within ±3% (r.m.s.). Moreover, comparison of experimental data and simulations has resulted in mapping of the longitudinal electric field of the unloaded wake up to 83 GV m−1 to a similar degree of accuracy. These results bode well for high-gradient, high-efficiency acceleration of electron bunches while preserving their emittance in such a cavity. PMID:27527569
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
In Part I of this work, an improved "second-order" homogenization theory was developed. This new theory makes use of generalized secant moduli that are intermediate between the standard secant and tangent moduli of the nonlinear phases, and that depend not only on the averages, or first-moments of the fields in the phases, but also on the second-moments of the field fluctuations, or phase covariance tensors. In this article, the theory, which is known to be exact to second-order in the heterogeneity contrast, is applied to the special cases of rigidly reinforced and porous materials. These are cases corresponding to infinite contrast where fairly explicit analytical expressions of the Hashin-Shtrikman and self-consistent-type may be generated for nonlinear composites. The results show that the new theory improves on the earlier theory (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) in at least two ways. First, the new theory satisfies rigorous bounds, even near the percolation limit, where field fluctuations become important, and the earlier second-order theory had been found to fail. Second, the new theory predicts fully compressible behavior for porous materials with an incompressible matrix phase, where the earlier theory had also been found to fail. In addition, the new estimates are found to be in better agreement with numerical simulations available from the literature.
Nonlinear saturation spectra of electric fields and density fluctuations in drift wave turbulence
NASA Technical Reports Server (NTRS)
Kelley, M. C.
1982-01-01
The detection of drift waves in the nonlinear evolution of a space plasma process driven at long wavelengths is considered, adducing measurements of the electric field and density fluctuation power spectra as evidence. Since the driving mechanism is clearly at long wavelengths, the detection of drift waves suggests that they may play an important role in the transfer of wave energy from long to short wavelengths in a low beta plasma. The saturated spectral density is compared with theoretical results in order to estimate the anomalous diffusion rate. The observed spectral form and amplitude is in excellent agreement with drift wave predictions.
NASA Astrophysics Data System (ADS)
Kikuchi, Takashi; Horioka, Kazuhiko
2016-06-01
A procedure to obtain a ratio of beam radii at final and initial states in arbitrary particle distributions is proposed, and is applied to the estimation of possible emittance growth for Gaussian and thermal equilibrium distributions. The ratios are estimated for Gaussian and thermal equilibrium distributions as a function of tune depression. The possible emittance growth as a function of tune depression and nonlinear field energy factor is also estimated with and without a constant radius ratio approximation. It is confirmed that the possible emittance growths are almost the same in comparison to the cases with and without the constant radius ratio approximation at each distribution.
NASA Astrophysics Data System (ADS)
Gapochka, M. G.; Denisov, M. M.; Denisova, I. P.; Kalenova, N. V.; Korolev, A. F.
2015-11-01
The paper is devoted to mathematical modeling of the nonlinear vacuum electrodynamics effect: the action of the strong magnetic field of a pulsar on the propagation of electromagnetic waves. It is shown that, due to the birefringence of the vacuum, for one normal wave, it takes more time to travel from a pulsar to a detector installed on astrophysical satellites than for the other normal wave. The delay of the pulse carried by the second normal wave relative to pulse carried by the first normal wave from the common point of origin to the satellite is calculated.
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-09-15
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.
φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Francés, Jorge; Bleda, Sergio; Bej, Subhajit; Tervo, Jani; Navarro-Fuster, Víctor; Fenoll, Sandra; Martínez-Gaurdiola, Francisco J.; Neipp, Cristian
2016-04-01
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
Volkova, E. A.; Popov, A. M. Tikhonova, O. V.
2013-03-15
The nonlinear polarization response of a quantum system modeling a silver atom in the field of high-intensity radiation in the IR and UV spectral ranges has been studied by direct numerical integration of a nonstationary Schroedinger equation. The domains of applicability of perturbation theory and polarization expansion in powers of the field intensity are determined. The contribution of excited atoms and electrons in a continuum to the atomic polarization response at the field frequency, which arises due to the radiation-induced excitation and photoionization processes, is analyzed. Features of the nonlinear response to an external field under conditions of atom stabilization are considered.
Varray, François; Ramalli, Alessandro; Cachard, Christian; Tortoli, Piero; Basset, Olivier
2011-07-01
The simulation of nonlinear propagation of ultrasound waves is typically based on the Kuznetsov-Zabolotskaya- Khokhlov equation. A set of simulators has been proposed in the literature but none of them takes into account a possible spatial 3-D variation of the nonlinear parameter in the investigated medium. This paper proposes a generalization of the angular spectrum method (GASM) including the spatial variation of the nonlinear parameter. The proposed method computes the evolution of the fundamental and second-harmonic waves in four dimensions (spatial 3-D and time). For validation purposes, the one-way fields produced by the GASM are first compared with those produced by established reference simulators and with experimental one-way fields in media with a homogeneous nonlinear parameter. The same simulations are repeated for media having an axial variation of the nonlinear parameter. The mean errors estimated in the focal region are less than 4.0% for the fundamental and 5.4% for the second harmonic in all cases. Finally, the fundamental and second-harmonic fields simulated for media having nonlinear parameter variations in the axial, lateral, and elevation directions, which cannot be simulated with other currently available methods, are presented. The new approach is also shown to yield a reduction in computation time by a factor of 13 with respect to the standard nonlinear simulator.
NASA Astrophysics Data System (ADS)
Kasper, R. G.
1985-02-01
Based on completed experimental electric-field scans and the corresponding finite-element field predictions, it appears that the finite-element numerical technique presents a strong analytical tool in calculating the nearfield (within 650 micrometers electric-field distributions about active microcells. This was analytically achieved with the new double membrane finite-element configuration representing nonlinear polarization and by using a local tangent slope (impedance) definition dependent on the local potential difference. The experimental determination of the normal current was realized with a newly developed scanning vibrating electrode technique. The finite-element model utilizes a priori measured uncoupled polarization curves for pure iron and pure copper. The current densities and the electric field intensity was calculated for all the grid points within the electrolyte and on its boundaries. Results appear to indicate that first order anodic mass loss can be predicted using finite-element predicted current density distributions on the anodic surface and the imposition of Faraday's law. The electric-field correlation established for the normal current-density vector provides the confidence to proceed in the evaluation of electric fields associated with pitting and crevice corrosion.
Quantifying wave-breaking dissipation using nonlinear phase-resolved wave-field simulations
NASA Astrophysics Data System (ADS)
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
Lazzaro, E.; Comisso, L.; Valdettaro, L.
2010-05-15
In tokamaks magnetic islands arise from an unstable process of tearing and reconnecting of helical field lines across rational surfaces. After a linear stage the magnetic instability develops through three characteristic nonlinear stages where increasingly complex topological alterations occur in the form of the magnetic islands. The problem of response of reconnection process to the injection of an external current suitably localized is addressed using a four-field model in a plane slab plasma, with a novel extension to account consistently of the relevant neoclassical effects, such as bootstrap current and pressure anisotropy. The results found have implications on the interpretation of the possible mechanism of present day experimental results on neoclassical tearing modes as well as on the concepts for their control or avoidance.
NASA Astrophysics Data System (ADS)
Wei, Nijun; Coffey, William T.; Déjardin, Pirre-Michel; Kalmykov, Yuri P.
External dc bias field effects on the nonlinear dielectric relaxation and dynamic Kerr effect of a system of permanent dipoles in a uniaxial mean field potential are studied via the rotational Brownian motion model. Postulated in terms of the infinite hierarchy of differential-recurrence equations for the statistical moments (the expectation value of the Legendre polynomials), the dielectric and Kerr effect ac stationary responses may be evaluated for arbitrary dc bias field strength via perturbation theory in the ac field. We have given two complementary approaches for treating the nonlinear effects. The first is based on perturbation theory allowing one to calculate the nonlinear ac stationary responses using powerful matrix methods. The second approach based on the accurate two-mode approximation [D.A. Garanin, Phys. Rev. E. 54, 3250 (1996)] effectively generalizes the existing results for dipolar systems in superimposed ac and dc fields to a mean field potential. The results apply both to nonlinear dielectric relaxation and dynamic Kerr effect of nematics and to magnetic birefringence relaxation of ferrofluids. Furthermore, the given methods of the solution of infinite hierarchies of multi-term recurrence relations are quite general and can be applied to analogous nonlinear response problems.
NASA Astrophysics Data System (ADS)
Farrugia, C. J.; Lavraud, B.; Torbert, R. B.; Argall, M.; Kacem, I.; Yu, W.; Alm, L.; Burch, J.; Russell, C. T.; Shuster, J.; Dorelli, J.; Eastwood, J. P.; Ergun, R. E.; Fuselier, S.; Gershman, D.; Giles, B. L.; Khotyaintsev, Y. V.; Lindqvist, P. A.; Matsui, H.; Marklund, G. T.; Phan, T. D.; Paulson, K.; Pollock, C.; Strangeway, R. J.
2016-06-01
We analyze plasma, magnetic field, and electric field data for a flux transfer event (FTE) to highlight improvements in our understanding of these transient reconnection signatures resulting from high-resolution data. The ˜20 s long, reverse FTE, which occurred south of the geomagnetic equator near dusk, was immersed in super-Alfvénic flow. The field line twist is illustrated by the behavior of flows parallel/perpendicular to the magnetic field. Four-spacecraft timing and energetic particle pitch angle anisotropies indicate a flux rope (FR) connected to the Northern Hemisphere and moving southeast. The flow forces evidently overcame the magnetic tension. The high-speed flows inside the FR were different from those outside. The external flows were perpendicular to the field as expected for draping of the external field around the FR. Modeling the FR analytically, we adopt a non-force free approach since the current perpendicular to the field is nonzero. It reproduces many features of the observations.
Measurements of Rayleigh-Taylor-Induced Magnetic Fields in the Linear and Non-linear Regimes
NASA Astrophysics Data System (ADS)
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.
Beninato, A.; Baglio, S.; Andò, B.; Emery, T.; Bulsara, A. R.; Jenkins, C.; Palkar, V.
2013-12-09
Multiferroic (MF) composites, in which magnetic and ferroelectric orders coexist, represent a very attractive class of materials with promising applications in areas, such as spintronics, memories, and sensors. One of the most important multiferroics is the perovskite phase of bismuth ferrite, which exhibits weak magnetoelectric properties at room temperature; its properties can be enhanced by doping with other elements such as dysprosium. A recent paper has demonstrated that a thin film of Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3} shows good magnetoelectric coupling. In separate work it has been shown that a carefully crafted ring connection of N (N odd and N ≥ 3) ferroelectric capacitors yields, past a critical point, nonlinear oscillations that can be exploited for electric (E) field sensing. These two results represent the starting point of our work. In this paper the (electrical) hysteresis, experimentally measured in the MF material Bi{sub 0.7}Dy{sub 0.3}FeO{sub 3}, is characterized with the applied magnetic field (B) taken as a control parameter. This yields a “blueprint” for a magnetic (B) field sensor: a ring-oscillator coupling of N = 3 Sawyer-Tower circuits each underpinned by a mutliferroic element. In this configuration, the changes induced in the ferroelectric behavior by the external or “target” B-field are quantified, thus providing a pathway for very low power and high sensitivity B-field sensing.
Aciktepe, T.; Akdeniz, K.G.; Barut, A.O.; Kalayci, J.
1988-01-01
For the conformally covariant coupled non-linear spinor-scalar field of the sigma-model type the authors show that the non-trivial vacuum instanton solutions have a geometric meaning as constant spinors on the five-dimensional hypercone. The quantized fields around these solutions correspond to the normal modes of the hypercone. A connection is thus established between field theory, particle spectrum of the fields and quantized excitations of a geometry (the hypercone).
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.
NASA Astrophysics Data System (ADS)
Timokhin, A. N.; Arons, J.
2013-02-01
. These discharges are similar to those encountered in previous calculations by Timokhin of pair creation when the surface has a high work function and cannot freely emit charge. In cases (b) and (c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current. The 1D results described here characterize the dependence of acceleration and pair creation on the magnitude and sign of current. The dependence on the spatial distribution of the current is a multi-dimensional problem, possibly exhibiting more chaotic behaviour. We briefly outline possible relations of the electric field fluctuations observed in the polar flows (both with and without pair creation discharges) to direct emission of radio waves, as well as revive the possible relation of the observed limit cycle behaviour to microstructure in the radio emission. Actually modelling these effects requires the multi-dimensional treatment, to be reported in a later paper.
NASA Astrophysics Data System (ADS)
Li, Yue; Zhu, Lei; Case Western Reserve University Team; Sichuan University Team
Understanding nonlinear dielectric behavior in polar polymers is crucial to their potential application as next genera tion high energy density and low loss dielectrics. In this work, we studied nonlinear dielectric properties of a biaxially oriented poly(vinylidene fluoride) (BOPVDF) film under both low and high electric fields. It was observed that the low-field dielectric nonlinearity for the BOPVDF disappeared above 10 Hz at room temperature, suggesting that the low-field dielectric nonlinearity originated from ionic migration of impurity ions rather than dipolar relaxation of the amorphous segments. Above the coercive field (EC ~70 MV/m), bipolar electric displacement-electric field (D-E) loop tests were used to extract the nonlinear behavior for pure PVDF crystals, which had a clear origin of ferroelectric switching of polar crystalline dipoles and domains and nonpolar-to-polar (α --> δ --> β) phase transformations. Using HVBDS, it was observed that the ferroelectric switching of polar crystalline dipoles and domains in BOPVDF above the EC always took place between 20 and 500 Hz, regardless of a broad range of temperature from -30 to 100 °C. This behavior was drastically different from the amorphous PVDF dipoles, which had a strong dependence on frequency over orders of magnitude. This work is supported by NSF(DMR-1402733).
Effect of a force-free end on the mechanical property of a biopolymer — A path integral approach
NASA Astrophysics Data System (ADS)
Zhou, Zicong; Joós, Béla
2016-08-01
We study the effect of a force-free end on the mechanical property of a stretched biopolymer. The system can be divided into two parts. The first part consists of the segment counted from the fixed point (i.e., the origin) to the forced point in the biopolymer, with arclength L f . The second part consists of the segment counted from the forced point to the force-free end with arclength ΔL. We apply the path integral technique to find the relationship between these two parts. At finite temperature and without any constraint at the end, we show exactly that if we focus on the quantities related to the first part, then we can ignore the second part completely. Monte Carlo simulation confirms this conclusion. In contrast, the effect for the quantities related to the second part is dependent on what we want to observe. A force-free end has little effect on the relative extension, but it affects seriously the value of the end-to-end distance if ΔL is comparable to L f . Project supported by the MOST and the NSERC (Canada).
NASA Astrophysics Data System (ADS)
Sun, Hao-Ran; Huang, Ka-Ma
2015-12-01
In this paper, an experimental set-up based on a novel microstrip cancellation circuit is presented for investigating the effects of external microwave fields on the dielectric properties of polar solution. The circuit consists of a 3 dB Wilkinson power combiner, a conventional 20 dB backward coupler, and a specially designed 20 dB single-sectioned forward coupler. Besides, in order to realize a uniform electric field in the tested solution, a nicked microstrip ring is designed in the circuit. An improvement of measurement sensitivity in the proposed circuit was obtained when compared to the conventional transmission lines method. We exploit interference cancellation processes to suppress the probing signal at the output port under the principle that two identical amplitude signals with 180° phase difference will completely cancel each other. The measurements are carried out at the frequency of 2.45 GHz, and the temperature effects caused by microwave heating are excluded by the flowing fluid. Experimental results show that the dielectric properties of DMSO-methanol/ethanol mixtures change at the electric field intensity of 105 V m - 1 and present a distinctly nonlinear dielectric change with the electric fields. The study of the microwave-material interaction has expanded our insights into the high-power microwave’s industry application.
NASA Astrophysics Data System (ADS)
Ponte Castañeda, Pedro
2002-04-01
This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of "linear comparison composites", the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castañeda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the "secant" moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the "tangent" moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work.
Hatsuki, Ryuji; Honda, Ayae; Kajitani, Masayuki; Yamamoto, Takatoki
2015-01-01
Our living sphere is constantly exposed to a wide range of pathogenic viruses, which can be either known, or of novel origin. Currently, there is no methodology for continuously monitoring the environment for viruses in general, much less a methodology that allows the rapid and sensitive identification of a wide variety of viruses responsible for communicable diseases. Traditional approaches, based on PCR and immunodetection systems, only detect known or specifically targeted viruses. We here describe a simple device that can potentially detect any virus between nanogap electrodes using nonlinear impedance spectroscopy. Three test viruses, differing in shape and size, were used to demonstrate the general applicability of this approach: baculovirus, tobacco mosaic virus (TMV), and influenza virus. We show that each of the virus types responded differently in the nanogap to changes in the electric field strength, and the impedance of the virus solutions differed depending both on virus type and virus concentration. These preliminary results show that the three virus types can be distinguished and their approximate concentrations determined. Although further studies are required, the proposed nonlinear impedance spectroscopy method may achieve a sensitivity comparable to that of more traditional, but less versatile, virus detection systems. PMID:26441875
Non-linear dynamics of viscoelastic liquid trilayers subjected to an electric field
NASA Astrophysics Data System (ADS)
Karapetsas, George; Bontozoglou, Vasilis
2014-11-01
The scope of this work is to investigate the non-linear dynamics of the electro-hydrodynamic instability of a trilayer of immiscible liquids. We consider the case of a polymer film which is separated from the top electrode by two viscous fluids. We develop a computational model and carry out 2D numerical simulations fully accounting for the flow and electric field in all phases. For the numerical solution of the governing equations we employ the mixed finite element method combined with a quasi-elliptic mesh generation scheme which is capable of following the large deformations of the liquid-liquid interface. We model the viscoelastic behavior using the Phan-Thien and Tanner (PTT) constitutive equation taking fully into account the non-linear elastic effects as well as a varying shear and extensional viscosity. We perform a thorough parametric study and investigate the influence of the electric properties of fluids, applied voltage and various rheological parameters. The authors acknowledge the support by the General Secretariat of Research and Technology of Greece under the action ``Supporting Postdoctoral Researchers'' (Grant Number PE8/906), co-funded by the European Social Fund and National Resources.
NASA Astrophysics Data System (ADS)
Schuch, Dieter
2014-04-01
Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Agapitov, O. V.; Drake, J. F.; Mozer, F.
2015-12-01
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.
NASA Technical Reports Server (NTRS)
Timokhin, A. N.; Arons, J.
2013-01-01
bursts of pair creation. These discharges are similar to those encountered in previous calculations by Timokhin of pair creation when the surface has a high work function and cannot freely emit charge. In cases (b) and (c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation are strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current.
NASA Astrophysics Data System (ADS)
Tukmakov, A. L.
2015-01-01
A model of a multivelocity multitemperature polydisperse gas suspension has been constructed with account taken of coagulation. Calculations of the dynamics of an aerosol of a polydisperse composition in an acoustic resonator have been done and the derived regularities have been described. A system of Navier-Stokes equations for a compressible heat-conducting gas was used to describe the motion of a carrier medium. The dynamics of dispersed fractions is described by a system of equations including continuity, momentum, and internal-energy equations. The equations of motion of the carrier medium and dispersed fractions have been written with account of the interphase exchange of momentum and energy. The Lagrangian model has been used to describe the process of coagulation. The change in the dispersity of the gas suspension in the nonlinear field of an acoustic resonator has been analyzed.
On some p-Laplacian equation with electromagnetic fields and critical nonlinearity in ℝN
NASA Astrophysics Data System (ADS)
Liang, Sihua; Zhang, Jihui
2015-04-01
In this paper, we consider the existence and multiplicity of solutions for p-Laplacian equation with electromagnetic fields and critical nonlinearity in ℝN: - ɛ p Δ p , A u + V ( x ) |u| p - 2 u = |u| p* - 2 u + h ( x , |u| p ) |u| p - 2 u for x ∈ ℝN, where Δ p , A u ( x ) ≔ div ( |u ∇ u + i A ( x ) u | p - 2 ( ∇ u + i A ( x ) u ) . By using Lions' second concentration compactness principle and concentration compactness principle at infinity to prove that the (PS)c condition holds locally and by variational method, we show that this equation has at least one solution provided that ɛ < E , for any m ∈ ℕ, it has m pairs of solutions if ɛ < E m , where E and E m are sufficiently small positive numbers.
Role of fluctuations and nonlinearities on field emission nanomechanical self-oscillators
NASA Astrophysics Data System (ADS)
Barois, T.; Perisanu, S.; Vincent, P.; Purcell, S. T.; Ayari, A.
2013-11-01
A theoretical and experimental description of the threshold, amplitude, and stability of a self-oscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current. The ac and dc components of the current and the phase stability are quantified. An ac to dc ratio above 100% and an Allan deviation of 1.3×10-5 at room temperature can be attained. Finally, it is shown that a simple nonlinear model cannot describe the equilibrium effective potential in the self-oscillating regime due to the high amplitude of oscillations.
McArthur, Duncan; Hourahine, Ben; Papoff, Francesco
2015-01-01
We model a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. Using exact mathematical formulae, we calculate numerically with a custom fortran code the effect of an external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. Data are provided in tabular, comma delimited value format and illustrate narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts. PMID:26601699
McArthur, Duncan; Hourahine, Ben; Papoff, Francesco
2015-11-24
We model a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. Using exact mathematical formulae, we calculate numerically with a custom fortran code the effect of an external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. Data are provided in tabular, comma delimited value format and illustrate narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts.
McArthur, Duncan; Hourahine, Ben; Papoff, Francesco
2015-01-01
We model a scheme for the coherent control of light waves and currents in metallic nanospheres which applies independently of the nonlinear multiphoton processes at the origin of waves and currents. Using exact mathematical formulae, we calculate numerically with a custom fortran code the effect of an external control field which enable us to change the radiation pattern and suppress radiative losses or to reduce absorption, enabling the particle to behave as a perfect scatterer or as a perfect absorber. Data are provided in tabular, comma delimited value format and illustrate narrow features in the response of the particles that result in high sensitivity to small variations in the local environment, including subwavelength spatial shifts. PMID:26601699
NASA Astrophysics Data System (ADS)
Fetisov, Y. K.; Srinivasan, G.
2008-07-01
This report is on hysteresis and switching associated with electric field (E) tuning of ferromagnetic resonance in a bilayer of yttrium iron garnet (YIG)-lead zirconate titanate (PZT). The tuning is facilitated by piezoelectricity of PZT and mechanical bonding with YIG. For E <2kV/cm, the frequency shift δf is linear with E. For E <10kV/cm a pronounced hysteresis is seen in δf versus E. For E >10kV/cm, a butterflylike dependence of δf with an abrupt switch in the sign and magnitude of δf are measured. The observations are attributed to nonlinearities of the piezoelectric deformation.
Vacuum polarization of massive spinor and vector fields in the spacetime of a nonlinear black hole
Matyjasek, Jerzy
2007-10-15
Building on general formulas obtained from the approximate renormalized effective action, the stress-energy tensor of the quantized massive spinor and vector fields in the spacetime of the regular black hole is constructed. Such a black hole is the solution to the coupled system of nonlinear electrodynamics and general relativity. A detailed analytical and numerical analysis of the stress-energy tensor in the exterior region is presented. It is shown that for small values of the charge as well as large distances from the black hole the leading behavior of the stress-energy tensor is similar to that in the Reissner-Nordstroem geometry. Important differences appear when the inner horizon becomes close to the event horizon. A special emphasis is put on the extremal configuration and it is shown that the stress-energy tensor is regular inside the event horizon of the extremal black hole.
Far-field optical imaging with subdiffraction resolution enabled by nonlinear saturation absorption
Ding, Chenliang; Wei, Jingsong
2016-01-01
The resolution of far-field optical imaging is required to improve beyond the Abbe limit to the subdiffraction or even the nanoscale. In this work, inspired by scanning electronic microscopy (SEM) imaging, in which carbon (or Au) thin films are usually required to be coated on the sample surface before imaging to remove the charging effect while imaging by electrons. We propose a saturation-absorption-induced far-field super-resolution optical imaging method (SAI-SRIM). In the SAI-SRIM, the carbon (or Au) layers in SEM imaging are replaced by nonlinear-saturation-absorption (NSA) thin films, which are directly coated onto the sample surfaces using advanced thin film deposition techniques. The surface fluctuant morphologies are replicated to the NSA thin films, accordingly. The coated sample surfaces are then imaged using conventional laser scanning microscopy. Consequently, the imaging resolution is greatly improved, and subdiffraction-resolved optical images are obtained theoretically and experimentally. The SAI-SRIM provides an effective and easy way to achieve far-field super-resolution optical imaging for sample surfaces with geometric fluctuant morphology characteristics. PMID:26727415
NASA Astrophysics Data System (ADS)
Moawad, S. M.; Ibrahim, D. A.
2016-08-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
Far-field optical imaging with subdiffraction resolution enabled by nonlinear saturation absorption
NASA Astrophysics Data System (ADS)
Ding, Chenliang; Wei, Jingsong
2016-01-01
The resolution of far-field optical imaging is required to improve beyond the Abbe limit to the subdiffraction or even the nanoscale. In this work, inspired by scanning electronic microscopy (SEM) imaging, in which carbon (or Au) thin films are usually required to be coated on the sample surface before imaging to remove the charging effect while imaging by electrons. We propose a saturation-absorption-induced far-field super-resolution optical imaging method (SAI-SRIM). In the SAI-SRIM, the carbon (or Au) layers in SEM imaging are replaced by nonlinear-saturation-absorption (NSA) thin films, which are directly coated onto the sample surfaces using advanced thin film deposition techniques. The surface fluctuant morphologies are replicated to the NSA thin films, accordingly. The coated sample surfaces are then imaged using conventional laser scanning microscopy. Consequently, the imaging resolution is greatly improved, and subdiffraction-resolved optical images are obtained theoretically and experimentally. The SAI-SRIM provides an effective and easy way to achieve far-field super-resolution optical imaging for sample surfaces with geometric fluctuant morphology characteristics.
Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes
Buividovich, P. V.
2011-02-15
We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all the histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. A stochastic solution of the self-consistency conditions can be implemented as a 'memory' of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the two-dimensional O(N) sigma model. The extension to non-Abelian lattice gauge theories is discussed.
Self-similar evolution of the nonlinear magnetic buoyancy instability
NASA Technical Reports Server (NTRS)
Shibata, K.; Tajima, T.; Matsumoto, R.
1990-01-01
A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k parallel to B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with the simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfven speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.
NASA Astrophysics Data System (ADS)
Trisnanto, Suko Bagus; Kitamoto, Yoshitaka
2016-02-01
The magnetization induced by oscillatory magnetic-field in a polydispersive superparamagnetic-suspension shows a nonlinearity which strongly depends on the applied frequency. Referring to the initially-measured complex magnetic-susceptibility in function of field-strength, the highly-nonlinear curve of dynamic magnetization at low frequency tends to be linear at higher frequency. Likewise, the dynamic susceptibility appears to be less field-strength dependent at higher frequency, emphasizing a frequency-dependence of magnetically-induced particle-dynamics. This finding is attributable to the imaginary part of magnetization which saturates at lower field-strength of low-frequency magnetic-field. Hence, Brownian relaxation losses should be constant after the saturation due to a confinement of particle rotations.
NASA Astrophysics Data System (ADS)
Gumber, Sukirti; Gambhir, Monica; Jha, Pradip Kumar; Mohan, Man
2016-10-01
We study the combined effect of hydrostatic pressure and magnetic field on electromagnetically induced transparency in quantum ring. The high flexibility in size and shape of ring makes it possible to fabricate a nearly perfect two-dimensional quantum structure. We also explore the dependence of frequency conversion, measured in terms of third order nonlinear susceptibility χ(3) , on coupling field, hydrostatic pressure and magnetic field. Although, a dip in χ(3) is observed with the introduction of strong coupling field, it renders the ring structure transparent to generated wave thus effectively enhancing the output of nonlinear frequency conversion process. At a fixed coupling strength, the output can be further enhanced by increasing the magnetic field while it shows an inverse relationship with pressure. These parameters, being externally controlled, provide an easy handle to control the output of quantum ring which can be used as frequency converter in communication networks.
NASA Astrophysics Data System (ADS)
Luo, Ma
The goal of this dissertation is to implement the spectral element method to calculate the electromagnetic properties of various semiconductor nano-structures, including photonic crystal, photonic crystal slab, finite size photonic crystal block, nano dielectric sphere. The linear electromagnetic characteristics, such as band structure and scattering properties, can be calculated by this method with high accuracy. In addition, I have explored the application of the spectral element method in nonlinear and quantum optics. The effort will focus on second harmonic generation and quantum dot nonlinear dynamics. The electromagnetic field can be simulated in both frequency domain and time domain. Each method has different application for research and engineering. In this dissertation, the first half of the dissertation discusses the frequency domain solver, and the second half of the dissertation discusses the time domain solver. For frequency domain simulation, the basic equation is the second order vector Helmholtz equation of the electric field. This method is implemented to calculate the band structure of photonic crystals consisting of dielectric material as well as metallic materials. Because the photonic crystal is periodic, only one unit cell need to be simulated in the computational domain, and a periodic boundary condition is applied. The spectral accuracy is inspected. Adding the radiation boundary condition at top and bottom of the computational region, the scattering properties of photonic crystal slab can be calculated. For multiple layers photonic crystal slab, the block-Thomas algorithm is used to increase the efficiency of the calculation. When the simulated photonic crystals are finite size, unlike an infinitely periodic system, the periodic boundary condition does not apply. In order to increase the efficiency of the simulation, the domain decomposition method is implemented. The second harmonic generation, which is a kind of nonlinear optical effect
NASA Technical Reports Server (NTRS)
Lobashov, A. A.; Mostepanenko, V. M.
1993-01-01
The theory of quantum effects in nonlinear dielectric media is developed. The nonlinear dielectric media is influenced by an external pumping field. The diagonalization of the Hamiltonian of a quantized field is obtained by the canonical Bogoliubov transformations. The transformations allow us to obtain the general expressions for the number of created photons and for the degree of squeezing. In the case of a plane pumping wave, for example, the results are calculated by using the zero order of the secular perturbation theory, with small parameters characterizing the medium nonlinearity. The Heisenberg equations of motion are obtained for non-stationary case and a commonly used Hamiltonian is derived from the first principles of quantum electrodynamics.
NASA Astrophysics Data System (ADS)
Bergmann, Rachelle Ann
The linear generation of electrostatic hydrogen cyclotron (EHC) waves in the auroral acceleration region near an altitude of 1R(,E) is examined. A field-aligned electron drift and an ion beam are included simultaneously in the plasma model. Each of these has the capability to excite EHC waves. Two assumptions are made, (1) that the plasma can be described by three Maxwellian species and, (2) that the properties of observed EHC waves are the same as the properties of the linearly excited modes. With these assumptions and a plasma model based on S3-3 satellite data, it is concluded that EHC waves driven by an electron drift compare more favorably with observed EHC waves than those driven by an ion beam. Further, the temperature of the drifting electrons should be on the order of the temperature of the stationary ions. Saturation of a linearly excited EHC wave by coherent decay to another EHC wave and an ion acoustic mode is considered. Frequency and wave number matching can be satisfied in this three -wave interaction if the daughter ion acoustic mode is oblique to the geomagnetic field. Many three-wave triads exist for a single parent. A calculation of the coupling coefficient between any three electrostatic waves in a uniformly magnetized plasma comprised of drifting Maxwellian species is derived. This is used to find the threshold electric field of a parent wave necessary for the daughter modes to have a positive non-linear growth rate. It is found that this threshold is below observed EHC wave amplitudes, and is zero when the parent EHC wave couples to a linearly marginally stable EHC daughter wave. Thus, this three-wave interaction may occur in the auroral acceleration region. A preliminary investigation into the temporal development of this interaction is conducted. Though the model is incomplete, the results indicate that this decay can act as a saturation mechanism for the linear growth. In the asymptotic state of the time development, it is the linearly
Nonlinear driven response of a phase-field crystal in a periodic pinning potential.
Achim, C V; Ramos, J A P; Karttunen, M; Elder, K R; Granato, E; Ala-Nissila, T; Ying, S C
2009-01-01
We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one- and two-dimensional systems. The model describes the lattice system as a continuous density field in the presence of a periodic pinning potential, allowing for both elastic and plastic deformations of the lattice. We first present results for phase diagrams of the model in the absence of a driving force. The nonlinear response to a driving force on an initially pinned commensurate phase is then studied via overdamped dynamic equations of motion for different values of mismatch and pinning strengths. For large pinning strength the driven depinning transitions are continuous, and the sliding velocity varies with the force from the threshold with power-law exponents in agreement with analytical predictions. Transverse depinning transitions in the moving state are also found in two dimensions. Surprisingly, for sufficiently weak pinning potential we find a discontinuous depinning transition with hysteresis even in one dimension under overdamped dynamics. We also characterize structural changes of the system in some detail close to the depinning transition.
Spectral-temporal receptive fields of nonlinear auditory neurons obtained using natural sounds.
Theunissen, F E; Sen, K; Doupe, A J
2000-03-15
The stimulus-response function of many visual and auditory neurons has been described by a spatial-temporal receptive field (STRF), a linear model that for mathematical reasons has until recently been estimated with the reverse correlation method, using simple stimulus ensembles such as white noise. Such stimuli, however, often do not effectively activate high-level sensory neurons, which may be optimized to analyze natural sounds and images. We show that it is possible to overcome the simple-stimulus limitation and then use this approach to calculate the STRFs of avian auditory forebrain neurons from an ensemble of birdsongs. We find that in many cases the STRFs derived using natural sounds are strikingly different from the STRFs that we obtained using an ensemble of random tone pips. When we compare these two models by assessing their predictions of neural response to the actual data, we find that the STRFs obtained from natural sounds are superior. Our results show that the STRF model is an incomplete description of response properties of nonlinear auditory neurons, but that linear receptive fields are still useful models for understanding higher level sensory processing, as long as the STRFs are estimated from the responses to relevant complex stimuli.
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines
Reale, D. V. Bragg, J.-W. B.; Gonsalves, N. R.; Johnson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2014-05-15
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
Spectral-temporal receptive fields of nonlinear auditory neurons obtained using natural sounds.
Theunissen, F E; Sen, K; Doupe, A J
2000-03-15
The stimulus-response function of many visual and auditory neurons has been described by a spatial-temporal receptive field (STRF), a linear model that for mathematical reasons has until recently been estimated with the reverse correlation method, using simple stimulus ensembles such as white noise. Such stimuli, however, often do not effectively activate high-level sensory neurons, which may be optimized to analyze natural sounds and images. We show that it is possible to overcome the simple-stimulus limitation and then use this approach to calculate the STRFs of avian auditory forebrain neurons from an ensemble of birdsongs. We find that in many cases the STRFs derived using natural sounds are strikingly different from the STRFs that we obtained using an ensemble of random tone pips. When we compare these two models by assessing their predictions of neural response to the actual data, we find that the STRFs obtained from natural sounds are superior. Our results show that the STRF model is an incomplete description of response properties of nonlinear auditory neurons, but that linear receptive fields are still useful models for understanding higher level sensory processing, as long as the STRFs are estimated from the responses to relevant complex stimuli. PMID:10704507
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar
2016-09-01
We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.
The quench map in an integrable classical field theory: nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Caudrelier, Vincent; Doyon, Benjamin
2016-11-01
We study the non-equilibrium dynamics obtained by an abrupt change (a quench) in the parameters of an integrable classical field theory, the nonlinear Schrödinger equation. We first consider explicit one-soliton examples, which we fully describe by solving the direct part of the inverse scattering problem. We then develop some aspects of the general theory using elements of the inverse scattering method. For this purpose, we introduce the quench map which acts on the space of scattering data and represents the change of parameter with fixed field configuration (initial condition). We describe some of its analytic properties by implementing a higher level version of the inverse scattering method, and we discuss the applications of Darboux–Bäcklund transformations, Gelfand–Levitan–Marchenko equations and the Rosales series solution to a related, dual quench problem. Finally, we comment on the interplay between quantum and classical tools around the theme of quenches and on the usefulness of the quantization of our classical approach to the quantum quench problem.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao E-mail: masato.minamitsuji@ist.utl.pt
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
NASA Astrophysics Data System (ADS)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled `spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
NASA Astrophysics Data System (ADS)
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.
Neukirch, T.; Wilson, F.; Harrison, M. G.
2009-12-15
A detailed discussion is presented of the Vlasov-Maxwell equilibrium for the force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)]. The derivation of the distribution function and a discussion of its general properties and their dependence on the distribution function parameters will be given. In particular, the distribution function can be single-peaked or multipeaked in two of the velocity components, with possible implications for stability. The dependence of the shape of the distribution function on the values of its parameters will be investigated and the relation to macroscopic quantities such as the current sheet thickness will be discussed.
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
Determination of Coronal Magnetic Fields from Vector Magnetograms
NASA Technical Reports Server (NTRS)
Mikic, Zoran
1997-01-01
During the course of the present contract we developed an 'evolutionary technique' for the determination of force-free coronal magnetic fields from vector magnetograph observations. The method can successfully generate nonlinear force- free fields (with non-constant-a) that match vector magnetograms. We demonstrated that it is possible to determine coronal magnetic fields from photospheric measurements, and we applied it to vector magnetograms of active regions. We have also studied theoretical models of coronal fields that lead to disruptions. Specifically, we have demonstrated that the determination of force-free fields from exact boundary data is a well-posed mathematical problem, by verifying that the computed coronal field agrees with an analytic force-free field when boundary data for the analytic field are used; demonstrated that it is possible to determine active-region coronal magnetic fields from photospheric measurements, by computing the coronal field above active region 5747 on 20 October 1989, AR6919 on 15 November 1991, and AR7260 on 18 August 1992, from data taken with the Stokes Polarimeter at Mees Solar Observatory, University of Hawaii; started to analyze active region 7201 on 19 June 1992 using measurements made with the Advanced Stokes Polarimeter at NSO/Sac Peak; investigated the effects of imperfections in the photospheric data on the computed coronal magnetic field; documented the coronal field structure of AR5747 and compared it to the morphology of footpoint emission in a flare, showing that the 'high- pressure' H-alpha footpoints are connected by coronal field lines; shown that the variation of magnetic field strength along current-carrying field lines is significantly different from the variation in a potential field, and that the resulting near-constant area of elementary flux tubes is consistent with observations; begun to develop realistic models of coronal fields which can be used to study flare trigger mechanisms; demonstrated that
Aburjania, G. D.; Machabeli, G. Z.; Kharshiladze, O. A.
2006-07-15
The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.
NASA Astrophysics Data System (ADS)
Mustafa, M.; Khan, Junaid Ahmad
2015-07-01
Present work deals with the magneto-hydro-dynamic flow and heat transfer of Casson nanofluid over a non-linearly stretching sheet. Non-linear temperature distribution across the sheet is considered. More physically acceptable model of passively controlled wall nanoparticle volume fraction is accounted. The arising mathematical problem is governed by interesting parameters which include Casson fluid parameter, magnetic field parameter, power-law index, Brownian motion parameter, thermophoresis parameter, Prandtl number and Schmidt number. Numerical solutions are computed through fourth-fifth-order-Runge-Kutta integration approach combined with the shooting technique. Both temperature and nanoparticle volume fraction are increasing functions of Casson fluid parameter.
Qin Hong; Davidson, Ronald C.
2011-08-15
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio-frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
NASA Astrophysics Data System (ADS)
Qin, Hong; Davidson, Ronald C.
2011-08-01
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio-frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
Hong Qin and Ronald C. Davidson
2011-07-19
In a linear trap confining a one-component nonneutral plasma, the external focusing force is a linear function of the configuration coordinates and/or the velocity coordinates. Linear traps include the classical Paul trap and the Penning trap, as well as the newly proposed rotating-radio- frequency traps and the Mobius accelerator. This paper describes a class of self-similar nonlinear solutions of nonneutral plasma in general time-dependent linear focusing devices, with self-consistent electrostatic field. This class of nonlinear solutions includes many known solutions as special cases.
NASA Astrophysics Data System (ADS)
Park, Kwangsoo
In this dissertation, a research effort aimed at development and implementation of a direct field test method to evaluate the linear and nonlinear shear modulus of soil is presented. The field method utilizes a surface footing that is dynamically loaded horizontally. The test procedure involves applying static and dynamic loads to the surface footing and measuring the soil response beneath the loaded area using embedded geophones. A wide range in dynamic loads under a constant static load permits measurements of linear and nonlinear shear wave propagation from which shear moduli and associated shearing strains are evaluated. Shear wave velocities in the linear and nonlinear strain ranges are calculated from time delays in waveforms monitored by geophone pairs. Shear moduli are then obtained using the shear wave velocities and the mass density of a soil. Shear strains are determined using particle displacements calculated from particle velocities measured at the geophones by assuming a linear variation between geophone pairs. The field test method was validated by conducting an initial field experiment at sandy site in Austin, Texas. Then, field experiments were performed on cemented alluvium, a complex, hard-to-sample material. Three separate locations at Yucca Mountain, Nevada were tested. The tests successfully measured: (1) the effect of confining pressure on shear and compression moduli in the linear strain range and (2) the effect of strain on shear moduli at various states of stress in the field. The field measurements were first compared with empirical relationships for uncemented gravel. This comparison showed that the alluvium was clearly cemented. The field measurements were then compared to other independent measurements including laboratory resonant column tests and field seismic tests using the spectral-analysis-of-surface-waves method. The results from the field tests were generally in good agreement with the other independent test results, indicating
Effect of nonlinear radiofrequency electromagnetic fields on the emittance of bunched beams
NASA Astrophysics Data System (ADS)
Phadte, D. S.; Patidar, C. B.
2013-07-01
Gap transformations are frequently used in ion Linac codes, to efficiently describe the particle dynamics. Using similar approach, we analyze the uniformly bunched beam passing through an axis-symmetric radiofrequency (RF) cavity. The method can be used for other distributions as well using a similar six dimensional analysis. The effect of non-linear RF field in radial and axial directions in an RF cavity and the finite phase width of the bunch, on the transverse and longitudinal emittance growth have been studied. The expressions obtained have been verified for the two types of cavity cells namely the zero mode DTL and pi mode CCL type used frequently in ion linacs. The results are seen to be valid for the entire maximum phase acceptance up to 360 degrees. Simulations with the equivalent beams of non-uniform distributions namely Waterbag and Gaussian show that at synchronous phases closer to the wave crest, the results give a good approximation of emittance growth in both planes for non-uniform beams.
NASA Astrophysics Data System (ADS)
Shi, Pengpeng; Jin, Ke; Zheng, Xiaojing
2016-04-01
Weak magnetic nondestructive testing (e.g., metal magnetic memory method) concerns the magnetization variation of ferromagnetic materials due to its applied load and a weak magnetic surrounding them. One key issue on these nondestructive technologies is the magnetomechanical effect for quantitative evaluation of magnetization state from stress-strain condition. A representative phenomenological model has been proposed to explain the magnetomechanical effect by Jiles in 1995. However, the Jiles' model has some deficiencies in quantification, for instance, there is a visible difference between theoretical prediction and experimental measurements on stress-magnetization curve, especially in the compression case. Based on the thermodynamic relations and the approach law of irreversible magnetization, a nonlinear coupled model is proposed to improve the quantitative evaluation of the magnetomechanical effect. Excellent agreement has been achieved between the predictions from the present model and previous experimental results. In comparison with Jiles' model, the prediction accuracy is improved greatly by the present model, particularly for the compression case. A detailed study has also been performed to reveal the effects of initial magnetization status, cyclic loading, and demagnetization factor on the magnetomechanical effect. Our theoretical model reveals that the stable weak magnetic signals of nondestructive testing after multiple cyclic loads are attributed to the first few cycles eliminating most of the irreversible magnetization. Remarkably, the existence of demagnetization field can weaken magnetomechanical effect, therefore, significantly reduces the testing capability. This theoretical model can be adopted to quantitatively analyze magnetic memory signals, and then can be applied in weak magnetic nondestructive testing.
NASA Astrophysics Data System (ADS)
Sigsbee, K.; Kletzing, C. A.; Pickett, J. S.; Gurnett, D. A.; Schwartz, S. J.; Lefebvre, B.; Lucek, E.; Fazakerley, A. N.; Kucharek, H.
2010-10-01
Langmuir wave characteristics in the Earth's foreshock were examined to identify possible nonlinear wave behavior for two case studies with data from the Cluster Wideband Data Plasma Wave Receiver. The occurrence rates of four types of power spectra near the foreshock edge were determined: (1) spectra with power at the local plasma frequency fpe only, (2) spectra with power at fpe and 2fpe, (3) spectra with double peaks near fpe, and (4) spectra with double peaks near fpe and peaks at low frequencies indicative of ion acoustic waves. For electric field waveform amplitudes between 0.1 and 22.0 mV/m, most power spectra fell into the fpe only and double-peaked categories. The maximum Langmuir wave amplitudes and bump-on-tail reduced electron distribution functions from Cluster PEACE data were more consistent with saturation of wave growth by electrostatic decay than modulational instabilities. However, few spectra had the double peaks near fpe and ion acoustic waves indicative of electrostatic decay, suggesting other processes may also be at work. For amplitudes greater than 22.0 mV/m, most power spectra fell into the fpe and 2fpe category, but many of the harmonics were too weak to be clearly distinguished from harmonics caused by instrumental effects.
Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions
NASA Astrophysics Data System (ADS)
Fujieda, S.; Mori, Y.; Nakazawa, A.; Mogami, Y.
2001-01-01
Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.
Effect of gravity field on the nonequilibrium/nonlinear chemical oscillation reactions.
Fujieda, S; Mori, Y; Nakazawa, A; Mogami, Y
2001-01-01
Biological systems have evolved for a long time under the normal gravity. The Belousov-Zhabotinsky (BZ) reaction is a nonlinear chemical system far from the equilibrium that may be considered as a simplified chemical model of the biological systems so as to study the effect of gravity. The reaction solution is comprised of bromate in sulfuric acid as an oxidizing agent, 1,4-cyclohexanedione as an organic substrate, and ferroin as a metal catalyst. Chemical waves in the BZ reaction-diffusion system are visualized as blue and red patterns of ferriin and ferroin, respectively. After an improvement to the tubular reaction vessels in the experimental setup, the traveling velocity of chemical waves in aqueous solutions was measured in time series under normal gravity, microgravity, hyper-gravity, and normal gravity using the free-fall facility of JAMIC (Japan Microgravity Center), Hokkaido, Japan. Chemical patterns were collected as image data via CCD camera and analyzed by the software of NIH image after digitization. The estimated traveling velocity increased with increasing gravity as expected. It was clear experimentally that the traveling velocity of target patterns in reaction diffusion system was influenced by the effect of convection and correlated closely with the gravity field.
NASA Astrophysics Data System (ADS)
Wang, Lin; Chen, Xiaoshuang; Hu, Yibin; Yu, Anqi; Lu, Wei
2014-10-01
Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high frequency oscillators up to the terahertz regime. Unlike conventional two-terminal NDC devices that rely on resonant tunneling and inter-valley transferring, in the present work, it has been shown that the universal NDC phenomenon of graphene-based FETs originates from their intrinsic nonlinear carrier transport under a strong electric field. The operation of graphene-NDC devices depends strongly on the interface between graphene and dielectric materials, the scattering-limited carrier mobility, and on the saturation velocity. To reveal such NDC behavior, the output characteristics of GFET are investigated rigorously, with both an analytical model and self-consistent transport equation, and with a multi-electrical parameter simulation. It is demonstrated that the contact-induced doping effect plays an important role in the operational efficiency of graphene-based NDC devices, rather than the ambipolar behavior associated with the competition between electron and hole conductances. In the absence of a NDC regime or beyond one, ambipolar transport starts at Vds > 2Vgs at the drain end, and as the dielectric layer begins to thin down, the kink-like saturation output characteristic is enhanced by the quantum capacitance contribution. These observations reveal the intrinsic mechanism of the NDC effect and open up new opportunities for the performance improvement of GFETs in future high-frequency applications, beyond the current paradigm based on two-terminal diodes.Recent observations of the negative differential conductance (NDC) phenomenon in graphene field-effect transistors (FET) open up new opportunities for their application in graphene-based fast switches, frequency multipliers and, most importantly, in high
Influence of 50 Hz magnetic field on human heart rate variability: linear and nonlinear analysis.
Tabor, Zbisław; Michalski, Józef; Rokita, Eugeniusz
2004-09-01
This study investigated the problem of the influence of 50 Hz magnetic field (MF) on human heart rate variability (HRV). The exposure system was a commercial device for magnetotherapy, generating field of the strength of 500 microT at the center of the coil, 150-200 microT at the position of human subjects' heart and 20-30 microT at the position of subjects' head. The exposure protocols, applied randomly, were either "half hour MF-off/half hour MF-on" or "half hour MF-off/half hour MF-off." The phonocardiographic (PhCG) signal of 15 volunteers were obtained during exposure and used for calculation of time-domain HRV parameters (mean time between heart beats (N-N), standard deviation of time between heart beats (SDNN), and the number of differences of successive beat-to-beat intervals greater than 50 ms, divided by the total number of beat-to-beat intervals (pNN50)) and nonlinear HRV measures (approximate entropy (ApEn), detrended fluctuation scaling exponents). The protocol MF-off/MF-on was applied in nine subjects. Repeated measures ANOVA (RMANOVA) performed for Mf-off/MF-off protocol indicated no statistical difference among four 15 min intervals of HRV data (P value >20% for all parameters except for N-N, where P = 3.7%). RMANOVA followed by the post hoc Tukey test performed for Mf-off/MF-on protocol indicated a statistically significant difference during MF on for N-N (8% increase, P <.1%), SDNN (40% increase, P = 1.1%), and pNN50 (110% increase, P <.1%). The results of the analysis indicate that the changes of these parameters could be associated with the influence of MF. PMID:15300734
Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
NASA Astrophysics Data System (ADS)
Leiva, Carlos; Plyushchay, Mikhail S.
2004-02-01
We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z2-graded Poisson, or quantum superalgebra, which may be treated as a nonlinear generalization of the osp(2|2)⊕su(2). In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is, in fact, the same osp(2|2) spin operator. As an odd integral, the osp(2|2) spin generates a nonlinear supersymmetry of De Jonghe, Macfarlane, Peeters and van Holten, and may be identified as a grading operator of the nonlinear superconformal algebra.
NASA Astrophysics Data System (ADS)
Sunil; Mahajan, Amit
2009-09-01
A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic field-dependent (MFD) viscosity, for stress-free boundaries. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effects of magnetic parameter, M3, solute gradient, S1 and MFD viscosity parameter, δ, on the subcritical instability region have also been analyzed.
NASA Astrophysics Data System (ADS)
Romero Kalmanovitz, Natalia
2009-12-01
The nonlinear behavior of low-dimensional electron systems has attracted a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. This work focuses on experimental results related to the nonlinear behavior of two dimensional electron systems. We first observed the non-linear zero-differential resistance state (ZDRS) that occurs for highly mobile two dimensional electron systems in response to a dc bias in the presence of a strong magnetic field applied perpendicular to the electron plane is suppressed. We found that it disappears gradually as the magnetic field is tilted away from the perpendicular at fixed filling factor. Good agreement is found with a model that considers the effect of the Zeeman splitting of Landau levels enhanced by the in-plane component of the magnetic field. Furthermore, we observed that when an electric field is applied to conductors, it heats electric charge carriers. It is demonstrated that an electric field applied to a conductor with a discrete electron spectrum produces a non-equilibrium electron distribution, which cannot be described by temperature. Such electron distribution changes significantly the conductivity of the electrons in a magnetic field, and forces them into a state with a zero differential resistance. Most importantly, the results demonstrate that in general, the effective overheating in the systems with discrete spectrum is significantly stronger than the one in systems with continuous and homogeneous distribution of the energy levels at the same input power. In the last part we observed non-linear behavior in a silicon MOSFET. Measurements of the rectification of microwave radiation at the boundary between two-dimensional electron systems separated by a narrow gap on a silicon surface for different temperatures, electron densities and microwave power, were performed. A theory is proposed that attributes the rectification to the thermoelectric
NASA Astrophysics Data System (ADS)
Hüter, Claas; Friák, Martin; Weikamp, Marc; Neugebauer, Jörg; Goldenfeld, Nigel; Svendsen, Bob; Spatschek, Robert
2016-06-01
We investigate nonlinear elastic deformations in the phase field crystal model and derived amplitude equation formulations. Two sources of nonlinearity are found, one of them is based on geometric nonlinearity expressed through a finite strain tensor. This strain tensor is based on the inverse right Cauchy-Green deformation tensor and correctly describes the strain dependence of the stiffness for anisotropic and isotropic behavior. In isotropic one- and two-dimensional situations, the elastic energy can be expressed equivalently through the left deformation tensor. The predicted isotropic low-temperature nonlinear elastic effects are directly related to the Birch-Murnaghan equation of state with bulk modulus derivative K'=4 for bcc. A two-dimensional generalization suggests K2D '=5 . These predictions are in agreement with ab initio results for large strain bulk deformations of various bcc elements and graphene. Physical nonlinearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformation, the magnitudes of the amplitudes depend on their relative orientation to the applied strain.
NASA Astrophysics Data System (ADS)
Sateesh, V. L.; Upadhyay, C. S.; Venkatesan, C.
2010-07-01
Polarization-electric-field (P-E) interaction results in rendering the stress tensor non-symmetric and in a nonlinear force term in the equilibrium equation. In this paper, an attempt is made to study these (P-E) nonlinear effects on the static response of laminated composite plates with piezo actuators. Further, this paper also focuses on finding the most effective piezo lay-up and ply orientation which gives the maximum deflections. Four different piezo lay-up configurations and three ply orientations are considered. It has been observed from the study that width-wise strips show more transverse bending and twisting. However, full length piezo layers show maximum longitudinal bending. The results of nonlinear analysis show a more considerable softening trend in deformations than that of the linear analysis in the case of longitudinal bending and twisting. In the case of transverse bending this nonlinear effect shows a hardening trend. Further, it has been observed that the influence of P-E nonlinearity depends on the stiffness of the core material, the geometric arrangement of piezo patches, the boundary conditions and the actuation voltage.
NASA Astrophysics Data System (ADS)
Zhu, J.; Winter, C. L.; Wang, Z.
2015-11-01
Computational experiments are performed to evaluate the effects of locally heterogeneous conductivity fields on regional exchanges of water between stream and aquifer systems in the Middle Heihe River basin (MHRB) of northwestern China. The effects are found to be nonlinear in the sense that simulated discharges from aquifers to streams are systematically lower than discharges produced by a base model parameterized with relatively coarse effective conductivity. A similar, but weaker, effect is observed for stream leakage. The study is organized around three hypotheses: (H1) small-scale spatial variations of conductivity significantly affect regional exchanges of water between streams and aquifers in river basins, (H2) aggregating small-scale heterogeneities into regional effective parameters systematically biases estimates of stream-aquifer exchanges, and (H3) the biases result from slow paths in groundwater flow that emerge due to small-scale heterogeneities. The hypotheses are evaluated by comparing stream-aquifer fluxes produced by the base model to fluxes simulated using realizations of the MHRB characterized by local (grid-scale) heterogeneity. Levels of local heterogeneity are manipulated as control variables by adjusting coefficients of variation. All models are implemented using the MODFLOW (Modular Three-dimensional Finite-difference Groundwater Flow Model) simulation environment, and the PEST (parameter estimation) tool is used to calibrate effective conductivities defined over 16 zones within the MHRB. The effective parameters are also used as expected values to develop lognormally distributed conductivity (K) fields on local grid scales. Stream-aquifer exchanges are simulated with K fields at both scales and then compared. Results show that the effects of small-scale heterogeneities significantly influence exchanges with simulations based on local-scale heterogeneities always producing discharges that are less than those produced by the base model
Linear and nonlinear stability in resistive magnetohydrodynamics
Tasso, H.
1994-09-01
A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its {open_quotes}nearness{close_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}unconditional{close_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.
A constant-alpha force-free-field analysis of the active region AR 4711 of February, 1986
NASA Technical Reports Server (NTRS)
Yang, Hai-Shou; Hong, Q. F.; Ding, Y. J.
1988-01-01
The theory of Yang et al. (1983) is used to analyze the large active region AR 4711 of Feb. 1986. This region stored between 0.01 x 10 to the 32nd and 5.36 x 10 to the 32nd erg of extractable free magnetic energy, sufficient to supply the energies of the observed flare activities in this region. The region was an energetic quadrupolar sunspot group, occurring during solar minimum; this group was strongly twisted and produced many intense flares.
Force-free currents and the Newman-Penrose tetrad of a Kerr black hole: Exact local solutions
NASA Astrophysics Data System (ADS)
Menon, Govind
2015-07-01
In a previous article we derived a class of solutions to the force-free magnetosphere in a Kerr background. Here, the streaming surface, defined by constant values of the toriodal component of the electromagnetic vector potential A , was generated by constant values of θ . The electromagnetic current vector flowed along the infalling principle null geodesic vector of the geometry. Subsequently, we generalized this to obtain an outgoing principle null geodesic vector as well. In this article, we derive solutions that are complimentary to the above-mentioned criteria. Namely, here the solution has a streaming surface generated by spheres of constant radial coordinate r , and the current vector is generated by linear combinations of m and m⋆, the remaining bases vectors in the Newman-Penrose null tetrad.
NASA Astrophysics Data System (ADS)
Bhattacharjee, A.; Germaschewski, K.; Wang, X.; Linde, T.; Rosner, R.; Siegel, A.
2002-12-01
There has been considerable interest in recent years in collisionless reconnection dynamics governed by the generalized Ohm's law in which electron inertia provides the mechanism for breaking field lines. It has been suggested in several theoretical studies that the nonlinear reconnection dynamics, to leading order, is independent of the mechanism that breaks field lines (that is, electron inertia). We test this suggestion carefully using the new Magnetic Reconnection Code (MRC) developed at the Center for Magnetic Reconnection Studies. The MRC is a new massively parallel code with Adaptive Mesh Refinement (AMR) that integrates the equations of Hall MHD. The use of AMR enables unprecedented levels of resolution of the current and vorticity layers and uncovers interesting secondary dynamics not seen in previous studies. We apply the MRC to the study of two problems, one involving free reconnection caused by a spontaneous and fast collisionless instability, the other involving forced reconnection induced by boundary perturbations on a stable plasma. In the case of free reconnection, over the range of parameters covered by our simulations, it is shown that the nonlinear reconnection rate is near-explosive, and furthermore, that the nonlinear magnetic island width is an invariant function of a dimensionless variable which is the product of the linear growth rate and time. Now, since the linear growth rate is a function of the ion sound radius as well as the electron skin depth, we conclude that the nonlinear reconnection rate is not independent of electron inertia. In the case of forced reconnection, after a slow growth phase, the dynamics exhibits an impulsive growth in the amplitude of the thin current sheet, and a subsequent current disruption mediated by secondary instabilities. These results, in which electron inertia provides the mechanism for breaking field lines, are contrasted with resistive Hall MHD simulations in which resistivity provides the mechanism for
Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; East, William E.; Blandford, Roger D.
2016-09-07
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 focusmore » 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. As a result, higher magnetization studies are promising and will be carried out in the future.« less
NASA Astrophysics Data System (ADS)
Yuan, Yajie; Nalewajko, Krzysztof; Zrake, Jonathan; East, William E.; Blandford, Roger D.
2016-09-01
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.
NASA Astrophysics Data System (ADS)
Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen
2016-05-01
A one-dimensional electrified viscoelastic model is built to study the nonlinear behavior of a slightly viscoelastic, perfectly conducting liquid jet under a radial electric field. The equations are solved numerically using an implicit finite difference scheme together with a boundary element method. The electrified viscoelastic jet is found to evolve into a beads-on-string structure in the presence of the radial electric field. Although the radial electric field greatly enhances the linear instability of the jet, its influence on the decay of the filament thickness is limited during the nonlinear evolution of the jet. On the other hand, the radial electric field induces axial non-uniformity of the first normal stress difference within the filament. The first normal stress difference in the center region of the filament may be greatly decreased by the radial electric field. The regions with/without satellite droplets are illuminated on the χ (the electrical Bond number)-k (the dimensionless wave number) plane. Satellite droplets may be formed for larger wave numbers at larger radial electric fields.
NASA Technical Reports Server (NTRS)
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.
NASA Astrophysics Data System (ADS)
Namboodiri, Mahesh; Khan, Tahirzeb; Karki, Khadga; Kazemi, Mehdi Mohammad; Bom, Sidhant; Flachenecker, Günter; Namboodiri, Vinu; Materny, Arnulf
2014-04-01
The combination of near-field microscopy along with nonlinear optical spectroscopic techniques is presented here. The scanning near-field imaging technique can be integrated with nonlinear spectroscopic techniques to improve spatial and axial resolution of the images. Additionally, ultrafast dynamics can be probed down to nano-scale dimension. The review shows some examples for this combination, which resulted in an exciton map and vibrational contrast images with sub-wavelength resolution. Results of two-color femtosecond time-resolved pump-probe experiments using scanning near-field optical microscopy (SNOM) on thin films of the organic semiconductor 3,4,9,10 Perylenetetracarboxylic dianhydride (PTCDA) are presented. While nonlinear Raman techniques have been used to obtain highly resolved images in combination with near-field microscopy, the use of femtosecond laser pulses in electronic resonance still constitutes a big challenge. Here, we present our first results on coherent anti-Stokes Raman scattering (fs-CARS) with femtosecond laser pulses detected in the near-field using SNOM. We demonstrate that highly spatially resolved images can be obtained from poly(3-hexylthiophene) (P3HT) nano-structures where the fs-CARS process was in resonance with the P3HT absorption and with characteristic P3HT vibrational modes without destruction of the samples. Sub-diffraction limited lateral resolution is achieved. Especially the height resolution clearly surpasses that obtained with standard microCARS. These results will be the basis for future investigations of mode-selective dynamics in the near-field.
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.
NASA Astrophysics Data System (ADS)
Dehghani, Z.; Saievar Iranizad, E.; Nadafan, M.
2015-01-01
Third order nonlinearity of Fe3O4 nanoparticles (NPs) doped in nematic liquid crystals (NLCs) was evaluated due to laser induced self-phase modulation. The influence of electric field on the nonlinear optical responses of the NLCs doped with Fe3O4 NPs was considered in different voltages. The measurements were performed for two commonly initial alignments (homogeneous and homeotropic) with different small compositional percentages of magnetic NPs. The experimental results show that the homogenous- aligned cell was considerably affected on the applied electric field while the nonlinearity of homeotropic-aligned NLCs with the Fe3O4 NPs did not approximately change in the presence of electric field.
NASA Astrophysics Data System (ADS)
Shi, L.; Yan, Z. W.
2016-06-01
In the present work, the optical properties of GaAs/AlxGa1-xAs/GaAs multi-shell ellipsoidal quantum dot heterostructures with a shallow hydrogenic impurity in the presence of an external electric field have been studied. The results show how the linear and nonlinear optical absorption coefficients and refraction index changes are changed by the variations of the size and shape of the multi-shell structure. Moreover, how the optical properties of this structure are affected by the electric field has also been shown. The physical reasons for the results have been discussed in detail.
Dynamics of atom-field probability amplitudes in a coupled cavity system with Kerr non-linearity
Priyesh, K. V.; Thayyullathil, Ramesh Babu
2014-01-28
We have investigated the dynamics of two cavities coupled together via photon hopping, filled with Kerr non-linear medium and each containing a two level atom in it. The evolution of various atom (field) state probabilities of the coupled cavity system in two excitation sub space are obtained numerically. Detailed analysis has been done by taking different initial conditions of the system, with various coupling strengths and by varying the susceptibility of the medium. The role of susceptibility factor, on the dynamics atom field probability has been examined. In a coupled cavity system with strong photon hopping it is found that the susceptibility factor modifies the behaviour of probability amplitudes.
Parazzini, Marta; Ravazzani, Paolo; Thuroczy, György; Molnar, Ferenc B; Ardesi, Gianluca; Sacchettini, Alessio; Mainardi, Luca Tommaso
2013-06-01
This study was designed to assess the nonlinear dynamics of heart rate variability (HRV) during exposure to low-intensity EMFs. Twenty-six healthy young volunteers were subjected to a rest-to-stand protocol to evaluate autonomic nervous system in quiet condition (rest, vagal prevalence) and after a sympathetic activation (stand). The procedure was conducted twice in a double-blind design: once with a genuine EMFs exposure (GSM cellular phone at 900 MHz, 2 W) and once with a sham exposure (at least 24 h apart). During each session, three-lead electrocardiograms were recorded and RR series extracted off-line. The RR series were analyzed by nonlinear deterministic techniques in every phase of the protocol and during the different exposures. The analysis of the data shows there was no statistically significant effect due to GSM exposure on the nonlinear dynamics of HRV.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
NASA Astrophysics Data System (ADS)
Chen, Chao; Xia, Jianghai; Liu, Jiangping; Feng, Guangding
2006-03-01
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
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
Tam, Leo K; Stockmann, Jason P; Galiana, Gigi; Constable, R Todd
2012-10-01
To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term null space imaging. The method is compared to conventional Cartesian SENSitivity Encoding as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The null space imaging approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding.
Tam, Leo K.; Galiana, Gigi; Stockmann, Jason P.; Constable, R. Todd
2012-01-01
To increase image acquisition efficiency, we develop alternative gradient encoding strategies designed to provide spatial encoding complementary to the spatial encoding provided by the multiple receiver coil elements in parallel image acquisitions. Intuitively, complementary encoding is achieved when the magnetic field encoding gradients are designed to encode spatial information where receiver spatial encoding is ambiguous, for example, along sensitivity isocontours. Specifically, the method generates a basis set for the null space of the coil sensitivities with the singular value decomposition (SVD) and calculates encoding fields from the null space vectors. A set of nonlinear gradients is used as projection imaging readout magnetic fields, replacing the conventional linear readout field and phase encoding. Multiple encoding fields are used as projections to capture the null space information, hence the term Null Space Imaging (NSI). The method is compared to conventional Cartesian SENSitivity Encoding (SENSE) as evaluated by mean squared error and robustness to noise. Strategies for developments in the area of nonlinear encoding schemes are discussed. The NSI approach yields a parallel imaging method that provides high acceleration factors with a limited number of receiver coil array elements through increased time efficiency in spatial encoding. PMID:22190380
NASA Astrophysics Data System (ADS)
Young-Gonzales, Amanda R.; Samanta, Subarna; Richert, Ranko
2015-09-01
For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.
Young-Gonzales, Amanda R; Samanta, Subarna; Richert, Ranko
2015-09-14
For glycerol and three monohydroxy alcohols, we have measured the non-linear dielectric effects resulting from the application and removal of a high dc bias electric field. The field effects are detected by virtue of a small amplitude harmonic field, from which time resolved changes in the dielectric loss are derived. The changes in permittivity are dominated by modifications of the time constants (rather than amplitudes) which display two contributions: a heating-like decrease of relaxation times that originates from the time dependent field when the bias is switched on and off and a slowing down of the dynamics resulting from the field induced reduction of configurational entropy. As observed for the electro-optical Kerr effect, the rise of the entropy change is slower than its decay, a feature that we rationalize on the basis of the quadratic dependence of the entropy change on polarization. For glycerol, the observed steady state level of the field induced shift of the glass transition temperature (+84 mK) matches the expectation based on the entropy change and its impact on dynamics via the Adam-Gibbs relation (+88 mK). For the alcohols, these non-linear effects rise and decay on the time scales of the prominent dielectric Debye process, underscoring the relation of these features to polarization anisotropy, opposed to mechanical or enthalpy relaxation which are orders of magnitude faster in these systems. A model is discussed which captures the observed magnitudes as well as time dependences in a near quantitative fashion. It is demonstrated that the high bias field modifies the response of polarization to the ac field, including a temporary change in the low field susceptibility.
2012-01-01
The exciton binding energy of an asymmetrical GaAs-Ga1−xAlxAs cylindrical quantum dot is studied with the use of the effective mass approximation and a variational calculation procedure. The influence on this quantity of the application of a direct-current electric field along the growth direction of the cylinder, together with that of an intense laser field, is particularly considered. The resulting states are used to calculate the exciton-related nonlinear optical absorption and optical rectification, whose corresponding resonant peaks are reported as functions of the external probes, the quantum dot dimensions, and the aluminum molar fraction in the potential barrier regions. PMID:22971418
Zapata, Alejandro; Acosta, Ruben E; Mora-Ramos, Miguel E; Duque, Carlos A
2012-01-01
: The exciton binding energy of an asymmetrical GaAs-Ga1-xAlxAs cylindrical quantum dot is studied with the use of the effective mass approximation and a variational calculation procedure. The influence on this quantity of the application of a direct-current electric field along the growth direction of the cylinder, together with that of an intense laser field, is particularly considered. The resulting states are used to calculate the exciton-related nonlinear optical absorption and optical rectification, whose corresponding resonant peaks are reported as functions of the external probes, the quantum dot dimensions, and the aluminum molar fraction in the potential barrier regions. PMID:22971418
Nonlinear frequency conversion of fields with orbital angular momentum using quasi-phase-matching
NASA Astrophysics Data System (ADS)
Shao, Guang-hao; Wu, Zi-jian; Chen, Jin-hui; Xu, Fei; Lu, Yan-qing
2013-12-01
We propose and investigate the quasi-phase-matched (QPM) nonlinear optical frequency conversion of optical vortices in periodically poled lithium niobate. Laguerre-Gaussian (LG) modes are used to represent the orbital angular momentum (OAM) states, characterized with the azimuthal and radial indices. Typical three-wave nonlinear interactions among the involved OAM modes are studied with the help of coupling wave equations. Being different from normal QPM process where the energy and quasimomentum conservations are satisfied, both of the azimuthal and radial indices of the OAM states stay constant in most of the cases. However, abnormal change of the radial index is observed when there is asynchronous nonlinear conversion in different parts of the beams. The QPM nonlinear evolution of fractional OAM states is also discussed showing some interesting properties. In comparison with the traditional birefringent phase matching, the QPM technique avoids the undesired walk-off effect to reserve high-quality LG modes. We believe the QPM is an effective way to convert, amplify, and switch OAM states in various optical vortex related applications.
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Ma, Yue
2016-09-01
The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for self-gravitating massive scalar fields, while existing methods only apply to massless scalar fields. First of all, by analyzing the structure of the Einstein equations in wave coordinates, we exhibit a nonlinear wave-Klein-Gordon model defined on a curved background, which is the focus of the present paper. For this model, we prove here the existence of global-in-time solutions to the Cauchy problem, when the initial data have sufficiently small Sobolev norms. A major difficulty comes from the fact that the class of conformal Killing fields of Minkowski space is significantly reduced in the presence of a massive scalar field, since the scaling vector field is not conformal Killing for the Klein-Gordon operator. Our method relies on the foliation (of the interior of the light cone) of Minkowski spacetime by hyperboloidal hypersurfaces and uses Lorentz-invariant energy norms. We introduce a frame of vector fields adapted to the hyperboloidal foliation and we establish several key properties: Sobolev and Hardy-type inequalities on hyperboloids, as well as sup-norm estimates, which correspond to the sharp time decay for the wave and the Klein-Gordon equations. These estimates allow us to control interaction terms associated with the curved geometry and the massive field by distinguishing between two levels of regularity and energy growth and by a successive use of our key estimates in order to close a bootstrap argument.
Detection and analysis of coherent groups in three-dimensional fully-nonlinear potential wave fields
NASA Astrophysics Data System (ADS)
Sanina, E. V.; Suslov, S. A.; Chalikov, D.; Babanin, A. V.
2016-07-01
We investigate the emergence of coherent groups in three-dimensional fully-nonlinear potential deep water waves whose initial spectrum is assumed to be of the JONSWAP type with directional distribution given by cos nθ, where n is the integer varying from 1 to 16. The analysis is based on the results of long-term wave simulations performed using a numerical solution of a three-dimensional Laplace equation for the velocity potential subject to nonlinear kinematic and dynamic boundary conditions at the free surface. The main characteristics of wave groups such as their average velocity, maximum group wave height, lifetime and length are analysed. The statistics of extreme waves occurring in the detected groups are discussed. Spatial and temporal scale characteristics of wave groups are compared to the previous results.
Mapping nonlinear receptive field structure in primate retina at single cone resolution.
Freeman, Jeremy; Field, Greg D; Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam; Simoncelli, Eero P; Chichilnisky, E J
2015-01-01
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits.
NASA Astrophysics Data System (ADS)
Singh, A.; Ctistis, G.; Huisman, S. R.; Korterik, J. P.; Mosk, A. P.; Herek, J. L.; Pinkse, P. W. H.
2015-01-01
We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high resolution in energy as well as in momentum using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are caused by a waveguide-specific near-field tip effect not previously reported, which can significantly phase-modulate the detected field.
NASA Astrophysics Data System (ADS)
Moon, Chanho; Kaneko, Toshiro; Itoh, Kimitaka; Ida, Katsumi; Kobayashi, Tatsuya; Inagaki, Shigeru; Itoh, Sanae-I.; Hatakeyama, Rikizo
2016-11-01
Turbulence in fluids and plasmas is ubiquitous in Nature and in the laboratory. Contrary to the importance of the ‘scale-free’ nature of cascade in neutral fluid turbulence, the turbulence in plasma is characterised by dynamics of distinct length scales. The cross-scale interactions can be highly non-symmetric so as to generate the plasma turbulence structures. Here we report that the system of hyper-fine electron-temperature-gradient (ETG) fluctuations and microscopic drift-wave (DW) fluctuations is strongly influenced by the sign of the gradient of the radial electric field through multiscale nonlinear interactions. The selective suppression effects by radial electric field inhomogeneity on DW mode induce a new route to modify ETG mode. This suppression mechanism shows disparity with respect to the sign of the radial electric field inhomogeneity, which can be driven by turbulence, so that it could be a new source for symmetry breaking in the turbulence structure formation in plasmas.
Singh, A.; Huisman, S. R.; Ctistis, G. Mosk, A. P.; Pinkse, P. W. H.; Korterik, J. P.; Herek, J. L.
2015-01-21
We have measured the photonic bandstructure of GaAs photonic-crystal waveguides with high resolution in energy as well as in momentum using near-field scanning optical microscopy. Intriguingly, we observe additional bands that are not predicted by eigenmode solvers, as was recently demonstrated by Huisman et al. [Phys. Rev. B 86, 155154 (2012)]. We study the presence of these additional bands by performing measurements of these bands while varying the incident light power, revealing a non-linear power dependence. Here, we demonstrate experimentally and theoretically that the observed additional bands are caused by a waveguide-specific near-field tip effect not previously reported, which can significantly phase-modulate the detected field.
Relativistic weak lensing from a fully non-linear cosmological density field
Thomas, D.B.; Bruni, M.; Wands, D. E-mail: marco.bruni@port.ac.uk
2015-09-01
In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- and B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.
NASA Technical Reports Server (NTRS)
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.
Watts, C.A.
1993-09-01
In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low dimensional chaos and simple determinism. Experimental date were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or low simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.
NASA Astrophysics Data System (ADS)
Zhou, Hao-Miao; Li, Meng-Han; Li, Xiao-Hong; Zhang, Da-Guang
2016-08-01
For a giant magnetostrictive rod under the action of multiple physical loads, such as an external magnetic field, temperature and axial pre-stress, this paper proposes a general one-dimensional nonlinear magneto-thermo-mechanical coupled constitutive model. This model is based on the Taylor expansion of the elastic Gibbs free energy of giant magnetostrictive material and thermodynamic relations from the perspective of macro continuum mechanics. Predictions made using this model are in good agreement with experimental data for magnetization and the magnetostrictive strain curve under the collective effect of pre-stress and temperature. Additionally, the model overcomes the drawback of the existing magneto-thermo-mechanical constitutive model that cannot accurately predict the magnetization and magnetostrictive strain curve for different temperatures and pre-stresses. Furthermore, the constitutive model does not contain an implicit function and is compact, and can thus be applied in both situations of tensile and compressive stress and to both positive and negative magnetostrictive materials, and it is thus appropriate for engineering applications. Comprehensive analysis shows that the model fully describes the nonlinear coupling properties of a magnetic field, magnetostrictive strain and elasticity of a magnetostrictive material subjected to stress, a magnetic field and heat.
NASA Astrophysics Data System (ADS)
Liu, Wu-Ming; Zhang, Wu-Shou; Pu, Fu-Cho; Zhou, Xin
1999-11-01
By using a stereographic projection of the unit sphere of magnetization vector onto a complex plane for the equations of motion, the effect of an external magnetic field for integrability of the system is discussed. The properties of the Jost solutions and the scattering data are then investigated through introducing transformations other than the Riemann surface in order to avoid double-valued functions of the usual spectral parameter. The exact multisoliton solutions are investigated by means of the Binet-Cauchy formula. The results showed that under the action of an external magnetic field nonlinear magnetization depends essentially on two parameters: its center moves with a constant velocity, while its shape changes with another constant velocity; its amplitude and width vary periodically with time, while its shape is also dependent on time and is unsymmetric with respect to its center. The orientation of the nonlinear magnetization in the plane orthogonal to the anisotropy axis changes with an external magnetic field. The total magnetic momentum and the integral of the motion coincident with its z component depend on time. The mean number of spins derivated from the ground state in a localized magnetic excitations is dependent on time. The asymptotic behavior of multisoliton solutions, the total displacement of center, and the phase shift of the jth peak are also analyzed.
NASA Astrophysics Data System (ADS)
Yesilgul, U.; Al, E. B.; Martínez-Orozco, J. C.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.; Ungan, F.; Kasapoglu, E.
2016-08-01
In the present study, the effects of electric and magnetic fields on the linear and third-order nonlinear optical absorption coefficients and relative change of the refractive index in asymmetric GaAs/GaAlAs double quantum wells under intense laser fields are theoretically investigated. The electric field is oriented along the growth direction of the heterostructure while the magnetic field is taken in-plane. The intense laser field is linear polarization along the growth direction. Our calculations are made using the effective-mass approximation and the compact density-matrix approach. Intense laser effects on the system are investigated with the use of the Floquet method with the consequent change in the confinement potential of heterostructures. Our results show that the increase of the electric and magnetic fields blue-shifts the peak positions of the total absorption coefficient and of the total refractive index while the increase of the intense laser field firstly blue-shifts the peak positions and later results in their red-shifting.
Magnetic field restructuring associated with two successive solar eruptions
Wang, Rui; Liu, Ying D.; Yang, Zhongwei; Hu, Huidong
2014-08-20
We examine two successive flare eruptions (X5.4 and X1.3) on 2012 March 7 in the NOAA active region 11429 and investigate the magnetic field reconfiguration associated with the two eruptions. Using an advanced non-linear force-free field extrapolation method based on the SDO/HMI vector magnetograms, we obtain a stepwise decrease in the magnetic free energy during the eruptions, which is roughly 20%-30% of the energy of the pre-flare phase. We also calculate the magnetic helicity and suggest that the changes of the sign of the helicity injection rate might be associated with the eruptions. Through the investigation of the magnetic field evolution, we find that the appearance of the 'implosion' phenomenon has a strong relationship with the occurrence of the first X-class flare. Meanwhile, the magnetic field changes of the successive eruptions with implosion and without implosion were well observed.
A filament supported by different magnetic field configurations
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Okuzumi, Satoshi; Inutsuka, Shu-ichiro
2015-02-01
The ionization state of the gas plays a key role in the magnetohydrodynamics (MHD) of protoplanetary disks. However, the ionization state can depend on the gas dynamics, because electric fields induced by MHD turbulence can heat up plasmas and thereby affect the ionization balance. To study this nonlinear feedback, we construct an ionization model that includes plasma heating by electric fields and impact ionization by heated electrons, as well as charging of dust grains. We show that when plasma sticking onto grains is the dominant recombination process, the electron abundance in the gas decreases with increasing electric field strength. This is a natural consequence of electron-grain collisions whose frequency increases with the electron's random velocity. The decreasing electron abundance may lead to a self-regulation of MHD turbulence. In some cases, not only the electron abundance but also the electric current decreases with increasing field strength in a certain field range. The resulting N-shaped current-field relation violates the fundamental assumption of the non-relativistic MHD that the electric field is uniquely determined by the current density. At even higher field strengths, impact ionization causes an abrupt increase of the electric current as expected by previous studies. We find that this discharge current is multi-valued (i.e., the current-field relation is S-shaped) under some circumstances, and that the intermediate branch is unstable. The N/S-shaped current-field relations may yield hysteresis in the evolution of MHD turbulence in some parts of protoplanetary disks.
Okuzumi, Satoshi; Inutsuka, Shu-ichiro
2015-02-10
The ionization state of the gas plays a key role in the magnetohydrodynamics (MHD) of protoplanetary disks. However, the ionization state can depend on the gas dynamics, because electric fields induced by MHD turbulence can heat up plasmas and thereby affect the ionization balance. To study this nonlinear feedback, we construct an ionization model that includes plasma heating by electric fields and impact ionization by heated electrons, as well as charging of dust grains. We show that when plasma sticking onto grains is the dominant recombination process, the electron abundance in the gas decreases with increasing electric field strength. This is a natural consequence of electron-grain collisions whose frequency increases with the electron's random velocity. The decreasing electron abundance may lead to a self-regulation of MHD turbulence. In some cases, not only the electron abundance but also the electric current decreases with increasing field strength in a certain field range. The resulting N-shaped current-field relation violates the fundamental assumption of the non-relativistic MHD that the electric field is uniquely determined by the current density. At even higher field strengths, impact ionization causes an abrupt increase of the electric current as expected by previous studies. We find that this discharge current is multi-valued (i.e., the current-field relation is S-shaped) under some circumstances, and that the intermediate branch is unstable. The N/S-shaped current-field relations may yield hysteresis in the evolution of MHD turbulence in some parts of protoplanetary disks.
Sabaeian, Mohammad Shahzadeh, Mohammadreza; Farbod, Mansoor
2014-12-15
In this work, the effects of vertical electric field on the electronic and optical properties of strained semi-spheroid-shaped InAs/GaAs quantum dot (QD) coupled to its wetting layer (WL) aimed to enhance the nonlinear optical properties were investigated. The dependence of energy eigenvalues of S- and P- states and intersubband P-to-S transition energy on applied electric field was studied. A ∼∓10 meV Stark shift in the intersubband P-to-S transition energy was calculated for a semi-spheroid-shaped QD with height of 5 nm and base-length of 20 nm when bias voltage was varied from 0 V to ±0.8V. The dependence of transition dipole moment and linear and nonlinear optical properties of the system on bias voltage was also studied. It was concluded that increasing the bias voltage from -0.8V to +0.8V leads to increase in figure of merit of the system from ∼0.153 to ∼0.198.
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. PMID:26740805
Mapping nonlinear receptive field structure in primate retina at single cone resolution
Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam
2015-01-01
The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. DOI: http://dx.doi.org/10.7554/eLife.05241.001 PMID:26517879
Wang, Shiwei; Zhao, Lisha; Zhang, Xiaolong; Shi, Zuosen; Cui, Zhanchen; Yang, Yanqiang
2009-08-15
This work focused on the development of a novel method for molecular level assembly and processing of inorganic-organic hybrid second-order nonlinear optical (SONLO) multilayer films. Aromatic diazo group linked silicon sol was first synthesized and used as a polycation. This oligomer was assembled into inorganic-organic hybrid SONLO multilayer films by electric-field-induced layer-by-layer assembly technique with a low molecular weight chromophore molecule as an anion. After UV irradiation, the electrostatic interaction between layers converted to covalent bonds. Large second-harmonic generation signal of the assembled film was observed, which confirmed that the chromophore in the film had a high degree of molecular orientation as assembled under the electric field. As the cross-linked structure and silicon oxygen meshwork in the films, the resulting inorganic-organic hybrid multilayer films displayed good thermal and chemical stability, and excellent NLO properties. PMID:19433327
NASA Astrophysics Data System (ADS)
Lu, Lin; Chang, Yunlong; Li, Yingmin; He, Youyou
2013-05-01
A transverse magnetic field was introduced to the arc plasma in the process of welding stainless steel tubes by high-speed Tungsten Inert Gas Arc Welding (TIG for short) without filler wire. The influence of external magnetic field on welding quality was investigated. 9 sets of parameters were designed by the means of orthogonal experiment. The welding joint tensile strength and form factor of weld were regarded as the main standards of welding quality. A binary quadratic nonlinear regression equation was established with the conditions of magnetic induction and flow rate of Ar gas. The residual standard deviation was calculated to adjust the accuracy of regression model. The results showed that, the regression model was correct and effective in calculating the tensile strength and aspect ratio of weld. Two 3D regression models were designed respectively, and then the impact law of magnetic induction on welding quality was researched.
Ultrafast Rotation of Light Fields Applied to Highly Non-Linear Optics
NASA Astrophysics Data System (ADS)
Quéré, Fabien
2014-05-01
Femtosecond laser beams can exhibit spatio-temporal couplings (STC), i.e. a temporal dependence of their spatial properties, or vice versa. Although these couplings have long been considered as detrimental for high-intensity and ultrafast experiments, moderate and controlled STC provide a powerful means of controlling high-intensity laser-matter interactions. This talk will first explain the basics of a particular STC, where the propagation direction of laser light rotates in time on the femtosecond time scale. Laser pulses with such ultrafast wavefront rotation can be used to generate attosecond pulses of light through non-linear optical processes. We show that these pulses, periodically generated in each laser cycle, can then be emitted in spatially separated beamlets. This effects provides a new type of light sources called attosecond lighthouses, and can be exploited for ultrafast measurements with femtosecond resolution, in a scheme called photonic streaking.
Kur'yanova, E V; Teplyi, D L; Zhukova, Yu D; Zhukovina, N V
2015-12-01
The basic behavioral activity of nonlinear rats was evaluated from the sum of crossed peripheral and central squares and peripheral and central rearing postures in the open fi eld test. This index was low (<20 episodes), intermediate (20-29 episodes), or high (>30 episodes). Male rats with high score of orientation and exploratory activity were characterized by higher indexes of total heart rate variability than rats with low or intermediate activity. Specimens with a greater contribution of VLF waves into the total power spectrum of heart rate variability were shown to dominate among the rats with high behavioral activity. Our results are consistent with the notions of a suprasegmental nature of VLF waves.
NASA Astrophysics Data System (ADS)
Dähmlow, Patricia; Müller, Stefan C.
2015-04-01
Labyrinth-like Turing patterns are investigated under the influence of an electric field. The patterns form in the ferroin-catalyzed Belousov-Zhabotinsky reaction embedded in the sodium-bis (2-ethylhexyl) sulfosuccinate (AOT) water-in-oil microemulsion. For two different values of the droplet fraction above and below the percolation transition of the system, the electric field induced drift of the patterns is different. Above the percolation transition, a linear increase of the drift velocity with increasing electric field strength is found. However, below the percolation transition, this increase shows an exponential behavior. The patterns are also observed to reorient under high electrical field strength, such that they are arranged perpendicular with respect to the field lines.
Steady-state axisymmetric nonlinear magnetohydrodynamic solutions with various boundary conditions
NASA Astrophysics Data System (ADS)
Wang, Lile; Lou, Yu-Qing
2014-04-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main-sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars, magnetars, isolated neutron stars, etc.] and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method and finite-element method schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso, finding that their separable semi-analytic non-linear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. Similar situations of multiple non-linear solutions with the same boundary conditions actually also happen to force-free magnetic field models of Low & Lou. The multiplicity of non-linear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as well as in the asymptotic behaviours approaching infinity, which may in turn explain why numerical solvers tend to converge to a non-linear solution with a lower energy than the corresponding separable semi-analytic one. By properly adjusting model parameters, we invoke semi-analytic and numerical solutions to describe different kinds of scenarios, including nearly parallel case and the situation in which the misalignment between the plasma flow and magnetic field is considerable. We propose that these MHD models are capable of describing the magnetospheres of MWDs as examples of applications with moderate conditions (including magnetic field) where the typical values of several important parameters are consistent with observations. Physical parameters can also be estimated based on such MHD models directly. We discuss the challenges
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K. . Inst. for Theoretical Physics); Sevrin, A. ); van Nieuwenhuizen, P. . Theory Div.)
1991-11-01
In this contribution to Tini Veltman's Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields ( the metric') are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K.; Sevrin, A.; van Nieuwenhuizen, P.
1991-11-01
In this contribution to Tini Veltman`s Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields (`the metric`) are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
NASA Astrophysics Data System (ADS)
Morais, C. V.; Zimmer, F. M.; Lazo, M. J.; Magalhães, S. G.; Nobre, F. D.
2016-06-01
The behavior of the nonlinear susceptibility χ3 and its relation to the spin-glass transition temperature Tf in the presence of random fields are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue λAT (replicon) on the random fields is analyzed. Particularly, in the absence of random fields, the temperature Tf can be traced by a divergence in the spin-glass susceptibility χSG, which presents a term inversely proportional to the replicon λAT. As a result of a relation between χSG and χ3, the latter also presents a divergence at Tf, which comes as a direct consequence of λAT=0 at Tf. However, our results show that, in the presence of random fields, χ3 presents a rounded maximum at a temperature T* which does not coincide with the spin-glass transition temperature Tf (i.e., T*>Tf for a given applied random field). Thus, the maximum value of χ3 at T* reflects the effects of the random fields in the paramagnetic phase instead of the nontrivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that χ3 still maintains a dependence on the replicon λAT, although in a more complicated way as compared with the case without random fields. These results are discussed in view of recent observations in the LiHoxY1 -xF4 compound.
Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration
NASA Astrophysics Data System (ADS)
Li, X. F.; Yu, Q.; Gu, Y. J.; Huang, S.; Kong, Q.; Kawata, S.
2015-08-01
The electromagnetic field in the electron "bubble" regime for ultra-intense laser wakefield acceleration was solved using the d'Alembert equations. Ignoring the residual electrons, we assume an ellipsoidal bubble forms under ideal conditions, with bubble velocity equal to the speed of light in vacuum. The general solution for bubble shape and electromagnetic field were obtained. The results were confirmed in 2.5D PIC (particle-in-cell) simulations. Moreover, slopes for the longitudinal electric field of larger than 0.5 were found in these simulations. With spherical bubbles, this slope is always smaller than or equal to 0.5. This behavior validates the ellipsoid assumption.
Electronic dynamics under effect of a nonlinear Morse interaction and a static electric field
NASA Astrophysics Data System (ADS)
Ranciaro Neto, A.; de Moura, F. A. B. F.
2016-11-01
Considering non-interacting electrons in a one-dimension alloy in which atoms are coupled by a Morse potential, we study the system dynamics in the presence of a static electric field. Calculations are performed assuming a quantum mechanical treatment for the electronic transport and a classical Hamiltonian model for the lattice vibrations. We report numerical evidence of the existence of a soliton-electron pair, even when the electric field is turned on, and we offer a description of how the existence of such a phase depends on the magnitude of the electric field and the electron-phonon interaction.
NASA Astrophysics Data System (ADS)
Moen, Erick K.; Beier, Hope T.; Thompson, Gary L.; Roth, Caleb C.; Ibey, Bennett L.
2014-03-01
Nonlinear optical probes, especially those involving second harmonic generation (SHG), have proven useful as sensors for near-instantaneous detection of alterations to orientation or energetics within a substance. This has been exploited to some success for observing conformational changes in proteins. SHG probes, therefore, hold promise for reporting rapid and minute changes in lipid membranes. In this report, one of these probes is employed in this regard, using nanosecond electric pulses (nsEPs) as a vehicle for instigating subtle membrane perturbations. The result provides a useful tool and methodology for the observation of minute membrane perturbation, while also providing meaningful information on the phenomenon of electropermeabilization due to nsEP. The SHG probe Di- 4-ANEPPDHQ is used in conjunction with a tuned optical setup to demonstrate nanoporation preferential to one hemisphere, or pole, of the cell given a single square shaped pulse. The results also confirm a correlation of pulse width to the amount of poration. Furthermore, the polarity of this event and the membrane physics of both hemispheres, the poles facing either electrode, were tested using bipolar pulses consisting of two pulses of opposite polarity. The experiment corroborates findings by other researchers that these types of pulses are less effective in causing repairable damage to the lipid membrane of cells.
NASA Astrophysics Data System (ADS)
Baghshahi, H. R.; Tavassoly, M. K.
2015-03-01
In this paper, we present a model which exhibits two identical Ξ-type three-level atoms interacting with a single-mode field with k-photon transition in an optical cavity enclosed by a Kerr medium. Considering full nonlinear formalism, it is assumed that the single-mode field, atom-field coupling and Kerr medium are all f-deformed. By using the adiabatic elimination method, it is shown that, the Hamiltonian of the considered system can be reduced to an effective Hamiltonian with two two-level atoms and f-deformed Stark shift. In spite of the fact that, the system seems to be complicated, under initial conditions which may be prepared for the atoms (coherent superposition of their ground and upper states) and the field (coherent state), the explicit form of the state vector of the entire system is analytically obtained. Then, the entanglement dynamics between different subsystems ( i.e. "field-two atoms", "atom-(field+atom)" and "atom-atom") are evaluated through appropriate measures like von Neumann entropy, tangle and concurrence. In addition, the effects of intensity-dependent coupling, deformed Kerr medium, detuning parameter, deformed Stark shift and multi-photon process on the considered entanglement measures are numerically analyzed, in detail. It is shown that the degree of entanglement between subsystems can be controlled by selecting the evolved parameters, suitably. Briefly, the Kerr medium highly decreases the amount of different considered measures of entanglement, especially for two-photon transition. This destructive effect preserves even when all other parameters are present, too. Furthermore, we find that the so-called entanglement sudden death and birth can occur in the atom-atom entanglement.
Speck, Thomas; Menzel, Andreas M; Bialké, Julian; Löwen, Hartmut
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
NASA Astrophysics Data System (ADS)
Castro, G.; Mascali, D.; Agnello, R.; Celona, L.; Leonardi, O.; Neri, L.; Nicolosi, D.; Torrisi, G.; Gammino, S.
2016-02-01
A characterization of wave-to-plasma interaction in a quasi-flat magnetostatic field at 3.75 GHz has been carried out by using a small-wire movable RF antenna, connected to a spectrum analyzer. The coupling between electromagnetic and electrostatic waves leads to a characteristic spectral emission in low frequency range and around the pumping wave frequency. The most relevant results consist in the broadening of the pumping wave spectrum above critical RF power thresholds and in the generation of sidebands of the pumping frequency, with corresponding components in low frequency domain. The non-linearities are accompanied by the generation of overdense plasmas and intense fluxes of X-rays.
Noe, G. Timothy; Lee, Joseph; Woods, Gary L.; Nojiri, Hiroyuki; Léotin, Jean; Kono, Junichiro
2013-12-15
We have developed a mini-coil pulsed magnet system with direct optical access, ideally suited for nonlinear and ultrafast spectroscopy studies of materials in high magnetic fields up to 30 T. The apparatus consists of a small coil in a liquid nitrogen cryostat coupled with a helium flow cryostat to provide sample temperatures down to below 10 K. Direct optical access to the sample is achieved with the use of easily interchangeable windows separated by a short distance of ∼135 mm on either side of the coupled cryostats with numerical apertures of 0.20 and 0.03 for measurements employing the Faraday geometry. As a demonstration, we performed time-resolved and time-integrated photoluminescence measurements as well as transmission measurements on InGaAs quantum wells.
Castro, G; Mascali, D; Agnello, R; Celona, L; Leonardi, O; Neri, L; Nicolosi, D; Torrisi, G; Gammino, S
2016-02-01
A characterization of wave-to-plasma interaction in a quasi-flat magnetostatic field at 3.75 GHz has been carried out by using a small-wire movable RF antenna, connected to a spectrum analyzer. The coupling between electromagnetic and electrostatic waves leads to a characteristic spectral emission in low frequency range and around the pumping wave frequency. The most relevant results consist in the broadening of the pumping wave spectrum above critical RF power thresholds and in the generation of sidebands of the pumping frequency, with corresponding components in low frequency domain. The non-linearities are accompanied by the generation of overdense plasmas and intense fluxes of X-rays. PMID:26931915
Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
Speck, Thomas; Menzel, Andreas M; Bialké, Julian; Löwen, Hartmut
2015-06-14
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results. PMID:26071703
NASA Astrophysics Data System (ADS)
Speck, Thomas; Menzel, Andreas M.; Bialké, Julian; Löwen, Hartmut
2015-06-01
Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.
Seidler, T.; Stadnicka, K.; Champagne, B.
2015-03-30
This contribution summarizes our current findings in the field of calculating and predicting the linear and second-order nonlinear electric susceptibility tensor components of organic crystals. The methodology used for this purpose is based on a combination of the electrostatic interaction scheme developed by Munn and his coworkers (RLFT) with high-level electronic structure calculations. We compare the results of calculations with available experimental data for several examples of molecular crystals. We show the quality of the final results is influenced by i) the chromophore geometry, ii) the method used for molecular properties calculations and iii) the partitioning scheme used. In conclusion we summarize further plans to improve the reliability and predictability of the method.
NASA Astrophysics Data System (ADS)
Tam, S. W.; Chang, T.; Kintner, P. M.; Klatt, E. M.
2008-12-01
ROMA (Rank-Ordered Multifractal Analysis) has the capabilities of deciphering the multifractal characteristics of intermittent fluctuations. The method allows one to understand the multifractal properties through global scale invariants. The utilities of ROMA, which combines the ideas of parametric rank ordering and single- parameter scaling of monofractals, were first demonstrated in its application to the results obtained from large-scale 2-D MHD simulations. In this study, we apply ROMA to the electric field fluctuations measured by the SIERRA sounding rocket in the auroral zone. The intermittent fluctuations span across time scales of multiple regimes that presumably reflect a change in the dominant physical processes. We extend the ROMA technique to take into account such nonlinear crossover behavior in the time scales, and obtain global scale invariants associated with the cross-regime multifractal spectra.
Ifantis, A; Papadimitriou, S
2003-10-01
This work investigates the nonlinear predictability of the Electro Telluric Field (ETF) variations data in order to develop new intelligent tools for the difficult task of earthquake prediction. Support Vector Machines trained on a signal window have been used to predict the next sample. We observe a significant increase at this short-term unpredictability of the ETF signal at about two weeks time period before the major earthquakes that took place in regions near the recording devices. The unpredictability increase can be attributed to a quick time variation of the dynamics that produce the ETF signal due to the earthquake generation process. Thus, this increase can be taken into advantage for signaling for an increased possibility of a large earthquake within the next few days in the neighboring region of the recording station.
Non-linear non-local molecular electrodynamics with nano-optical fields.
Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul
2015-10-28
The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.
Detection of radio-frequency magnetic fields using nonlinear magneto-optical rotation
NASA Astrophysics Data System (ADS)
Ledbetter, M. P.; Acosta, V. M.; Rochester, S. M.; Budker, D.; Pustelny, S.; Yashchuk, V. V.
2007-02-01
We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of 100pG/Hz (rms) in a 3.5-cm -diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as 25pG/Hz (rms).
Bubble shape and electromagnetic field in the nonlinear regime for laser wakefield acceleration
Li, X. F.; Yu, Q.; Huang, S.; Kong, Q.; Gu, Y. J.; Kawata, S.
2015-08-15
The electromagnetic field in the electron “bubble” regime for ultra-intense laser wakefield acceleration was solved using the d'Alembert equations. Ignoring the residual electrons, we assume an ellipsoidal bubble forms under ideal conditions, with bubble velocity equal to the speed of light in vacuum. The general solution for bubble shape and electromagnetic field were obtained. The results were confirmed in 2.5D PIC (particle-in-cell) simulations. Moreover, slopes for the longitudinal electric field of larger than 0.5 were found in these simulations. With spherical bubbles, this slope is always smaller than or equal to 0.5. This behavior validates the ellipsoid assumption.
Detection of radio-frequency magnetic fields using nonlinear magneto-optical rotation
Ledbetter, M. P.; Acosta, V. M.; Rochester, S. M.; Budker, D.; Pustelny, S.; Yashchuk, V. V.
2007-02-15
We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high-frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. Based on experimentally measured signal-to-noise ratio, we demonstrate a sensitivity of 100 pG/{radical}(Hz) (rms) in a 3.5-cm-diameter paraffin coated cell. Assuming detection at the photon shot-noise limit, we project a sensitivity as low as 25 pG/{radical}(Hz) (rms)
Non-linear non-local molecular electrodynamics with nano-optical fields.
Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul
2015-10-28
The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields. PMID:26520498
Nonlinear inversion for wave fields monitoring data in hierarchic heterogeneous media
NASA Astrophysics Data System (ADS)
Hachay, Olga; Khachay, Andrey; Khachay, Oleg
2016-04-01
Geological medium is an open system which is influenced by outer and inner factors that can lead it to a unstable state. That non stability is as a rule occurred locally and these zones are named as dynamically active elements, which are indicators of potential catastrophic sources. These objects differ from the embedded geological medium by their structural forms, which often are of hierarchical type. The process of their activisation can be searched, using wave fields monitoring. For that purpose it is needed to develop new algorithms of modeling wave fields propagation through the local objects with hierarchical structure. Also it is needed to develop new theory of interpretation the distribution of wave fields for defining the contours of these local hierarchical objects. It had been constructed an algorithm for 3D modeling electromagnetic field for arbitrary type of source of excitation in N-layered medium with a hierarchic conductive intrusion, located in the layer number J. It had been constructed algorithms for 2D modeling of sound diffraction and linear polarized transversal seismic wave on an intrusion of hierarchic structure, located in the layer number J of N-layered elastic medium. We used the method of integral and integral-differential equations for a space frequency presentation of wave fields distribution. It is developed an algorithm for constructing the equation of theoretical inverse problem for 2-D electromagnetic field of E and H polarization and linear polarized longitudinal elastic wave by excitation of the N-layered conductive or elastic medium with hierarchic conductive or elastic inclusion located in the ν -th layer. From the theory it is obviously that for such complicated medium each wave field contains its own information about the inner structure of the hierarchical inclusion. Therefore it is needed to interpret the monitoring data for each wave field apart, and not mixes the data base. These results will be the base for constructing
Non-linear magnetic behavior around zero field of an assembly of superparamagnetic nanoparticles.
de Montferrand, Caroline; Lalatonne, Yoann; Bonnin, Dominique; Motte, Laurence; Monod, Philippe
2012-05-21
The MIAplex® device is a miniaturized detector, devoted to the high sensitive detection of superparamagnetic nanoprobes for multiparametric immunoassays. It measures a signal corresponding to the second derivative of the magnetization around zero field. Like any new technology, the real success of the MIAplex® detector can only be exploited through a deep understanding of the magnetic signature. In this letter, we study the magnetic behavior around zero-field of diluted lab-made and commercial ferrofluids by comparing together conventional SQUID magnetization and MIAplex® signature. PMID:22441242
Interaction between emerging magnetic flux and the ambient solar coronal field
NASA Astrophysics Data System (ADS)
Cheung, M.; Derosa, M.
2008-12-01
We study the interaction between emerging magnetic flux and pre-existing coronal field by means of numerical simulations using the magneto-frictional method. By advancing the induction equation, the magneto-frictional method models the coronal magnetic field as a quasi-static sequence of non-linear force- free field configurations evolving in response to photospheric driving. A general feature of the simulations is the spontaneous formation of tangential discontinuities, interfaces where the field line torsional coefficient changes abruptly across separate domains of connectivity. Since the method evolves the vector potential, we can follow the evolution of the relative magnetic helicity and examine its relation to the magnetic free energy. Other tools, such as the squashing factor of Titov and Démoulin, are also used to study the topology of the field configurations.
Structural analysis of the SDSS Cosmic Web - I. Non-linear density field reconstructions
NASA Astrophysics Data System (ADS)
Platen, Erwin; van de Weygaert, Rien; Jones, Bernard J. T.; Vegter, Gert; Calvo, Miguel A. Aragón
2011-10-01
This study is the first in a series in which we analyse the structure and topology of the Cosmic Web as traced by the Sloan Digital Sky Survey (SDSS). The main issue addressed in the present study is the translation of the irregularly distributed discrete spatial data in the galaxy redshift survey into a representative density field. The density field will form the basis for a statistical, topological and cosmographic study of the cosmic density field in our Local Universe. We investigate the ability of three reconstruction techniques to analyse and investigate web-like features and geometries in a discrete distribution of objects. The three methods are the linear Delaunay Tessellation Field Estimator (DTFE), its higher order equivalent Natural Neighbour Field Estimator (NNFE) and a version of the Kriging interpolation adapted to the specific circumstances encountered in galaxy redshift surveys, the Natural Lognormal Kriging technique. DTFE and NNFE are based on the local geometry defined by the Voronoi and Delaunay tessellations of the galaxy distribution. The three reconstruction methods are analysed and compared using mock magnitude- and volume-limited SDSS redshift surveys, obtained on the basis of the Millennium simulation. We investigate error trends, biases and the topological structure of the resulting fields, concentrating on the void population identified by the Watershed Void Finder. Environmental effects are addressed by evaluating the density fields on a range of Gaussian filter scales. Comparison with the void population in the original simulation yields the fraction of false void mergers and false void splits. In most tests DTFE, NNFE and Kriging have largely similar density and topology error behaviour. Cosmetically, higher order NNFE and Kriging methods produce more visually appealing reconstructions. Quantitatively, however, DTFE performs better, even while being computationally far less demanding. A successful recovery of the void population on
NASA Astrophysics Data System (ADS)
Hu, Q.; Qiu, J.; Krucker, S.; Wang, L.; Wang, B.; Chen, Y.; Moestl, C.
2014-12-01
We report on the detailed and systematic study of field-line twist and length distributions within magnetic flux ropes embedded in Interplanetary Coronal Mass Ejections (ICMEs). In particular we will utilize energetic electron burst observations at 1 AU together with associated type III radio emissions detected by the Wind spacecraft to provide unique measurements of magnetic field-line lengths within selected ICME events. These direct measurements will be compared with flux-rope model calculations to help assess the fidelity of different models and to provide diagnostics of internal structures. The Grad-Shafranov reconstruction method will be utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model and the commonly known Lundquist (linear force-free) model to reveal the close relation between the field-line twist and length in cylindrical flux ropes, based on in-situ Wind spacecraft magnetic field and plasma measurements. We show that our initial analysis of field-line twist indicates clear deviation from the Lundquist model, but better consistency with the Gold-Hoyle model. We will also discuss the implications of our analysis of flux-rope structures on the origination and evolution processes in their corresponding solar source regions.
Unsteady three-dimensional thermal field prediction in turbine blades using nonlinear BEM
NASA Technical Reports Server (NTRS)
Martin, Thomas J.; Dulikravich, George S.
1993-01-01
A time-and-space accurate and computationally efficient fully three dimensional unsteady temperature field analysis computer code has been developed for truly arbitrary configurations. It uses boundary element method (BEM) formulation based on an unsteady Green's function approach, multi-point Gaussian quadrature spatial integration on each panel, and a highly clustered time-step integration. The code accepts either temperatures or heat fluxes as boundary conditions that can vary in time on a point-by-point basis. Comparisons of the BEM numerical results and known analytical unsteady results for simple shapes demonstrate very high accuracy and reliability of the algorithm. An example of computed three dimensional temperature and heat flux fields in a realistically shaped internally cooled turbine blade is also discussed.
Automodelling solutions of the Higgs-field nonlinear wave equation in the de Sitter space.
NASA Astrophysics Data System (ADS)
Dyshko, A. L.; Konyukhova, N. B.; Voronov, N. A.
2000-04-01
The effect of the expansion of the Universe on such classical physical objects as spherical bubbles is studied. The authors look for automodelling solutions to scalar Higgs-field equation in the de Sitter space and compare them with the bubble type solutions in the thin-wall approximation. The automodelling bubbles could be considered as critical or singular ones because they collapse in an infinite time. Multinodal solutions as enclosed bubbles are discovered numerically.
NASA Astrophysics Data System (ADS)
Borisov, V. I.; Galanin, A. L.; Liubchenko, V. E.; Rogashkov, A. S.; Telegin, A. A.
1988-10-01
Experimental results are presented on InP Gunn diodes in intense microwave fields. Two important features of such devices which distinguish them from GaAs devices were found: (1) microwave oscillation at an active-layer electron density of about 10 to the 17th/cu cm and (2) the substantial heating of the near-cathode region of the active layer, leading to characteristic changes in the I-V characteristics.
NASA Astrophysics Data System (ADS)
Veranda, M.; Bonfiglio, D.; Cappello, S.; Chacón, L.; Escande, D. F.
2013-07-01
Helical self-organized reversed-field pinch (RFP) regimes emerge both numerically—in 3D visco-resistive magnetohydrodynamic (MHD) simulations—and experimentally, as in the RFX-mod device at high current (IP above 1 MA). These states, called quasi-single helicity (QSH) states, are characterized by the action of a MHD mode that impresses a quasi-helical symmetry to the system, thus allowing a high degree of magnetic chaos healing. This is in contrast with the multiple helicity (MH) states, where magnetic fluctuations create a chaotic magnetic field degrading the confinement properties of the RFP. This paper reports an extensive numerical study performed in the frame of 3D visco-resistive MHD which considers the effect of helical magnetic boundary conditions, i.e. of a finite value of the radial magnetic field at the edge (magnetic perturbation, MP). We show that the system can be driven to a selected QSH state starting from both spontaneous QSH and MH regimes. In particular, a high enough MP can force a QSH helical self-organization with a helicity different from the spontaneous one. Moreover, MH states can be turned into QSH states with a selected helicity. A threshold in the amplitude of MP is observed above which is able to influence the system. Analysis of the magnetic topology of these simulations indicates that the dominant helical mode is able to temporarily sustain conserved magnetic structures in the core of the plasma. The region occupied by conserved magnetic surfaces increases reducing secondary modes' amplitude to experimental-like values.
Nonlinear theory of a free electron laser with a helical wiggler and an axial guide magnetic field
NASA Astrophysics Data System (ADS)
Ginzburg, N. S.; Peskov, N. Yu.
2013-09-01
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.
Nonlinear dynamics of a sinusoidally driven pendulum in a repulsive magnetic field
NASA Astrophysics Data System (ADS)
Siahmakoun, Azad; French, Valentina A.; Patterson, Jeffrey
1997-05-01
The dynamics of a sinusoidally driven pendulum in a repulsive magnetic field is investigated theoretically and experimentally. The experimental data are acquired using a shaft encoder interfaced to a PC which measures the angular displacement of the pendulum as a function of time. Both the theoretical simulations and the experimental measurements exhibit regions of periodic and chaotic behavior, depending on the system parameters. Amplitude jumps, hysteresis, and bistable states are also observed. The simplicity of the apparatus makes this experiment suitable for an advanced undergraduate laboratory.
Smith, S.J.
1985-01-01
In the experimental program described, we deliberately broaden a well-stabilized single mode laser beam by introducing fluctuations to the laser frequency, in order to synthesize laser power spectra for which the fluctuations are well-characterized to all orders in a statistical sense. With this technique we are able to produce single mode laser fields which have nearly Lorentzian power spectra at one limit, essentially Gaussian power spectra at the other limit, and which may be varied continuously between these two limits. 16 refs., 6 figs.
NASA Astrophysics Data System (ADS)
Karabulut, Ibrahim; Paspalakis, Emmanuel
2016-07-01
We study theoretically the intensity-dependent nonlinear optical properties of an asymmetric coupled quantum well under a static electric field. Effects such as nonlinear absorption, optical rectification and refractive index are investigated theoretically by using the density matrix equations including the permanent dipole terms. Our results show that the effects of the permanent dipoles on the corresponding optical processes depend crucially on the direction and strength of the static electric field, especially for large optical intensities. Another interesting result of this work is that the nonlinear optical spectra studied here saturate with an increasing optical intensity and specifically the optical spectra in the case that the permanent dipoles are considered reach saturation for lower intensities than when the permanent dipoles are not considered.
NASA Astrophysics Data System (ADS)
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.
Bykov, Andrei M.; Osipov, Sergei M.; Ellison, Donald C.; Vladimirov, Andrey E. E-mail: osm2004@mail.ru E-mail: avenovo@gmail.com
2014-07-10
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-Alfvénic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (∼eV) injected at the viscous subshock to the escape of the highest energy CRs (∼PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification, and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.
Ong, P. V.; Kioussis, Nicholas; Amiri, P. Khalili; Wang, K. L.
2016-01-01
Voltage-induced switching of magnetization, as opposed to current-driven spin transfer torque switching, can lead to a new paradigm enabling ultralow-power and high density instant-on nonvolatile magnetoelectric random access memory (MeRAM). To date, however, a major bottleneck in optimizing the performance of MeRAM devices is the low voltage-controlled magnetic anisotropy (VCMA) efficiency (change of interfacial magnetic anisotropy energy per unit electric field) leading in turn to high switching energy and write voltage. In this work, employing ab initio electronic structure calculations, we show that epitaxial strain, which is ubiquitous in MeRAM heterostructures, gives rise to a rich variety of VCMA behavior with giant VCMA coefficient (~1800 fJ V−1m−1) in Au/FeCo/MgO junction. The heterostructure also exhibits a strain-induced spin-reorientation induced by a nonlinear magnetoelastic coupling. The results demonstrate that the VCMA behavior is universal and robust in magnetic junctions with heavy metal caps across the 5d transition metals and that an electric-field-driven magnetic switching at low voltage is achievable by design. These findings open interesting prospects for exploiting strain engineering to harvest higher efficiency VCMA for the next generation MeRAM devices. PMID:27424885
NASA Astrophysics Data System (ADS)
Ong, P. V.; Kioussis, Nicholas; Amiri, P. Khalili; Wang, K. L.
2016-07-01
Voltage-induced switching of magnetization, as opposed to current-driven spin transfer torque switching, can lead to a new paradigm enabling ultralow-power and high density instant-on nonvolatile magnetoelectric random access memory (MeRAM). To date, however, a major bottleneck in optimizing the performance of MeRAM devices is the low voltage-controlled magnetic anisotropy (VCMA) efficiency (change of interfacial magnetic anisotropy energy per unit electric field) leading in turn to high switching energy and write voltage. In this work, employing ab initio electronic structure calculations, we show that epitaxial strain, which is ubiquitous in MeRAM heterostructures, gives rise to a rich variety of VCMA behavior with giant VCMA coefficient (~1800 fJ V‑1m‑1) in Au/FeCo/MgO junction. The heterostructure also exhibits a strain-induced spin-reorientation induced by a nonlinear magnetoelastic coupling. The results demonstrate that the VCMA behavior is universal and robust in magnetic junctions with heavy metal caps across the 5d transition metals and that an electric-field-driven magnetic switching at low voltage is achievable by design. These findings open interesting prospects for exploiting strain engineering to harvest higher efficiency VCMA for the next generation MeRAM devices.
Chaikovsky, S. A.; Datsko, I. M.; Labetskaya, N. A.; Rybka, D. V.; Ratakhin, N. A.; Oreshkin, V. I.
2015-11-15
The paper presents the results of an experimental study of the skin explosion of cylindrical conductors of diameter 1–3 mm (copper, aluminum, titanium, steel 3, and stainless steel) at a peak magnetic field of 200–600 T. The experiments were carried out on the MIG pulsed power generator at a current of up to 2.5 MA and a current rise time of 100 ns. The surface explosion of a conductor was identified by the appearance of a flash of extreme ultraviolet radiation. A minimum magnetic induction has been determined below which no plasma is generated at the conductor surface. For copper, aluminum, steel 3, titanium, and stainless steel, the minimum magnetic induction has been estimated to be (to within 10%) 375, 270, 280, 220, and 245 T, respectively.
ERIC Educational Resources Information Center
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…
Topological complexity and tangential discontinuity in magnetic fields
Janse, A. M.; Low, B. C.; Parker, E. N.
2010-09-15
This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities (TDs). This property proposed and demonstrated by Parker [Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)] is explained in terms of (i) the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and (ii) the hyperbolic nature of the partial differential equation for the twist function {alpha} of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.
NASA Astrophysics Data System (ADS)
Mirus, Kevin Andrew
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Mirus, K.A.
1998-06-01
In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.
Stability of bumps in piecewise smooth neural fields with nonlinear adaptation
NASA Astrophysics Data System (ADS)
Kilpatrick, Zachary P.; Bressloff, Paul C.
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Strubbe, David A.; Andrade, Xavier; Rubio, Angel; Louie, Steve G.
2009-03-01
Chloroform is often used as a solvent and reference when measuring non-linear optical properties of organic molecules. We calculate directly the non-linear susceptibilities of liquid chloroform at optical frequencies, using molecular dynamics and the Sternheimer equation in time-dependent density-functional theory [X. Andrade et al., J. Chem. Phys. 126, 184106 (2007)]. We compare the results to those of chloroform in the gas and solid phases, and experimental values, and make an ab initio calculation of the local-field factors which are needed to extract molecular properties from liquid calculations and experimental measurements.
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.
NASA Astrophysics Data System (ADS)
Donoso, Guillermo; Ladera, Celso L.
2012-11-01
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.
NASA Astrophysics Data System (ADS)
Gassenmeier, M.; Sens-Schönfelder, C.; Eulenfeld, T.; Bartsch, M.; Victor, P.; Tilmann, F.; Korn, M.
2016-03-01
To investigate temporal seismic velocity changes due to earthquake related processes and environmental forcing in Northern Chile, we analyse 8 yr of ambient seismic noise recorded by the Integrated Plate Boundary Observatory Chile (IPOC). By autocorrelating the ambient seismic noise field measured on the vertical components, approximations of the Green's functions are retrieved and velocity changes are measured with Coda Wave Interferometry. At station PATCX, we observe seasonal changes in seismic velocity caused by thermal stress as well as transient velocity reductions in the frequency range of 4-6 Hz. Sudden velocity drops occur at the time of mostly earthquake-induced ground shaking and recover over a variable period of time. We present an empirical model that describes the seismic velocity variations based on continuous observations of the local ground acceleration. The model assumes that not only the shaking of large earthquakes causes velocity drops, but any small vibrations continuously induce minor velocity variations that are immediately compensated by healing in the steady state. We show that the shaking effect is accumulated over time and best described by the integrated envelope of the ground acceleration over the discretization interval of the velocity measurements, which is one day. In our model, the amplitude of the velocity reduction as well as the recovery time are proportional to the size of the excitation. This model with two free scaling parameters fits the data of the shaking induced velocity variation in remarkable detail. Additionally, a linear trend is observed that might be related to a recovery process from one or more earthquakes before our measurement period. A clear relationship between ground shaking and induced velocity reductions is not visible at other stations. We attribute the outstanding sensitivity of PATCX to ground shaking and thermal stress to the special geological setting of the station, where the subsurface material
Ryasnyansky, Aleksandr; Palpant, Bruno; Debrus, Solange; Ganeev, Rashid; Stepanov, Andrey; Can, Nurdogan; Buchal, Christoph; Uysal, Sibel
2005-05-10
The nonlinear absorption of nanocomposite layers based on ZnO implanted with Cu+ ions with an energy of 160 keV in implantation doses of 10(16) and 10(17) ions/cm2 was investigated. The values of the nonlinear absorption coefficient were measured by the Z-scan method at a wavelength of 532 nm by use of nanosecond and picosecond laser pulses. Possible optical applications of these materials are discussed.
Tautz, R. C.; Lerche, I.
2015-11-15
This note considers the evolution of steady isothermal flow across a uniform magnetic field from an analytic standpoint. This problem is of concern in developments of magnetic fields in the solar corona and for prominence dynamics. Limiting behaviors are obtained to the nonlinear equation describing the flow depending on the value of a single parameter. For the situation where the viscous drag is a small correction to the inviscid flow limiting structures are also outlined. The purpose of the note is to show how one can evaluate some of the analytic properties of the highly nonlinear equation that are of use in considering the numerical evolution as done in Low and Egan [Phys. Plasmas 21, 062105 (2014)].
NASA Astrophysics Data System (ADS)
Lim, Hyung Jin; Kim, Yongtak; Koo, Gunhee; Yang, Suyoung; Sohn, Hoon; Bae, In-hwan; Jang, Jeong-Hwan
2016-09-01
In this study, a fatigue crack detection technique, which detects a fatigue crack without relying on any reference data obtained from the intact condition of a target structure, is developed using nonlinear ultrasonic modulation and applied to a real bridge structure. Using two wafer-type lead zirconate titanate (PZT) transducers, ultrasonic excitations at two distinctive frequencies are applied to a target inspection spot and the corresponding ultrasonic response is measured by another PZT transducer. Then, the nonlinear modulation components produced by a breathing-crack are extracted from the measured ultrasonic response, and a statistical classifier, which can determine if the nonlinear modulation components are statistically significant in comparison with the background noise level, is proposed. The effectiveness of the proposed fatigue crack detection technique is experimentally validated using the data obtained from aluminum plates and aircraft fitting-lug specimens under varying temperature and loading conditions, and through a field testing of Yeongjong Grand Bridge in South Korea. The uniqueness of this study lies in that (1) detection of a micro fatigue crack with less than 1 μm width and fatigue cracks in the range of 10–20 μm in width using nonlinear ultrasonic modulation, (2) automated detection of fatigue crack formation without using reference data obtained from an intact condition, (3) reliable and robust diagnosis under varying temperature and loading conditions, (4) application of a local fatigue crack detection technique to online monitoring of a real bridge.
NASA Astrophysics Data System (ADS)
Lim, Hyung Jin; Kim, Yongtak; Koo, Gunhee; Yang, Suyoung; Sohn, Hoon; Bae, In-hwan; Jang, Jeong-Hwan
2016-09-01
In this study, a fatigue crack detection technique, which detects a fatigue crack without relying on any reference data obtained from the intact condition of a target structure, is developed using nonlinear ultrasonic modulation and applied to a real bridge structure. Using two wafer-type lead zirconate titanate (PZT) transducers, ultrasonic excitations at two distinctive frequencies are applied to a target inspection spot and the corresponding ultrasonic response is measured by another PZT transducer. Then, the nonlinear modulation components produced by a breathing-crack are extracted from the measured ultrasonic response, and a statistical classifier, which can determine if the nonlinear modulation components are statistically significant in comparison with the background noise level, is proposed. The effectiveness of the proposed fatigue crack detection technique is experimentally validated using the data obtained from aluminum plates and aircraft fitting-lug specimens under varying temperature and loading conditions, and through a field testing of Yeongjong Grand Bridge in South Korea. The uniqueness of this study lies in that (1) detection of a micro fatigue crack with less than 1 μm width and fatigue cracks in the range of 10-20 μm in width using nonlinear ultrasonic modulation, (2) automated detection of fatigue crack formation without using reference data obtained from an intact condition, (3) reliable and robust diagnosis under varying temperature and loading conditions, (4) application of a local fatigue crack detection technique to online monitoring of a real bridge.
NASA Astrophysics Data System (ADS)
Shao, Xuefei; Fu, Yiming; Chen, Yang
2015-05-01
Based on the higher order shear deformation theory and the geometric nonlinear theory, the nonlinear motion equations, to which the effects of the positive and negative piezoelectric and the thermal are introduced by piezoelectric fiber metal laminated (FML) plates in an unsteady temperature, are established by Hamilton’s variational principle. Then, the control algorithm of negative-velocity feedback is applied to realize the vibration control of the piezoelectric FML plates. During the solving process, firstly, the formal functions of the displacements that fulfilled the boundary conditions are proposed. Then, heat conduction equations and nonlinear differential equations are dealt with using the differential quadrature (DQ) and Galerkin methods, respectively. On the basis of the previous processing, the time domain is dispersed by the Newmark-β method. Finally, the whole problem can be investigated by the iterative method. In the numerical examples, the influence of the applied voltage, the temperature loading and geometric parameters on the nonlinear dynamic response of the piezoelectric FML plates is analyzed. Meanwhile, the effect of feedback control gain and the position of the piezoelectric layer, the initial deflection and the external temperature on the active control effect of the piezoelectric layers has been studied. The model development and the research results can serve as a basis for nonlinear vibration analysis of the FML structures.
NASA Astrophysics Data System (ADS)
Tsai, T.; Chang, C.; Lyu, L.
2006-12-01
Nonlinear evolutions of electrostatic (ES) and electromagnetic (EM) instabilities in a field-aligned counter- streaming plasma are studied by means of a full particle code simulation and a Vlasov simulation. Our simulation results show that field-aligned counter-streaming plasma can lead to fast growing electrostatic two- stream instability to heat electrons along the background magnetic field directions. If the background magnetic field is not strong enough, the field-aligned heating can easily make the system unstable to the electromagnetic fire-hose instability. The nonlinear kinetic Alfven waves generated by the fire-hose instability can isotropize the electron pressure and heat ions by both ion-cyclotron instability and non-adiabatic ion gyro- reflections. Additional instabilities generated by the gyro-reflecting events can heat the plasma in a very efficient way. The importance of the cross-scale coupling between the ES instabilities and the EM instabilities in the space plasmas with counter-streaming plasma flows will be discussed.
NASA Astrophysics Data System (ADS)
Gavrilyuk, A. P.; Karpov, S. V.
2009-09-01
Optical nonlinearities in aggregates of nanoparticles formed in silver hydrosols (SHs) are studied under pico- and nanosecond pulsed laser excitation. The dependence of the nonlinear refractive index n 2 on the degree of hydrosol aggregation is studied experimentally at the wavelength λ=1.064 μm. It is found that n 2 changes sign when the degree of hydrosol aggregation is increased. Various physical effects occurring in resonant domains of the aggregates are analyzed using a simple physical model of two bound silver nanoparticles. The theory takes into account thermal, elastic, electrostatic, and light-induced effects. Experimental results are discussed in the context of this theory.
Sonnino, Giorgio; Peeters, Philippe
2004-09-01
This paper forms a part of a series of manuscripts which we intend to submit for publication in the near future, aiming to test the validity of the thermodynamic field theory (TFT), previously formulated, comparing the theoretical results with experimental data. In this particular case, we shall analyze the Hall effect. As known, when a magnetic field is applied at right angles to the direction of an electric current or a thermal gradient, galvano- and thermomagnetic effects appear in the material. In this paper, we shall show that if we study these effects in nonlinear regime, the TFT foresees an interesting effect: the nonlinear Hall effect. This prediction is herein submitted to experimental verifications. In this paper, we shall analyze this effect studying materials with weak thermoelectric power coefficients. We shall show the agreement between the theoretical predictions of the TFT and experiments. Experimental curves related to the nonlinear Hall effect allow us to determine the order of magnitude of the constant chi introduced in the TFT.
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2015-01-01
This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number. PMID:26714259
Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir
2015-01-01
This article investigates the magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid subject to the convective boundary condition. Flow is generated due to a nonlinear stretching of the surface in two lateral directions. Temperature and nanoparticles concentration distributions are studied through the Brownian motion and thermophoresis effects. Couple stress fluid is considered electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed via boundary layer approach. Nonlinear ordinary differential systems are constructed by employing suitable transformations. The resulting systems have been solved for the convergent series solutions of velocities, temperature and nanoparticles concentration profiles. Graphs are sketched to see the effects of different interesting flow parameters on the temperature and nanoparticles concentration distributions. Numerical values are computed to analyze the values of skin-friction coefficients and Nusselt number. PMID:26714259
Zaytsev, Kirill I. Katyba, Gleb M.; Yakovlev, Egor V.; Yurchenko, Stanislav O.; Gorelik, Vladimir S.
2014-06-07
A novel approach for the enhancement of nonlinear optical effects inside globular photonic crystals (PCs) is proposed and systematically studied via numerical simulations. The enhanced optical harmonic generation is associated with two- and three-dimensional PC pumping with the wavelength corresponding to different PC band-gaps. The interactions between light and the PC are numerically simulated using the finite-difference time-domain technique for solving the Maxwell's equations. Both empty and infiltrated two-dimensional PC structures are considered. A significant enhancement of harmonic generation is predicted owing to the highly efficient PC pumping based on the structural light focusing effect inside the PC structure. It is shown that a highly efficient harmonic generation could be attained for both the empty and infiltrated two- and three-dimensional PCs. We are demonstrating the ability for two times enhancement of the parametric decay efficiency, one order enhancement of the second harmonic generation, and two order enhancement of the third harmonic generation in PC structures in comparison to the nonlinear generations in appropriate homogenous media. Obviously, the nonlinear processes should be allowed by the molecular symmetry. The criteria of the nonlinear process efficiency are specified and calculated as a function of pumping wavelength position towards the PC globule diameter. Obtained criterion curves exhibit oscillating characteristics, which indicates that the highly efficient generation corresponds to the various PC band-gap pumping. The highest efficiency of nonlinear conversions could be reached for PC pumping with femtosecond optical pulses; thus, the local peak intensity would be maximized. Possible applications of the observed phenomenon are also discussed.
Li, Mengmeng; Dai, Ying; Ma, Xiangchao; Li, Zhujie; Huang, Baibiao
2015-07-21
Recent experiments have demonstrated that the typical nonlinear optical material K3B6O10Br can be an excellent photocatalyst under ultraviolet (UV) light irradiation. To understand the origin of the photocatalytic activity and further improve its photocatalytic efficiency to develop alternative photocatalysts, the built-in electric field and the electron effective mass and their synergistic effect on transfer and the separation of carriers in K3B6O10X (X = Br, Cl) were investigated by means of first-principles calculations. Our results show that the built-in electric field and the smallest effective mass of holes in K3B6O10Br are both along the [001] direction. In contrast, the effective masses of electrons are isotropic because of the spherically symmetric s orbitals at the conduction band minimum (CBM). Therefore, the electric field can promote efficient transfer and separation of the photogenerated carriers along the [001] direction. As a consequence, the synergistic effect of built-in electric field and the isotropy of the electron effective mass results in the {001} surface, to which most of the carriers will accumulate, showing the highest photocatalytic activity. Similar results can also be obtained for a K3B6O10Cl crystal considering the analogous structure with that of K3B6O10Br. The present study may provide theoretical insight to develop the photocatalytic performance of nonlinear optical materials.
Friction and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Manini, N.; Braun, O. M.; Tosatti, E.; Guerra, R.; Vanossi, A.
2016-07-01
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.
BOOTSTRAPPING THE CORONAL MAGNETIC FIELD WITH STEREO: UNIPOLAR POTENTIAL FIELD MODELING
Aschwanden, Markus J.; Sandman, Anne W.
2010-09-15
We investigate the recently quantified misalignment of {alpha}{sub mis} {approx} 20{sup 0}-40{sup 0} between the three-dimensional geometry of stereoscopically triangulated coronal loops observed with STEREO/EUVI (in four active regions (ARs)) and theoretical (potential or nonlinear force-free) magnetic field models extrapolated from photospheric magnetograms. We develop an efficient method of bootstrapping the coronal magnetic field by forward fitting a parameterized potential field model to the STEREO-observed loops. The potential field model consists of a number of unipolar magnetic charges that are parameterized by decomposing a photospheric magnetogram from the Michelson Doppler Imager. The forward-fitting method yields a best-fit magnetic field model with a reduced misalignment of {alpha}{sub PF} {approx} 13{sup 0}-20{sup 0}. We also evaluate stereoscopic measurement errors and find a contribution of {alpha}{sub SE} {approx} 7{sup 0}-12{sup 0}, which constrains the residual misalignment to {alpha}{sub NP} {approx} 11{sup 0}-17{sup 0}, which is likely due to the nonpotentiality of the ARs. The residual misalignment angle, {alpha}{sub NP}, of the potential field due to nonpotentiality is found to correlate with the soft X-ray flux of the AR, which implies a relationship between electric currents and plasma heating.
NASA Astrophysics Data System (ADS)
Moosavi, S. H. S.; Moini, R.; Sadeghi, S. H. H.; Kordi, B.
2011-06-01
In this paper an improved antenna theory (AT) model with nonlinearly varying resistive loading and fixed inductive loading is used to electromagnetically simulate lightning strikes to tall structures. Measurement data captured from Toronto's CN tower are used to verify the validity of the new model. Both the return stroke channel (RSC) and the tower are modeled by straight thin conducting wires. The wire model of the channel is assumed to have distributed nonlinear resistive elements as a function of current and time, adopted from the numerical models of a spark channel and consequent shockwave from a lightning discharge, yielding a varying value of the channel radius from the base to the cloud along the RSC. Such distributed elements are used to take into account the current attenuation while propagating along the channel and varying propagation speeds lower than the speed of light. RSC current distribution and radiated electromagnetic fields in near, intermediate, and far range distances predicted by the proposed model are compared with those obtained from the measurement data and with those of the original AT model and the AT with fixed inductive loading (ATIL-F) model. Current wave propagation speed profile in RSC and tower is investigated as a function of height as well. The effects of applying different tower geometry models are also studied. It is shown that the new model is able to reproduce one of the characteristic features of the electromagnetic fields radiated by lightning, namely, the far-field inversion of polarity with a zero crossing occurring in the tens of microseconds range. We have also investigated the effect of nonlinearity of the channel assumed in the new model. It is shown that among the electromagnetic models, distributed nonlinear resistance along the channel leads to a zero crossing in the tens of microseconds range even for large values of resistance. It is also shown that decreasing the nonlinearity results in the predictions
NASA Astrophysics Data System (ADS)
Robles-Uriza, A. X.; Reyes Gómez, F.; Mejía-Salazar, J. R.
2016-09-01
We report the existence of multiple omnidirectional defect modes in the zero-nbar gap of photonic stacks, made of alternate layers of conventional dielectric and double-negative metamaterial, with a polaritonic defect layer. In the case of nonlinear magnetic metamaterials, the optical bistability phenomenon leads to switching from negligible to perfect transmission around these defect modes. We hope these findings have potential applications in the design and development of multichannel optical filters, power limiters, optical-diodes and optical-transistors.
Dupret, K.; Delande, D.
1996-03-01
We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the {open_quote}{open_quote}nonlinear wave-packet dynamics{close_quote}{close_quote} [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. {bold 67}, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. {copyright} {ital 1996 The American Physical Society.}
Barseghyan, Manuk G; Restrepo, Ricardo L; Mora-Ramos, Miguel E; Kirakosyan, Albert A; Duque, Carlos A
2012-01-01
: The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum. PMID:23021497
NASA Astrophysics Data System (ADS)
Tavassoly, M. K.; Rastegarzadeh, M.
2016-10-01
In this paper based on a generalization of the Jaynes-Cummings model we solve the dynamical Hamiltonian describing the interaction between a (Λ or V-type) three-level atom and a single-mode field in the "full nonlinear regime" and then the analytical form of state vector of the system is explicitly obtained. In this manner, we encountered with "intensity-dependent detuning" as well as "intensity-dependent atom-field coupling" in our two models. Via choosing an appropriate deformation function (which imposes nonlinearity to the system) we consider the influence of Kerr-like medium from which the resonance condition for a selected number of quanta is achieved (selective transition is occurred). Furthermore, by these considerations, we may find the optimum values for atom-field coupling constants which provide a regular periodic behavior of probability amplitudes for the two considered atomic systems. Moreover, to show this periodic time behavior, the temporal evolution of the probability of the allowed atomic transitions as well as the Mandel parameter (as a non-classical sign) is depicted for various circumstances. As is observed, complete revivals may appear in some particular situations.
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
Nonlinear Optics and Applications
NASA Technical Reports Server (NTRS)
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.
NASA Astrophysics Data System (ADS)
Chinone, N.; Yamasue, K.; Honda, K.; Cho, Y.
2013-11-01
Scanning nonlinear dielectric microscopy (SNDM) can evaluate carrier or charge distribution in semiconductor devices. High sensitivity to capacitance variation enables SNDM to measure the super-high-order (higher than 3rd) derivative of local capacitance-voltage (C-V) characteristics directly under the tip (dnC/dVn,n = 3, 4, ...). We demonstrate improvement of carrier density resolution by measurement of dnC/dVn,n = 1, 2, 3, 4 (super-higher-order method) in the cross-sectional observation of metal-oxide-semiconductor field-effect-transistor.
Magnetic Field-line Twist and Length Distributions inside Interplanetary Magnetic Flux Ropes
NASA Astrophysics Data System (ADS)
Hu, Qiang; Qiu, Jiong; Krucker, Sam
2015-04-01
We report on the detailed and systematic study of field-line twist and length distributions within magnetic flux ropes embedded in Interplanetary Coronal Mass Ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model and the commonly known Lundquist (linear force-free) model to reveal the close relation between the field-line twist and length in cylindrical flux ropes, based on in-situ spacecraft magnetic field and plasma measurements. In particular, we utilize energetic electron burst observations at 1 AU together with associated type III radio emissions detected by the Wind spacecraft to provide unique measurements of magnetic field-line lengths within selected ICME events. These direct measurements are compared with flux-rope model calculations to help assess the fidelity of different models and to provide diagnostics of internal structures. We show that our initial analysis of field-line twist indicates clear deviation from the Lundquist model, but better consistency with the Gold-Hoyle model. By using the different flux-rope models, we conclude that the in-situ direct measurements of field-line lengths are consistent with a flux-rope structure with spiral field lines of constant and low twist, largely different from that of the Lundquist model, especially for relatively large-scale flux ropes. We will also discuss the implications of our analysis of flux-rope structures on the origination and evolution processes in their corresponding solar source regions.
[Nonlinear magnetohydrodynamics
Not Available
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.
Davidson, R.C.; Chen, C.
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
NASA Astrophysics Data System (ADS)
Fernández, Leandro; Onorato, Miguel; Monbaliu, Jaak; Toffoli, Alessandro
2015-04-01
This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing laboratory experiments, field measurements and numerical simulations. It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics and second order based statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh = 1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if kh < 1.36. In this regard, the aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, laboratory experiments in a large wave basin, numerical experiments solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and field experiments at the Lake George experimental site (Australia) have been compared to assess the role of third order nonlinearity, and particularly modulational instability, on wave statistics. Herein, we present a comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between laboratory experiments, simulations and in-situ data which provides a confrontation between the numerical results and real observations in laboratory and field conditions.
NASA Astrophysics Data System (ADS)
Aschwanden, Markus J.; Sun, Xudong; Liu, Yang
2014-04-01
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 EN and potential energy EP but find up to a factor of 4 discrepancy in the free energy E free = EN – EP 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.
Aschwanden, Markus J.; Sun, Xudong; Liu, Yang E-mail: xudongs@stanford.edu
2014-04-10
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{sub N} and potential energy E{sub P} but find up to a factor of 4 discrepancy in the free energy E {sub free} = E{sub N} – E{sub P} and up to a factor of 10 discrepancy in the decrease of the free energy ΔE {sub 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.
Karzova, M.; Cunitz, B.; Kreider, W.; Bailey, M.; Yuldashev, P.; Andriyakhina, Y.; Sapozhnikov, O.; Khokhlova, V.
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.
NASA Astrophysics Data System (ADS)
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.
Karzova, M.; Cunitz, B.; Yuldashev, P.; Andriyakhina, Y.; Kreider, W.; Sapozhnikov, O.; Bailey, M.; Khokhlova, V.
2016-01-01
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 transducer output to provide stronger pushing force; however, nonlinear acoustic saturation effect 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 low power pressure beam scans. 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. PMID:27087711
Bell, T.F.
1986-04-01
Using a recently developed theory, we calculate the wave magnetic field amplitude threshold B/sub tau/ necessary to allow the nonlinear trapping of energetic gyroresonant and Landau resonant electrons by VLF whistler mode waves in the magnetosphere, propagating at an arbitrary angle, psi, with respect to the earth's magnetic field, B/sub 0/. This theory predicts that the amplitude threshold is governed near the magnetic equatorial plane by the gradient of psi with respect to distance, z, along B/sub 0/. Using commonly accepted models of the magnetosphere and computer raytracing techniques, we determine the function psi(z) for magnetic shells in the range 2< or =L< or =5 and for frequencies 5 kHz< or =f< or =17.8 kHz.
EXTRAPOLATION OF THE SOLAR CORONAL MAGNETIC FIELD FROM SDO/HMI MAGNETOGRAM BY A CESE-MHD-NLFFF CODE
Jiang Chaowei; Feng Xueshang E-mail: fengx@spaceweather.ac.cn
2013-06-01
Due to the absence of direct measurement, the magnetic field in the solar corona is usually extrapolated from the photosphere in a numerical way. At the moment, the nonlinear force-free field (NLFFF) model dominates the physical models for field extrapolation in the low corona. Recently, we have developed a new NLFFF model with MHD relaxation to reconstruct the coronal magnetic field. This method is based on CESE-MHD model with the conservation-element/solution-element (CESE) spacetime scheme. In this paper, we report the application of the CESE-MHD-NLFFF code to Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) data with magnetograms sampled for two active regions (ARs), NOAA AR 11158 and 11283, both of which were very non-potential, producing X-class flares and eruptions. The raw magnetograms are preprocessed to remove the force and then inputted into the extrapolation code. Qualitative comparison of the results with the SDO/AIA images shows that our code can reconstruct magnetic field lines resembling the EUV-observed coronal loops. Most important structures of the ARs are reproduced excellently, like the highly sheared field lines that suspend filaments in AR 11158 and twisted flux rope which corresponds to a sigmoid in AR 11283. Quantitative assessment of the results shows that the force-free constraint is fulfilled very well in the strong-field regions but apparently not that well in the weak-field regions because of data noise and numerical errors in the small currents.
Deriving Potential Coronal Magnetic Fields from Vector Magnetograms
NASA Astrophysics Data System (ADS)
Welsch, Brian T.; Fisher, George H.
2016-08-01
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Ampère's law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplace's equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, "least-squares" potential field, which minimizes the integrated square of the residual between the potential and actual fields. We also explore weighting the residuals in the fit by spatially uniform measurement uncertainties. This has advantages both in not overfitting the radial field used for the Neumann BC, and in maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of active region 11158, and find that residual discrepancies between the observed and potential fields are significant, and they are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid-potential fields have significantly less energy than the Neumann fields in every case - by more than 10^{32} erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
Mehdian, H. Kargarian, A.; Hajisharifi, K.
2015-06-15
In this paper, the effect of an external inhomogeneous magnetic field on the high intensity laser absorption rate in a sub-critical plasma has been investigated by employing a relativistic electromagnetic 1.5 dimensional particle-in-cell code. Relying on the effective nonlinear phenomena such as phase-mixing and scattering, this study shows that in a finite-size plasma the laser absorption increases with inhomogeneity of the magnetic field (i.e., reduction of characteristic length of inhomogeneous magnetic field, λ{sub p}) before exiting a considerable amount of laser energy from the plasma due to scattering process. On the other hand, the presence of the external inhomogeneous magnetic field causes the maximum absorption of laser to occur at a shorter time. Moreover, study of the kinetic results associated with the distribution function of plasma particles shows that, in a special range of the plasma density and the characteristic length of inhomogeneous magnetic field, a considerable amount of laser energy is transferred to the particles producing a population of electrons with kinetic energy along the laser direction.
Kirtman, Bernard; Springborg, Michael; Rérat, Michel; Ferrero, Mauro; Lacivita, Valentina; Dovesi, Roberto; Orlando, Roberto
2015-01-22
An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.
NASA Astrophysics Data System (ADS)
Gu, Zhan
1998-09-01
A new localized smoothing filter based on the least squares is proposed in this study. It has been found the use of an appropriate smoothing method is critical to the success of numerical prediction of separating flow problems with nonlinear turbulence models. The new smoothing filter effectively eliminated numerical fluctuations due to the nonlineality of the turbulence model and the higher order approximation. The efficiency of using this scheme is very attractive; less than 20% more CPU time is needed for the extra computation in simulations. Modification has been made to the nonlinear model to take into consideration of low Reynolds number effects. The two-dimensional turbulent recirculating flow field behind a V-shaped bluff body has been investigated numerically. Similar bluff bodies are used in combustion chambers for flame stabilization. The study helps to gain a comprehensive understanding of the mechanism of the flame stability and major factors that affect this stability, and thereby establishes a more reasonable physical model. The validation test of turbulent flow over a backward facing step shows that the modified nonlinear turbulence model significantly improved the overall prediction. Predicted results for both mean flow field and turbulence quantities agreed very well experimental results. The prediction error for the characteristic reattachment length has been reduced from 18% to 4% compared with the experimental data. The results of simulation of flow field behind the bluff body are also improved by using this model. The degree of improvement varies for different flow variables. Parametric investigation of the flow field by varying the shape and size of the bluff body is also performed. It has been found that the axial distributions of normalized reverse mass flow rate for different configurations are similar. The maximum reverse mass flow rate increases monotonically with the base height as well as with the included angle of the bluff body, but
Magnetic field line lengths inside interplanetary magnetic flux ropes
NASA Astrophysics Data System (ADS)
Hu, Qiang; Qiu, Jiong; Krucker, Sam
2015-07-01
We report on the detailed and systematic study of field line twist and length distributions within magnetic flux ropes embedded in interplanetary coronal mass ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model to reveal the close relation between the field line twist and length in cylindrical flux ropes, based on in situ Wind spacecraft measurements. We show that the field line twist distributions within interplanetary flux ropes are inconsistent with the Lundquist model. In particular, we utilize the unique measurements of magnetic field line lengths within selected ICME events as provided by Kahler et al. () based on energetic electron burst observations at 1 AU and the associated type III radio emissions detected by the Wind spacecraft. These direct measurements are compared with our model calculations to help assess the flux rope interpretation of the embedded magnetic structures. By using the different flux rope models, we show that the in situ direct measurements of field line lengths are consistent with a flux rope structure with spiral field lines of constant and low twist, largely different from that of the Lundquist model, especially for relatively large-scale flux ropes.
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.
Werner, René; Schmidt-Richberg, Alexander; Handels, Heinz; Ehrhardt, Jan
2014-08-01
Accurate and robust estimation of motion fields in respiration-correlated CT (4D CT) images, usually performed by non-linear registration of the temporal CT frames, is a precondition for the analysis of patient-specific breathing dynamics and subsequent image-supported diagnostics and treatment planning. In this work, we present a comprehensive comparison and evaluation study of non-linear registration variants applied to the task of lung motion estimation in thoracic 4D CT data. In contrast to existing multi-institutional comparison studies (e.g. MIDRAS and EMPIRE10), we focus on the specific but common class of variational intensity-based non-parametric registration and analyze the impact of the different main building blocks of the underlying optimization problem: the distance measure to be minimized, the regularization approach and the transformation space considered during optimization. In total, 90 different combinations of building block instances are compared. Evaluated on proprietary and publicly accessible 4D CT images, landmark-based registration errors (TRE) between 1.14 and 1.20 mm for the most accurate registration variants demonstrate competitive performance of the applied general registration framework compared to other state-of-the-art approaches for lung CT registration. Although some specific trends can be observed, effects of interchanging individual instances of the building blocks on the TRE are in general rather small (no single outstanding registration variant existing); the same level of accuracy is, however, associated with significantly different degrees of motion field smoothness and computational demands. Consequently, the building block combination of choice will depend on application-specific requirements on motion field characteristics.
Malanushenko, A.; Schrijver, C. J.; DeRosa, M. L.; Wheatland, M. S.
2014-03-10
The shapes of solar coronal loops are sensitive to the presence of electrical currents that are the carriers of the non-potential energy available for impulsive activity. We use this information in a new method for modeling the coronal magnetic field of active region (AR) 11158 as a nonlinear force-free field (NLFFF). The observations used are coronal images around the time of major flare activity on 2011 February 15, together with the surface line-of-sight magnetic field measurements. The data are from the Helioseismic and Magnetic Imager and Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The model fields are constrained to approximate the coronal loop configurations as closely as possible, while also being subject to the force-free constraints. The method does not use transverse photospheric magnetic field components as input and is thereby distinct from methods for modeling NLFFFs based on photospheric vector magnetograms. We validate the method using observations of AR 11158 at a time well before major flaring and subsequently review the field evolution just prior to and following an X2.2 flare and associated eruption. The models indicate that the energy released during the instability is about 1 × 10{sup 32} erg, consistent with what is needed to power such a large eruptive flare. Immediately prior to the eruption, the model field contains a compact sigmoid bundle of twisted flux that is not present in the post-eruption models, which is consistent with the observations. The core of that model structure is twisted by ≈0.9 full turns about its axis.
Sedaghat, M.; Ettehadi-Abari, M.; Shokri, B. Ghorbanalilu, M.
2015-03-15
Laser absorption in the interaction between ultra-intense femtosecond laser and solid density plasma is studied theoretically here in the intensity range Iλ{sup 2}≃10{sup 14}−10{sup 16}Wcm{sup −2}μm{sup 2}. The collisional effect is found to be significant when the incident laser intensity is less than 10{sup 16}Wcm{sup −2}μm{sup 2}. In the current work, the propagation of a high frequency electromagnetic wave, for underdense collisional plasma in the presence of an external magnetic field is investigated. It is shown that, by considering the effect of the ponderomotive force in collisional magnetized plasmas, the increase of laser pulse intensity leads to steepening of the electron density profile and the electron bunches of plasma makes narrower. Moreover, it is found that the wavelength of electric and magnetic fields oscillations increases by increasing the external magnetic field and the density distribution of electrons also grows in comparison with the unmagnetized collisional plasma. Furthermore, the spatial damping rate of laser energy and the nonlinear bremsstrahlung absorption coefficient are obtained in the collisional regime of magnetized plasma. The other remarkable result is that by increasing the external magnetic field in this case, the absorption coefficient increases strongly.
NASA Astrophysics Data System (ADS)
Qi, Yusheng; Yue, Dick
2015-11-01
We use direct nonlinear phase-resolved simulations based on a High-Order Spectral (HOS) method (Dommermuth & Yue 1987) to understand and quantify wave-breaking dissipation in the evolution of general irregular short-crested wave-fields. We achieve this by incorporating a robust phenomenological-based wave breaking model in HOS simulations to account for energy dissipation. This model can automatically simulate the onset of wave breaking, and the simulated wave-breaking dissipation strength differentiates corresponding to different wave breaking type (such as spilling or plunging breaking waves). 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, which provides the times, locations and intensity of wave breaking events. From the dissipation field we further calculate the distribution of total length of breaking wave front per unit surface area per unit increment of breaking velocity (Phillips 1985), and obtain qualitative agreement with Phillips theoretical power-law.
Anomalous resistivity and the evolution of magnetic field topology
NASA Technical Reports Server (NTRS)
Parker, E. N.
1993-01-01
This paper explores the topological restructuring of a force-free magnetic field caused by the hypothetical sudden onset of a localized region of strong anomalous resistivity. It is shown that the topological complexity increases, with the primitive planar force-free field with straight field lines developing field lines that wrap half a turn around each other, evidently providing a surface of tangential discontinuity in the wraparound region. It is suggested that the topological restructuring contributes to the complexity of the geomagnetic substorm, the aurora, and perhaps some of the flare activity on the sun, or other star, and the Galactic halo.
NASA Astrophysics Data System (ADS)
Zhang, Li
2015-11-01
Based on the compact density matrix approach, the linear and nonlinear refractive index change (RIC) and optical rectification (OR) coefficients in a GaN-based step QW with strong built-in electric field (BEF) have been theoretically deduced and investigated in detail. The analytical electronic state is derived by the two airy functions. And the band nonparabolicity is taken into account by using an energy dependence effective mass (EDEM) method. Numerical calculations on a four-layer AlN/GaN/AlxGa1-xN/AlN step QW are performed, and the curves for the geometric factors, the linear, the nonlinear, the total RICs and the OR coefficients as functions of the structural parameters of the step QW are discussed. The features for these curves were specified and reasons for the features were explained reasonably. It is found that the decreasing of well width Lw, and step barrier width Lb and the doped concentration x in step barrier will result in the significant enhancement of the RICs. With the decrease of Lw, Lb and x, the resonant photon energies of RIC and OR coefficients have obvious blue-shift. Moreover, the RIC and OR coefficients behave different dependence on the structural parameters of the GaN-based step QWs. The profound physical reasons are also analyzed.
Davidson, R.C.; Lee, W.W.; Stoltz, P.
1997-08-01
This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field B{sup sol}(x). The analysis is based on the nonlinear Vlasov-Maxwell equations in the electrostatic approximation, assuming a thin beam with characteristic beam radius r{sub b} {much_lt} S. The results are applied to investigate the nonlinear evolution of the generalized entropy, mean canonical angular momentum {l_angle}P{sub {theta}}{r_angle}, center-of-mass motion for {l_angle}X{r_angle} and {l_angle}Y{r_angle}, mean kinetic energy (1/2) {l_angle}X{sup {prime}2} + Y{sup {prime}2}{r_angle}, mean-square beam radius {l_angle}X{sup 2} + Y{sup 2}{r_angle}, and coupled rate equations for the unnormalized transverse emittance {epsilon}(s) and root-mean-square beam radius R{sub b}(s) = {l_angle}X{sup 2} + Y{sup 2}{r_angle}{sup 1/2}. Global energy balance is discussed, and the coupled rate equations for {epsilon}(s) and R{sub b}(s) are examined for the class of axisymmetric beam distributions F{sub b}.
NASA Astrophysics Data System (ADS)
Rawlinson, Z. J.; Townend, J.; Arnold, R.; Bannister, S.
2012-09-01
The accuracy with which geophysical observations are made is inherently determined by the geometry of the observation network, and typically depends on a highly non-linear relationship between data and earth parameters. Statistical experimental design provides a means of optimizing the network geometry to provide maximum information about parameters of interest. Here, we re-derive the nonlinear experimental design DN optimization method, without the need for the usual assumption of a multivariate normal model of data uncertainties. We demonstrate the criterion's utility by applying it to the problem of seismic network expansion in the active Kawerau geothermal field, Taupo Volcanic Zone, New Zealand. The design calculations maximize the ratio of the hypocentre data generalized variance (attributable to resolvable spatial separation of earthquakes) to the measurement error generalized variance (attributable to observational uncertainties), and incorporate realistic 3-D velocity and attenuation models, surface noise sources, and both P- and S-wave data. In geologically complex areas, statistical experimental design provides a means of objectively deploying finite observational resources to target areas of particular interest while taking into account environmental and logistical factors.
Nonlinear diffusion and superconducting hysteresis
Mayergoyz, I.D.
1996-12-31
Nonlinear diffusion of electromagnetic fields in superconductors with ideal and gradual resistive transitions is studied. Analytical results obtained for linear and nonlinear polarizations of electromagnetic fields are reported. These results lead to various extensions of the critical state model for superconducting hysteresis.
Bennett, Kochise Mukamel, Shaul
2014-01-28
The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N{sup 2}.
Bennett, Kochise; Mukamel, Shaul
2014-01-28
The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).
NASA Technical Reports Server (NTRS)
Wheeler, A. A.; Mcfadden, G. B.; Coriell, S. R.; Hurle, D. T. J.
1990-01-01
The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, the demarcation between supercritical and subcritical behavior is calculated as a function of processing conditions and material parameters. The bifurcation behavior is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.
NASA Astrophysics Data System (ADS)
Barseghyan, M. G.; Duque, C. A.; Niculescu, E. C.; Radu, A.
2014-02-01
We study the laser field effects on the intersubband optical absorption and the refractive index changes in a GaAs/AlGaAs quantum wire with equilateral triangle cross section. The wire is under the action of a laser beam which is assumed to be non-resonant with the semiconductor structure and linearly polarized perpendicularly to the triangle side. In the effective mass approximation and for a finite potential barrier we calculate the subband states by using a finite element method. Linear, non linear and total absorption coefficients and refractive index changes are calculated as functions of the laser field for the allowed intersubband transitions. Two polarizations of the pump radiation, parallel and perpendicular to the laser field direction, are discussed.
NASA Technical Reports Server (NTRS)
Abraham-Shrauner, B.
1986-01-01
Upper hybrid drift waves are found as a special solution to a Vlasov-Maxwell plasma which has a longitudinal electric field and a perpendicular uniform magnetic field. A single-species plasma with a constant-density mobile neutralizing background supports spatially varying disturbances that oscillate at the upper hybrid frequency. The general functional dependences of the electric field, the plasma number density, and the one-particle distribution function for the special case are found from more general Vlasov-Maxwell equations invariant under a Lie group point transformation. The one-particle distribution function for the plasma is a function of the Liouville invariant, which is the energy in the generalized Bernstein-Greene-Kruskal (BGK) reference frame, and the momentum in the drift direction.
Li, Haipeng; Xu, Hu; Shen, Xiaopeng; Han, Kui; Bi, Zetong; Xu, Runfeng
2016-01-01
We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light. PMID:27305957
NASA Astrophysics Data System (ADS)
Li, Haipeng; Xu, Hu; Shen, Xiaopeng; Han, Kui; Bi, Zetong; Xu, Runfeng
2016-06-01
We investigated the electronic properties and second hyperpolarizabilities of hydrogenated silicon nanoclusters (H-SiNCs) by using the density functional theory method. The effects of cluster size, external electric field and incident frequency on the second hyperpolarizability were also examined, respectively. We found that small H-SiNCs exhibit large second hyperpolarizability. With the increase of the number of silicon atoms in H-SiNCs, the frontier molecular orbital energy gap decreases, attributed to the enhancement of the second hyperpolarizability. Interestingly, we also found the electric-field-induced gigantic enhancement of the second hyperpolarizability for H-SiNCs due to the change of electron density distributions. In addition, our results demonstrate a significant dependence on the frequency of incident light.
NASA Astrophysics Data System (ADS)
Auzinsh, M.; Berzins, A.; Ferber, R.; Gahbauer, F.; Kalvans, L.; Mozers, A.; Spiss, A.
2015-05-01
We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the D2 line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments, laser-induced fluorescence components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components, we were able to see structures not visible in the difference graphs, which give deeper insight into the processes responsible for these signals. We studied how these signals are dependent on intensity and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions. The theoretical curves described the experimental measurements satisfactorily, reproducing even small features in the shapes of the curves.
NASA Technical Reports Server (NTRS)
Bell, T. F.
1986-01-01
A recently developed theory is used to calculate the wave magnetic field amplitude threshold, B-tau, necessary to allow the nonlinear trapping of energetic gyroresonant and Landau resonant electrons by VLF whistler mode waves in the magnetosphere propagating at an arbitrary angle, psi, with respect to the earth's magnetic field. A detailed raytracing study is carried out to establish the variation of psi with position along each magnetic shell in the range L = 2-5 and for frequencies 5-17.8 kHz. It is found that the minimum values of B-tau along each L shell generally occur at points of second-order resonance. In general, for nonducted fixed frequency signals there is only one point of second-order resonance on each L shell, and this is located within a few degrees of the magnetic equator. However, over a narrow range of L, there are as many as three points of second-order resonance and as many as three associated minima in B-tau. At least one of these points is located more than 10 deg from the magnetic equator.
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
Coronal magnetic fields produced by photospheric shear
NASA Technical Reports Server (NTRS)
Sturrock, P. A.; Yang, W.-H.
1987-01-01
The magneto-frictional method is used for computing force free fields to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear, by a simple functional form.
Banerjee, Tanmoy; Biswas, Debabrata
2013-12-01
We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.
NASA Astrophysics Data System (ADS)
Banerjee, Tanmoy; Biswas, Debabrata
2013-12-01
We explore and experimentally demonstrate the phenomena of amplitude death (AD) and the corresponding transitions through synchronized states that lead to AD in coupled intrinsic time-delayed hyperchaotic oscillators interacting through mean-field diffusion. We identify a novel synchronization transition scenario leading to AD, namely transitions among AD, generalized anticipatory synchronization (GAS), complete synchronization (CS), and generalized lag synchronization (GLS). This transition is mediated by variation of the difference of intrinsic time-delays associated with the individual systems and has no analogue in non-delayed systems or coupled oscillators with coupling time-delay. We further show that, for equal intrinsic time-delays, increasing coupling strength results in a transition from the unsynchronized state to AD state via in-phase (complete) synchronized states. Using Krasovskii-Lyapunov theory, we derive the stability conditions that predict the parametric region of occurrence of GAS, GLS, and CS; also, using a linear stability analysis, we derive the condition of occurrence of AD. We use the error function of proper synchronization manifold and a modified form of the similarity function to provide the quantitative support to GLS and GAS. We demonstrate all the scenarios in an electronic circuit experiment; the experimental time-series, phase-plane plots, and generalized autocorrelation function computed from the experimental time series data are used to confirm the occurrence of all the phenomena in the coupled oscillators.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Large scale reconstruction of the solar coronal magnetic field
NASA Astrophysics Data System (ADS)
Amari, T.; Aly, J.-J.; Chopin, P.; Canou, A.; Mikic, Z.
2014-10-01
It is now becoming necessary to access the global magnetic structure of the solar low corona at a large scale in order to understand its physics and more particularly the conditions of energization of the magnetic fields and the multiple connections between distant active regions (ARs) which may trigger eruptive events in an almost coordinated way. Various vector magnetographs, either on board spacecraft or ground-based, currently allow to obtain vector synoptic maps, composite magnetograms made of multiple interactive ARs, and full disk magnetograms. We present a method recently developed for reconstructing the global solar coronal magnetic field as a nonlinear force-free magnetic field in spherical geometry, generalizing our previous results in Cartesian geometry. This method is implemented in the new code XTRAPOLS, which thus appears as an extension of our active region scale code XTRAPOL. We apply our method by performing a reconstruction at a specific time for which we dispose of a set of composite data constituted of a vector magnetogram provided by SDO/HMI, embedded in a larger full disk vector magnetogram provided by the same instrument, finally embedded in a synoptic map provided by SOLIS. It turns out to be possible to access the large scale structure of the corona and its energetic contents, and also the AR scale, at which we recover the presence of a twisted flux rope in equilibrium.
Callen, J. D.
2002-11-04
The primary efforts this year have focused on exploring the nonlinear evolution of localized interchange instabilities, some extensions of neoclassical tearing mode theory, and developing a model for the dynamic electrical conductivity in a bumpy cylinder magnetic field. In addition, we have vigorously participated in the computationally-focused NIMROD and CEMM projects.